Illustrated Dictionary of
Electronic Materials and Devices
Concise Student Edition (v.2.0)
Safa Kasap
University of Saskatchewan
Canada
Harry Ruda
University of Toronto
Canada
Motorola’s prototype flat panel display based on the
Fowler-Nordheim field emission principle. (Courtesy of Dr.
Babu Chalamala, Flat Panel Display Division, Motorola.)
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
2
PREFACE
The title Illustrated Dictionary of Electronic Materials: Concise Student Edition reflects exactly
the contents of this dictionary. It is not meant to be an encyclopedia in this field but rather a selfcontained semiquantitative description of terms and effects that frequently turn up in electronic
materials science. The first edition of dictionaries like this usually have many terms missing.
Indeed, we have missed many terms but we have also described many; though, undoubtedly, our
own biased selection. There is always a compromise in life between perfection and practicality.
We tried to keep the descriptions at the semiquantitative level so that they can be understood at
the undergraduate level. Difficult definitions have illustrations to convey the concepts. At the
same time, illustrations tend to take much space and we did not want this dictionary to be so
thick that it would be cumbersome to use.
One of us (SOK) would like to express his special thanks to his colleague and friend Professor
Charbel Tannous (University of Brest, France) who generously provided some of the definitions
(marked [CT]) and, with his incisive criticisms, kept challenging the authors to come up with
better definitions; a faultless friend and a great professor.
Please feel free to e-mail us your comments for improving this dictionary. Although we may not
be able to reply individually, we do read all our email messages and take note of suggestions and
comments. If you would like to have an online access to a Color Illustrated Dictionary of
Electronic Materials and Devices, you can do so at http://ElectronicMaterials.Usask.Ca.
Safa Kasap
Saskatoon
Harry Ruda
Toronto
“I know you believe you understand what you think I said,
but I am not sure you realize that what you heard is not
what I meant”
Alan Greenspan
Chairman of US Federal Reserve
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
3
Absorption coefficient α characterizes the loss of photons as light propagates along a certain
direction in a medium. It is the fractional change in the intensity of light per unit
distance along the propagation direction, that is,
δI
α=−
Iδx
where I is the intensity of the radiation. The absorption coefficient depends on the
photon energy or wavelength λ. Absorption coefficient α is a material property. Most
of the photon absorption (63%) occurs over a distance 1/α and 1/α is called the
penetration depth δ.
Photon energy (eV)
5 4
1
3
1
2
0.9
0.8
0.7
108
Ge
1 107
In0.7Ga0.3As0.64P0.36
In0.53Ga0.47As
Si
1 106
GaAs
(m-1)
InP
1 105
a-Si:H
1 104
1 103
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Wavelength ( m)
Absorption coefficient ( ) vs. wavelength ( ) for various semiconductors
(Data selectively collected and combined from various sources.)
Absorption is the loss in the power of an electromagnetic radiation that is traveling in a
medium. The loss is due to the conversion of light energy to other forms of energy, e.g.
lattice vibrations (heat) during the polarization of the molecules of the medium, local
vibrations of impurity ions, excitation of electrons from the valence band to the
conduction band etc.
Acceleration a is the rate of change of an object's velocity, dv/dt. When a net force F acts on a
body, it imparts acceleration to that body, i.e. the velocity of the body changes, either
increasing or decreasing. In classical physics, the force F and the acceleration a are
treated by F = ma where m is the mass of the body (called the inertial mass) and a is its
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
4
acceleration. Acceleration is a vector quantity that has a magnitude as well as a direction,
thus a = dv/dt.
Acceptance angle, or the maximum acceptance angle is the largest possible light launch angle
from the fiber axis. Light waves within the acceptance angle that enter the fiber become
guided along the fiber core. If NA is the numerical aperture of a step index fiber, and
light is launched from a medium of refractive index no, then maximum acceptance angle
αmax is given by
NA
sin α max =
no
Total acceptance angle is twice the maximum acceptance angle and is the total angle
around the fiber axis within which all light rays can be launched into the fiber.
Acceptance cone is a cone with its height aligned with the fiber axis and its apex angle twice the
acceptance angle so that light rays within this cone can enter the fiber and then
propagate along the fiber.
Acceptor atoms are dopants that have one less valency than the host atom. They therefore
accept electrons from the valence band (VB) and thereby create holes in the VB which
leads to p > n and hence to a p-type semiconductor.
Electron energy
B atom sites every 106 Si atoms
x Distance
Ec
Ea
Ev
into crystal
B–
h+
B–
B–
B–
~0.05 eV
VB
Energy band diagram for a
p-type Si doped with 1
ppm B. There are acceptor
energy levels just above Ev
around B– sites. These
acceptor levels accept
electrons from the valence
band (VB) and therefore
create holes in the VB.
Accumulation in a MOS (metal-oxide-semiconductor) device occurs when an applied voltage
to the gate (or metal electrode) of a MOS device causes the semiconductor under the
oxide to have a greater number of majority carriers than the equilibrium value.
Majority carrier have been accumulated at the surface of the semiconductor under the
oxide.
Acetic acid (CH3COOH) is an acid (a component of vinegar) that is used for etching
semiconductors. [H.R.]
Activated complex occurs temporarily during a transformation or reaction when the reactant
atoms or molecules come together to form a particular arrangement (intermediate
between reactants and products) which has a higher potential energy than the reactants.
The state of the reactant atoms / molecules in the activated complex is the termed the
activated state. The potential energy barrier between the activated state and the reactants
is the activation energy.
Activated state occurs temporarily during a transformation or reaction when the reactant atoms
or molecules come together to form a particular arrangement (intermediate between
reactants and products) which has a higher potential energy than the reactants. The
potential energy barrier between the activated state and the reactants is the activation
energy.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
5
Activation energy is the potential energy barrier that prevents a system from changing from
state to another. For example, if two atoms A and B get together to form a product AB,
the activation energy is the potential energy barrier against the formation of this product.
It is the minimum energy which the reactant atom or molecule must have to be able to
reach the activated state and hence form the product. The probability that a system has
an energy equal to the activation energy is proportional to the Boltzamnn factor: exp(−
EA/kT), where EA is the activation energy, k is the Bolztamann constant and T is the
temperature (Kelvins).
Active device is a device that exhibits gain (current or voltage or both) and has a directional
function. Transistors are active devices whereas resistors, capacitors and inductors are
passive devices.
Active region is the region in a medium where direct electron hole pair (EHP) recombination
takes place. For light emitting diodes (LED) it is the region where most EHP
recombination takes place. In the laser diode it is the region where stimulated
emissions exceeds spontaneous emission and absorption. It is the region where
coherent emission dominates.
Adiabatic process is that in which there is no heat exchange with the surroundings. The only
interaction with the surroundings is the mechanical work done on or by the system.
During an adiabatic process, the change in the internal energy, ∆U, is a result of the
mechanical work done by or on the system. If ∆W is the work done by the system, then
∆U+∆W=0. In practice adiabatic processes are approximated by insulating the system
with a good thermal insulator, or carrying out the process quickly so that there is not
enough time for heat flow. The compressions stroke in the internal combustion engine is
an example of an approximate adiabatic processes in which the compression of the gas in
the cylinder takes place quickly and hence adiabatically which raises the internal energy
and hence the temperature.
AlInP alloys are III-V semiconductor ternary alloys that are commonly used for fabricating
optoelectronic devices. A direct bandgap of 1.35 eV to 3.58 eV occurs if the ratio of
aluminum to indium in the alloys is varied from 0 to 1. Alloys with aluminum fraction
of 0.49 are lattice matched to GaAs, a readily available substrate material commonly used
for high speed electronic and optoelectrnic devices. Alloys of this
composition(Al0.49In0.51P) have an indirect bandgap of 2.33 eV at 300 K. [H.R.]
AlInAs alloys are III-V semiconductor ternary alloys that are commonly used for fabricating
optoelectronic devices. A direct bandgap of 0.36 eV to 3.07 eV occurs if the ratio of
aluminum to indium in the alloys is varied from 0 to 1. Alloys with aluminum fraction
of 0.48 are lattice matched to InP, a readily available substrate material commonly used
for fabricating long wavelength semiconductor laser diodes and photodetectors. Alloys
of this composition (Al0.49In0.51As) have a direct bandgap of 1.45 eV at 300 K. [H.R.]
Alloy is a metal that contains more than one element. Brass is an alloy of Cu and Zn.
Alloy spiking also known as junction spiking, occurs when silicon diffuses into and dissolves
in an electrode metal, resulting in a poor contact between the electrode and the silicon
(which is usually in the form of a silicide). When this occurs near a junction, the contact
metal can penetrate the junction causing junction leakage commonly called spiking. Alloy
spiking is commonly found for an aluminum contact metal, and in order to prevent
spiking from occurring, a diffusion barrier, for example, titanium nitride, is used. [H.R.]
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
6
Aluminides are materials formed as a result of the chemical reaction of aluminum with other
materials. [H.R.]
Ammonia (NH3) is a toxic and flammable gas that is used to form silicon nitride using a
chemical vapor deposition (CVD) process. [H.R.]
Ammonium fluoride (NH4F) is a salt that is used as a buffering agent in the buffered oxide
etching process. [H.R.]
Ammonium hydroxide (NH4OH) is the base that is formed when ammonia is dissolved in
water. [H.R.]
Amorphous solid exhibits no crystalline structure or long range order. It only posses a short
range order in that the nearest neighbors of an atom are well defined by virtue of
chemical bonding requirements. See glass.
Amorphous silicon (a-Si) is a noncrystalline form of silicon in which the structure lacks the
long range order of crystalline Si (c-Si) even though in a-Si, on average, each Si atom
prefers to bond with four neighbors. The difference is that the relative angles between the
Si-Si bonds in a-Si deviate considerably from those in the crystal which obey a strict
geometry. Therefore as we move away from a reference atom eventually the periodicity
for generating the crystalline structure is totally lost. Furthermore, because the Si-Si
bonds do not follow the equilibrium geometry, the bonds are strained and some are even
missing simply because forming a bond causes a large bond bending. Consequently the
a-Si structure has many voids and incomplete bonds or dangling bonds. One way to
reduce the density of broken bonds is to use hydrogen to simply terminate a bond.
Since hydrogen only has one electron it can attach itself to a broken bond and repair it or
passivate the dangling bond. The structure resulting from hydrogen in amorphous silicon
is called hydrogenated amorphous Si (a-Si:H). Many electronic devices such as a-Si:H
solar cells are based on depositing a-Si with H to obtain a-Si:H in which the hydrogen
concentration is typically 10 at.%. The process involves the decomposition of silane gas,
SiH4, in an electrical plasma in a vacuum chamber. The process is called plasmaenhanced chemical vapor deposition (PECVD). The advantage of a-Si:H is that it
can be grown on large areas for such applications as photovoltaic cells, falt panel actrive
matrix arrays (as in flat panel displays) and photoconductor drums used in some
photocopying machines.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
7
H
Dangling
bond
H
H
H
H
H
(b) Two dimensional schematic
(a) Two dimensional
schematic representation representation of the structure of
amorphous silicon. The structure
of a silicon crystal
has voids and dangling bonds
and there is no long range order.
(c) Two dimensional
schematic representation of
the structure of hydrogenated
amorphous silicon. The
number of hydrogen atoms
shown is exaggerated.
Silicon can be grown as a semiconductor crystal or as an amorphous
semiconductor film. Each line represents an electron in a bond. A full
covalent bond has two lines and a broken bond has one line.
Ampere's circuital law is an integral relationship between the magnetic field around a closed
path and the total current enclosed (threaded) by the that field. It is particularly useful in
relating the magnetic field intensity H and the conduction current I enclosed. If we
integrate the tangential component of H around any closed path we find the enclosed
current due to the flow of conduction electrons (Around a closed circuit, ∫Hdl = I).
Amphoteric dopant refers to the electrical activity of a given chemical species in a crystalline
semiconductor. Such a species is said to be amphoteric if it is able to act as either a
donor or acceptor impurity in a given crystalline semiconductor, depending on the site it
occupies in the crystal structure. For example, silicon is an amphoteric dopant in GaAs
since it can occupy, by substitution, either arsenic or gallium atomic sites. When it
occupies arsenic sites it acts as an acceptor-like dopant, while it behaves as a donor-like
dopant when occupying gallium sites. [H.R.]
Angstrom (Å) is 10-10 meters.
Angular momentum, L, about a point O is defined by L = p × r where p is the linear
momentum and r is the position vector of the body from O. For a circular orbit around
O, the angular momentum is orbital and L = pr = mvr. Newton's Second Law in terms of
angular momentum becomes, dL/dt = τ where τ is the applied torque about the same
point O. In classical mechanics, in the absence of an external torque, the angular
momentum of a body is conserved. In a central force field, i.e. when the force
experienced by a body is always directed to pass through O, that is the force F is directed
along r, L is also conserved (this is the so-called central field theorem). In quantum
mechanics, the orbital angular momentum of an electron in an atom is quantized via
L=h√[l(l +1)] where l is orbital quantum number of the electron, l = 0,1,2,...,(n−1)
and n the principal quantum number.
Anion is an atom that has gained negative charge by virtue of accepting an electron or electrons.
Usually nonmetal atoms can gain electrons easily to becomes anions. Anions become
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
8
attracted to the anode (positive terminal) in ionic conduction. Typical anions are the
halogen ions, F−, Cl−, Br−, I−.
Anisotropy (optical) refers to the fact that the refractive index n of a crystal depends on the
direction of the electric field in the propagating light beam. The velocity of light in a
crystal depends on the direction of propagation and on the state of its polarization, i.e.
the direction of the electric field. Most noncrystalline materials such as glasses and
liquids, and all cubic crystals are optically isotropic, that is the refractive index is the
same in all directions. For all classes of crystals excluding cubic structures, the refractive
index depends on the propagation direction and the state of polarization. The result of
optical anisotropy is that, except along certain special directions, any unpolarized light
ray entering such a crystal breaks into two different rays with different polarizations and
phase velocities. When we view an image through a calcite crystal, an optically
anisotropic crystal, we see two images, each constituted by light of different polarization
passing through the crystal, whereas there is only one image through an optically
isotropic crystal. Optically anisotropic crystals are called birefringent because an
incident light beam may be doubly refracted. Experiments and theories on “most
anisotropic crystals”, i.e. those with the highest degree of anisotropy, show that we can
describe light propagation in terms of three refractive indices, called principal
refractive indices n1, n2 and n3, along three mutually orthogonal directions in the
crystal, say x, y and z called principal axes. These indices correspond to the polarization
state of the wave along these axes. Crystals that have three distinct principal indices also
have two optic axes and are called biaxial crystals. On the other hand, uniaxial crystals
have two of their principal indices the same (n1 = n2) and only have one optic axis.
Uniaxial crystals, such as quartz, that have n3 > n1 and are called positive, and those
such as calcite that have n3 < n1 are called negative uniaxial crystals.
A line viewed through a cubic sodium chloride (halite) crystal (optically isotropic) and a
calcite crystal (optically anisotropic).
Anode is the electrode where oxidation takes place; the substance looses its electrons. For
example in the electrolysis of aqueous sodium sulfate, at the anode, water is
decomposed and its hydrogen oxidized: 2H2O(l) → O2(g) + 4H+(aq) + 4e-. In
electronics, anode is simply a positive electrode; attracts electrons or negative ions,
anions.
Antiferromagnetic materials have crystals in which alternating permanent atomic spin
magnetic moments are equal in magnitude but point in opposite directions (antiparallel)
which leads to no net magnetization of the crystal.
Antiferromagnetism - An assembly of magnetic moments interacting with a negative
exchange integral will minimize their energy by adopting an anti-parallel configuration.
The net total magnetization is zero. It is possible to consider the entire crystal as made
of two inter-penetrating sub-lattices containing moments all parallel inside each sublattice, but with the total magnetization of each sub-lattice opposite to one another. [C.T.]
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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Antimony (Sb) is a metal that is used to form the semiconductors, indium antimonide, gallium
antimonide and aluminum antimonide, and alloys formed from these binary compounds.
Antimony is also used as an n-type dopant for silicon, especially when using ion
implantation. [H.R.]
Antireflection coating is a thin dielectric layer coated on an optical device or component to
reduce the reflection of light and increase the transmitted light intensity.
Antisite defect is a type of point defect that occurs in a crystalline material when component
atoms are misplaced by substituting for each other. For example, in a compound
semiconductor such as GaAs, two types of antisite defects can occur- an arsenic atom
occupying a gallium atom site, known as an arsenic antisite defect, or a gallium atom
occupying an arsenic atom site, known as a gallium antisite defect. Since in the case of
an antisite defect, the atom which occupies a given site differs from its regular occupant,
there will be a difference in the valence charge density, and as a result, such defects often
result in the formation of acceptor or donor-like defect states. [H.R.]
Argon (Ar) is a chemically inert, nontoxic gas that is used in purging, annealing and
sputtering processes. Argon is also used as an inert gas in silicon bulk crystal growth.
[H.R.]
Arrhenius temperature dependence implies that the rate of change in a physical or chemical
process, or the particular property under observation, has an exponential temperature
dependence of the form
∆H 
Rate = C exp −
 RT 
where C is a constant, R is the gas constant, T is the temperature (in Kelvins) and ∆H is
the activation energy of associated with the process, in J mol-1.
Arsenic (As) is a semi-metallic solid that is a main component in a number of technologically
important III-V semiconductors. These include gallium arsenide, aluminum arsenide, and
indium arsenide. Arsenic is also a commonly used n-type dopant, especially using ion
implantation. [H.R.]
Arsine (AsH3) is a highly toxic, flammable gas that is used as a source of arsenic for the
metal-organic vapor deposition (MOCVD) and chemical vapor deposition (CVD)
of III-V arsenic containing semiconductors. It is also used as a source for n-type doping
of silicon by diffusion, as well as by ion implantation. [H.R.]
Ashing is the removal of photoresist from a substrate as a result of high temperature
oxidation. [H.R.]
Atomic mass (or relative atomic mass or "atomic weight", Mat) of an element is the
average atomic mass, in atomic mass units (u), of all the naturally occurring isotopes
of the element. Atomic masses are listed in the Periodic Table. The amount of an element
which has 6.022 × 1023 atoms (the Avogadro number of atoms) has a mass in grams
equal to the atomic mass.
Atomic mass number (A) is the number of protons and neutrons in the nucleus. If Z is the
atomic number and N is the neutron number then A = Z+N.
Atomic mass unit (amu) is a convenient atomic mass unit that is equal to 1/12 of the mass of a
neutral carbon atom which has a mass number A = 12 (6 protons and 6 neutrons). It has
been found that amu = 1.66054 × 10−27 kg. It is equivalent to 10-3 / NA where NA is the
Avogadro number.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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Atomic number (Z) is the number of protons in the nucleus of an atom.
Atomic packing factor is the fraction of volume in the crystal actually occupied by atoms.
Attenuation (α) is the decrease in the optical power of a traveling wave, or a guided wave in a
dielectric waveguide, in the direction of travel. If Po is the optical power at some location
O, and if it is P at a distance L from O along the direction of propagation then the
attenuation coefficient is defined by α = 10L-1log(P/Po).
Avalanche breakdown is the enormous increase in the reverse current in a pn junction when
the applied reverse field is sufficiently high to cause the generation of electron hole pairs
by impact ionization in the space charge layer.
Avalanche multiplication factor M of an avalanche photodiode (APD) is defined as
I
Multiplied photocurrent
M=
= ph
Primary unmultiplied photocurrent I pho
where Iph is the APD photocurrent that has been multiplied and Ipho is the primary or
unmultiplied photocurrent.
Avalanche noise is the excess noise in the photocurrent of an avalanche photodiode due to
the statistics of the multiplication process occurring in the avalanche region. The
avalanche process does nor occur continuously and smoothly in time but as discrete
events whose frequency of occurrence fluctuates in the avalanche region about some
mean value. Thus the multiplication M fluctuates about a mean value. The result of the
statistics of impact ionization is an excess noise contribution, called avalanche noise,
to the multiplied shot noise. The noise current in an avalanche photodiode (APD) is
given by,
in-APD = [2e(Ido + Ipho)M2FB]1/2
where F is called the excess noise factor and is a function of M and the impact ionization
probabilities (called coefficients). Generally, F is approximated by the relationship F ≈
Mx where x is an index that depends on the semiconductor, the APD structure and the
type of carrier that initiates the avalanche (electron or hole). For Si APDs, x is 0.3 - 0.5
whereas for Ge and III-V (such as InGaAs) alloys it is 0.7 - 1.
Avalanche photodiode (APD) is a photodiode with a depletion region in which the field is
sufficiently large for an avalanche multiplication of photogenerated charge carriers by
impact ionization. The avalanche process in the APD occurs over a limited region of
the depletion layer and the photodiode design allows only the multiplication of one type
of carrier for example electrons for Si.
Average energy, Eav of an electron in a metal is determined by the Fermi-Dirac statistics and
the density of states, and is 3/5EF where EF is the Fermi energy. It increases with the
Fermi energy and also with the temperature. Eav of an electron in the conduction band
is 3/2kT as if the electrons were obeying Maxwell-Boltzmann statistics. This is only true
for a nondegenerate semiconductor.
Avogadro's number (NA) is the number of atoms in exactly 12 grams of Carbon-12. It is
6.022 x 1023. Since atomic mass is defined as 1/12 of the mass of the carbon-12 atom,
NA number of atoms of any substance has a mass equal to the atomic mass, Mat, in
grams.
Backgrinding is the process of mechanically thinning a wafer to remove stress cracks, as well
as improve heat dissipation in a finished device. [H.R.]
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
11
Ballistic electrons refers to electrons with an elastic mean free path le that considerably
exceeds the dimensions of a sample, or the dimensions of some constraining channel, L,
in which these electrons move. That is, when le>>L, the electrons will be able to move
through such a material, or in such a channel without suffering any scattering, and are
said to move ballistically. [H.R.]
Band offset or band discontinuities can occur at a heterojunction as a result of a difference in
the electron affinities of each of the heterojunction materials. If the electron affinities of
each material are χΑ and χB, respectively, then the conduction band offset, ∆Ec will be
given by q(χΑ − χB), where q the electron charge (1.602×10-19 C). Moreover, if the
energy bandgaps of the two materials are Eg,A and Eg,B, respectively, then the valence
band offset ∆Ev will be given by
∆Ev = {|Eg,A − Eg,B| − ∆Ec}.
Note that the sum of the band offsets in the conduction and valence band equal the
difference in the bandgaps between the two materials of the heterojunction. [H.R.]
Bandwidth, or optical bandwidth, is the range of modulation frequencies up to some
maximum frequency ƒop where the optical transmission characteristic of the fiber falls by
a factor of 3 dB. The optical bandwidth is roughly the same as the bit rate capacity B and,
similarly to BL, ƒopL, called the bandwidth-length product, remains approximately
constant and a property of the fiber.
Base spread resistance (rbb′) is an effective resistance that represents the voltage drop from the
external base terminal (B) to the actual base point (B'). It is the voltage VB'E that controls
the collector current.
Base width modulation (the Early effect) is the modulation of the base width by the voltage
appearing across the base-collector junction. An increase in the base to collector voltage
increases the collector junction depletion layer width which results in the narrowing of
the base width, hence increasing the collector current.
Bessel function Jn(x) of order n is a mathematical function that is a solution to the differential
equation
x2y′′ + xy′ + (x2 − n2)y = 0
where prime represents differentiation with respect to x, i.e. y′ = dy/dx, and n is a constant
(independent of x and y). Bessel functions are either tabulated or graphed for various
orders. Jn(x) looks like a damped sinusoidal wave. The electric field in cylindrical
waveguides, coaxial cables, step index optical fibers, are generally described by Bessel
functions. For example, for step index fibers, zeros of the Bessel function Jn(x) point to
those values of the V-number at which various modes, with the exception of the
fundamental mode, are cut-off (cannot propagate). For example, the LP11 (l = 1, m = 1)
mode is cut off when J0(x) = 0 or when V = 2.405.
Bias is a term used to describe the application of a continuous (dc) voltage across, or a current
through, a device that puts the device in a desirable operating condition. For example,
applying a reverse dc voltage across a pin photodiode establishes the necessary electric
field and puts the pin into a desirable operating condition.
Bimolecular reaction is a single step reaction that involves a direct interaction between two
molecules.
Binary phase diagram is a phase diagram for an alloy with only two components.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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Bipolar junction transistor (BJT) is a transistor whose normal operation is based on the
injection of minority carriers from the emitter into the base region and their diffusion
to the collector where they give rise to a collector current. The voltage between the base
and the emitter controls the collector current; this is the transistor action.
Birefringent crystals such as calcite are optically anisotropic which leads to an incident light
beam becoming separated into ordinary (o-) and extraordinary (e-) waves with
orthogonal polarizations; incident light becomes doubly refracted because these two
waves experience different refractive indicesno and ne. There is no double refraction for
light propagation along the optic axis. If we were to cut a plate from a calcite crystal so
that the optic axis (along z) would be parallel to two opposite faces of the plate, then a ray
entering at normal incidence to one of these faces would not diverge into two separate
waves. The o- and e-waves would travel in the same direction but with different speeds.
The waves emerge in the same direction as well which means that we would see no
double refraction. This optical arrangement is used in the construction of various optical
retarders and polarizers as discussed below. If we were to cut a plate so that the optic
axis was perpendicular to the plate face, then both the o and e-way would be traveling at
the same speed and along the same direction which means we would not again see any
double refraction (see also anisotropy)
Two polaroid analyzers are placed with their transmission axes, along the long edges, at
right angles to each other. The ordinary ray, undeflected, goes through the left polarizer
whereas the extraordinary wave, deflected, goes through the right polarizer. The two
waves therefore have orthogonal polarizations.
Optic axis
Incident ray
Principal section
Principal section
E//
e-wave
e-ray
o-ray
A calcite rhomb
o-wave
E
Incident wave
Optic axis
(in plane of paper)
An EM wave that is off the optic axis of a calcite crystal splits into two waves called ordinary
and extraordinary waves. These waves have orthogonal polarizations and travel with different
velocities. The o-wave has a polarization that is always perpendicular to the optical axis.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
z , ne
Optic axis
13
x , no
Ee-wave
Ee-wave
E
y
z
Eo-wave
(a)
x , no
Eo-wave
(b)
Optic axis
y , no
(a) A birefringent crystal plate with the optic axis parallel to the plate surfaces. (b) A
birefringent crystal plate with the optic axis perpendicular to the plate surfaces.
Bismuth (Bi) is a brittle metal that is used for n-type doping of silicon using ion
implantation. [H.R.]
Bit is the basic unit of information in digital communication systems and corresponds to the
presence or absence of pulses.
Bit rate is the rate at which bits are transmitted in a digital communications system.
Maximum rate at which the digital data can be transmitted along the fiber is the bit rate
capacity, B (bits per second) and is directly related to the dispersion characteristics of
the fiber.
Bit rate × distance (BL) is the product of the bit rate capacity and fiber length. Generally, the
dispersion or time spread of an optical pulse increases with distance and the bit rate
capacity consequently decreases with distance. In multimode fibers, B decreases
approximately linearly with L so that BL is nearly constant and fiber characteristic.
Strictly, however, BL is not constant (especially for single mode fibers) and one should
compare BL products of fibers of comparable length.
Black body is a hypothetical (an ideal) body that absorbs all the electromagnetic radiation
falling onto it and therefore appears to be black at all wavelengths. When heated, a black
body emits the maximum possible radiation at that temperature. A small hole in the wall
of a cavity maintained at a uniform temperature emits radiation that approximately
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
corresponds to that from a black body .
14
Iλ
3000 K
Hot body
Spectral irradiance
Escaping black body
radiation
Classical theory
Planck's radiation law
2500 K
Small hole acts as a black body
0
1
2
λ ( µm)
3
4
5
Schematic illustration of black body radiation and its characteristics. Spectral irradiance
vs wavelength at two temperatures (3000K is about the temperature of the incandescent
tungsten filament in a light bulb).
Black body radiation is the distribution of radiation energy as a function of wavelengths
emerging from a hot black body such as a small hole in a cavity. The maximum amount
of radiation intensity that can be emitted by an object is called the black body radiation.
Although, in general, the radiated intensity depends on the material's surface, a radiation
emitted from a cavity with a small aperture is independent of the material of the cavity
and corresponds very closely to black body radiation. Spectral irradiance Iλ is the
emitted radiation intensity (power per unit area) per unit wavelength so that Iλdλ is the
intensity in a small range of wavelengths, dλ. Planck’s black body radiation law
describes the wavelength dependence of Iλ as
2πhc 2
Iλ =
hc  

λ5 exp
−1

λkT  

where k is Boltzmann’s constant, T is the temperature (Kelvins), h is the Planck
constant, c is the speed of light.
Bloch wall is a magnetic domain wall.
Bohr magneton (β) is a useful elementary unit of magnetic moment on the atomic scale. It is
equal to the magnetic moment of one electron spin along an applied magnetic field, β =
eh /2me.
Boltzmann energy distribution, see Boltzmann statistics
Boltzmann statistics describes the behavior of a collection of particles (e.g. gas atoms) in
terms of their energy distribution. It specifies the number of particles, N(E), with an
energy E through N(E) ∝ exp(−E /kT) where k is Boltzmann’s constant and T is the
temperature (Kelvins). The description is non-quantum mechanical in the sense that there
is no restriction to how many particles can have the same state (the same wavefunction)
with an energy E. It applies when there are only a few particles compared with the
number of possible states so that the likelihood of two particles having the same state
becomes negligible. This is generally the case for thermally excited electrons in the
conduction band of a semiconductor where there are many more states than number of
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
15
electrons. The kinetic energy distribution of gas molecules in a tank obeys the Boltzman
statistics.
E
exp(–E/kT)
The Boltzmann energy distribution describes the
statistics of particles, e.g. electrons, when the
particles do not interact with each other, i.e. when
there are very few electrons compared with the
number of available states.
E2
E1
0
N1
N2
N(E)
Boltzmann’s constant k is the gas constant per atom or per molecule, that is, the gas constant
divided by Avogadro’s number (k = R/NA); k = 1.38×10-23 J K-1. (3/2kT is the mean
kinetic energy associated with the translational motions of gas molecules in a gas
cylinder at temperature T).
Bond energy or binding energy between two atoms is the work (or energy) needed to
infinitely separate the two atoms from their equilibrium separation in the molecule or
solid.
Boron (B) is a nonmetallic element that is used as a p-type dopant for silicon using ion
implantation, and commonly as a p-type dopant for III-V semiconductors using
molecular beam epitaxy (MBE). [H.R.]
Boron trichloride (BCl3) is a toxic, nonflammable, corrosive gas that is used to etch metals
and silicides. It is also a source of boron for p-type doping of silicon by ion
implantation. [H.R.]
Boron trifluoride (BF3) is a toxic gas that is used as a source of boron for p-type doping of
silicon using ion implantation. [H.R.]
Boron trioxide (B2O3) is added to silica glass to form B-doped silica to modify (decrease) the
refractive index.
Boule is a body of crystallized material formed from a melt growth technique. The boule is
normally entirely single crystal material, and assumes a shape characteristic of the
particular process from which it was formed. Thus, Czochralski grown boules are
typically solid rods of materials with an approximately circular cross-section, while
boules grown by the horizontal Bridgeman process typically are rods with a D-shaped
cross-section. Subsequent slicing of the boule into thin wafers is used to form
substrates onto which devices are patterned. [H.R.]
Boundary conditions relate the normal and tangential components of the electric field next to
the boundary. The tangential component must be continuous through the boundary.
Suppose that En1 is the normal component of the field in medium 1 at the boundary and
εr1 is the relative permittivity in medium 1. Using a similar notation for medium 2,
then the boundary condition is εr1En1 = εr2En2.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
16
Boundary
Et1
Et2
En1
En2
Boundary conditions between dielectrics. Et is the
tangential and En is the normal electric field to the
boundary Subscripts 1 and 2 refer to dielectrics 1 and 2.
r1En1 = r2En2 and Et1 = Et2
V
Bridgeman growth is a commonly use bulk crystal growth method, and is based on
directional solidification induced by a temperature gradient at a seed/melt interface. This
growth method can be carried out in a vertical or horizontal configuration with respect to
the vector of gravitational force. Material growth occurs in a high purity crucible that
contains both a seed crystal and source material. Typically crucibles are made from either
high purity quartz or pyrolytic boron nitride. Often the crucible system is loaded into a
sealed and evacuated quartz tube that also contains in a separate zone, a source of the
volatile constituent of the material being prepared. By independently controlling the
temperature of the crucible and the volatile constituent material, any losses of volatile
material can be precisely compensated for, resulting in exceptionally high quality and
high purity material. While this technique is ideally suited for the growth of III-V
compounds with highly volatile components at their melting points, it does have some
significant disadvantages. These include, the constraints of the crucible which can lead to
strain in the grown crystal due to differential thermal expansion, as well as a D-shape for
the material grown as a result of material solidifying assuming the profile of the base of
the crucible. Significant economical implications for the technique relate to difficulties in
scaling the process up to prepare large boules. [H.R.]
Brass is a copper rich Cu-Zn alloy.
Brewster's angle or polarization angle (θp) is the angle of incidence which results in the
reflected wave having no electric field in the plane of incidence (plane defined by the
incident ray and the normal to the surface). The electric field oscillations are in the plane
perpendicular to the plane of incidence.
Bronze is a copper rich Cu-Sn alloy.
Buffered oxide etch (BOE) is the process of removing a silicon dioxide layer from a silicon
wafer, without removing any silicon. The etch consists of a hydrofluoric acid solution
that is buffered with ammonium fluoride. [H.R.]
Built-in voltage (Vo) is the voltage across a pn junction, going from p to n-type
semiconductor, in an open circuit. It is not the voltage across the diode which is made up
of Vo as well as the contact potential at the metal electrode to semiconductor junctions.
Cathode is where reduction takes place; the substance gains electrons. For example, in the
electrolysis of aqueous sodium sulfate, at the cathode, water is decomposed and its
oxygen reduced: 2H2O + 2e- → H2(g) + 2OH+(aq) + 4e-. In elkectronics, Cathode is
simply a negative electrode; emits electrons, or attracts positive charges, that is, cations.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
17
Cathode-ray tube (CRT) is a vacuum tube device that uses an electron beam to provide an
image on a luminous screen. Thermionically emitted electrons from a heated cathode at
one end of the tube are accelerated by ring shaped anodes (hollow cylinders) which form
an electrostatic lens system to focus the beam. Electrons pass through the anode rings
and form a beam that strikes the enlarged end of the tube. The latter is coated on the
inside with a fluorescent material (a phosphor) so that the region struck by the electron
beam becomes luminous. A negative voltage applied to a grid between the cathode and
the anode controls the intensity of the electron beam. The cathode (including the
filament), grid and the anode assembly is termed an electron gun. The electron beam
from the electron gun can be deflected by x and y-deflection plates or by magnetic coils.
Cation is an atom that has gained positive charge by virtue of loosing an electron or electrons.
Usually metal atoms can lose electrons easily to becomes cations. Cations become
attracted to the cathode (negative terminal) in ionic conduction as in gaseous
discharge. Alkali metals, Li, Na, K, .. easily lose their valence electron to become cations.
Li+, Na+, K+,......
CdS is a II-VI semiconductor compound which can assume either the zinc blende crystal
structure with lattice constant a = 0.414 nm, or wurtzite crystal structure, having a direct
bandgap of Eg = 2.42 eV and density ρ = 4.82 g cm-3. [H.R.]
CdSe is a II-VI semiconductor compound having the wurtzite crystal structure with lattice
constant a = 0.430 nm, and with a direct bandgap of Eg = 1.73 eV and density ρ = 5.81 g
cm-3. [H.R.]
CdTe is a II-VI semiconductor compound having the zinc blende crystal structure with lattice
constant a = 0.648 nm, and with a direct bandgap of Eg = 1.58 eV and density ρ = 6.20 g
cm-3. [H.R.]
Centrosymmetric crystals have a unit cell with a center of symmetry. If we draw a vector r
from point O to any charge and then reverse the vector, i.e. make it −r, we will find the
same charge. If, on the other hand, we do not find the same charge when we reverse the
vector, then the unit cell is non- centrosymmetric.; r and −r point on to different ions.
Non-centrosymmetric crystals exhibit piezoelectricity.
r
r
O
r
O
r
(a) Centrosymmetric
(b) Non-centrosymmetric
Ceric ammonium nitrate (NH4)2[Ce(NO3)6] is an etching solution for chrome that is used in
the manufacturing of reticules made from cerium IV and ammonium nitrate. [H.R.]
Channel is the conducting strip between the source and drain regions of a MOSFET.
Charge is a physical property that characterizes the electrostatic state of the body through the
extent of electrostatic interaction between the body and another charged body. A charge
can be positive or negative and it is always in multiples of the fundamental electronic
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
18
charge e, that is Q = ±eN where N is an integer. Two oppositely charged objects attract
each other and two same-charge objects repel each other. The fundamental law that
characterizes the forces between static charges is Coulomb's law which states that the
force F between two charges Q1 and Q2 separated by a distance r is given by F =
Q1Q2/[4πεor2] where εo is the absolute permittivity or the permittivity of free space.
When the charges are in a dielectric medium we have to include the polarization of the
medium and its effect on the coulombic force which can be done by replacing εo by εoεr
where εr is the relative permittivity of the body assumed to isotropic.
Chemical potential µ or Gibbs free energy per atom G of a system or a substance is the
potential energy per atom for doing non pV (non-mechanical) work, for example
electrical or magnetic work. It is the change in the chemical potential (or change in Gibbs
free energy per atom) that results in non-pV work to be done. For example in a battery,
the EMF, V, that is available is the change ∆µ. The term chemical potential (potential
energy) is used because the work comes about typically through chemical changes.
Chemical vapor deposition (CVD) is a chemical process by which reaction between gaseous
reactants results in products that are deposited as solid. It is a growth technique used to
deposit thin layers of material on a substrate. Typically, a crystalline substrate is chosen
leading to epitaxial growth of the deposited material. Growth occurs when a heated
substrate is placed in a stream of vapor containing species that react on or close to the hot
substrate surface, leading to deposition. Often, the reaction vessel is made from high
purity quartz that is non-reactive and does not lead to contamination of the deposited
material. Substrates are usually heated by placing them on a graphite susceptor which is
heated by induction; that is, a radio-frequency radiation generated in a coil wound around
the exterior of the reaction vessel induces heating of the susceptor. The gases chosen for
a given process depend on the choice of material that is to be deposited. For example, to
deposit silicon SiCl4 (i.e., silicon-tetrachloride), SiH2Cl2 (i.e., dichloro-silane), SiHCl3
(i.e., trichloro-silane) and SiH4 (i.e., silane) are commonly used compounds. For the
chlorine-based compounds, the decomposition occurs on the hot substrate by chemical
reduction of the compound with hydrogen. The overall chemical reaction for the case of
SiCl4 may be written as: SiCl4(Gas) + H2(Gas) ⇔ Si(Epitaxial) + 4 HCl(Gas). Typically,
temperatures in excess of about 1000 oC are required for deposition, principally because
of the need for a minimum temperature before Si atoms deposited on the surface can
migrate and find their mimimum energy lattice sites. Doping of epilayers is
accomplished by introducing controlled quantities of hydrides of the dopants into the
gas stream; the most commonly used gases are PH3 (i.e., phosphine), AsH3 (i.e.,
arsine) and B2H6 (i.e., diborane). In practice, doping is found to be a linear function of
the concentration of dopant to Si-based molecules in the feedstock over a wide range of
concentrations. This makes achieving controlled doping levels relatively simple. The
technique is relatively simple and controllable, and since deposition can occur on a
number of substrates (held on the same susceptor) simultaneously, it is also highly
economical. [H.R.]
Chemical-mechanical polishing (CMP) involves the use of a slurry compound to
microscopically polish the surface of a wafer by both abrasion and chemical etching,
prior to its use as a substrate. The term chemical-mechanical planarization refers to
the use of a similar type of slurry compound to microscopically plane a device layer.
[H.R.]
Chip is a piece (or a volume) of a semiconductor crystal which contains many integrated active
and passive components to implement a circuit.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
19
Chromatic dispersion is due to the dispersion of a traveling pulse of light along an optical
fiber as a result of the wavelength dependence of the propagation characteristics and
waveguide properties but excluding multimode dispersion. Chromatic dispersion arises
as a result of the range of wavelengths in the emission spectrum of the emitter (e.g.
LED or laser diode) that are coupled into the fiber. It is the combination of material
dispersion and waveguide dispersion.
Citric acid (C6H8O7) is an organic acid that is produced from lemons, limes and pineapples.
Citric acid is a colorless, odorless, crystalline powder with a melting point of 153 °C. It is
used in a variety of semiconductor etching solutions. [H.R.]
Cladding is the dielectric layer that surrounds the dielectric core of an optical waveguide.
Clausius-Mossotti equation relates the dielectric constant (εr), a macroscopic property, to the
polarizability (α), a microscopic property.
Clean dry air (CDA) is air that has been compressed, dried (i.e., using either a refrigerant or a
desiccant dryer) and filtered. A typical CDA system operates at ± 120 psi, has a dew
point of less then 40 °F and contains no particles of size larger than 0.015 µm. [H.R.]
Cleanroom is an environment in which humidity, temperature and contamination are kept under
precise control. Cleanrooms are rated by the concentration of dust particles in them, in
units of numbers of particles contained in one cubic foot of air. Usual designations
(given in order of increasing cleanliness) are Class 10,000, Class 1000, Class 100, Class
10 and Class 1. The tolerances on temperature and humidity control also become more
stringent as the class rating decreases. For example, the typical specification for a Class 1
cleanroom is a temperature of 70 °F ± 0.5 °F and a relative humidity of 50% ± 5%.
[H.R.]
Cleavage plane refers to a preferred crystallographic plane for a crystalline material to fracture,
resulting in a characteristic fracture surface. That is, cleaved materials exhibit atomically
smooth and flat surfaces corresponding to specific atomic planes, after fracture.
Typically, materials will favor the most densely packed atomic planes (or so-called closepacked planes) for cleavage, as the energy involved in moving opposing planes of atoms
over each other is often lower than for other planes. This may be attributed to the
relatively small displacements required for a unit of interplanar displacement on such
planes. For example, the most densely packed planes for silicon are the {111} family of
planes on which cleavage often occurs. [H.R.]
Cluster tool is a tool capable of performing a series of processes on a wafer by making use of
typically two to five individual process chambers. Wafers are typically loaded automated
into the cluster tool and shuttled back and forth between the individual process chambers.
[H.R.]
Cobalt silicide is an important silicide that is used extensively for self-aligned masking
technology and has one of the lowest resistivities of all of the refractory metal silicides
(i.e., 18 to 25 µΩ cm). It also has a high value for its binary eutectic temperature (lowest
binary alloy melting temperature), 1195 °C, suitable for device processing. [H.R.]
Coercivity or the coercive field Hc measures the ability of a magnetized material to resist
demagnetization. It is the required reverse applied field that would remove any remanent
magnetization, i.e. demagnetize the material.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
20
Coherent radiation (or light) consists of waves that have the same wavelength and always
have the same phase difference with respect to each other at all times.
Cohesive energy is the energy needed to take a solid apart into constituent parts that are
infinitely separated from each other (i.e. do not interact). Usually the constituent parts are
atoms. Atomic cohesive energy would be the energy required to take a solid apart into
its constituent atoms, for example, disassemble a copper crystal into individual copper
atoms. On the other hand, the cohesive energy of solid nitrogen (indeed, any van der
Waals solid) is more conveniently defined as the energy needed to break it into
individual isolated N2 molecules.
Collector junction is the metallurgical junction between the base and the collector of a
bipolar transistor.
Compensated semiconductor contains both donors and acceptors in the same crystal region
which compensate for each other's effects. For example, if there are more donors than
acceptors, Nd > Na, then some of the electrons released by donors are captured by
acceptors and the net effect is that Nd − Na number of electrons per unit volume are left in
the conduction band.
Complementarity principle suggests that the wave model and the particle model are
complementary models in that one model alone cannot be used to explain all the
observations in nature. For example, the electron diffraction phenomenon is best
explained by the wave model whereas in the Compton experiment the electron is treated
as it were a particle, i.e. it is deflected by an impinging photon which imparts an
additional momentum to the electron.
Complementary MOS (CMOS) device uses a combination of NMOS (n-channel MOS) and
PMOS (p-channel MOS) transistors to implement solid state switches.
Complex relative permittivity (εr' + jεr'') has a real part (εr') that determines the charge
storage ability and an imaginary part (εr'') that determines the energy losses in the
material as a result of the polarization mechanism. The real part determines the
capacitance through C= εo εr'A/d and the imaginary part determines the electric power
dissipation per unit volume as heat by E 2ωεoεr'', where E is the electric field, ω is the
angular frequency and εo is the absolute permittivity.
(b)
(a)
2.7
PET at 115°C
2.65
r'
2.6
r'
2.55
2.5
r''
2.45
2.4
2.35
1
10
2
10
3
10
Frequency (Hz)
10
4
0.045
40
0.04
30
20
0.035
r''
0.03
10
0.025
-10
0.02
105
KCl
r'
r''
0
-20
0
1
2
3
4
5
6
7
8
9
10
12
Frequency ( 10 Hz)
Real and imaginary parts of the dielectric constant, r' and r'', vs frequency
for (a) a polymer, PET, at 115°C and (b), an ionic crystal, KCl, at room
temperature. Both exhibit relaxation peaks but for different reasons.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
21
Compton effect is the scattering of a high energy photon by a "free" electron. The Compton
effect is experimentally observed when an X-ray beam is scattered from a target that
contains many conduction ("free") electrons such as a metal or graphite. When an X-ray
photon interacts with a conduction electron in a metal it becomes deflected just as if it
were a "particle" with a certain momentum p. The photon loses some of its energy to the
electron and therefore suffers a reduction in the frequency from υ to υ'. From the
Compton experiment, the momentum of the photon has been shown to conform to p =
h/λ (De Broglie relationship).
Conduction band (CB) is a band of energies for the electron in a semiconductor where it can
gain energy from an applied field and drift and thereby contribute to electrical
conduction. The electron in the CB behaves as of were a "free" particle with an effective
mass, me*.
Conductivity is a measure of the rate at which charge carriers (e.g. electrons) are transported in
a material under an applied field. It is the reciprocal of resistivity. Conductivity is the
current density flowing through a material per unit applied electric field, that is, the
conductivity σ is defined by
J = σE
where J is the current density and E is the applied field. The conductivity also indicates
the rate at which electrical energy from the applied field is converted to heat in a material
as charge carries, driven by the field, collide with lattice vibrations, impurities, defects etc.
This power dissipation in the material due to charge flow is called Joule heating and the
power Pvol per unit volume dissipated in the material is
Pvol = JE = σE2.
The conductivity σi due to the transport of a given species i of charge carriers (such as
electrons) depends on the drift mobility of carriers µi, their concentration ni and the
charge qi each carrier has,
σi = qiniµi.
The total conducivity is the sum of conductivities due to each species of charge carriers.
Congruent transformation, such as congruent melting or congruent evapoation, refers to a
change in the phase without a change in the composition of the material. The
composition remains the same during the transformation. On the other hand, if a material
is heated through melting (or evaporation) and its composition changes with time, the
process is said to be an incongruent transformation. Most II-VI semiconductors
evaporate congruently. That is, the composition of the vapor remains in the same
stoichiometric proportions as the solid, for a given temperature of evaporation (i.e., equal
fractions of group II and group VI materials, in both the solid and vapor phases). [H.R.]
Continuity equation is an equation that describes the rate of change with time in the
concentration of one type of carrier (i.e., either electrons or holes). In particular the
continuity equation describing the time rate of change for a process that resulted in an
excess concentration of holes ∆p, above the equilibrium concentration po, would include
terms describing a spatial variation in the current density, generation and
recombination. The current density in general has a drift contribution, arising from an
electric field, and a diffusion contribution arising from a concentration gradient Suppose
that at one instant the hole concentration p(x,t) as a function of distance x in a sample is
as shown in the figure. Assume that there is no variation in p lateral, along y and z
directions. Consider a small elemental volume of thickness δx, then
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
22
Net rate of increase in hole concentration in the elemental volume δx
= Rate of increase due to spatial change (decrease) in the current
+ Rate of generation (Gn)
− Rate of recombination (Rn)
p(x,t)
Arbitrary hole concentration p(x,t)
profile in a semiconductor.
Consider an elemental volume x
at x. The net rate of change of p
depends on the change in the
current density Jh, generation Gh
and recombination Rh processes
within this element. is the
electric field in the sample.
Instantaneous hole
concentration
Gh
Jh(x)
Rh
Jh(x+ x)
x
x
In mathematical form, the continuity equation for holes at one point in a sample where
the current density Jh due the drift and diffusion of these holes is,
1 ∂Jh
∂∆p ∂p
=
=−
+ Gh − Rh
∂t
∂t
e ∂x
where p and ∆p are the instantaneous and excess electron concentrations respectively, Gh
and Rh refer to the generation and recombination rates for holes, e is the charge of a
hole (electron charge) , and Jh refers to the hole current. If drift and diffusion processes
are included in the description of the hole transport equation, then the hole current
density Jh can be written as,
∂p
Jh = eµh pE − eDh
∂x
where µh, Dh are the drift mobility and diffusivity of holes, and E is the electric field,
respectively. Note that the first term on the right hand side refers to drift, while the
second term refers to diffusion (from Fick’s first law). The continuity equation can be
derived directly from Maxwell’s equations, and in particular, Ampere’s law.
Consider a sample in which the electric field E is uniform and an excess hole
concentration ∆p has been created at a time t = 0 at some location by suitable means (e.g.
by photoexcitation). Suppose that the recombination time for the excess holes is τh, then
the rate of recombination Rh is ∆p/τh and the above two equations combine to give,
∂∆p
∂∆p
∂ 2 ∆p ∆p
µ
D
= − hE
+ h
−
∂t
∂x
∂x 2
τh
The excess holes simply drift, diffuse and recombine with electrons at the same
as indicated in the figure. If the initial excess hole concentration is a simple delta
function, then the excess hole concentration is given by
 ( x − µhEt )2 
 t 
Nh
∆p( x, t ) =
exp
−
exp − 


1/ 2
( 4πDht )
4 Dht 
 τh 

where Nh is the total number of excess holes initially injected per unit area. The hole
concentration profile shifts, that is drifts, along x with a velocity dx/dt = vd = µhE.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
23
p(x,t)
t=0
t1 > 0
t2 > t1
x
If we inject excess holes in a sample at one position, then in the
presence of an electric field , this charge packet drifts and at the
same time broadens due to diffusion. The area under the p profile
remains constant only if there is no recombination or extraction at
an electrode.
[H.R.]
Cooper pair is a "quasi-particle" formed by the mutual of two electrons with opposite spins and
opposite linear momenta below a critical temperature. It has a charge of −2e and a mass
of 2me but no net spin. It does not obey Fermi-Dirac statistics. The electrons are held
together by the induced distortions and vibrations of the lattice of positive metal ions
with which the electrons interact.
Coordination number (CN) is the nearest number of atoms surrounding a given atom in a
crystal, or given structure. In the body centered cubic (BCC) crystal structure, each atom
has eight neighbors. The center atom in the BCC unit cell has 8 nearest neighbors
because there are eight corners.
Corona discharge is a local discharge in a gaseous atmosphere where the field is sufficiently
high to cause dielectric breakdown, for example, by avalanche ionization.
Cotton-Mouton effect is the inducement of birefringence in a material due to the application of
a magnetic field, analogous to the electro-optic Kerr effect. For example, when a
magnetic field is applied to a liquid, the molecules may become aligned resulting in an
optical anisotropy. The induced change in the refractive index is proportional to the
square of the magnetic field.
Covalent bond is the sharing of a pair of valence electrons between two atoms. For example
in H2, the two hydrogen atoms share their electrons so that each has a closed shell.
Critical angle (θc) is the angle of incidence that results in a refracted wave at 90û when the
incident wave is traveling in a medium of lower refractive index and is incident at a
boundary with a material with a higher refractive index.
Critical electric field is the field in the space charge (or depletion) region at reverse breakdown
(avalanche or Zener)
Critical magnetic field, Bc, is the maximum field that can be applied to a superconductor
without destroying the superconducting behavior. Bc decreases from its maximum value
at absolute zero to zero at Tc.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
24
Critical temperature, Tc, is a temperature that separates superconducting state from the normal
state. Above Tc the substance is in the normal state with a finite resisitivity but below Tc it
is in the superconducting state with zero resisitivity.
Critical thickness in epitaxy refers to the maximum thickness that an epitaxially deposited
film can have before the elastic mismatch energy reaches a critical value and results in the
formation of so called misfit dislocations to accommodate this mismatch energy. That is,
when the lattice constant of the substrate and epitaxial layer differ, the atomic planes in
the epitaxial material attempt to maintain continuity with those of the substrate. However,
the elastic distorsion of the atomic planes in the epitaxial layer, results in stored strain
energy in the film, that is eventually sufficient (for a sufficiently thick film) to permit
misfit dislocations to be nucleated. If b is the Burgers vector of the dislocation, hc is the
critical thickness, f is the misfit strain and υ is Poisson’s ratio, then hc is given by,
b
  hc  
hc =
+1
ln
8π (1 + υ ) f   b  
For the case of semiconductor epitaxial growth on (100) surfaces, the most common type
of misfit dislocation is the 60o type, whose direction and Burgers vector both lie along
<110> type directions at 60o to each other − the maximum strain reduction occurs in this
case when the dislocations form at the substrate-epitaxial layer interface. [H.R.]
Crystal is a three dimensional periodic arrangement of atoms or molecules or ions. A
characteristic property of the crystal structure is its periodicity and a degree of
symmetry. For each atom the number of neighbors and their exact orientations are well
defined, otherwise the periodicity will be lost. There is therefore a long range order
resulting from strict adherence to a well defined bond length and relative bond angle (or
exact orientation of neighbors). An infinite periodic array of geometric points in space
defines a space lattice or simply a lattice. Strictly, a lattice does not contain any atoms or
molecules because it is simply an imaginary array of geometric points. A crystal is
obtained from the lattice by placing an identical group of atoms (or molecules) at each
lattice point. The identical group of atoms is called the basis of the crystal structure;
conceptually
Crystal = Lattice + Basis
Crystal momentum of the electron in a crystal is hk where k is the “wavevector” of the
electron in the crystal, that is ψ(x) =U(x)exp(jkx) is a solution of the Scrödinger equation
given the periodic potential energy for the particular crystal of interest. Such a solution
is a traveling wave with a wavevector k and that is spatially modulated by U(x). The rate
of change of hk is equal to the sum of all external forces only thus hk represents what we
understand as the momentum of a particle. However, in this case the electron is in the
crystal and subject to a periodic potential energy; hence the name crystal momentum. In
general, hk is not the true momentum of the electron because the rate of change of hk is
not equal to the total force, including internal forces. Nonetheless, we can treat hk in most
cases as a “momentum”.
Crystallization is a process by which crystals of a substance are formed from another phase
of that substance, for example, from the melt by solidification just below the fusion
temperature or by condensation of the molecules from the vapor phase onto a substrate.
The crystallization process initially requires the formation of small nuclei of the crystal
phase which contain a limited number (perhaps 103-104) of atoms or molecules of the
substance. Following nucleation, the nuclei grow by atomic diffusion from the melt to
the nuclei.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
25
Curie temperature (TC) is the critical temperature at which the ferromagnetic and ferrimagnetic
properties are lost. Above the Curie temperature the material behaves as if it were
paramagnetic.
Czochralski (CZ) growth is a type of melt growth technique commonly used for preparing
boules of electronic materials such as silicon. The CZ growth method was first
introduced by J. Czochralski in 1918, and involves dipping a single crystal seed into the
melt, and after equilibriating it with the melt, withdrawing it at a constant rate while
simultaneously rotating it. In this approach, material crystallizes onto the cooler seed
crystal and as the seed is slowly withdrawn further material continuously deposits onto
the seed. For a given material system and operating conditions, reducing the pulling rate
can be used to increase the boule diameter. Typical pulling speeds for Si are about 10-20
cm/hour using rotation rates of about 10 revolutions per minute. A great advantage of
this technique is that the boule grows unconstrained (i.e., not in a crucible as would be
the case for Bridgeman growth) and therefore avoids issues related to relative
expansion on cooling. [H.R.]
Dark current of a photodetector is the dc current that flows in the absence of light when it is
carrying a bias voltage. In a pn junction photodiode, the bias voltage is a reverse bias
across the device, and the dark current depends strongly on the temperature. There are
two contributions to the dark current which are the diffusion of minority carriers in
the neutral regions and the thermal generation of electron hole pairs (EHPs) in the space
charge layer (SCL). Both depend strongly on the temperature and the dark current
increases exponentially with increasing temperature, typically as a thermally activated
process, i.e. Idark ~ exp(−Eg/ηkT) where η is 1 if the reverse current is controlled by
minority carrier diffusion in the neutral regions and 2 if it is controlled by thermal
generation of EHPs in the SCL, Eg is the bandgap of the semiconductor material, k is
Boltzmann’s constant and T is the temperature (K). See reverse diode current.
De Broglie relationship relates the wave-like properties (e.g. wavelength, λ) of matter to its
particle-like properties (e.g. momentum, p) via λ = h / p where h is Planck’s constant, λ
is the wavelength associated with wave-like properties and p is the momentum associated
with particle-like properties. For example, a stream of electrons, each with a momentum
p, can be made to be diffracted from a single crystal just like an X-ray (electromagnetic
wave) thereby exhibiting a wavelike property with a wavelength λ.
Debye equations attempt to describe the frequency response of the complex relative
permittivity, εr'+jεr '', of a dipolar medium through the use of a single relaxation time
τ to describe the sluggishness of the dipoles driven by the external ac field.
Debye length λd is the distance beyond which a given charge is effectively ‘screened’ − that is,
particles at distances beyond λd are not influenced by the charge. The Debye length
describes how mobile charges respond to a non-uniform potential variation, by spatially
re-distributing themselves to modify the potential and effectively screen out the potential
variation at larger distances. The dependence of the potential φ(r) associated with an
isolated charge Ze as a function of radial position r from the charge is given by
Coulomb’s Law as,
Ze
φ (r ) =
4πεr
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
26
where ε = εrεo is the permittivity of the medium, εr is the relative permittivity and εo is
the absolute permittivity. The redistribution of mobile charges around this isolated charge
will result in the charge appearing to be neutralized or ‘screened’ at distances beyond λd,
with a resultant change in the potential distribution φ′(r) for the screened charge of,
 r
Ze
φ ′( r ) =
exp − 
4πεr
 λd 
The Debye length in a plasma describes the screening of a point charge by a
sheath of positive and negative ions, aligning themselves so as to shield the influence of
the charge Ze from the rest of the plasma. The Coulomb potential near this charge can be
seen to be reduced, with the potential dropping to zero for r >> λd. In this case, λd is
given by,
−1
 e 2 no  1 1   2
λd = 
 − 
ε
k
 Te Ti  

where k is Boltzmann’s constant, and Te and Ti are the effective temperature of
electrons and ions in the plasma, respectively, and no is the initial ion concentration in the
plasma. In the derivation of the above equation, it is assumed that the distance between
ions in the plasma is much less that λd, resulting in the need for many such ions to
effectively screen a given charge Ze.
In the case of semiconductors, there are a number of examples of how the term
Debye length is applied. One example is the case of a fixed ionized impurity,
representing the charge Ze in the first equation, with εr referring to the relative
permittivity of the semiconductor As discussed above, free charges will spatially
distribute themselves to shield this charge from other carriers, modifying the potential −
this typically occurs in the vicinity of depletion regions of pn junctions and Schottky
barriers. The general expression for the Debye length under these circumstances is given
by,
1/ 2
 kTε 
=
λd  2

 e ( n + p) 
where T is the temperature of the material, and n and p refer to the concentration of free
electrons and holes in the material, respectively. [H.R.]
Debye temperature is a characteristic temperature of a particular crystal above which nearly all
the atoms are vibrating in accordance of the kinetic molecular theory, that is, each atom
has an average energy (potential + kinetic) of 3kT due to atomic vibrations, and the heat
capacity is determined by the Dulong-Petit rule.
Degenerate semiconductor has so many dopants that the electron concentration in the
conduction band (CB), or hole concentration in the valence band (VB), is comparable
with the density of states in the band. Consequently the carriers interact with each other
and Fermi-Dirac statistics must be used. The Fermi level is either in the CB for a n+
type degenerate, or in the VB for a p+ type degenerate semiconductor. The superscript +
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
27
indicates a heavily doped semiconductor.
E
CB
Impurities
forming a band
(E)
EF n
Ec
Ev
a
CB
Ec
Ev
EFp
VB
b
(a) Degenerate n-type semiconductor. Large number of donors form a band
that overlaps the conduction band (CB). (b) Degenerate p-type
semiconductor. (E) is the density of states, Ec and Ev are the conduction
and valence band edges and EFn is the fermi level.
Deionization (DI) is one of the primary processes used in the production of ultra-pure water.
Such water is an essential ingredient in the wet-chemical processing of semiconductors.
The key step in the process is ion exchange, which is a process that uses resins in bead
form to exchange acceptable ions (e.g., sodium or hydrogen) for unwanted ions (e.g.,
calcium and magnesium). [H.R.]
Density of states, g(E), is the number of electron states (e.g. wavefunctions, ψ(n,l,ml,ms))
per unit energy per unit volume. g(E)dE is thus the number of states in the energy range
E to E+dE per unit volume.
Density of vibrational states g(ω) is the number of lattice vibrational modes per unit angular
frequency range; g(ω)dω is the total number of lattice vibrational modes in the frequency
range ω to ω + dω.
Depletion (space charge) layer capacitance is the incremental capacitance (dQ/dV) due to the
change in the exposed dopant charges in the depletion layer as a result of the change in
the voltage across the pn junction.
Depletion MOSFET is a MOSFET device that already has a conducting channel between the
source and the drain in the absence of a gate voltage. In the depletion mode of operation
the applied gate voltage reduces the conductance of the channel and hence reduces the
drain current. In the enhancement mode of operation the gate voltage polarity enhances
the conductance of the source to drain channel and increases the drain current.
Detectivity is the reciprocal of noise equivalent power (NEP).
Diamagnetic material has a negative magnetic susceptibility and reduces or repels applied
magnetic fields. Superconductors are perfect diamagnets which repel the applied
field. Many substances possess weak diamagnetism so that the applied field is slightly
decreased within the material.
Diborane (B2H6) is a toxic and pyrophoric gas that is used as a source of boron for p-type
doping of silicon by ion implantation as well as during chemical vapor deposition
(CVD) of silicon. [H.R.]
Dichlorosilane (H2SiCl2) is a flammable and corrosive liquid that is used to form both silicon
dioxide and silicon nitride using chemical vapor deposition (CVD). It is also used
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
28
to grow silicon layers epitaxially using CVD. Dichlorosilane is a chlorine containing
material that will readily react with any moisture to form hydrochloric acid. [H.R.]
Dichroism is a phenomenon in which the optical absorption in a substance depends on the
direction of propagation and the state of polarization of the light beam. A dichroic
crystal is an optically anisotropic crystal in which either the e-wave or the o-wave is
heavily attenuated (absorbed).
Die is an individual device that is cut (usually by scribing) from a wafer before it is packaged.
[H.R.]
Dielectric is a material in which energy can be stored by the polarization of the molecules. It
is a material that increases the capacitance or charge storage ability of a capacitor. Ideally
it is a non-conductor of electrical charge so that an applied field does not cause a flow of
charge but instead relative displacement of opposite bound charges and hence
polarization of the medium.
Dielectric loss is the electrical energy lost as heat in the polarization process in the presence
of an applied ac field (an alternating electronic field). The energy is absorbed from the ac
voltage and converted to heat during the polarizations of the molecules. It should not be
confused with conduction loss σE 2 or V2/R.
Dielectric mirror is made from alternating high and low refractive index quarter-wave thick
multilayers. Such dielectric mirrors provide a high degree of wavelength selective
reflectance at the required free surface wavelength λ if the thicknesses of alternating
layers d1 and d2 with refractive indices n1 and n2 are such that
n 1d 1 + n 2d 2 = 1/2λ
which then leads to the constructive interference of all partially reflected waves at the
interfaces.
Dielectric strength is the maximum field (Ebr) that can be sustained in a dielectric beyond
which dielectric breakdown ensues, i.e. there is a large conduction current through the
dielectric shorting the plates.
Diffusion is a random process by which particles move from high concentration regions to low
concentration regions. There is a flow of particles of a given species from high to low
concentration regions by virtue of their random motions. Diffusion is a process by which
atoms migrate by virtue of their random thermal motions. Consider an impurity atoms in
an interstitial void in a two dimensional hypothetical crystal lattice. The impurity atom
has four neighboring voids to jump into. If θ is the angle with respect to the x-axis then
these voids are at directions θ = 0° 90°, 180° and 270°. Each jump is in random direction
along one of these four angles. As the impurity atom jumps from void to void it leaves its
original location at O and after N jumps, after time t, it has been displaced from O to O′.
If each step is a distance a either parallel to x or parallel to y, then after N steps, the mean
square distance L2 from O to O′. is
L2 = a2N.
If the rate of jumps is ϑ (jumps per second) then N jumps take a time t = N/ϑ. Thus the
mean square distance diffused by the impurity in time t is
L2 = a2ϑt = 2Dt
1
2
where D = /2a ϑ is defined as the diffusion coefficient. The rate of jumps, or the jump
frequency, depends on the probability that the impurity has sufficient energy to break its
bonds and move into the neighboring void. The potential energy barrier that must be
overcome is the activation energy EA of the diffusion process. The jump frequency ϑ is
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
29
therefore proportional to the Boltzmann factor exp(−EA/kT), where k is Boltzmann’s
constant and T is the temperature, and the diffusion coefficient is thermally activated.
After N jumps
O
a
y
= 90°
a
= 180°
= 0°
L
x
= 270°
O
In two dimensional diffusion, an impurity atom has four site choices for
jumping (diffusing) into a neighboring interstitial vacancy. After N jumps,
the impurity atom would have been displaced from the original position at O
to O . L is the root mean square distance diffused after N jumps, or in time t.
Diffusion (storage) capacitance is the pn junction capacitance due to the injection and
storage of minority carriers in the neutral regions when a forward bias is applied.
Diffusion coefficient is a measure of the rate at which atoms diffuse. It depends on the nature
of the diffusion process and typically it is temperature dependent. It is defined as the
diffusion flux per unit concentration gradient. See diffusion.
Diffusion couple refers to two materials that are brought together at an interface, about which
inter-diffusion occurs , i.e. the counter movement of species across the interface.
Typically, at elevated temperatures, and given sufficient time, diffusion occurs to reduce
concentration gradients, and equalize the concentration of species, about the interface. If
the diffusivities of the counter moving species are different, there will be a net flow of
matter about the interface, resulting in the physical location of the interface neing
displaced. [H.R.]
Diffusion of an impurity in a solid is the random motion of the impurity from one site to
another as a result of its exchange of energy with crystal vibrations. Diffusion of atoms
in a solid is a thermally activated process. Suppose that he impurity atom is at an
interatomic void A in the crystal, called an interstitial site. For the impurity atom to
move from A to take up a new position at the neighboring void at B, it must push the host
neighbors apart as it moves across. This requires energy in much the same way as
toppling the filing cabinet. There is therefore a potential energy barrier EA to the motion
of this atom from A to B. Both the host and the impurity atoms in the solid are vibrating
about their equilibrium positions with a distribution of energies and also continually
exchanging energies which leads to energy fluctuations. In thermal equilibrium, at any
instant, we can expect the energy distribution of the atoms to obey the Boltzmann
distribution law. The average kinetic energy per atom, which is vibrational, is on the order
of kT, where k is Boltzmann’s constant and T is the temperature, and this certainly will
not allow the impurity to simply overcome the PE barrier EA because typically EA is much
greater than kT. The rate of jump, called the diffusion, of the impurity from A to B
depends on two factors. First is the number of times the atom tries to go over the
potential barrier, which is the vibrational frequency υo in the AB direction. Secondly, it
depends on the probability that it has sufficient energy to overcome the PE barrier. Only
during those times when the atom has an energy greater than the potential energy barrier
EA = UA* − UA will it jump across from A to B. During this diffusion process, the atom
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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attains an activated state A* with an energy EA above UA, so that the crystal internal
energy is higher than UA. Suppose that there are N impurity atoms. At any instant,
according to the Boltzmann distribution, nEdE of these will have kinetic energies in the
range E to E + dE so that the probability that an impurity atom has an energy E greater
than EA is
Number of impurities with E > E A
Probability( E > E A ) =
Total number of impurities
∞
∫ nE dE
 E 
= A exp − A 
N
 kT 
where A is a dimensionless constant that has only a weak temperature dependence. The
rate of jumps, jumps per seconds, or simply the frequency of jumps ϑ from void to void
is
ϑ = (Frequency of attempt along AB)(Probability of E >EA)
 E 
ϑ = Avo exp − A  ; E A = U A * − U A
 kT 
Probability( E > E A ) =
A
A*
EA
B
U = PE(x)
UA*
A*
EA
UA= UB
A
B
X
Displacement
Diffusion of an interstitial impurity atom in a crystal from one
void to a neighboring void. The impurity atom at position A
must posses an energy EA to push the host atoms away and move
into the neighboring void at B.
Digital communications is the transmission of information in the form of pulses from one
location to another. Typically, an analog signal is sampled at fixed intervals and the value
at each interval is put into a binary code containing 1s and 0s and the coded information
is then transmitted as pulses (1 corresponding the presence and 0 to the absence of a
pulse). Thus the analog signal is digitized and sent by pulses.
Diode (short diode) is a pn junction in which the neutral regions are shorter than the
minority carrier diffusion lengths.
Dipolar (orientational) polarization arises when randomly oriented polar molecules in a
dielectric are rotated and aligned by the application of a field so as to give rise to a net
average dipole moment per molecule. In the absence of the field the dipoles (polar
molecules) are randomly oriented and there is no average dipole moment per molecule.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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In the presence of the field the dipoles are rotated, some partially and some fully, to align
with the field and hence give rise to a net dipole moment per molecule.
Dipolar relaxation equation describes the time response of the induced dipole moment per
molecule in a dipolar material in the presence of a time dependent applied field. The
response of the dipoles depends on their relaxation time which is mean time required
to dissipate the stored electrostatic energy in the dipole alignment to heat through lattice
vibrations or molecular collisions.
Dipole relaxation (dielectric resonance) occurs when the frequency of the applied ac field is
such that there is maximum energy transfer from the ac voltage source to heat in the
dielectric through the alternate polarization and depolarization of the molecules by the
ac field. The stored electrostatic energy is dissipated through molecular collisions and
lattice vibrations (in solids). The peak occurs when the angular frequency of the ac field
is the reciprocal of the relaxation time.
Direct recombination capture coefficient B is a material constant that characterizes the rate of
recombination of excess injected carriers in a direct bandgap semiconductor. Suppose
that excess electrons and holes have been injected, as would be in a pn-junction under
forward bias, and that ∆np is the excess electron concentration and ∆pp is the excess
hole concentration in the neutral p-side of a GaAs pn junction. Injected electron and
hole concentrations would be the same to maintain charge neutrality, that is, ∆np = ∆pp.
Thus, at any instant,
np = npo + ∆np = instantaneous minority carrier concentration,
and
pp = ppo + ∆np = instantaneous majority carrier concentration.
The instantaneous recombination rate will be proportional to both the electron and hole
concentrations at that instant , that is nppp. Suppose that the thermal generation rate of
electron hole pairs is Gthermal. The net rate of change of ∆np is then,
∂∆np/∂t = −Bnppp + Gthermal
where B is a constant called the direct recombination capture coefficient. In equilibrium
∂∆np/∂t = 0 and np = npo and pp = ppo, where the subscript o refers to thermal equilibrium
concentrations, so that Gthermal = Bnpoppo. Thus, the rate of change in ∆np is
∂∆np/∂t = −B(nppp − npoppo)
Dislocation is a line imperfection within a crystal that extends over many atomic distances. See
edge dislocation and screw dislocation.
Dispersion in fiber optics is the spread in time, known as temporal broadening, of an
infinitesimally thin optical pulse as it propagates along the fiber. The temporal
broadening is due the different propagation characteristics of different wavelength
components of light that are coupled into the fiber and propagate along the guide. Due to
the dispersion effect there is an upper limit for the rate at which we can transmit light
pulses along a fiber.
Dispersion relation relates the angular frequency ω and the wavevector k of waves that are
allowed to exist in a given system. For example, in a crystal lattice, the coupling of atomic
oscillations leads to a particular relationship between ω and k which determines the
allowed lattice waves and their group velocities. The dispersion relation is crystal
structure specific, that is, it depends on the lattice, basis and bonding. In a dielectric
medium which experiences an applied electric field of angular frequency ω, the
polarization and hence the relative permittivity εr depend on the frequency ω; and εr =
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
32
εr(ω) is the dielectric dispersion relation. In optical materials, the dispersion relation is a
relationship between the refractive index n and the wavelength λ of the electromagnetic
wave, n = n(λ); the wavelength usually refers to the free-space wavelength.
Domain wall energy is the excess energy in the domain wall as a result of the gradual
orientations of the neighboring spin magnetic moments of atoms through the wall region.
It is the work done in establishing a wall by breaking up a single domain into two
domains with different orientations of magnetization. Domain wall energy is the excess
energy due to the excess exchange interaction energy, magnetocrystalline
anisotropy energy and magnetostrictive energy in the wall region.
Domain wall is a region between two neighboring magnetic domain of differing orientations
of magnetization.
Donor atoms are dopants in the semiconductor that have a valency one more than the host
atom. They therefore donate electrons to the conduction band (CB) and thereby create
electrons in the CB which leads to n > p and hence to an n-type semiconductor (n is the
electron concentration in the CB and p is the hole concentration in the valence band
(VB)).
Arsenic doped Si crystal.
The four valence electrons
of As allow it to bond just
like Si but the fifth electron
is left orbiting the As site.
The energy required to
release to free fifth-electron
into the CB is very small.
As+
Electron Energy
e–
Ec
~0.03 eV E
d
Energy band diagram for an n-type Si
doped with 1 ppm As. There are
donor energy levels just below Ec
around As+ sites.
CB
As+
As+
As+
As+
Ev
x Distance into
crystal
As atom sites every 106 Si atoms
Dopant is an element that is incorporated in trace amounts into bulk crystals to form doped
wafers, or into epitaxial layers to influence their conductivity type (i.e., n- or p- type) and
their resistivity. Dopants are classified as being of either acceptor or donor type. [H.R.]
Doping is the process in which dopants are incorporated into bulk crystals or thin layers of
semiconductors by using a variety of processes. These include, doping during bulk
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
33
material or layer fabrication (so called in-situ doping), and also use of diffusion and ion
implantion. These approaches all are designed to permit the controlled introduction of
precise amounts of an impurity to create n- or p-doped material. Using masking,
implantation and diffusion processes permit the doping of only selected regions of
material. [H.R.]
Doppler effect is the change in the measured frequency of a wave due to the motion of the
source relative to the observer. If the source is moving towards the observer the
frequency increases (wavelength decreases), and it decreases when the source is moving
away. As a fast train approaches an observer, its whistle becomes higher in pitch
(frequency) and as the train moves away from the observer, its pitch becomes lower. The
true source frequency remains the same but more waves arrive at the observer per second
when the source is moving toward the observer than when it is moving away. In the case
of electromagnetic radiation, if v is the relative velocity of the source object toward the
observer and υo is the source frequency, then the measured electromagnetic wave
frequency υ is υ = υo[1+(v/c)], for (v/c) << 1.
Drift mobility is the drift velocity per unit applied field. If µd is the mobility then the defining
equation is vd=µdE where vd is the drift velocity and E is the electric field.
Drift velocity is the average velocity, over all the conduction electrons in the conductor, in the
direction of an applied electrical force (F = −eE for electrons). In the absence of an
applied field, all the electrons are moving around randomly and the average velocity, over
all the electrons, in any direction is zero. With an applied field, Ex, there is a net velocity
per electron, vdx, in the opposite direction to the field where vdx depends on Ex via
vdx=µdEx where µd is the drift mobility.
Drive-in diffusion is the second step in the semiconductor fabrication process to form a
controlled profile of impurities in a semiconductor device structure. The first step is the
so-called predeposition step in which a shallow layer (typically a few tenths of a micron
deep) of the desired dopant species are introduced into the crystal by diffusion. The
drive-in step is a higher temperature step which is used to diffuse this latent impurity
profile deeper into the structure in a controlled way. The predeposition step will typically
result in the chosen impurity being dissolved in the surface layer to a concentration
determined by the equilibrium solid-solubility of that species in the host material. Since
the drive-in process does not involve introducing any additional source of the chosen
impurity, this process results in a lower concentration of the impurity diffused deeper
into the semiconductor host material. If the predeposition impurity profile is assumed to
be close to a delta function, then the solution of the diffusion equation for the
concentration C(x,t) profile as a function of depth x and time t, will be given by,
 x2 
Q
C( x, t ) =
exp −

 4 Dt 
πDt
where Q is the total dose of impurities (number per unit area), and D is their diffusivity.
This is a so-called Gaussian profile with the surface concentration given by the preexponential term. [H.R.]
Dry etching is a gas-phase based process for material removal. Typically, this refers to
processes conducted under vacuum and involving beams of ions or electrons to cause
material removal. Two types of processes are often distinguished - namely, physical and
reactive etching. In the former case, the process is sometimes referred to as sputtering.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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In the case of the latter type of process, the etching can result from a chemical reaction
occurring between incident species and surface atoms. Processes commonly in use for
semiconductor dry etching that fall in the latter class are reactive ion etching (RIE) and
chemically-assisted ion beam etching (CAIBE). Both of these processes rely on a
plasma of excited ions to react either directly (i.e., in the case of RIE) or indirectly
through the mediation of a reactive gas that is excited by the plasma ions (i.e., in the case
of CAIBE). Dry etching processes are typically known for their ability to remove
material independent of any underlying crystallographic structure - that is, purely as a
function of the geometry of the sample being etched with respect to the orientation of the
etching species. This is often termed an anisotropic etching process. [H.R.]
Dry plasma etching is the process of using a chemically-reactive ionized gaseous plasma to
etch a semiconductor. [H.R.]
Easy direction is the crystal direction along which the atomic magnetic moments (due to spin)
are spontaneously and most easily aligned. Exchange interaction energy is lowest
(hence favorable) when the alignment of atomic spin magnetic moments is in this
direction in the crystal. For the iron crystal it is one of the six [100] directions (cube
edge).
Eddy current loss is the Joule energy loss (I2R) in a ferromagnetic material subjected to
changing magnetic fields (in ac fields).The varying magnetic field induces voltages in
the ferromagnetic material which drive currents (called eddy currents) which generates
Joule heating due to I2R.
Eddy currents are the induced conduction currents flowing in a ferromagnetic material as a
result of varying (ac) magnetic fields.
Edge dislocation is a line imperfection within a crystal which occurs when there is an
additional but a short plane of atoms which does not extend as much as its neighbors.
The edge of the plane constitutes a line of atoms where the bonding is irregular and
defines a line imperfection that is called an edge dislocation.
Compression
Tension
Dislocation in a crystal is a line defect which is accompanied by
lattice distortion and hence a lattice strain around it. Around the
dislocation there is a strain field as the atomic bonds have been
compressed above and stretched below the islocation line
Edge emitting LEDs (ELED) has the emitted radiation emerging from an area on an edge of
the crystal i.e. from an area on a crystal face perpendicular to the active layer. ELEDs
provide a greater intensity light and also a beam that is more collimated than the surface
emitting LEDs. The light is guided to the edge of the crystal by a dielectric waveguide
formed by wider bandgap semiconductors surrounding a double heterostructure. The
recombination of injected carriers occurs in the InGaAs active region which has a
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
35
bandgap Eg ≈ 0.83 eV. Recombination is confined to this layer because the surrounding
InGaAsP layers, confining layers, have a wider bandgap (Eg ≈ 1 eV) and the
InGaAsP/InGaAs/InGaAsP layers form a double heterostructure. The light emitted in the
active region (InGaAs) spreads into the neighboring layers (InGaAsP) which act to
contain the light and guide it along the crystal to the edge. InP has a wider bandgap (Eg ≈
1.35 eV) and thus a lower refractive index than InGaAsP. The two InP layers adjoining
the InGaAsP layers therefore act as cladding layers and thereby confine the light to the
DH structure. Generally some kind of lens system is used to conveniently couple the
emitted radiation from an ELED into a fiber. For example, a hemispherical lens attached
to the fiber end can be used for collimating the beam into the fiber. A graded index
(GRIN) rod lens is a glass rod that has a parabolic refractive index profile across its
cross-section with the maximum index on the rod axis. It is like a large diameter short
length graded index "fiber" (typical diameters are 0.5 - 2 mm). A GRIN rod lens can be
used to focus the light from an ELED into a fiber. This coupling is particularly useful for
single mode fibers inasmuch as their core diameters are typically ~10 µm. The output
spectra from surface and edge emitting LEDs using the same semiconductor material is
not necessarily the same. The first reason is that the active layers have different doping
levels. Second is the self-absorption of some of the photons guided along the active
layer as in ELED. Typically the linewidth of the output spectrum from an ELED is less
than that from a SLED. In set of experiments, for example, an InGaAsP ELED operating
near 1300 nm was observed to have a linewidth of 75 nm whereas the corresponding
SLED had a linewidth of 125 nm.
60-70 m
L
Su
bs
tra
te
Stripe electrode
Insulation
p+-InP (Eg = 1.35 eV, Cladding layer)
p+-InGaAsP (Eg 1 eV, Confining layer)
n-InGaAs (Eg 0.83 eV, Active layer)
n+-InGaAsP (Eg 1 eV, Confining layer)
n+-InP (Eg = 1.35 eV, Cladding/Substrate)
Electrode
2
1
Current
paths
Substrate
Light beam
3
200-300 m
Active region (emission region)
Schematic illustration of the the structure of a double heterojunction stripe
contact edge emitting LED
Effective density of states (Nc) at the conduction band edge is a quantity that represents all
the states in the conduction band per unit volume as if they were all at Ec. Similarly Nv
which is the effective density of states at the valence band edge is a quantity that
represents all the states in the valence band per unit volume as if they were all at Ev.
Effective electron mass, me*, represents the inertial resistance of an electron inside a crystal
against an acceleration imposed by an external force such as the applied electric field. If
Fext = eEx is the external applied force due to the applied field Ex then the effective mass,
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
36
me*, determines the acceleration of the electron by eEx = me*a. It takes into account the
effect of the internal fields on the motion of the electron. In vacuum where there are no
internal fields, me* is obviously the mass in vacuum, me. Effective mass of an electron is
a quantum mechanical quantity that behaves like the inertial mass in classical mechanics,
F = ma in that it measures the objects resistance to acceleration. It relates the acceleration
a of an electron in the conduction band to the applied external force Fext by Fext = me*a.
The external force is most commonly the force of an applied electric field, eEx, and
excludes all internal forces within the crystal . Similarly the effective mass of a hole in the
valence band is its inertial mass against acceleration imposed by an external force. We
should note that the internal fields depend on the location of the electron and its effect on
the motion of the electron can only be determined by solving the Schrödinger equation
with the appropriate potential energy term V. The effective mass me* depends inversely
on the curvature of the E vs. k behavior, i.e.
−1
2
*
2 d E 
me = h  2 
 dk 
which shows that a high curvature represents a light me* and a broad curvature represents
a heavy me*. For example, GaAs E vs. k diagram for the conduction band has a central
valley Γ that has a sharp curvature and a satellite valley L that has a small curvature. The
electron effective mass is small in Γ but large in L. Consequently the electron drift
mobility, inversely proportional to the effective mass, is high in Γ and low in L.
E
Central
valley
L
Ec
me* = 0.35me
L
E ≈ 0.3 eV
CB
Eg
Ev
Satellite
valley
me* = 0.07me
VB
–k
k
[111]
n-type GaAs has the
conduction electrons in
the central valley at low
fields. These have a light
effective mass of 0.07me.
At sufficiently high fields
some of these electrons
can be scattered to the
satellite valley where
they have a heavy
effective mass of 0.35me.
[111]
Effusion cell provides a source of a species that is used in molecular beam epitaxy (MBE). It
is often called a Knudsen source as shown schematically in the figure. The Knudsen cell
consists of a heating system made of (A) refractory materials such as tantalum and
molybdenum (which produce negligible emissions until heated to temperatures in excess
of about 1500 οC and which are non reacting with typical III-V source/dopant materials)
and (B) a high purity inert crucible (usually of high purity graphite or boron nitride) to
contain the source material. The source cell also has provisions for a thermocouple to
accurately monitor and control the source temperature (typically within about 0.1 οC).
The Knudsen cells have small apertures (typically about 2 to 3 cm in diameter, depending
on the cell volume) to permit the molecules of the heated source to escape. For such a
source, the flux of molecules Js (Molecules cm-2 s-1) escaping through the source
aperture per second and measured at a distance L (in cm) from the source orifice, is given
by,
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
37
pA
L MT
where A is the source aperture area in cm2, p is the pressure in the source in Torr, M is
the molecular weight of the effusing source species and T is the absolute temperature of
the material inside the source. It is assumed that the flux Js is measured at the center of
the plane normal to the source beam. If the flux is measured at points displaced from this
origin, but still on the same plane, it would follow a cosine-law dependence on the angle
subtended to the center of the source orifice, θ, i.e., J(θ) = Jscos4θ. This relationship is
obeyed as long as the mean free path of species becomes comparable to, or less than,
the orifice diameter; above this pressure the flow changes from molecular type flow to
viscous flow. As an example of the operation of a source, consider a source of pure
gallium that is used for growing GaAs by MBE. The vapor pressure of gallium pGa
originating from such a source may be approximated by the Clausius-Clapeyron
equation, which in this case gives pGa (Torr) ≈ 2.856×108 exp (− 31581/T), where T is
the absolute temperature of the gallium source. Thus, for a typical gallium cell
temperature in the range of 930 to 980 °C for GaAs growth, pGa is in the range between
1.134×10-3 and 3.233 ×10-3 Torr, typically resulting in a gallium flux on the substrate of
1.5×1015 and 4.2×1015 gallium atoms/cm2. For successful growth of GaAs, an arsenic
flux of about 10 times that for gallium is required. MBE growth usually requires at least
one effusion cell to create a flux of each elemental species. Thus, to grow a ternary
compound such as AlGaAs, requires at least three cells. In addition, effusion cells are
also used for dopant sources. [H.R.]
Einstein coefficients A21, B12 and B21 are constants that are used in describing the rates of
spontaneous emission, absorption and stimulated emission respectively between
two energy levels E1 and E2 where E2 > E1. For example, the rate of spontaneous
emission from E2 and E1 is proportional to the number of atoms N2 at E2 so that
spontaneous transition rate is A21N2. The rate of upward transitions from E1 to E2 by
photon absorption is proportional to the number of atoms N1 at E1 and also to the
number of photons with energy hυ = E2 − E1 i.e. absorption rate is B12N1ρ(hυ) where
B12 is the Einstein B12 coefficient, and ρ(hυ) is the photon energy density per unit
frequency which represents the number of photons per unit volume with an energy hυ (
= E2 − E1). The Einstein coefficients are interrelated. For example, if E1 and E2 have the
same degeneracy, then B12 = B21 and A21/B21 = 8πhυ3/c3. In the above expressions, h is
Planck’s constant, υ is the radiation frequency, c is the speed of light.
Js = 1.118 × 10 22
2
Einstein relation relates the diffusion coefficient D of a given species of charge carriers to
their drift mobility µ via D/µ = kT/q where q is the charge of the carrier, k is
Boltzmann’s constant and T is the temperature.
Elastic modulus or Young's modulus (Y) indicates the ease with which a solid can be
elastically deformed. The greater is Y, the more difficult it is to elastically deform the
solid. When a solid of length L is subjected to a tensile stress, σ (force per unit area), it
will extend elastically by an amount δL. δL/L is the strain, ε. Stress and strain are
related by σ = Yε so that Y is the stress needed per unit elastic strain. The elastic
modulus depends on the crystal direction. For a polycrystalline material it is an average
value over various crystal directions.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
38
Electric dipole moment exists when a positive charge +Q is separated from a negative charge Q. Even though the net charge is zero, there is nonetheless an electric dipole moment, p,
given by p = Qx where x is the distance vector from -Q to +Q. Just as two charges exert
a coulomb force on each other, two dipoles also exert a force on each other which
depends on the magnitudes of the dipoles, their separation and orientation.
Electric susceptibility (χe) is a material quantity that measures the extent of polarization in
the material per unit field. It relates the amount of polarization, P, at a point in the
dielectric to the field, E, at that point via P = χeεoE. If εr is the relative permittivity
then χe = εr − 1. Vacuum has no electric susceptibility.
Electrical conductivity (σ) is a property of a material that quantifies the ease with which
charges flow inside the material along an applied electric field or a voltage gradient. It is
the inverse of electrical resistivity, ρ. Since charge flow is due a voltage gradient, σ is
the rate of charge flow through unit area per unit voltage gradient; J = σE, where J is the
current density and E is the electric field. The power dissipated as heat per unit volume
in a conductor of conductivity σ is given by Joule’s law, that is σE2. In a metal where
the conduction electron concentration is n, and the electron drift mobility is µ, the
conductivity is given by σ = enµ, where e is the electronic charge. In a semiconductor
there are both electrons in the conduction band (CB) and holes in the valence band
(VB) contributing to electrical conduction and the conductivity is
σ = enµe + epµh
where n is the electron concentration in the CB, p is the hole concentration in the VB, µe
is the drift mobility of electrons in the CB, and µh is the drift mobility of holes in the
VB.
Electro-optic effects refer to changes in the refractive index of a material induced by the
application of an external electric field, which therefore “modulates” the optical
properties; the applied field is not the electric field of any light wave, but a separate
external field. We can apply such an external field by placing electrodes on opposite
faces of a crystal and connecting these electrodes to a battery. The presence of such a
field distorts the electron motions in the atoms or molecules of the substance, or distorts
the crystal structure resulting in changes in the optical properties. For example, an
applied external field can cause an optically isotropic crystal such as GaAs to become
birefringent. In this case, the field induces principal axes and an optic axis. Typically
changes in the refractive index are small. The frequency of the applied field has to be
such that the field appears static over the time scale it takes for the medium to change its
properties, that is respond, as well as for any light to cross the substance. The electrooptic effects are classified according to first and second order effects. If we were to take
the refractive index n to be a function of the applied electric field E, that is n = n(E), we
can of course expand this as a Taylor series in E. The new refractive index n′ is
n′ = n + a1E + a2E2 + ...
where the coefficients a1 and a2 are called the linear electro-optic effect and second order
electro-optic effect coefficients. Although we would expect even higher terms in the
expansion of the above equation, these are generally very small and their effects
negligible within highest practical fields. The change in n due to the first E term is called
the Pockels effect. The change in n due to the second E2 term is called the Kerr effect,
and the coefficient a2 is generally written as λK where K is called the Kerr coefficient.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
39
Thus, the two effects are
∆n = a1E
∆n = a2E2 = (λK)E2
All materials exhibit the Kerr effect. It may be thought that we will always find some
(non-zero) values for a1 for all materials but this is not true and only certain crystalline
materials exhibit the Pockels effect. If we apply a field E in one direction to a crystal and
then reverse the field and apply −E then ∆n should change sign. If the refractive index
increases for E, it must decrease for −E. Reversing the field should not lead to an
identical effect (the same ∆n). The structure has to respond differently to E and −E.
There must therefore be some asymmetry in the structure to distinguish between E and −
E. In a noncrystalline material, ∆n for E would be the same as ∆n for −E as all directions
are equivalent in terms of dielectric properties. Thus a1 = 0 for all noncrystalline
materials (such as glasses and liquids). Similarly, if the crystal structure has a center of
symmetry then reversing the field direction has an identical effect and a1 is again zero.
Only crystals that are noncentrosymmetric exhibit the Pockels effect . For example a
NaCl crystal (centrosymmetric) exhibits no Pockels effect but a GaAs crystal
(noncentrosymmetric) does.
Electrochemical cell is a device for converting chemical energy to electrical energy. It consists
of two half cells so that one allows oxidation of a substance and the other reduction.
Electrode is a conducting material, such as a metal, by which electrons are transferred to or from
the electrolyte (ionic solution) with which it is contact.
Electrolysis is the use of electrical energy to produce a chemical change by virtue of lowering
the Gibbs free energy for the reaction by ∆G = −∆WE where ∆WE is the electrical energy
input.
Electrolyte is an ionic solution that conducts electricity by the movement of these ions.
Electromechanical breakdown and electrofracture is a breakdown process which directly or
indirectly involves electric field induced mechanical weakening, e.g. crack propagation, or
mechanical deformation, that eventually lead to dielectric breakdown. The breakdown
process starts as a result of mechanical deformations or mechanical weakening in the
presence of a large field but the eventual breakdown may be different, e.g. mechanical
deformation may lead to thermal breakdown.
Electron affinity, χ is the energy required to remove an electron from the bottom of the
conduction band Ec to the vacuum level.
Electron hole pair (EHP) creation energy gauges the sensitivity of a high energy particle or
X-ray radiation detector in terms of the energy absorbed from the incident radiation per
free electron hole pair that is collected. Stated differently, it is the energy that the material
absorbs from the incident beam to generate a free electron and a free hole (or one
electron of collected charge in the external circuit). High sensitivity means that the
amount of radiation energy required, denoted as W±, to create a single free EHP must be
as low as possible because the free (or collectable) charge ∆Q generated from an incident
radiation of energy ∆E is simply e∆E/W±. All experiments on examining the amount of
charge generated by high energy particles, including X-rays, have shown that this charge
depends on the incident radiation energy, i.e. ∆Q ∝ ∆E. This has lead to the introduction
of an EHP creation energy (W±). The creation of EHPs by an X-ray photon first
involves the generation of an energetic primary electron from an inner core shell, for
example, the K-shell. As this energetic photoelectron travels in the solid it causes
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
40
ionizations along its track and hence the creation of many EHPs. For many
semiconductors the energy W± required to create and electron hole pair has been shown
to depend on the energy bandgap Eg via the Klein rule
W ± ≈ 2.8E g + E phonon.
where Ephonon is a phonon energy term. Ephonon is expected to be small (~0.5 eV) so that
typically W± is close to 2.8Eg. Further in many crystalline semiconductors, just like the
optical quantum efficiency, W± is field independent and well defined. This W± is so
well defined in crystalline semiconductors, such as high purity Ge, ZnCdTe, for example,
that they are used in spectrometers to measure the energy of the incident X-rays or high
energy charged particles. Que and Rowlands argued that if one relaxes the conservation
of k rule as required for amorphous semiconductors then the EHP creation energy
should be about 2.2Eg + Ephonon where the latter is again a small phonon energy term.
18
Diamond
16
Klein rule:W ± ≈ 2.8Eg + 0.5 eV
14
12
SiC
W± 10
(eV) 8
PbO
GaP
GaSe
AlSb
CdTe
GaAs
6
4
Que and Rowlands
AgCl
a-Se
Si
InSb
PbS
W± ≈ 2.2Eg + 0.5 eV
TlBr
AgBr
PbI2
HgI2
a-Si:H
2
Ge
0
0
1
2
3
4
Band gap (eV)
5
6
EHP creation energy W± vs energy bandgap for semiconductors (for a-Se W± is field
dependent and the value plotted is extrapolated to very large fields so that W± is
“intrinsic” or saturated EHP creation energy).
Electronegativity is a relative measure of the ability of an atom to attract electrons to form an
anion. Fluorine is the most highly electronegative atom as it most easily accepts an
electron to become an anion (F-). Typically halogens (F, Cl, Br, I) are electronegative
elements. In HCl, for example, the Cl atom is more electronegative than the H atom and
therefore attracts the electrons more than the H proton. Cl therefore acquires a net
negative charge and the hydrogen proton becomes exposed. The molecule therefore has
a permanent dipole moment.
Electronic bond polarization is the displacement of valence electrons in the bonds in
covalent solids (e.g. Ge, Si). It is a collective displacement of the electrons in the bonds
with respect to the positive nuclei.
Electronic polarization is the displacement of the electron cloud of an atom with respect to the
positive nucleus. Its contribution to the relative permittivity of a solid is usually small.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
41
Emissivity ε of a surface represents the efficiency with which a heated surface emits radiation
with respect to radiation emitted from a black body at the same temperature. Consider a
unit area of a surface of interest and a unit area of a black body. These surfaces emit
electromagnetic (EM) energy (radiation),
ε=
Rate of EM energy emitted froma surface
Rate of EM energy emitted froma black body at the same temperature
The radiation power emitted from a surface is given by Stefan's Law:
Pradiated = εσA(T4 - To4)
where σ is Stefan's constant (= 5.67 × 10−8 W m-2 K-4), ε is the emissivity of the surface,
A is the surface area, T is the temperature of the surface and To is the ambient
temperature.
Emitter junction is the metallurgical junction between the emitter and the base of a bipolar
junction transistor.
Emitter of a bipolar transistor is one of the two similarly doped (e.g. both n-type) regions that
surrounds the oppositely doped (p-type) base and injects minority carriers into the
base when the emitter-base junction is forward biased.
Endothermic reaction absorbs heat from its surroundings.
Energy density is the amount of energy per unit volume. In a region where the electric field is
E, the energy stored per unit volume is 1/2εoE 2. This is the energy density, ρE.
Energy of the electron in the crystal, whether in the conduction band (CB) or valence
band (VB), depends on its momentum hk through the E-k behavior determined by the
solutions to Schrödinger equation for the particular crystal structure (with a particular
periodic potential energy). E-k behavior is most conveniently represented graphically
through E-k diagrams. For example, for an electron at the bottom of the CB, E increases
as (hk)2/(2me*) where hk is the momentum and me* is the effective mass of the electron
which is determined from the E-k behavior. The quantity hk is called the crystal
momentum of the electron because the rate of change of hk is the external applied force
on the electron, d(hk)/dt = Fexternal, and not the actual force which is the sum of external
and internal forces. E-k diagrams are essentially plots of electron energy vs. crystal
momentum of the electron.
E
CB
Ec
Direct Band Gap
Electrons
Eg
Holes
Ev
E - k diagram for a direct bandgap
semiconductor such as GaAs. The
minimum of the CB is directly above the
maximum of the VB.
VB
–k
k
Enhancement
MOSFET is a MOSFET device
that needs a gate to source voltage, above the
threshold voltage, to form a conducting channel between the source and the drain. In
absence of a gate voltage there is no conduction between the source and drain. In its
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
42
usual mode of operation the gate voltage enhances the conductance of the source to drain
inversion layer and increases the drain current.
Enthalpy (H) is a measure of the total energy of the system which includes the internal energy,
U, and also the energy due to its volume because changes in the latter involves work; H =
U + PV. Quite often we equate the enthalpy of the substance to the "heat content" of a
substance at constant pressure since the heat exchange at constant pressure is equal to
the enthalpy change; ∆H = (∆Q)P.
Entropy is an extensive property of the system that measures its degree of randomness. The
more chaotic the system, higher is its entropy. It is kind of a muddle factor. Suppose that
for a given internal energy U, the number of distinguishable ways the constituents (e.g.
molecules) of a systrem can be arranged is W. This is the number of different ways you
can distribute the atoms in the system to get the same energy U. Then the entropy of the
system per mole is defined by the equation
S = klnW
where k is the Boltzmann constant. A perfect crystal at absolute temperature of zero
will have all the atoms at well defined sites and there is only one distinguishable
arrangement of atoms for that energy. Changing the places of atoms in the crystal does
not lead to a different distinguishable state. Thus the entropy at absolute zero of
temperature for a perfect crystal is zero. Suppose, however, that the crystal has one
vacancy due to one of the atoms taken to the surface. Then this vacancy can be in any of
the N places and there are N different distiniguishable combinations of atoms with the
vacancy at various sites. Thus W = N and S = klnN and the entropy has now increased.
With the introduction of this one vacancy, the structure becomes more random. There is
a vacancy somewhere in the crystal and this can be anywhere and there are some N such
distinct possibilities.
The entropy of a substance also increases with the temperature. For example, in a
gas more and more molecules attain higher energies as the temperature is raised by virtue
of the Maxwell-Boltzmann distribution broadening with the temperature. There is
therefore a larger distribution of molecules over the possible energies with increasing
temperature which means that there is more chaos in the system i.e. more variation in the
molecular energies. Consequently, the entropy increases. When heat energy ∆Q is added
to a material, initially at temperature T, its entropy increases by an amount defined by
∆Q
∆S =
T
in units of J K-1. Suppose that the system changes from a state A to state B. The change
can be reversible or irreversible. ∆S is defined as the heat absorbed by the system ∆Q, as
if the system went through a reversible change, per unit temperature. Since in equilibrium
at T = 0 K, the entropy is zero, the entropy S at some arbitrary temperature T, is given by,
T
∆Q
dT
T
0
All real solids at a finite temperature will have a certain degree of disorder,
leading to it possessing so-called configurational entropy. It can also be said that any
irreversible change is one that produces an increase in the entropy of the system.
The Second Law of Thermodynamics states that in all spontaneous processes, i.e.
those occurring naturally, the entropy of the system and its surroundings must always
increase. The entropy of a system and its surrounding during chemical and physical
processes increases. Nature prefers systems to increase their entropy - nature likes
randomness. It has profound implications from biology to computer engineering. If we
define the universe as the system of interest and its immediate surroundings, then the
S = S0 +
∫
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
43
entropy of the universe must always increase during a spontaneous process. For
reversible changes, those which occur infinitely slowly, the entropy of the universe
remains unchanged. If ∆Ssystem and ∆Ssurroundings are the entropy changes for the system
and its surroundings during a physical or chemical change, then according to the Second
Law
∆Ssystem + ∆Ssurroundings ≥ 0.
[H.R.]
Entropy of mixing ∆Sm refers to the entropy change associated with forming an intimate
mixture of two or more distinct species (e.g., atoms) as compared with the same number
of such species in isolation. Assuming for example the two species are A and B atoms,
from the definition of entropy S = klnW, the following expression can be written:
W
∆S m = k B log e A ,B
W AWB
where WA,B refers to the number of ways of arranging A and B atoms in the intimate
mixture, and WA and WB refer to the number of ways of arranging just A atoms, and just
B atoms, in isolation, respectively. Since all A and B atoms can be assumed to be
identical, all of the arrangements of A atoms (or indeed B) atoms in the isolated case of
only A atoms (or only B atoms), are equivalent, and indeed, WA = WB = 1. Statistical
thermodynamics can be used to evaluate an expression for WA,B and hence ∆Sm in this
example. The result for 1 mole is
∆Sm = −R[XAln(XA) + XBln(XB)]
where R is the ideal gas constant, and XA and XB are the atomic fractions of A and B,
respectively, with XA + XB = 1. The higher the degree of randomness in a system, the
higher the entropy. In the mixture example, the largest number of ways of arranging a
system of A and B atoms occurs when there are equal numbers of A and B atoms, or = XB
= 0.5: in this case, the argument in the square brackets above, has its maximum value of
−0.693, with other compositions of the mixture corresponding to a higher (less negative)
value for the entropy of mixing. [H.R.]
Epitaxy is usually defined as the growth of a layer of single crystal material on top of a single
crystal substrate in such a way that the crystalline structure of the substrate is preserved
in the layer. [H.R.]
Equilibrium between two systems requires mechanical, thermal and chemical equilibrium.
Mechanical equilibrium means that the pressure should be the same in the two systems
so that one does not expand at the expense of the other and thermal equilibrium implies
that both should have the same temperature. To have chemical equilibrium, we also need
the two systems to have the same Gibbs free energy per particle. Equilibrium within a
single phase substance (e.g., steam only or hydrogen gas only) implies uniform
pressure and temperature within the system.
Equilibrium state of a system is that in which the pressure and temperature in the system are
uniform throughout. We say that the system possesses mechanical and thermal
equilibrium.
Erf diffusion function refers to the use of the error function to describe the diffusion of heat
and mass in various media. Consider the diffusion of atoms from a region where the
concentration is constant. Suppose that a material is initially confined to a finite region x
< 0 at concentration C = C0 and with concentration C = 0 elsewhere (i.e., for x > 0), for
time t = 0. The solution of the diffusion equation (Fick’s second law), describing the
movement of diffusing atoms of given species into a host medium, under these boundary
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
44
conditions, is usually written in terms of the complementary error function erfc as
follows:
 x 
C( x, t ) = Co erfc

 2 Dt 
where D is the diffusivity of the diffusing atoms in the host medium. Other problems
concerning diffusion also commonly have solutions that can be expressed in terms of the
error function or the complementary error function. [H.R.]
Error function is a standard mathematical function for which there are extensive tables
available, which is usually written as erf(z) and defined as follows:
z
2
erf( z ) =
exp( −ϕ 2 )dϕ
π 0
The error function has the following properties: − erf(z) = erf(−z), erf(0) = 0 and erf(∞)
= 1. This function, and the so-called complementary error function erfc(z) = 1−erf(z),
are used extensively in simplifying analytical solutions for heat and mass diffusion in
solids. [H.R.]
∫
Eutectic composition is the alloy composition of two elements that results in the lowest
melting temperature compared with any other composition. Eutectic solid has a structure
that is a mixture of two phases. The eutectic structure is usually special, e.g. of lamellae
type.
Evanescent wave is the wave that propagates in a lower refractive index medium, along the
boundary with a higher refractive index medium, when a wave traveling in the medium of
higher refractive index is incident at the boundary at an angle equal to or greater than the
critical angle. The amplitude of the evanescent wave decreases exponentially with
distance from the boundary into the medium with a lower refractive index.
Evaporation refers to the process of deposition of a material by heating it (by using, for
example, a resistively heated crucible, an electric filament or electron beam heating) under
high-vacuum (between 5×10-5 Torr and 1×10-7 Torr) conditions. This causes the
material to vaporize resulting in a flux of atoms being emitted. This flux of material
(evaporating from the source) is then allowed to condense on a substrate surface,
usually by withdrawing a protective shutter mounted in front of the substrate surface.
Typically, wafers are held in a semispherical or "planetary" system that permits a
multitude of wafers to be exposed to the same evaporating source during a given process
(i.e., without the need for a separate pumpdown sequence). [H.R.]
Excess carrier concentration is the excess concentration above the thermal equilibrium value.
Excess carriers are generated by an external excitation such as photogeneration.
Exchange integral (Jij) is the strength of the magnetic interactions between neighboring atoms,
i and j. It is essentially a Coulomb interaction between the electrons that were exchanged
between the i and j sites. The associated exchange energy between sites i and j is given
by −2JijMi⋅Mj, where Mi and Mj are the magnetization at the i and j sites, respectively.
If Jij > 0, energy is minimized when the moments are parallel, and if Jij < 0, antiparallel
configuration of the moments is favored. [C.T.]
Exchange interaction energy (Eex) is a kind of coulombic interaction energy between two
neighboring electrons and positive metal ions that depends on the relative spin
orientations of the electrons as a consequence of the Pauli exclusion principle. Its
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
45
exact origin is quantum mechanical. Qualitatively, different spins lead to different
electron wavefunctions, different negative charge distributions and hence different
coulombic interactions. In ferromagnetic crystals Eex is negative when the neighboring
electron spins are parallel.
Exciton is an electron bound to a hole in a crystalline solid, such as a semiconductor, analogous
to the binding of electron and proton in a hydrogen atom. The carriers, bound by their
mutual electrostatic attraction, may migrate through the crystal and eventually recombine
with the emission of a photon. Unlike the hydrogen atom, Coulomb attraction occurs
between an electron and hole having relatively low effective mass, as compared with
hydrogen’s nuclear mass; thus, the exciton reduced mass is small, and given the high
dielectric constant of typical crystalline materials, as compared with free space, the
exciton binding energy is relatively small. Since the electron and hole in an exciton must
move through the crystal together, their translational velocities must be identical: that is,
dE
dE
h
=h
and thus excitons are only found at critical points in E(k)
dk electron,CB
dk hole,VB
where the curvature of the conduction and valence bands are equal. For highly n-type
material, Coulomb repulsion between free electrons and electrons in the exciton reduce
the range over which the exciton can form (i.e., through the so-called screened Coulomb
interaction). A similar argument applies for highly p-type materials. In materials with
strong internal fields, bands bend together exerting a counter-force on the electron and
hole in the exciton (i.e., pulling them apart in opposite directions) - when the applied field
to the exciton exceeds the internal field binding the exciton together, the exciton
dissociates. For the case of a crystal under mechanical deformation, the energy bands
either move together or move apart. In both cases, the electron and hole experience a
force tending to move them in the same direction, and the exciton can then move in a
common direction. If there is a local deformation potential, the exciton will drift to a
location of minimum energy gap, in response to the band bending. Exciton complexes
can also form that involve more than just a single electron and hole; possible complexes
that can form include fixed charges (e.g., ionized and un-ionized donors and acceptors),
as well as multiple electrons and holes. Such complexes may be electrically neutral (i.e.,
termed excitonic molecules), or electrically charged (i.e., termed excitonic ions). When
excitons are formed, bound to neutral impurities (e.g., a hole to a neutral donor), the
excitonic ion in this case is called a bound-exciton, as the associated exciton appears to
be trapped to this impurity. In bulk semiconductors, excitons are usually only observable
in high purity samples and at cryogenic temperatures owing to their relatively small
binding energies. However, in heterostructures such as quantum wells, quantum
confinement significantly enhances the exciton binding energy, allowing excitonic
transitions to be used at room temperature to develop optoelectronic devices such as
optoelectronic switches. [H.R.]
Exothermic reaction releases heat to the environment. An endothermic reaction absorbs heat
from the environment.
Extensive property depends on the size (or extent) of the substance. The larger the size of the
system, the greater is the extensive property. Typical extensive properties are volume,
mass, surface area, internal energy, enthalpy, entropy. We can define an intensive
property that is derived from an extensive property.
External discharges are discharges or shorting currents over the surface of the insulator when
the conductance of the surface increases as a result of surface contamination, e.g.
excessive moisture, deposition of pollutants, dirt, dust, salt spraying etc. Eventually the
contaminated surface develops sufficient conductance to allow discharge between the
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
46
electrodes at a field below the normal breakdown strength of the insulator. This type of
dielectric breakdown over the surface of the insulation is termed surface tracking.
Extrinsic semiconductor is a semiconductor that has been doped so that the concentration of
one type of charge carriers far exceeds that of the other. Adding donor impurities
releases electrons into the conduction band and the concentration of electrons (n) in the
conduction band (CB) far exceeds the concentration of holes (p) in the valence band
(VB) and the semiconductor becomes n-type. When acceptor impurities are added, these
acceptors accept electrons from the VB and thereby create holes in the VB so that the
hole concentration (p) far exceeds the electron concentration (n); the semiconductor
becomes p-type. The mass action law, np = ni2, remains valid in extrinsic
semiconductors as long as the semiconductor is in the dark and in thermal equilibrium.
Thus, adding donors to increase n concomitantly also decreases p by the same ratio.
CB
Ec
EFi
Ev
Ec
EFn
Ev
Ec
EFp
Ev
VB
Energy band diagrams for (a) intrinsic (b) n-type and (c) p-type semiconductors. In all cases,
np = ni2. Note that donor and acceptor energy levels are not shown. CB = conduction band,
VB = valence band, Ec = CB edge, Ev = VB edge, EF = Fermi level in intrinsic
semiconductor, EFn = Fermi level in n-type semiconductor, EFp = Fermi level in p-type
semiconductor,
Face centered cubic (FCC) lattice is that which has one lattice point at each corner of a cube
and one at the center of each face. If there is a chemical species (an atom or a molecule)
at each lattice point then the structure is a FCC crystal structure.
Faraday effect, originally observed by Michael Faraday (1845), is the rotation of the plane of
polarization of a light wave as it propagates through a medium that has been placed in a
magnetic field that is parallel to the light propagation direction. When an optically
inactive material such as glass is placed in a strong magnetic field and then a plane
polarized light is sent along the direction of the magnetic field, it is found that the
emerging light’s plane of polarization has been rotated. The magnetic field can be
applied, for example, by inserting the material into the core of a magnetic coil - a solenoid
The induced specific rotatory power (θ/L) has been found to be proportional to the
magnitude of applied magnetic field, B. The amount of rotation θ is given by
θ = ϑBL
where B is the magnetic field (flux density), L is the length of the medium, and ϑ is the
so-called Verdet constant. It depends on the material and the wavelength. The Faraday
effect is typically small. A magnetic field of ~0.1 T causes a rotation of about 1° through
a glass rod of length 20 mm. It seems to appear that an “optical activity” has been
induced by the application of a strong magnetic field to an otherwise optically inactive
material. There is however an important distinction between the natural optical activity
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
47
and the Faraday effect. The sense of rotation θ in the Faraday effect, for a given material
(Verdet constant), depends only on the direction of the magnetic field B. If ϑ is positive,
for light propagating parallel to B, the optical field E rotates in the same sense as an
advancing right-handed screw pointing in the direction of B. The direction of light
propagation does not change the absolute sense of rotation of θ. If we reflect the wave to
pass through the medium again, the rotation increases to 2θ.
Faraday's law of induction states that whenever the total magnetic flux threading a circuit
changes it induces a voltage in that circuit. The induced voltage is such that it tries to
oppose the change in the flux (Lenz's law). Ferromagnetic materials have the ability
of possessing large permanent magnetizations even in the absence of an applied field.
An unmagnetized ferromagnetic material normally has many magnetic domains whose
magnetizations add to give no overall magnetization. However, in a sufficiently strong
magnetizing field, the whole ferromagnetic substance becomes one magnetic domain in
which all the atomic spin magnetic moments are aligned to give a large magnetization
along the field. Some of this magnetization is retained even after the removal of the field.
Fermi energy (EF) or level may be defined in several equivalent ways. Fermi level is the energy
level corresponding to the energy required to remove an electron from the
semiconductor; there need not be any actual electrons at this energy level. The energy
needed to remove an electron defines the work function Φ. We can define the Fermi
level to be Φ below the vacuum level. EF can also be defined as that energy value below
which all states are full and above which all states are empty at absolute zero of
temperature. EF can also be defined through a difference. A difference in the Fermi
energy, ∆EF, in a system is the external electrical work done per electron either on the
system or by the system just as electrical work done when a charge e moves through a
electrostatic potential energy (PE) difference is e∆V. It can be viewed as a fundamental
material property. In more advanced texts it is refereed to as the chemical potential of
the semiconductor.
Fermi-Dirac statistics determines the probability of occupancy of a state at an energy level E
by an electron. It takes into account that when we are considering a collection of
electrons, they must obey the Pauli Exclusion Principle. The Fermi-Dirac function
quantifies this probability via
1
f ( E) =
E − EF 
1 + exp
 kT 
where EF is the Fermi energy, k is Boltzmann’s constant and T is the temperature
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
48
(Kelvins).
E
T2 > T1
T=0
EF
T1
0
1
/
2
1
The Fermi-Dirac function. f(E), describes the
statistics of electrons in a solid. The electrons
interact with each other and the environment
so that they obey the Pauili Exclusion
Principle.
f(E)
Ferrimagnetic materials possess crystals that contain two sets of atomic magnetic moments
that oppose each other but one set has greater strength and therefore there is a net
magnetization of the crystal. An unmagnetized ferrimagnetic substance normally has
many magnetic domains whose magnetizations add to give no overall magnetization.
However, in a sufficiently strong magnetizing field, the whole ferromagnetic substance
becomes one magnetic domain with a large magnetization along the field. Some of this
magnetization is retained even after the removal of the field.
Ferrimagnetism is the intermediate case between ferromagnets and antiferromagnets. Like the
case of an antiferromagnet, one considers the crystal as made of two sub-lattices, with
total magnetizations opposing one another. The magnitude of each magnetization is
different resulting into a net total magnetization. [C.T.]
Ferrites are ferromagnetic materials that are ceramics with insulating properties. They are
therefore used in HF applications where eddy current losses are significant. Their
general composition is (MO)(Fe2O3) where M is typically a divalent metal. For
magnetically soft ferrites M is typically Fe Mn, Zn, Ni whereas for magnetically hard
ferrites M is typically Sr or Ba. Hard ferrites such as BaOFe2O3 have the hexagonal
crystal structure with a high degree of manetocrystalline anisotropy and therefore
possess high coercivity (difficult to demagnetize).
Ferroelectricity is the occurrence of spontaneous polarization in certain crystals such as
barium titanate. Ferroelectric crystals have a permanent polarization P as a result of
spontaneous polarization. The direction of P can be defined by the application of an
external field. Many ferroelectric materials are oxides of the type ABO3, e.g. BaTiO3,
LiNbO3, where A and B are typically metallic elements. A-site and B-site refer to the
sites of the atoms A and B in the crystal.
Ferromagnetic materials possess crystals that contain two sets of atomic magnetic moments
that oppose each other but one set has greater strength and therefore there is a net
magnetization of the crystal. An unmagnetized ferromagnetic substance normally has
many magnetic domains whose magnetizations add to give no overall magnetization.
However, in a sufficiently strong magnetizing field, the whole ferromagnetic substance
becomes one magnetic domain with a large magnetization along the field. Some of this
magnetization is retained even after the removal of the field.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
49
Ferromagnetism - An assembly of magnetic moments interacting with a positive exchange
integral will minimize their energy by adopting a common parallel configuration with a
net large value of the total magnetization. [C.T.]
Field effect transistor (FET) is a transistor whose normal operation is based on controlling
the conductance of a channel between two electrodes by the application of an external
field. The effect of the applied field is to control the current flow. The current is due to
majority carrier drift from the source to the drain and is controlled by the voltage
applied to the gate.
Field emission is the tunneling of an electron from the surface of a metal into vacuum due to
the application of a strong electric field. (typically E > 109 V m−1)
Fill factor (FF) is a figure of merit for solar cells and is defined as
I V
FF = m m
IscVoc
where Im and Vm are the photocurrent and voltage when maximum power is being
delivered to the load, and Isc andVoc are the short circuit photocurrent and open circuit
voltage . It is clearly advantageous to have FF as close to unity as possible but the
exponential pn junction properties prevent this. Typically FF values are in the range 7085% and depend on the device material and structure. See photovoltaic I-V
characteristics.
Filter is a device that allows only certain frequencies (or wavelengths) to pass and others to be
blocked. Filters typically have a certain resonant frequency υo and a bandwidth ∆υ
around υo such that input (incoming) signals within this ∆υ are passed.
Flat results from grinding a sections of an ingot after properly orienting the boule using X-ray
diffraction. After the ingot is cut into wafers, this process leaves a flat section to the
perimeter of an otherwise circular section wafer, that is used to identify the specific
crystallographic orientation of the wafer. [H.R.]
Floating-zone growth is one of the principal techniques used for preparing Si single crystals.
Similar to the Czochralski technique, boules are grown without the use of a crucible
and thus problems such as oxygen incorporation in crystals grown using other
techniques employing quartz crucibles, are alleviated. In this process, a single crystal
seed is mated to a high purity polycrystalline rod of the same material (e.g., silicon) and
clamped at both ends to permit the assembly to be rotated. A thin radio-frequency (RF)
heated zone melts a strip of material, with material solidifying in just ahead and just
behind the thermal front. The process is initiated adjacent to the seed crystal and
proceeds by moving the RF heated zone slowly up the length of the polycrystalline bar
causing the polycrystalline material to transform to single crystal material. The crystal
diameter can be controlled by the rate at which polycrystalline material is fed into the RF
zone. The levitation effect resulting from RF heating permits more of the melt to be
supported than would be possible by surface tension effects alone, resulting in a
capability to grow larger diameter crystals. The method is most suitable for materials
which possess high surface tension and low density in the molten phase. Typical float
zone grown Si crystals have about 100 times lower oxygen concentrations than liquid
encapsulated Czochralski (LEC) grown crystals. The float zone technique, however,
does not lend itself to growth of semiconducting compounds containing high vapor
pressure elements. [H.R.]
Flux is a term used to describe the rate of flow through a unit area. If ∆N is the number of
particles flowing through an area A in time ∆t, then particle flux, Γ, is defined by Γ = ∆N /
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
50
(A∆t). If an amount of radiation energy ∆E flows through an area A in time ∆t, energy
flux is ΓE=∆E / (A∆t) which defines the intensity of an electromagnetic wave.
Forward bias is the application of an external voltage to a pn junction such that the positive
terminal is connected to the p-side and negative to the n-side. The applied voltage reduces
the built-in potential.
Fourier's law states that the rate of heat flow through a sample, due to thermal conduction, is
proportional to the temperature gradient (dT/dx) and the cross sectional area (A) i.e. If Q′
is the rate of heat flow, then Q′ = −κA(dT/dx) where κ is the thermal conductivity.
Free energy, or Gibbs free energy, G, is a measure of a system's ability to do non-PV work,
that is electrical or magnetic work, as the result of a chemical or physical change. t is an
extensive property of the system. For all spontaneous processes at constant
temperature and pressure the change in the free energy must be negative, ∆G < 0. This
arises from the Second Law of Thermodynamics. In equilibrium G is a minimum. Free
energy of a pure substance per particle is the chemical potential µ = G/N where N is
the number of particles in the system. For two systems in equilibrium, µ must be
uniform, i.e. ∆µ = 0 in going from one to the other system, otherwise the change in µ will
result in external electrical work.
Frenkel defect is an imperfection in an ionic crystal which occurs when an ion moves into an
interstitial site thereby creating a vacancy in its original site. The imperfection is
therefore a pair of point defects.
Frenkel pair is a pair of point defects formed in a crystalline material with a degree of ionic
bonding. If the crystalline material is a compound MX consisting of M and X atoms, for
example, then Frenkel pairs can exist on either the M- or X-sublattice; if the defect pair is
formed on the M-sublattice, it corresponds to an M atom being displaced from its normal
site to an adjacent interstitial site. This displacement results in the formation of a vacant
M-site and an M atom on the interstitial site. Relative to the neutral crystal, prior to the
displacement, the vacant M-site will hold a negative charge and the M atom on the
interstitial site will hold a positive charge of equal magnitude. Such types of defects can
form during ion implantation, or during irradiation of a device with high-energy
particles (e.g., electrons, ions or neutrons), for example, in space. [H.R.]
Fuel cell is an electrochemical cell in which substances which are oxidized and reduced are
fed continuously (and separately) to the anode and cathode.
Full width at half maximum (FWHM) is the width on the abscissa between half maximum
points of the ordinate. Suppose that y vs. x has a maximum y = ymax at x = xo and then
falls to half the maximum value 1/2ymax at x = x2 and x = x1, where x2 > xo > x1. Then
FWHM is ∆x of y vs. x between the half point 1/2ymax so that ∆x = x2 − x1.
Fundamental mode is the lowest order mode that can exist in a dielectric guide and it is the
traveling electric field pattern that has no nodes in the transverse direction to the
waveguide axis (nodes are locations where the electric field is zero).
Fusion is the melting of a solid. The fusion temperature is the melting temperature of a solid.
Gain is the output signal per unit input signal. For voltages , GV = Vout/Vin and for optical signals
with power P, usually, Gop = Pout/Pin.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
51
Gallium (Ga) is a metal that is the primary constituent in a number of III-V semiconductors
such as gallium arsenide and gallium aluminum arsenide, gallium phosphide and gallium
antimonide. Gallium is also commonly used as a p-type dopant for silicon using ion
implantation. Gallium has an unusually low melting point of 29.75 °C or 85.5 °F at
atmospheric pressure. [H.R.]
Gauss's law is a fundamental law of physics (one of Maxwell's equations) that relates the
surface integral of the electric field over a closed (hypothetical) surface to the sum of all
the charges enclosed within the surface. If En is the field normal to a small surface area
dA and Qtotal is the enclosed total charge then over the whole closed surface
εo ∫EndA = Qtotal
where the integration is over the whole closed surface. If there is a dielectric medium,
then we can use
εoεr ∫EndA = Qfree
where Qfree represents the sum of all free charges (excluding polarization charges)
within the surface. This equation applies to an isotropic medium in which εr is
independent of the direction of the field. Gauss’s law in point form relates the gradient
of the electric field at a point to the charge density ρ at that point, i.e. in a one
dimensional problem (as through the space charge region of a pn junction) the gradient
would be dE/dx, and
εoεr dE/dx = ρnet
Charges inside
the surface
n
dA
Gauss Law: The surface integral
of the electric field normal to the
surface is the total charge
enclosed. Field is positive if it is
coming out, negative if it is going
into the surface.
Surface
Gaussian or normal error distribution, refers to a mathematical function g(x) of the
following form:
 1  x − µ2
1
g( x ) =
exp −

σ 2π
 2 σ  
where µ and σ refer to the mean and standard deviation, respectively. The half-width of
the distribution has a value of 2.354σ. This is one of the most important probability
distribution functions for use in statistical analysis of data. The form of g(x) is chosen so
that the area under the curve is unity (i.e., g( x )dx = 1), and thus g(x) is a normalized
distribution function. [H.R.]
∫
Gibbs phase rule is an expression for the number of phases that can co-exist in equilibrium in
a system under specified conditions, and is given by:
P=C+N−F
where P refers to the number of phases present, C is the number of components, N is the
number of non-compositional variables (i.e., temperature and pressure), and F is the
number of degrees of freedom. F is the number of variables (as defined for N above) that
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
52
must be specified to achieve a given state of the system. As an example, consider a phase
diagram describing the possible phases that can form for different fractions x of silicon
and germanium atoms (i.e., alloys of the form, Si1-xGex) as a function of temperature.
The number of components C is 2 (i.e., Si is one component and Ge is the other), and the
number of non-compositional variables N is 1 (i.e., temperature is the variable under
consideration); thus, P = 3 − F in this case. Experimental data show that for all x, but
over a limited temperature range, silicon atoms can be incorporated into a germanium
crystal, or vice versa - this is known as compete solid solubility, and is the basis of
current interest in preparing Si1-xGex alloys, with their associated high charge carrier
mobility (as compared with silicon) for electronic devices. In this case, the solid solution
is a single phase with P = 1; therefore, F = 2, implying that two variables need to be
specified to define under what thermodynamic conditions these solid solutions can form.
These two variables are the composition x and the temperature, as discussed above,
consistent with Gibbs phase rule. [H.R.]
Ge-Si alloys are semiconducting alloys that form as a result of the complete solid solubility of
silicon in germanium and vice versa. For all fractions of silicon in these alloys, a
diamond lattice structure forms. These alloys are important materials for
microelectronics, owing to their significantly higher charge carrier mobilities as
compared with silicon, while being compatible with existing silicon based integrated
circuit manufacturing technology. One limitation of such alloys is that the lattice constant
of the alloys significantly different from that of silicon with the addition of germanium,
and limits the useful range of alloy compositions that can be prepared on silicon without
the introduction of dislocations and other interfacial strain related defects that can
degrade device performance. [H.R.]
Glass is a term that can be used generically to refer to a non-crystalline substance below the
glass transition temperature (Tg) or more specifically to a range of inorganic
(noncrystalline) materials composed of such oxides as SiO2, B2O3, Na2O, P2O5 etc. The
glass structure has no long range order of the crystal, but exhibits only short range
order; we can identify the nearest neighbors of an atom because its valency requirements
in forming bonds must be satisfied.
Silicon (or Arsenic) atom
Oxygen (or Selenium) atom
Crystalline and amorphous
structures illustrated
schematically in two
dimensions.
(a) A crystalline solid reminiscent to
crystalline SiO2.(Density = 2.6 g cm-3)
(b) An amorphous solid reminiscent to vitreous silica
(SiO2) cooled from the melt (Density = 2.2 g cm-3 )
Glass transition (transformation) temperature Tg is usually a narrow temperature range
over which the properties of a material change from solid-like, below Tg, to liquid-like
behavior, above Tg. For example, the heat capacity of a glass is solid like (small) below
Tg and liquid like (high) above Tg. The transition is not always very clear and sometime
the distinction between solid-like and liquid-like behavior is made in terms of the
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
53
viscosity of the material. Below the glass transition temperature, the viscosity of the
structure is so great that over the time scale of observation there is no significant flow
(one may, of course, argue that over thousands of years there may be indeed be a
noticeable flow but this will not change our general view of the substance in our lifetime).
Any shearing stress below Tg results in an elastic response due to the stretching of
bonds, and on removal of the stress the glass returns to its original shape. This is a
typical solid-like behavior and for all practical purposes we view the structure below Tg
as that of a solid. The glass transition temperature is not actually a unique temperature
where the liquid on cooling suddenly becomes glass but a temperature range in which the
liquid-like behavior gradually changes over to a solid-like behavior as the substance is
cooled. It depends not only on the viscosity of the material, which in turn depends on the
bonding and structure, but also on the rate of cooling. Clearly, if the cooling is very slow
then the atomic arrangements can follow the demands of the cooling rate much more
closely and the structure exhibits liquid like behavior to lower temperatures. If the
cooling rate is too slow then there may be sufficient time for atomic diffusions to form
the crystal.
Graded bandgap refers to alloy systems in which the bandgap is varied by varying the
composition (i.e., fraction of a component in the alloy). If the composition is changed
gradually through a structure, the bandgap changes gradually in response, leading to a
so-called grading of the bandgap as a function of position in the structure. Such an
approach is useful in tailoring the response of carriers within a device, as gradient (with
respect to position) of the bands, corresponds to an internal electric field suitable for
causing carrier drift. In addition, grading the bandgap also will alter the optical response
of the structure, and is commonly used in optoelectronic devices to enhance performance.
[H.R.]
Graded index optical fiber has a core refractive index that is graded gradually, i.e. changes
continuously, towards the cladding. Typically in a graded index fiber, the refractive
index profile is approximately parabolic to minimize modal dispersion.
Grain boundary is a surface region between differently oriented adjacent grain crystals. The
grain boundary contains lattice mismatch between adjacent grains.
Foreign impurity
Self-interstitial type atom
Void, vacancy
Strained bond
Grain boundary
Broken bond
(dangling bond)
The grain boundaries have broken bonds, voids, vacancies, strained
bonds and "interstitial" type atoms. The structure of the grain boundary
is disordered and the atoms in the grain boundaries have higher
energies than those within the grains.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
54
Grain is an individual crystal within a polycrystalline material. Within a grain the crystal
structure and orientation are the same everywhere and the crystal is oriented in one
direction only.
Ground state is the state of the electron with the lowest energy.
Group index (Ng) represent the factor by which the group velocity of a group of waves in a
dielectric medium is reduced with respect to propagation in free space, i.e. Ng = vg / c
where vg is the group velocity.
Group is a vertical column in the periodic table. The halogens (F, Cl, Br, I, At) are Group VII
elements.
Group velocity (vg) is the velocity with which a group of waves of closely spaced wavelengths
(called a wave packet) travel in a medium. It is the velocity with which the energy in the
group of waves is propagated in the medium. The group velocity in free space is the
same as the velocity of light, c, in vacuum.
Gyromagnetic ratio (γ) is the ratio of the magnetic moment of an electron to its angular
momentum. It depends whether the angular momentum is due to orbital motion, spin
or both. The term can also apply to a nucleus in which case it is the nuclear gyromagnetic
ratio.
Hall effect is a phenomenon that occurs in a conductor carrying a current when it is placed in a
magnetic field perpendicular to the current. The charge carriers in the conductor
become deflected by the magnetic field and give rise to an electric field (Hall field) that is
perpendicular to both the current and magnetic field. If the current density, Jx, is along x
and the magnetic field, Bz, is along z, then the Hall field is either along +y or −y
depending on the polarity of the charge carriers in the material.
Jy = 0
VH
Bz
V
y
eEH
Jx
EH
Ex
vdx
Jx
z
evdxBz
A
Bz
The current flow is along the xdirection. The externally applied
magnetic field is along the zx
direction. The Lorentz force
evdxBz is along y. This force
initially accumulates electrons
near the bottom of the conductor
until equiliribrium is reached as
shown in this figure.
V
Hall coefficient (RH) is a parameter that gauges the magnitude of the Hall effect. If Ey is
the electric field set up in the y-direction due to a current density, Jx, along x and a
magnetic field, Bz, along z, then RH = Ey/JxBz. For a sample in which there are only one
species of mobile charge carriers, e.g. electrons in a metal, the hole coefficient RH
depends on the carrier concentration, n (for negative charges) or p (for positive charges),
and also on their sign,
1
1
RH = −
or
RH = +
en
ep
The sign of RH therefore indicates polarity of the charge carriers in a sample. Hall effect
in a semiconductor where there are both electrons and holes results in the deflection of
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
55
both electrons and holes toward the bottom surface of the sample and consequently the
Hall voltage depends on the relative concentrations and mobilities of electrons and holes.
If concentrations of electrons and holes are n and p respectively and the electron and hole
drift mobilities are µe and µh, RH in semiconductors is given by
RH =
pµ h2 − nµe2
or
RH =
p − nb 2
e( pµ h + nµe ) 2
e( p + nb ) 2
where b = µe/µh. It is clear that the Hall coefficient depends on both the drift mobility
ratio and the concentrations of holes and electrons. In the extrinsic region of a doped
semiconductor, typically either p >> n or n >> p. Assuming that b is not drastically
different than 1, then for p-type semiconductors, RH =1/ep, and for n-type
semiconductors, RH = −1/en.
Hall probes are used for high precision magnetometry. They are typically based on Hall
generators made of high-mobility compound semiconductors, such as InSb and InAs. A
high carrier mobility is crucial for achieving high sensitivity, low offset, and low noise.
These problems are usually overcome through digital signal processing. [C.T.]
Hard direction is the crystal direction along which it is hardest to align the atomic spin
magnetic moments relative to the easy direction. Exchange interaction energy, Eex,
favors the easy direction most (Eex is most negative) and favors the hard direction least
(Eex is least negative).
Hard magnetic materials characteristically have high remanent magnetizations (Br) and
high coercivities (Hc) so that once magnetized they are difficult to demagnetize. They are
suitable for permanent magnet applications. They have broad B-H hysteresis loops. See
soft magnetic materials.
B
Hard
–H
H
Soft
Soft and hard magnetic materials
–B
Hard magnetic particles are small particles of various shapes that have high coercivity due to
having a single magnetic domain with high magnetocrystalline anisotropy energy,
or possessing substantial shape anisotropy (aspect ratio - length to width ratio).
Harmonic oscillator is an oscillating system, for example, two masses joined by a spring, that
can be described by simple harmonic motion. In quantum mechanics, the energy of a
harmonic oscillator is quantized and can only increase or decrease by a discrete amount
hω. The minimum energy of a harmonic oscillator is not zero but 1/2hω, called the zeropoint energy.
Hazardous production material (HPM) is a term used to describe solids, liquids and gases
that are hazardous to people if handled without any protection. Subclasses of HPM
include acids, bases, toxics, flammables, combustables, oxidizers and pyrophorics. [H.R.]
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
56
Heat capacity at constant volume is the increase in the internal energy of a system per degree
increase in the temperature of the system, i.e. CV = (∂U /∂T)V where U is the total internal
energy of the system (kinetic energy and potential energy) and the subscript V
indicates constant volume. For most metals, the heat capacity per mole obeys the
Dulong-Petit rule, that is Cmole = 3R where R is the gas constant. At room temperature
Cmole is approximately 25 J mole-1 for all metals. The Dulong-Petit rule is based on the
kinetic molecular of matter and the Maxwell equipartition of energy theorem. In general
the molar heat capacity Cm of a solid can be determined from the Debye heat capacity
expression which, in graphical form, is shown in the accompanying figure. This graph
represents the molar heat capacity of all solids as a function of temperature, normalized
with respect to the Debye temperature TD. The Debye temperature is a characteristic
temperature of a particular crystal above which nearly all the atoms are vibrating in
accordance of the kinetic molecular theory. For example, for silicon, TD = 625 K, and
at room temperature, T = 300 K, T/TD = 0.48 and Cm is about 0.81(3R) or 20J mole-1.
This point is on the temperature sensitive portion of the Debye curve which means that
Cm depends on the temperature. For example, diamond has Debye temperature of 1860
K and its atomic mass is 12 g mole-1. At room temperature, T = 300 K, T/TD = (300
K)/(1860 K) = 0.16 and Cm is only 0.24(3R) = 6 J mol-1.
1
25
0.9
Cm = 3R
Cu
0.8
20
Si (TD = 625 K)
0.7
0.6
15
Cm/(3R) 0.5
0.4
10
Cm
J mol-1
0.3
0.2
5
Diamond
(TD = 1860 K)
0.1
0
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
T / TD
Debye molar heat capacity curve. The dependence of the molar heat
capacity Cm on temperature with respect to the Debye temperature: Cm vs.
T/TD. For Si, TD = 625 K so that at room temperature (300 K), T/TD = 0.48
and Cm is only 0.81(3R).
Heat is the amount of energy that is transferred from one system to another (or between the
system and its surroundings) as a result of a temperature difference. It is not a new
form of energy but rather the transfer of energy from one body to another by virtue of
the random motions of their molecules. When a hot body is in contact with a cold body,
heat is transferred from the hot to the cold body. What is actually transferred is the
excess mean kinetic energy of the molecules in the hot body. Molecules in the hot body
have higher kinetic energy and vibrate more violently and, as a result of the collisions
between the molecules, there is a net transfer of energy from the hot to the cold body
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
57
until the molecules in both bodies have the same mean kinetic energy; when their
temperatures are the same.
Henry’s law applies to a dilute solution of solute atoms in a solvent. In such a solution, the
concentration of the solute atoms is very small and these atoms are, on average, to be
found at relatively large distances from one another. Thus, the solute atoms are not able
to interact with each other very effectively, and Henry’s law is based on the proposition
that these interactions can be neglected. Under this assumption, the partial pressure of
solute atoms above the solution, pA, should scale in proportion to the number of solute
atoms in the solution, or for a fixed volume of solution, the concentration of solute atoms
in the solution, XA, i.e. pA = βXA, where β is a constant for a given solute and solution.
This equation is known as Henry’s Law. [H.R.]
Heteroepitaxy refers to epitaxial growth where the layer of material grown on top of the
substrate and the substrate itself are different materials. An example of this would be a
single crystal layer of InGaAsP grown on top of a single crystal GaAs substrate. [H.R.]
Heterogeneous mixture is a mixture in which the individual components remain physically
separate and possess different chemical and physical properties. It is a mixture of
different phases.
Heterojunction is a junction between different semiconductor materials, for example between
GaAs and GaAlAs ternary alloy. There may or may not be a change in the doping.
The doping in the wider bandgap semiconductor is denoted with a capital letter, N or P,
and that in the narrower bandgap semiconductor with lower case n or p.
Heterostructure Laser Diodes have a thin narrower bandgap semiconductor layer sandwiched
between two wider bandgap semiconductors so that there are two heterojunctions. The
wider Eg layers provide potential energy steps and hence carrier confinement within the
narrower Eg layer and also provide a step change in the refractive index and hence optical
confinement. The sandwiched narrower Eg layer acts as the active region in which the
electron and hole concentrations are sufficiently high to lead to stimulated emission.
High-purity (HP) and ultra-high-purity (UHP) are terms that are used to refer to solids,
liquids and gases that contain only trace amounts of impurities. The quantity of these
impurities are usually measured in units of ppm (parts-per-million), ppb (parts-perbillion) and ppt (parts-per-trillion). [H.R.]
Hole (h+) is a missing electron in an electronic state that is in the valence band. Intuitively, it is
a missing electron in a bond between two neighboring atoms in the semiconductor
crystal. The region around this “ruptured” bond is a net positive charge of +e. It can
drift in an applied field because an electron in a neighboring bond can tunnel into this
vacant site and thereby cause the positively charge bond-vacancy to become displaced,
shifted. Thus holes contribute to electrical conduction in semiconductors as well. In a full
valence band there is no net contribution to the current. There are equal number of
electrons (e.g. at b and b') with opposite momenta. If there is an empty state, hole, at b at
the top of the valence band (VB) then the electron at b' contributes to the current. The
reason that the presence of a hole makes conduction possible is the fact that the momenta
of all the VB electrons are cancelled except that at b’. Thus, we can consider the net result
of the motions of all the electrons in the VB just by exmining the behavior of the missing
electron at b’ and assigning to it a positive charge +e and an effective mass mh*
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
(a)
CB
+
h
e–
+
h
58
+
h
(d)
+
Eg
h
VB
+
h e–
+
h
(b)
+
h
e–
+
h
(e)
e–
(c)
+
h
+
h
(f)
A pictorial illustration of a hole in the valence band wandering around the
crystal due to the tunneling of electrons from neighboring bonds.
E
Ev
b'
b
VB
–k
k
E
b'
b
VB
–k
In a full valence band there is no net
contribution to the current. There are equal
number of electrons (e.g. at b and b') with
opposite momenta. (b) If there is an empty
state (hole) at b at the top of the band then
the electron at b' contributes to the current.
k
Homoepitaxy refers to epitaxial growth where the layer of material grown on top of the
substrate and the substrate itself are of the same material. An example of this would be
a layer of GaAs single crystal grown on a single crystal GaAs substrate. [H.R.]
Homogeneous mixture is a mixture of two or more chemical species in which the chemical
properties (e.g. composition) and physical properties (e.g. density, heat capacity) are
uniform throughout. A homogeneous mixture is a solution.
Homojunction is a junction between differently doped regions of the same semiconducting
material, for example a pn junction in the same silicon crystal; there is no change in the
bandgap energy, Eg.
Hopping electron conduction in a solid involves a localized electron around an atomic site
tunneling or jumping over a potential energy barrier to a neighboring site as a result
of lattice vibrations perturbing its surroundings. Thus hopping conduction is a
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
59
thermally assisted jump from one local site to another nearby site and does not involve
the drift of electrons as if they were free in the conduction band with occasional
scattering. The mobility for hopping conduction is much smaller than that for drift in the
conduction band.
Horizontal and vertical Bridgeman (HB and VB) growth are two commonly used forms
of Bridgeman growth in which growth occurs parallel (VB) to or perpendicular to the
vector of gravitational force (HB). [H.R.]
Hume-Rothery rules are empirical rules determining the formation of a solid solution
between two elements. These rules state that for such a solid solution to form, (a) each
element should have the same valence, (b) the crystal structure of each element, in
isolation, should be the same, (c) the elements should not react to form a compound, and
(d) the atomic radii of each of the elements should not differ by more than 15%. These
rules can provide a useful guideline for selecting pairs of elements that exhibit solid
solubility. [H.R.]
Hund's rule states that electrons in a given subshell, nl, try to occupy separate orbitals
(different ml) and keep their spins parallel (same ms). In doing so they achieve a lower
energy than pairing their spins (different ms) and occupying the same orbital (same ml).
Hydrochloric acid (HCl) is a poisonous solution of hydrogen chloride gas in water. It is a
commonly used component in etching solutions for electronic materials. [H.R.]
Hydrofluoric acid (HF) is an extremely hazardous acid used to etch silicon dioxide. HF is
particularly dangerous because it results in no immediate or apparent reaction to contact
with skin. However, within a short period of contact to HF, the HF causes severe burns
and in extreme cases of prolonged exposure, it leads to leeching of calcium from a
person’s bones. [H.R.]
Hydrogen (H2) is a non-toxic flammable gas that is used as a reactant gas with trichlorosilane
to form epitaxial silicon. It is also commonly used as a transport agent to transport metalorganic precursors from their bubblers to the reactor in the case of metal-organic
chemical vapor deposition (MOCVD). Thermal oxides of silicon are commonly
grown using H2O that is produced by the combustion of high-purity hydrogen and
oxygen. Hydrogen is also used as a reducing gas to scavenge oxygen. Oxygen reduction
prevents the formation of silicon dioxide as an impurity in epitaxial silicon layers.
[H.R.]
Hydrogen chloride (HCl) is a corrosive gas that is used in etching, oxidation, passivation
and epitaxial growth. [H.R.]
Hydrogen peroxide (H2O2) is an unstable and strong oxidizer, that is soluble in water and
alcohol, and is used as a catalyst in special etching solution formulations, including for
example, the piranha etch. [H.R.]
Hydrogenated amorphous Si (a-Si:H) see amorphous silicon.
Hysteresis loop is the magnetization (M) vs. applied magnetic field intensity (H) or B vs.
H behavior of a ferromagnetic (or ferromagnetic) substance as it is repeatedly
magnetized and demagnetized through one cycle.
Hysteresis loss is the energy loss involved in magnetizing and demagnetizing a ferromagnetic
(or ferromagnetic) substance. It arises from various energy losses involved in the
irreversible motions of the domain walls. Hysteresis loss per unit volume of specimen
is the area of the B-H hysteresis loop.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
60
Impact ionization is the process by which a high electric field accelerates a free charge carrier
(electron in the conduction band) which then impacts with a Si-Si bonds to generate a
free electron hole pair. The impact excites an electron from the band edge (Ev) to the
conduction band edge (Ec).
Implanation damage is associated with the ion implantation process. Accelerated ions (e.g.,
dopant species) impinging on a target material decelerate and lose energy through
interactions with electrons in the target, as well as by collisions with target nuclei. If a
given implant species have sufficient momentum, then its collisions with the target nuclei
can lead to target atoms being displaced from their normal sites. The type of point
defects that are formed will depend on the energetics of the process involved, including
energy of formation and migration of given defects, their pairing energy, target
temperature, and the flux and total dose of the implanting species. Implantation damage
is the term used to describe the extent by which point defect concentrations are
augmented as a result of the implantation process. Typically, a common type of
implantation damage is that of the formation of defect pairs such as an interstitialvacancy pair, when a target atom is knocked off its normal site (leading to a vacancy
formation) and comes to rest in between normal lattice sites (leading to the formation of
an interstitial defect). Rapid thermal annealing is commonly used to help reduce the
concentration of implant-related defects. Since, in this process, heat is applied for a
relatively short duration, only a very limited amount of diffusion is allowed to occur.
The process is designed to be sufficient to recover the damage, but not to permit sharp
device doping profiles to be significantly disturbed. [H.R.]
Incremental conductance (gd) is the change in the forward current per unit change in the
voltage across the diode, dI/dV. Incremental resistance is the inverse of the incremental
conductance.
Indium (In) is a soft metal that is the primary constituent in a number of important III-V
semiconductors including indium phosphide, indium arsenide and indium antimonide. It
is also used as a source for p-type doping of silicon by ion implantation. [H.R.]
Induced polarization is the polarization of a molecule as a result of its placement in an
electric field. The induced polarization is along the direction of the field. If the molecule
is already polar then induced polarization is the additional polarization that arises due to
the applied field alone and it is directed along the field.
Inductance is a property of an electrical circuit and its medium which characterizes the total
amount of magnetic flux that is set up in the medium per unit current in the circuit. If a
current I is flowing through an electrical circuit and it links (threads) a total amount of
magnetic flux Φtotal then the inductance of this circuit, whether it is a single conductor or
a complicated circuit, is given by L = Φtotal/I. Magnetic energy stored in an inductor
carrying a current I is Emag = (1/2)LI2. The greater the inductance of a circuit, the more
magnetic energy is stored per unit current.
Ingot is a solid bar of material that can be either a single crystal or polycrystalline. The latter
case is commonly called a boule. Polycrystalline ingots of silicon are commonly used as
feed material in the floating zone growth process. [H.R.]
Initial permeability (µriµo) is the initial slope of the B vs. H characteristic of an unmagnetized
ferromagnetic (or ferromagnetic) material and typically represents the magnetic
permeability under very small applied magnetic fields. Initial relative permeability
(µri) is the relative permeability of an unmagnetized ferromagnetic (or ferromagnetic)
material under very small applied fields.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
61
Injection (electrode) limited current through a solid occurs when the current flow is limited
by the rate at which the electrical contacts can inject carriers into the sample. As the
applied field increases, the potential energy barrier against the injection of carriers from
the electrode into the sample is lowered by the Schottky effect .
Injection electroluminescence, see light emitting diode.
Injection laser diode see laser diode.
Injection pumping is the achievement of population inversion in a region of a
semiconductor laser device by injecting sufficiently large number electrons (in the
conduction band) and holes (in the valence band) by virtue of passing a sufficiently
large current.
Instantaneous irradiance is the instantaneous flow of energy per unit time per unit area and is
given by the instantaneous value of the Poynting vector, S = v2εoεrE×B, where v is the
velocity of the electromagnetic wave in the medium (v2 = c2/εr), εr is the relative
permittivity, E is the electric field and B is the magnetic field.
Insulation Aging is a term used to describe the physical and chemical deterioration in the
properties of the insulation so that its dielectric breakdown characteristics worsen with
time. Aging therefore determines the useful life of the insulation.
Integrated circuit (IC) is a chip of a semiconductor crystal in which many active and passive
components have been integrated together to form a sophisticated circuit.
Integrated optics refers to the integration of various optical devices and components on a single
common substrate, for example, lithium niobate, just as in integrated electronics all the
necessary devices for a given function are integrated in the same semiconductor crystal
substrate (chip). There is a distinct advantage to implementing various optically
communicated devices, e.g. laser diodes, waveguides, splitters, modulators,
photodetectors and so on, on the same substrate as it leads to miniaturization and also to
an overall enhancement in performance and usability (typically).
Intensity is the flow of energy per unit area per unit time. It is equal to energy flux. If ρE is the
energy density and the v is the velocity of propagation of a wave then instantaneous
intensity I is vrE. For an electromagnetic wave the instantaneous intensity is cεoE2 where
c is the light velocity and E is the instantaneous electric field given by E = Eosin(kx−ωt).
The average intensity, Iav, the mean energy flow per unit area per unit time, is given by
1
/2cεoEo2. In the photonic interpretation of light, the intensity is given by I = hυΓph where
hυ is the photon energy and Γph is the photon flux (number of photon flowing per unit
area per unit second).
Intensive property of a substance is independent of its size. Typical intensive properties are
pressure (P), temperature (T), electric and magnetic field intensities (E and H). We can
define an intensive property that is derived from an extensive property by normalizing
the latter with respect to the mass of the substance. For example, specific volume is the
volume of the substance per unit mass. Lower case is normally used for specific
properties: v = V / M.
Interband absorption in direct bandgap semiconductors such as III-V semiconductors (e.g.
GaAs, InAs, InP, GaP) and in many of their alloys (e.g. InGaAs, GaAsSb) is a photon
absorption process in which there is no assistance from lattice vibrations. The photon
is absorbed and the electron is excited directly from the valence band to the
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
62
conduction band without a change in its k-vector (or its crystal momentum hk)
inasmuch as the photon momentum is very small. The change in the electron momentum
from the valence band (VB) to the conduction band (CB) is
hkCB − hkVB = photon momentum ≈ 0.
This process corresponds to a vertical transition on the E-k diagram, that is electron
energy (E) vs. electron momentum (hk) in the crystal). The absorption coefficient of
these semiconductors rises sharply with decreasing wavelength from λg as for GaAs and
InP. Interband absorption in indirect bandgap semiconductors such as Si and Ge, is a
photon absorption process for photon energies near and above the bandgap (Eg) energy
and requires the absorption and emission of lattice vibrations, that is phonons, during
the absorption process. If K is the wavevector of a lattice wave (lattice vibrations travel
in the crystal), then hK represents the momentum associated with such a lattice vibration,
that hK is a phonon momentum. When an electron in the valence band is excited to the
conduction band there is a change in its momentum in the crystal and this change in the
momentum cannot be supplied by the momentum of the incident photon which is very
small. Thus, the momentum difference must be balanced by a phonon momentum:
hkCB − hkVB = phonon momentum = hK.
The absorption process is said to be indirect as it depends on lattice vibrations which in
turn depend on the temperature. Since the interaction of a photon with a valence electron
needs a third body, a lattice vibration, the probability of photon absorption is not as high
as in a direct transition. Furthermore, the cut-off wavelength is not as sharp as for direct
bandgap semiconductors. During the absorption process, a phonon may be absorbed or
emitted. If ϑ is the frequency of the lattice vibrations then the phonon energy is hϑ. The
photon energy is hυ where υ is the photon frequency. Conservation of energy requires
that the
hυ = Eg ± hϑ
Thus, the onset of absorption does not exactly coincide with Eg, but typically it is very
close to Eg inasmuch as hϑ is small (< 0.1 eV). The absorption coefficient initially rises
slowly with decreasing wavelength from about λg.
E
E
CB
Ec
CB
Eg
Direct Band Gap
Photon
Indirect Band Gap, Eg
Ec
Ev
Photon
Ev
VB
–k
VB
k
(a) GaAs (Direct bandgap)
Phonon
–k
k
(b) Si (Indirect bandgap)
(a) Photon absorption in a direct bandgap semiconductor. (b) Photon absorption
in an indirect bandgap semiconductor (VB, valence band; CB, conduction band)
Interfacial polarization occurs whenever there is an accumulation of charge at an interface
between two materials or between two regions within a material. Grain boundaries and
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
63
electrodes are regions where generally charges accumulate and give rise to this type of
polarization.
Internal discharges are partial discharges that take place in microstructural voids, cracks or
pores within the dielectric where the gas atmosphere (usually air) has lower dielectric
strength. A porous ceramic for example would experience partial discharges if the field
is sufficiently large. Initially the pore size (or the number of pores) may be small and the
partial discharge insignificant but with time the partial discharge erodes the internal
surfaces of the void. Partial discharges can locally melt the insulator and can easily cause
chemical transformations. Eventually and usually an electrical tree type of discharge
develops from a partial discharge that has been eroding the dielectric. The erosion of the
dielectric by the partial discharge propagates like a branching tree. The "tree branches"
are erosion channels, filaments of various sizes, in which gaseous discharge takes place
and forms a conducting channel during operation.
Internal quantum efficiency (ηint) of a light emitting diode gauges what fraction of electron
hole recombinations in the forward biased pn junction are radiative and therefore lead
to photon emission. Nonradiative transitions are those in which and electron and a hole
recombine through a recombination center such as a crystal defect or an impurity and
emit phonons (lattice vibrations). By definition,
Rate of radiative recombination
ηint =
Total rate of recombination (radiative and nonradiative)
1
τr
ηint =
or
1
1
+
τ r τ nr
where τr is the mean lifetime of a minority carrier before it recombines radiatively and
τnr is the mean lifetime before it recombines via a recombination center without emitting a
photon. The total current I is determined by the total rate of recombinations whereas the
number of photons emitted per second (Φph) is determined by the rate of radiative
recombinations. Thus,
Φ ph Pop(int) / hυ
Photons emitted per second
=
=
ηint =
Total carriers lost per second I / e
I /e
where Pop(int) is the optical power generated internally (not yet extracted), e is the
electronic charge, and hυ is the photon energy.
Internal quantum efficiency of a photodetector is the number of free electron hole pairs
photogenerated per absorbed photon ; this is not per incident photon on the device.
Inasmuch as internal quantum efficiency is defined in terms of per absorbed photon, it is
greater than external quantum efficiency which is defined in terms per incident photon;
not all incident photons are absorbed.
Internal reflection is the reflection of an electromagnetic (EM) wave initially traveling in a
medium of high refractive index n1 at the boundary with a medium of lower refractive
index n2 (< n1); a light wave traveling in n1 is reflected at the boundary n1-n2 (some of the
energy may however be transmitted). For example, internal reflection occurs when a light
wave traveling in water is incident on the water-air surface and becomes reflected.
Interstitial site (interstice) is an unoccupied space between the atoms (or ions or molecules)
in the crystal.
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64
Intrinsic breakdown or electronic breakdown commonly involves the avalanche multiplication
of electrons (and holes in solids) by impact ionization in the presence of high electric
fields. The large number of free carriers generated by the avalanche of impact ionizations
leads to a runaway current between the electrodes and hence insulation breakdown.
Intrinsic carrier concentration (ni) is the electron concentration in the conduction band of
an intrinsic semiconductor (an ideal perfect crystal that has not been doped). The
hole concentration in the valence band is equal to the electron concentration. The
intrinsic concentration is a material property that depends on the energy bandgap Eg and
the temperature and can be written as
ni2 = NcNvexp(−Eg/kT)
where Nc and Nv are the effective densities of states at the conduction and valence band
edges, Eg is the badgap, k is Boltzmann’s constant and T is the absolute temperature.
Intrinsic semiconductor has equal number of electrons and holes due to thermal generation
across the bandgap, Eg. It corresponds to a pure semiconductor crystal in which there
are no impurities and crystal defects to cause an effective doping of the crystal.
Inversion occurs when an applied voltage to the gate (or metal electrode) of a MOS device
causes the semiconductor under the oxide to develop a conducting layer (or a channel)
at the surface of the semiconductor. The conducting layer has opposite polarity carriers
to the bulk semiconductor and is hence termed an inversion layer.
Ion is an atom that has a net charge associated with it as a result of gaining or losing electron(s).
The loss of one or more electrons results in the production of positively charged ion(s)
[i.e., cation(s)]. The gain of one or more electrons results in the production of negatively
charged ion(s) [i.e., anion(s)]. [H.R.]
Ion implantation is a process that is used to bombard a sample in vacuum with ions of a given
species of atoms. First the dopant atoms are ionized in vacuum and then accelerated
them applying voltage differences to impinge on a sample to be doped. The sample is
grounded to neutralize the implanted ions.
Ionic conduction is the migration of ions in the material as a result of field directed diffusion.
When a positive ion in an interstitial site jumps to a neighboring interstitial site in the
direction of the field it lowers its potential energy which is a favorable process. If it
jumps in the opposite direction then it has to do work against the force of the field which
is undesirable. Thus the diffusion of the positive ion is directed along the field.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
65
Ionic crystals are solids that have cations (positive ions, e.g. Na+) and anions (negative ions, e.g.
Cl−) arranged in a period array. In ionic solids the cations and the anions attract each
other non-directionally. The crystal structure depends on how closely the opposite ions
can be brought together and how best the same ions can avoid each other while
maintaining long range order, or maintaining symmetry. It depends on the relative charge
and size per ion. It is very simple to demonstrate the importance of the size effect in two
dimensions. If we have identical coins, say pennies (1 cent coins), we can make at most
six pennies touch one penny. On the other hand if we have to bring quarters (25 cent
coins) to touch one penny, we can at most, have five quarters touch the penny. But this
arrangement cannot be extended to construct a two dimensional crystal with periodicity.
To fulfill the long range symmetry requirement of crystals we can only use four quarters
to touch the penny and thereby build a two dimensional "penny-quarter" crystal which is
shown in the figure. In the two dimensional crystal, a penny has four quarters as nearest
neighbors and similarly a quarter has four pennies as nearest neighbors. A convenient
unit cell is a square cell with 1/4 of a penny at each corner and a full quarter at the center.
The three dimensional equivalent of the unit cell of the penny-quarter crystal is the NaCl
unit cell. The Na+ ion is about half the size of the Cl− ion which permits 6 nearest
neighbors while maintaining long range order. The table below lists the cation-anion
radius ratio and the corresponding crystal structure.
Ratio of radii = 1
Ratio of radii = 0.75
25¢
1¢
25¢
Unit cell
1¢
1¢
Nearest neighbors = 6 Nearest neighbors = 4
A two-dimensional crystal of
pennies and quarters
Packing of coins on a table top to build a two dimensional crystal.
Ionic radius ratio is R+/R−. CN is coordination number
R +/R −
< 0.155
0.155−0.225
0.225−0.414
0.414−0.732
0.732−1
CN
2
3
4
6
8
ZnS
NaCl
CsCl
Example
Ionic polarization is the relative displacement of oppositely charged ions in an ionic crystal
that results in the polarization of the whole material. Typically ionic polarization is
important in ionic crystals below the infrared wavelengths.
Ionization energy is the energy required to ionize an atom, e.g. remove an electron.
Ionized impurity scattering limited mobility is the mobility of the electrons when their motion
is limited by scattering from the ionized impurities in the semiconductor (e.g. donors and
acceptors).
Irradiance (average) is the average flow of energy per unit time per unit area where averaging
is typically carried out by the light detector (over many oscillation periods). Average
irradiance can also be defined mathematically by the average value of the Poynting vector
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
66
S = v2εoεrE×B over one period; Saverage = 1/2cεonEo2 where Eo is the amplitude of the
electric field, c is the speed of light, εr is the relative permittivity, n is the refractive
index (εr1/2), E is the electric field and B is the magnetic field. The instantaneous
irradiance can only be measured if the power meter can respond more quickly than the
oscillations of the electric field, and since this is in the optical frequencies range, all
practical measurements invariably yield the average irradiance because all detectors have
a response rate much slower than the frequency of the wave.
Irreversible process is that in which during the process the system goes through
nonequilibrium states; the pressure and temperature are not uniform.
Isolated system is a system for which there is no energy exchange in the form of heat or work
with the surroundings. Thus for changes in the state of an isolated system, if U is the
internal energy, ∆U = 0.
Isomorphous means that the structure is the same everywhere (iso, uniform; morphous,
structure)
Isomorphous phase diagram is that for an alloy which shows unlimited solid solubility.
Isothermal process is that in which the temperature of the system remains constant throughout
the process. The temperature will remain constant if the system is in thermal equilibrium
which requires very slow (in theory, almost infinitely slow) changes in the pressure and
volume. The system can exchange energy as heat and work with its surroundings so
that both ∆Q and ∆W can be finite. In practice, isothermal changes are executed by
thermally contacting the system with a very large body of constant temperature and
carrying out the process sufficiently slowly. "How slowly" depends on the actual size of
the system.
Isotopes of an element have the same atomic number Z (the same number of protons) but differ
in N and A. They have different numbers of neutrons in the nucleus and hence different
atomic mass numbers.
Isotropic substance has the same property in all directions of space.
Jerk is the rate of change of an object's acceleration, that is the amount of change in its
acceleration per unit time. When a body experiences a change da in its acceleration in a
small time interval dt, it experiences a jerk da/dt. The greater the change in the
acceleration per unit time, the larger is the jerk. Put differently, jerk is the rate of change
of force acting on a body; the higher this change, the greater the jerk. Jerk is a vector
quantity that has a magnitude and a direction. [Note: Author's definition adopted from a
Physics Teacher article.]
Joule's Law relates the power dissipated in a current carrying conductor to the applied field and
the current density so that P = JE = σE2.
Joule heating is the heating of a conductor as a result of passing a current through it. When a
current is passed through a crystal, electrical energy is converted to more energetic
atomic vibrations of the crystal due to the collisions of charge carriers with crystal
vibrations, impurities and defects. Thus, there is an increases in the internal energy of the
material which means that the temperature of the crystal increases. The excess energy is
lost to the ambient through thermal conduction, radiation, convection etc, and this excess
energy that is generated is what defined as "heat".
k is the wavevector of the electron's wavefunction. In a crystal the electron wavefunction,
ψ(x), is a modulated traveling wave of the form, ψk(x) = Uk(x)exp(−jkx) where k is the
wavevector and Uk(x) is a periodic function which depends on the PE of interaction
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
67
between the electron and the lattice atoms. k identifies all possible states, ψk(x), that are
allowed to exist in the crystal. hk is called the crystal momentum of the electron as its
rate of change is the externally applied force to the electron, d(hk)/dt = Fexternal.
Kerr effect is a second order electro-optic effect in which an applied strong electric field
modifies the refractive index in such a way that the refractive index change is
proportional to the square of the applied field. For example, when a strong field is
applied to an otherwise optically isotropic material such as glass (or liquid), the change
in the refractive index will be due only to the Kerr effect, since such materials exhibit no
Pockels effect. If Ea is the applied field, then the change in the refractive index for
polarization parallel to the applied field is given by
∆n = λKEa2
where K is the Kerr coefficient. Suppose that we arbitrarily set the z-axis of a Cartesian
coordinate system along the applied field. The applied field distorts the electron motions
(orbits) in the constituent atoms and molecules, including those valence electrons in
covalent bonds, in such a way that it becomes “more” difficult for the electric field in
the light wave to displace electrons parallel to the applied field direction. Thus a light
wave with a polarization parallel to the z-axis will experience a smaller refractive index,
reduced from its original value no to ne. A light waves with polarizations orthogonal to the
z-axis will experience the same refractive index no. The applied field thus induces
birefringence with an optic axis parallel to the applied field direction. The material
becomes birefringent for waves traveling off the z-axis. The polarization modulator and
intensity modulator concepts based on the Pockels cell can be extended to the Kerr
effect. In the Kerr case, the applied field again induces birefringence. The Kerr phase
modulator uses the fact that the applied field along z induces a refractive index ne parallel
to the z-axis whereas that along the x-axis will still be no. The light components Ez and Ez
then travel along the material with different velocities and emerge with a phase difference
∆φ resulting in an elliptically polarized light. However, the Kerr effect is small as it is a
second order effect, and therefore only accessible for modulation use at high fields. The
advantage, however, is that, all materials, including glasses and liquids, exhibit the Kerr
effect and the response time in solids is very short, much less than nanoseconds leading
to high modulation frequencies (greater than GHz). See also electro-optic effects.
Ea
z
z
no
ne
x
Ez
E
no
y
Input
light
Ea
y
Ex
Output
light
x
(a) An applied electric field, via the Kerr effect, induces birefringences in
an otherwise optically istropic material. no and ne are the ordinary and
extraordinary refractive indices (b) A Kerr cell phase modulator.
Kinetic molecular theory assumes that the atoms and molecules of all substances (gases,
liquids and solids) above absolute zero of temperature are in constant motion.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
68
Monatomic molecules (e.g. He, Ne) in a gas exhibit constant and random translational
motion whereas the atoms in a solid exhibit constant vibrational motion.
Large Scale Integration (LSI) is a type of semiconductor fabrication technology. Typically it
refers to individual dies that have between 100 and 1000 devices on them. The
technology produces circuits with densities intermediate between that of Very Large
Scale Integrated circuits (VLSI) and Small Scale Integrated circuits (SSI). [H.R.]
Larmor frequency (ωL) is the angular frequency of the precession of a magnetic moment in
an applied magnetic field. One can draw an analogy with the angular frequency of the
precession of a spinning top around the gravitational field of the earth.
LASER (Light Amplification by Stimulated Emission of Radiation) is a device within
which photon multiplication by stimulated emission produces an output radiation that
is nearly monochromatic and coherent (vis-à-vis incoherent stream of photons from
tungsten light bulb). Furthermore, the output beam has very little divergence. Laser
operation is first based on achieving population inversion between two energy levels
in the medium which populates an excited energy level at E2 with a large number of
atoms compared with a lower energy level E1. The process that establishes population
inversion is called pumping. In an optically pumped laser, the lasing medium must have
at least three suitable energy levels. For example, in the ruby laser, the Cr3+ ions in the
ground state at E1 are optically pumped, by photons of energy hυ13 = (E3−E1) from a
xenon flash, to an energy level E3 from where they decay to an energy level E2, above E1,
which eventually becomes more populated than the E1. When an atom falls from the
excited level, E2, to a less populated lower energy level, E1, it emits a photon of energy
hυ21 = (E2−E1), which can impact with another excited atom and cause it to emit a photon
with the same frequency by stimulated emission. Two photons are then obtained that are
in phase and are traveling in the same direction which can impact on a third atom and
cause further stimulated emission thereby collect another coherent photon. The
stimulated emission of other excited atoms gives rise to a stream of photons which are in
phase and are traveling in the same direction. By enclosing the medium within an optical
cavity (e.g. two parallel mirrors), it is possible to reflect the photons backwards and
forwards in the medium to build-up the photon density. One of the mirrors of the cavity
is partially silvered to allow some of the radiation to escape as a laser light output.
Laser diode equation relates the output optical power Po to the diode current density J (or
current I) above the threshold current density Jth. In simple terms,
 hc 2τ ph W (1 − R ) 
Po = 
( J − Jth )
2enλ


where R is the reflectance of the optical cavity reflectors, n is the refractive index, λ is
the wavelength, W is the width of the active region and τph is the photon decay time in
the cavity; the power in a light wave, in the absence of amplification, decreases as exp(−
ατx) which is equivalent to a decay in time as exp(−t/τph) where τph = n/(cατ) and αt is
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
69
the total attenuation coefficient representing all these loss mechanisms.
n Po
nth
Threshold population
inversion
n
Po = Lasing output power ∝ Nph
I
Ith
Simplified and idealized description of a semiconductor laser
diode based on rate equations. Injected electron concentration
n and coherent radiation output power P o vs. diode current I.
Laser diode external differential quantum efficiency ηEDQE, of a laser diode is defined as
 e  dP
Increase in number of output photons from diode ( per unit second)
ηEDQE =
=  o
Increase in number of injected electrons into diode ( per unit second)  Eg  dI
where Po is the emitted optical power, Eg is the bandgap of the active region
semiconductor and I is the diode current.
Laser diode external power efficiency ηEPE, of the laser diode is defined by
Optical output power
E 
ηEPE =
= ηEQE  g 
 eV 
Electical input power
where ηEQE is the laser diode external quantum efficiency, Eg is the bandgap of the
active region semiconductor and V is the diode voltage.
Laser diode external quantum efficiency ηEQE, is defined as
Number of output photons from the diode ( per unit second) ePo
ηEQE =
=
Eg I
Number of injected electrons into diode ( per unit second)
where Po is the emitted optical power, Eg is the bandgap of the active region
semiconductor and I is the diode current.
Laser diode is a semiconductor diode which emits coherent radiation in contrast to an LED
(light emitting diode) which emits incoherent radiation. Laser diodes operate on the
principle of stimulated emission resulting from electron hole pair injection and direct
recombination under forward bias.
Latent heat of fusion is the energy needed per mole (or per unit mass) to melt a material. This
is also the enthalpy of fusion ∆Hf.
Lattice is a regular array of points in space with a periodicity. Strictly, a lattice does not contain
any atoms or molecules because it is simply an imaginary array of geometric points.
There are fourteen distinct lattices in the three dimensional space. When an atom or
molecule is placed at each lattice point the resulting regular structure is the crystal
structure. The atom, molecule or group of atoms that are placed at each lattice point is
called a basis. In logical terms,
Crystal = Lattice + Basis.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
70
The unit cell of the two-dimensional lattice in Figure 1.70a is a square which is
characterized by the length a of one of the sides; a is called a lattice parameter. A given
lattice can generate different patterns of atoms depending on the basis. The lattice in
Figure 1 with the two-atom basis as is in Figure 2 produces the crystal in Figure 3.
Although the latter crystal appears as a body centered square (similar to BCC in threedimension) it is nonetheless a simple square lattice with two atoms comprising the basis.
Suppose that the basis had only one atom, then the crystal would appear as the simple
square lattice in Figure 1 (with each point now being an atom). The patterns in Figures 1
and 3 are different but the underlying lattice is the same. Because of the same lattice, the
two crystals would have certain identical symmetries. For example, for both crystals, a
rotation by 90° about a lattice point would produce the same crystal structure. To fully
characterize the crystal, we also have to specify the locations of the basis-atoms in the
unit cell as in Figure 4. By convention, we place a Cartesian coordinate system at the
rear-left corner of the unit cell with the x and y axes along the square edges. We indicate
the coordinates (xi,yi) of each i-th atom in terms of the lattice parameters along x and y.
Thus, the atoms in the unit cell in Figure 4 are at (0, 0) and at (1/2, 1/2).
Crystal
Lattice
Basis
placement
in unit cell
(0,0)
y
Basis
a
a
(1/2,1/2)
90°
Unit cell
x
Unit cell
4
1
2
3
1. A simple square lattice. The unit cell is a square with a side a. 1. Basis has two
atoms. 3. Crystal = Lattice + Basis. The unit cell is a simple square with two atoms.
4. Placement of basis atoms in the crystal unit cell.
Lattice energy of an ionic crystal is the total energy of the crystal when all its constituent ions
are brought from infinity (where they are all isolated from each other) to construct the
crystal. It is the energy that is liberated when isolated and independent ions are brought
together to form the crystal. From example when 1 mole of Cs+ and Cl− ions are brought
together to form the CsCl crystal structure, 657 kJ mol-1 is liberated so the lattice energy
is −657 kJ mol-1 (or −6.8 eV per Cs+-Cl- ion pair).
Lattice matching refers to the relationship between the lattice parameter of an epitaxial layer
and the substrate on which it is prepared, for a given temperature. If the lattice parameters
of these materials differ significantly, the lattice planes on either side of the interface
must bend to accommodate the difference. The amount of lattice plane bending that a
given set of materials can accommodate depends on the elastic stiffness of both materials,
as well as the epitaxial layer thickness. Thus, the difference in the lattice parameters
produces a strain at the interface between the layer and substrate, commonly referred to
as the mismatch strain. Beyond a critical mismatch strain, the planes at either side of the
interface can no longer deform together or coherently, resulting in the formation of misfit
dislocations. These defects are often highly detrimental to device performance, since they
can act as non-radiative recombination centers. The usual way to define the lattice
mismatch ε, is in terms of the average lattice parameter of layer and substrate aaverage,
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
71
where aaverage ≡ 12 ( aepilayer + asubstrate ), and
a
− asubstrate
ε = epilayer
aaverage
As a guide, for ε ≤ 10 −3 , epitaxial growth can occur coherently, whereas for larger
mismatch strains, there is an increased tendency to generate misfit dislocations, and
nucleation and epilayer growth become increasingly difficult. The issue of lattice
matching is further complicated by the fact that although materials may be lattice matched
to each other at one temperature (e.g., the growth temperature), they may be mismatched
at another (e.g., on cooling, due to thermal expansion coefficient mismatch). [H.R.]
Lattice parameter mismatch describes the difference in the unit cell dimensions between
layers in an epitaxial layer structure or between an epitaxial layer and the single crystal
substrate on which it is being prepared. It is assumed that the all materials have the
same crystallographic space group. Epitaxial growth requires that the lattice
parameters for both substrate and epilayer must be closely matched. Otherwise, any
difference between the lattice parameters will require the lattice planes on either side of
the interface to bend to accommodate the differences. The amount of lattice plane
bending and how much of it can be tolerated will depend on the elastic stiffness’ of both
the substrate and the layer, as well as the actual layer thickness grown. Thus the
difference in the lattice parameters results in a strain at the interface between the layer
and substrate, commonly refered to as the mismatch strain. Beyond a critical mismatch
strain, the planes at either side of the interface can no longer deform together or
coherently, resulting in the formation of misfit dislocations. These defects are often
highly detrimental in device applications, since they can act as non-radiative
recombination centers or deep traps. The usual way to define the lattice mismatch ε, is
in terms of the average lattice parameter of layer and substrate aaverage,
aaverage ≡ 12 ( aepilayer + asubstrate ).
As a guide, for ε ≤ 10 −3 , epitaxial growth can occur coherently, whereas for larger
mismatch strains, there is an increased tendency to generate misfit dislocations, and
nucleation and epilayer growth become increasingly difficult. The issue of lattice
matching is further complicated by the fact that although materials may be lattice
matched at one temperature (e.g., the growth temperature), they may be mismatched at
another (e.g., on cooling, due to thermal expansion coefficient mismatch). [H.R.]
Lattice parameters are the lengths of the sides of the unit cell and the angles between the
sides.
Lattice scattering limited mobility is the mobility of the electrons when their motion is limited
by scattering from thermal vibrations of the lattice atoms.
Lattice wave is a wave in a crystal due to coupled oscillations of the atoms. Lattice waves may
be traveling or stationary waves.
Law of the junction relates the injected minority carrier concentration just outside the
depletion layer to the applied voltage. For holes in the n-side, that is for minority carriers,
it is, pn(0) = pnoexp(eV/kT) where pn(0) is the hole concentration just outside the
depletion layer, pno is the equilibrium hole concentration (both in the n-side), V is the
external applied voltage, k is Boltzmann’s constant and T is the temperature (K).
Lead frame is a formed copper strip, typically that is plated with silver or palladium. The lead
frame also comprised the surface for attaching the die and provides points for attaching
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
72
leads. Wire bonding and packaging are then used to complete the manufacture of the
given component. [H.R.]
LED characteristics typically refer to the emitted light spectral characteristics in terms of
spectral intensity vs. wavelength, output light intensity vs. diode current, current-voltage
characteristics and the angular variation of the emitted light intensity. There may be
other additional associated characteristics as well such as changes in the light output
characteristics with temperature etc. The width of the output light spectrum depends not
only on the temperature but also on LED material, whether direct or indirect bandgap
semiconductor is used. Typically the output spectral with corresponds to a few kBT in the
energy distribution of the emitted photons. Typical current-voltage characteristics
exhibit a turn-on or the cut-in voltage from which point the current increases sharply
with voltage. The turn-on voltage depends on the semiconductor and generally increases
with the energy bandgap Eg. For example, typically, for a blue LED it is about 3.5 - 4.5
V, for a yellow LED, it is about 2 V, and for a GaAs infrared LED it is around 1 V.
Relative
intensity
(b)
(a)
(c)
V
Relative light intensity
655nm
1.0
0.5
0
600
2
1
24 nm
I (mA)
0
650
700
0
20
40
I (mA)
0
0
20
40
(a) A typical output spectrum (relative intensity vs. wavelength) from a red GaAsP LED.
(b) Typical output light power vs. forward current. (c) Typical I-V characteristics of a
red LED. The turn-on voltage is around 1.5V.
Light emitting diode (LED) is a semiconductor diode which emits incoherent radiation.
LEDs operate on the principle of spontaneous emission resulting from electron hole
pair injection and direct recombination under forward bias. Consider what happens
when a p-n+ junction is forward biased. As soon as a forward bias V is applied across
this junction, this voltage drops across the depletion region since this is the most resistive
part of the device. Consequently, the built-in potential Vo is reduced to Vo − V which then
allows the electrons from the n + side to diffuse, or become injected, into the p-side. The
hole injection component from p into the n + side is much smaller than the electron
injection component from the n + to p-side. The recombination of injected electrons in the
depletion region as well as in the neutral p-side results in the spontaneous emission of
photons. Recombination primarily occurs within the depletion region and within a
volume extending over the diffusion length Le of the electrons in the p-side. This
recombination zone is frequently called the active region. The phenomenon of light
emission from electron-hole pair (EHP) recombination as a result of minority carrier
injection as in this case is called injection electroluminescence. Because of the statistical
nature of the recombination process between electrons and holes, the emitted photons are
in random directions; they result from spontaneous emission processes in contrast to
stimulated emission. The LED structure has to be such that the emitted photons can
escape the device without being reabsorbed by the semiconductor material. This means
the p-side has to be sufficiently narrow or we have to use heterostructure devices as
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
73
discussed below,
Electron energy
(a)
EF
Ev
n+
p
Ec
eVo
Ec
EF
Eg
eVo
Distance into device
n+
p
Eg
(b)
h ≈ Eg
Ev
V
Electron in CB
Hole in VB
(a) The energy band diagram of a p-n+ (heavily n-type doped) junction without any bias. Builtin potential Vo prevents electrons from diffusing from n+ to p side. (b) The applied bias reduces
Vo and thereby allows electrons to diffuse, be injected, into the p-side. Recombination around
the junction and within the diffusion length of the electrons in the p-side leads to photon
emission.
Linear Combination of Atomic Orbitals (LCAO) is a method to obtain the electron
wavefunction in the molecule from a linear combination of individual atomic
wavefunctions. For example when two H atoms, A and B, come together, the electron
wavefunctions in H2, based on LCAO are
ψa = ψ1s(A) + ψ1s(B)
ψb = ψ1s(A) − ψ1s(B)
where ψ1s(A) andψ1s(B) are atomic wavefunctions centered around the H-atoms A and B
respectively. The ψa and ψb represent molecular orbital wavefunctions for the
electron; they reflect the behavior of the electron, or its probability distribution, in the
molecule.
Liquid phase epitaxy (LPE) is an epitaxial deposition technique for preparing crystalline
layers of material, suitable for subsequent processing to form electronic devices. To
produce a epitaxial layer by LPE, a substrate is chosen that is closely lattice matched to
the layer material that is to be grown. The substrate is immersed in a solution containing
the required solute to form the epitaxial layer. Since growth occurs at a relatively low
temperature compared with the melting point of the substrate and epitaxial layer, the
equilibrium amount of solute that can be dissolved in the solution to saturate it, is
relatively low. Reducing the temperature of the solution results in an excess of solute at
the lower temperature (due to the reduction in solubility of solvent with decreasing
temperature), known as a supersaturation. The supersaturation can be relieved by
precipation of the excess solute onto a substrate, leading to epitaxial growth. Doping of
epilayers can easily be achieved by dissolving selected species into the solution being
used for growth. These impurites are then incorporated into the growing epitaxial layer,
doping it. A series of epitaxial layers can be grown sequentially on top of one another in
a given process, by using a so-called slider system. In this case, a series of solutions with
different dopants in each, or different alloy compositions (to prepare alloy layers such
as, for example, AlGaAs), can be placed over the substrate or another epitaxial layer, and
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
74
growth from that solution initiated. Thus complex multilayer structures (both homoepitaxial and hetero-epitaxial) can be prepared. Since the growth process operates at
relatively low temperatures, the solubility of extraneous impurities is low and high purity
materials can be prepared. Moreover, for many device applications, control over layer
thickness is important. Since at the low growth temperatures, the growth rate (controlled
by diffusion of species to the growing interface) is slow, it is easy to control layer
thickness to the level of fractions of a micron. The technique has been successfully used
to prepare high power laser diodes, solar cells and photodiodes. However, for many
applications, difficulties with scaling up this technique to simultaneously deposit a
plurality of epitaxial layers, has led to a decline in the use of this approach as compared
with vapor phase based epitaxial growth techniques. [H.R.]
Lithography is a process by which a pattern is defined on the surface of the wafer which
identifies the crystal regions to be doped or metallic interconnections.
Local field (Eloc) is the true field experienced by a molecule in a dielectric which arises from
the free charges on the plates and all the induced dipoles all around the molecule. The
true field at a molecule is not simply the applied field (V/d) because of the field of the
neighboring induced dipoles. In cubic crystals and liquids the local field is given by Eloc
= E + P/3εo
Long diode is a pn junction with neutral regions longer than the minority carrier diffusion
lengths.
Lorentz force is the force experienced by a moving charge in a magnetic field. When a charge
q is moving with a velocity v in a magnetic field B then it experiences a force, F, that is
proportional to the magnitude of its charge, q, its velocity, v and the field B such that
F=qv×B.
Loss tangent or tanδ is the ratio of the imaginary part to the real part, εr''/εr '. The angle δ is the
phase angle between the capacitive current and the total current. If there is no dielectric
loss then the two currents are the same and δ = 0.
Luminescence, in general terms, is the emission of light as a result of an excited electron
transitting down to the ground energy level. In a semiconductor, this would correspond
to the recombination of an electron and a hole; the excited electron is the conduction
band (CB) electron and its ground state corresponds to a hole in the valence band
(VB) . In contrast, light emitted from an ordinary light bulb is due to the heating of the
metal filament. The emission of radiation from a heated object is called incandescence. In
luminescence, emission of radiation requires the initial excitation of electrons. If the
electron excitation is due to photon absorption, then the process is identified as
photoluminescence. The direct electron-hole recombination mechanism generally occurs
very quickly. For example, typical minority carrier lifetimes are in the range of
nanoseconds so that light emission from a semiconductor stops within nanoseconds after
the removal of excitation. Such luminescence processes are normally identified as
fluorescence. The emission of light from a fluorescent tube is actually a fluorescence
process. The tube contains a gas mixture of argon and mercury. The Ar and Hg gas
atoms become excited by the electrical discharge process and emit light mainly in
ultraviolet region which is absorbed by the fluorescent coating on the tube. The excited
electrons in the fluorescent coating material then recombine emitting light in the visible
spectrum. There are also materials, called phosphors, from which light emission may
continue for milliseconds to hours after the cessation of excitation. These slow
luminescence processes are normally referred to as phosphorescence.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
CB
Thermalization
Ec
Trapping
Et
Eg
Excited State
h <Eg
Luminescent Center
(Activator)
Ground State
h >Eg
Recombination
Ev
75
Optical absorption generates an
EHP. The electron thermalizes and
then becomes trapped at a local
center and thereby removed from
the CB. Later it becomes detrapped
and wanders in the CB again.
Eventually it is captured by a
luminescent center where it
recombines with a hole emitting a
photon. Traps therefore delay
recombination.
VB
Consider a semiconductor that has localized states that are electron traps and temporarily
capture an electron from the conduction band and thereby immobilizes it. After a while a
strong lattice vibration returns the electron back into the conduction band (by thermal
excitation). The traps may be due to crystal defects or they may be added impurities.
The time the electron spends trapped at Et depends on the energy depth of the trap from
the conduction band, Ec−Et. Initially the incident photon excites a valence band electron
to the conduction band. The electron then thermalizes, i.e. loses the excess energy as it is
collides with lattice vibrations, and falls close to Ec. As the electron wanders in the
conduction band it becomes captured by a trap at Et. It remains captured until a strong
lattice vibration excites it back into the conduction band. The electron wanders around
again in the conduction band and eventually it becomes trapped in an excited state of a
luminescent center or an activator. Typically, luminescent centers are intentionally added
impurities or crystal defects such as interstitials or vacancies. The electron then falls
down in energy to the ground state of the activator releasing a photon. Later the electron
at the ground state recombines with a wandering hole in the valence band band. Thus the
activator acts as a radiative recombination center. With some impurities the energy that
is released when the electron falls down to the ground state is in the form of lattice
vibrations so that the impurity acts as a nonradiative recombination center. The time
interval between photogeneration and recombination can be quite long if the electron
remains captured at Et for a considerable length of time. In fact, the electron may become
trapped and detrapped many times before it finally recombines so that the emission of
light can persist for a relatively long time after the cessation of excitation. There are many
examples of phosphors with various activators. For example, ZnS is a typical phosphor
material. Small amounts of Cu in the ZnS phosphor acts as an activator with
luminescence occurring in the green region. Mn, on the other hand, is an activator which
gives luminescence in the red region. It is also possible to excite electrons into the CB by
bombarding the material with a high energy electron beam. If these electrons recombine
with holes and emit light then the process is called cathodoluminescence. This is the
mechanism which allows us to view the electron beam trace on the screen of a CRT
(cathode-ray tube). The electron beam excites EHPs in the phosphor coating on the
CRT screen. In the case of color CRT displays, typically the screen is coated uniformly
with three sets of phosphor dots which exhibit cathodoluminescence in the blue, red and
green wavelengths. In electroluminescence an electric current, either ac or dc, is used to
excite electrons into the CB which then recombine with holes and emit light. For example
passing a current through certain semiconducting phosphors such as ZnS doped with
Mn causes light emission by electroluminescence. The emission of light from an light
emitting diode (LED) is an example of injection electroluminescence in which the
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applied voltage causes charge carrier injection and recombination in a device (diode) that
has a junction between a p-type and an n-type semiconductor.
Magnetic dipole moment µm is the product IA of current I flowing in a circuit loop and the
area A of the loop. Qualitatively it measures the strength of magnetic field put out by a
current loop and also the extent of interaction of the current loop with an externally
applied magnetic field. If un is the unit vector in the direction of an advance of a screw if
it is turned in the direction of the current loop then as a vector the magnetic moment is
defined by µm = I A un. It is normal to the surface of the loop. Magnetic moment in a
magnetic field experiences a torque that tries to rotate µm to align it with the field. In a
non-uniform field the magnetic moment experiences a force that attracts it to greater
fields. Magnetic moment of an atom is due to the orbital motions of the electrons and the
electron spins. Due to the negative charge of the electron, the magnetic moment is in the
opposite direction to angular momentum. In many magnetic materials, the magnetic
properties arise from individual atoms possessing unpaired electron spins.
Magnetic domain is a region of a ferromagnetic (or ferromagnetic) crystal which has
spontaneous magnetization, i.e. magnetization in the absence of an applied field, due to
the alignment of all magnetic moments.
Magnetic field intensity, or magnetizing field H gauges the magnetic strength of external
conduction currents (e.g. currents flowing in the windings) in the absence of a material
medium. It excludes the magnetization currents that become induced on the surfaces
of any material placed in a magnetic field. µoH is the magnetic field in the in free space
and is considered to be the applied magnetic field. The terms intensity or strength
distinguish H from B which is simply called the magnetic field.
Magnetic field of a propagating electromagnetic radiation is related to its electric field E. In an
isotropic medium of refractive index n, (n = √(relative permittivity)), the magnetic
field B = E/v where v = c/n = c/√(εr) is the phase velocity in the medium which is
assumed to be nonmagnetic.
Magnetic field, magnetic induction or magnetic flux density (B) is a field that is generated by
a current carrying conductor which produces a force on current carrying conductor
elsewhere. Equivalently we can define it as the field generated by a moving charge that
acts to produce a force on a moving charge elsewhere. The force is called the Lorentz
force and is given by F = qv × B where v is the velocity of the particle with charge q.
The magnetic field B in a material is the sum of the applied field intensity, µoH, and that
due to the magnetization of the material, µoM. Thus B = µo (H + M).
Magnetic flux (Φ) represents to what extent magnetic field lines are "flowing" through a
given area perpendicular to the field lines. If δA is a small area perpendicular to the
magnetic field B and B is constant over δA then the flux δΦ through δA is defined by δΦ
= BδA. Total flux through any closed surface is zero, i.e. §BdA = 0.
Magnetic flux density or magnetic induction (B) is a vector field quantity that describes the
magnitude and direction of the magnetic force that is exerted on a moving charge or on a
current carrying conductor. The magnetic force is essentially the Lortentz force and
excludes the electrostatic force qE. If the amount of magnetic flux density flowing
through an area ∆A is B then the magnetic flux, Φ, through ∆A is defines as Φ = B∆A.
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Magnetic liquid encapsulated Czochralski (Magnetic LEC or MLEC) is a modified form
of liquid encapsulated Czochralski (LEC) growth in which a magnetic field
applied to the melt to reduce melt temperature fluctuations. Typically peak temperature
fluctuation amplitudes can be about 10 to 20 oC in the absence of an applied field. On
applying magnetic fields in excess of 1 kOe, these temperature fluctuations are damped
down to a level of about 0.1 oC. This approach has enabled boules with greatly improved
crystal quality and homogeneity to be prepared. [H.R.]
Magnetic permeability (µ) is a property of the medium that characterizes the strength of the
magnetic flux density, B, that exists in the medium due to an applied magnetic field
strength, H, i.e. µ = B/H. H depends only on the external currents and is determined by
Ampere's Law whereas B depends on both H that gives rise to it and the medium itself.
We can only determine effects due to B. In vacuum, B = µoH where µo is called the
permeability of free space (4π x 10−7 H.m−1). When a material medium is involved µ is
written as µoµr where µr is the relative permeability of the material. µr is a
dimensionless constant that characterizes the contribution of the atoms of the material to
the total magnetic flux density, B, in the medium.
Magnetic quantum number, ml, specifies the component of the orbital angular
momentum, Lz, in the direction of a magnetic field along z so that Lz = ±hml where ml
can be a negative or positive integer from −l to +l including 0, i.e. −l, −(l−1),...,0,...,(l−
1),l. The orbital, ψ, of the electron depends on ml as well as on n and l. The ml,
however, generally determines the angular variation of ψ.
Magnetic Random Access Memory (MRAM) is the magnetic counterpart of the electronic
RAM. Usually RAM is used for non permanent storage of temporary data. MRAM
opens up the possibility of having permanent storage of temporary data. This might be
used in the case of system crash or some other event during which data must be
recovered. [C.T.]
Magnetic resonance is resonance absorption of electromagnetic radiation when an atom with
a magnetic moment is placed in a magnetic field. For example, in the presence of an
applied field B the energy of a single unpaired electron is split into two levels separated
by ∆E which depends on the strength of B. The electron will normally be in the lower
energy level with its magnetic moment aligned with B. An incident electromagnetic
radiation of energy ∆E will be absorbed by the electron which will flip its spin (rotate its
magnetic moment) and jump to the higher energy level. The energy absorbed from the
radiation rotates the magnetic moment against applied field.
Magnetic susceptibility (χm) indicates the ease with which the material becomes magnetized
under an applied magnetic field. It is the magnetization induced in the material per
unit magnetizing field, χm = M/H.
Magnetization current (Im) is a bound current per unit length that exists on the surface of a
substance due to its magnetization. It is not, however, due to the flow free charges but
arises in the presence of an applied magnetic field as a result of the orientations of the
electronic motions in the constituent atoms. In the bulk these electronic motions cancel
each other and there is no net bulk current but on the surface they add to give a bound
surface current Im per unit length which is equal to the magnetization, M, of the
substance.
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Magnetization or magnetization vector (M) represents the net magnetic moment per unit
volume of material. In the presence of a magnetic field, individual atomic moments tend
to align with the field which results in a net magnetization. Magnetization of a
specimen can be represented by the flow of currents on the surface over a unit length of
the specimen. M = Im where Im is the surface magnetization current per unit length.
Magnetization reversal/switching deals with the storage of data in a magnetic medium. In a
storage medium, a zero/one bit is represented by a magnetization having a definite
direction. The zero/one bit transition is represented by a switching of the direction of the
magnetization from one direction to another. [C.T.]
Magneto-optic effects are changes in the optical properties due to the application of an external
magnetic field.
Magnetocrystalline anisotropy energy (K) is the energy needed to rotate the magnetization
of a ferromagnetic (or ferromagnetic) crystal from its natural easy direction to a hard
direction. For example, it takes and energy of 40 mJ.cm-3 to rotate the magnetization of
tan iron crystal from the easy direction [100] to the hard direction [111].
Magnetocrystalline anisotropy is the anisotropy associated with magnetic properties such as
the magnetization in different directions in a ferromagnetic (or ferromagnetic) crystal.
Atomic spins prefer to align along certain directions in the crystal which are called easy
directions. The direction along which it is most difficult to align the spins is called the
hard direction. For example, in the iron crystal all atomic spins prefer to align along
one of [100] directions (easy directions) and it is most difficult to align the spins along
one of the [111] directions (hard directions).
Magnetometer is an instrument for measuring the magnitude of a magnetic field. Some
instruments can also measure the direction of the magnetic field as well.
Magnetostatic energy is the potential energy stored in an external magnetic field. It takes
external work to establish a magnetic field and this energy is said to be stored in the
magnetic field. Magnetic energy per unit volume at a point in free space is given by
Evol(air) = 1/2µoH2 = B2/(2µo).
Magnetostriction is the change in the length of a ferromagnetic (or ferromagnetic) crystal as a
result of its magnetization. An iron crystal placed in a magnetic field along an easy
direction becomes longer along this direction but contracts in the transverse direction.
Magnetostriction energy is the strain energy in the crystal due to magnetostriction, i.e. work
done in straining the crystal when it becomes magnetized.
Majority carriers are electrons in an n-type and holes in a p-type semiconductor.
Maser (Microwave Amplification by Stimulated Emission of Radiation) is a device in
which stimulated emission amplifies or generates a microwave radiation (wavelength
>100 µm). The principle of operation is the same as that for a laser.
Mask is a high contrast pattern on a transparent plate that identifies the processing pattern (e.g.
diffusion regions) needed on the wafer surface. For example, a typical mask may be a
quartz plate with a patterned chromium film on it.
Mass action law in semiconductor science refers to the law np = ni2 which is valid under
thermal equilibrium conditions and in the absence of external biases and illumination.
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Material dispersion is the spread in the velocities of different wavelength waves in a
dielectric medium due to the wavelength dependence of the refractive index of the
medium. As long as the propagating electromagnetic wave is not monochromatic (single
wavelength),and the medium has a group index that changes with the wavelength, there
will always be material dispersion.
Matthiessen's rule gives the overall resistivity of a metal as the sum of individual resistivities
due to scattering from thermal vibrations, impurities, crystal defects. If the resistivity due
to scattering from thermal vibrations is denoted by ρT and resistivities due to scattering
from crystal defects and impurities can be lumped into a single resistivity term, ρR, called
the residual resistivity, then ρ = ρT + ρR.
Maximum relative permeability (µrmax) is the maximum relative permeability of a
ferromagnetic (or ferrimagnetic) material.
Maxwell’s equations are a set of equations that describe the space and time dependence of the
electric and magnetic fields in a medium through partial derivatives. In an isotropic
dielectric material with a relative permittivity εr, Maxwell’s equations lead to a wave
equation for the electric field E.
∂ 2E ∂ 2E ∂ 2E
∂ 2E
+
+
=
ε
ε
µ
o r o
∂x 2 ∂y 2 ∂z 2
∂t 2
where εo and µo are the permittivity and permeability of free space. It is assumed that the
dielectric material is nonmagnetic, i.e µr = 1. The solution of this equation is an
electromagnetic wave that is traveling with a velocity v given by
1
v=
ε oε r µo
See electromagnetic wave.
Mean free path is the mean distance traversed by an electron between scattering events. If τ is
the mean free time between scattering events, and u is the mean speed of the electron,
then the mean free path, l = uτ.
Mean free time is the average time it takes to scatter a conduction electron. If ti is the free time
between collisions (between scattering events) for an electron labeled as i, then τ = ti
averaged over all the electrons. The drift mobility is related to the mean free time by µd
= eτ / me. The reciprocal of the mean free time is the mean probability per unit time that a
conduction electron will be scattered, or, put differently, the mean frequency of scattering
events.
Mechanical work is qualitatively defined as the energy expended in displacing a constant force
through a distance. When a force F is moved a distance dx, work done dW=F.dx. When
we lift a body such as an apple of mass m (100g) by a distance h (1m), we do work by
and amount F∆x=mgh (1J) which is then stored as the gravitational potential energy of
the body. We have transferred energy from ourselves to the potential energy of the body
by exchanging energy with it in the form of work. Further, in lifting the apple, the
molecules have been displaced in orderly fashion, all upwards. Work therefore involves
an orderly displacement of atoms and molecules of a substance in complete contrast to
heat. See PV Work.
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Meissner effect is the repulsion of all magnetic flux from the interior of a superconductor.
The superconductor behaves as if it were a perfect diamagnet with χm = −1.
B
B
B off
Superconductor
I
I
T > Tc
T < Tc
Perfect conductor
T < Tc
The Meissner effect. A superconductor cooled below its critical
temperature expels all magnetic field lines from the bulk by setting up
a surface current. A perfect conductor ( = ∞) shows no Meissner
effect.
Melt growth refers to a class of techniques for the crystallization of a material from a liquid
phase (a Melt) at the material’s melting temperature. A large variety of technologically
important electronic materials can be prepared using melt growth including, for example,
Si, Ge, GaAs, InP, InSb, GaP and CdTe. Different melt growth techniques are suitable,
depending on the specific requirements for the material to be prepared: these include
Czochralski, liquid encapsulated Czochralski (LEC), magnetic LEC, horizontal
and vertical Bridgeman and the floating-zone growth techniques. [H.R.]
Metal-oxide-semiconductor transistor (MOST) is a field effect transistor in which the
conductance between the source and drain is controlled by the voltage applied to the gate
electrode which is insulated from the channel by an oxide layer.
Metalization refers to the use of sputtering or chemical vapor deposition (CVD) processes
to create conductors by applying a thin layer of metal to a device. This may be a single
metal such as aluminum, gold or platinum, or may be an alloy such as gold-germanium,
or may involve a multi-layer structure of different metals. [H.R.]
Metallic bonding is the binding of the metal atoms in the crystal through the attraction
between the positive metal ions and the mobile valence electrons in the crystal. The
valence electrons permeate the space between the ions.
Metallurgical junction is where there is an effective junction between the p-type and n-type
doped regions in the crystal. It is where the donor and acceptor concentrations are equal
or where there is a transition from n- to p-type doping.
Metalorganic chemical vapor deposition (MOCVD) is a type of CVD process in which
metalorganic species are used as source gases for the deposition process. This is
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currently one of the techniques of choice for fabricating epitaxial layers of compound
semiconductors. The other technique being MBE. For example, to grow the III-V alloy
compounds AlGaAs, the usual choice of feedstock gas are metal-organics of the group
III elements (Ga and Al) and hydrides of the group V elements. These chemicals must
satisfy several requirements to be suitable for growth; (a) they must decompose at the
growth temperature (typically in the range between 500 and 800 oC) to permit
incorporation into a growing layer to occur, (b) they must be gaseous or have high vapor
pressures at room temperature, such that they can easily be transported through tubes
from the sources to the reaction vessel, and (c) they must be available with reasonable
purity. Metalorganic sources typically used in this case include the two gallium sources,
trimethyl-gallium (TMGa) and triethyl-gallium (TEGa) and the aluminum sources
trimethyl-aluminum (TMAl) and triethyl-aluminum (TEAl). The usual hydride source of
arsenic is AsH3 (arsine). These source gases are fed into a gas manifold prior to
entering the reaction vessel to provide a homogeneous feedstock composition which, in
turn, assists in producing epitaxial layers with a more homogeneous composition. A key
feature of MOCVD systems is the ability to rapidly switch the gas phase composition
feeding the reaction chamber. These well-controlled compositional changes have made
superlattice growth and abrupt doping profiles attainable and have been instrumental in
the success of MOCVD for advanced optoelectronic device development. Key to this
capability is the use of mass flow controllers that can precisely control the flow of each
gas supplied to the system manifold, coupled with fast acting control valves. The
chemical reaction that occur on a hot substrate using TMGa as a gallium source at
about 700 oC is (CH3)3Ga + AsH3 ⇒ GaAs + 3CH4 while a similar reaction could have
been written for TMAl. Thus, simple mixing of TMGa and TMAl can yield the whole
range of AlGaAs alloys: (1-x)TMGa + xTMAl + AsH3 ⇒ AlxGa1-xAs + 3CH4.
Dopants are added to the gas feedstock in the same manner as other components.
Typically, either metal-organic group II sources, or group IV and group VI hydrides are
used as the p- and n-type doping sources for III-V growth. This approach permits
growth and doping on a number of substrates in a single growth run, and is therefore
offers higher throughput. One problem with MOCVD is that many of the growth
parameters of inter-dependent, leading with problems in controlling the process. Another
issue of concern with MOCVD is the handling of toxic and flammable gases. In spite of
its limitations, MOCVD can produce layers of almost any III-V compound as well as
high quality superlattices and heterostructures with quality matching that of both liquid
phase epitaxy (LPE) and molecular beam epitaxy (MBE). The total cost of an
MOCVD system (including safety equipment) is about an order of magnitude higher
than for an LPE system, but about half that of an MBE system. [H.R.]
Micron (µm) is the unit of linear measurement equal to 1/1,000,000 (millionth) of a meter. It is
equivalent to 0.00003927 inches, or 1,000 nanometers, or 10,000 angstroms. A human
hair is approximately 100 microns in diameter. [H.R.]
Miller indices (hkl) are indices that conveniently identify parallel planes in the crystal.
Suppose that a plane has the intercepts x1, y1 and z1 in terms of the lattice parameters a,
b and c, with the x, y and z axes. For a plane passing through the origin one simply shift
the origin or considers another parallel plane. Then (hkl) are obtained by taking
reciprocals of x1, y1 and z1 and reducing these to a set of smallest integers.
Minority carrier diffusion length (L) is the mean distance a minority carrier diffuses
before recombination, L = √[Dτ] where D is the diffusion coefficient and τ is the
minority carrier lifetime.
Minority carrier injection is the flow of electrons into the p-side and holes into the n-side of a
pn junction when a voltage is applied to reduce the built-in voltage across the
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junction. It can also refer to an increase in the minority carrier concentration due to
photogeneration.
Minority carrier lifetime (τ) is the mean time for a minority carrier to disappear by
recombination. 1/τ is the mean probability per unit time that a minority carrier
recombines with a majority carrier. Suppose that excess electrons and holes have been
injected, as would be in a pn-junction under forward bias, and that ∆np is the excess
electron, minority carrier, concentration and ∆pp is the excess hole, majority carrier,
concentration in the neutral p-side of a GaAs pn junction. Injected electron and hole
concentrations would be the same to maintain charge neutrality, that is, ∆np = ∆pp. In
many instances the rate of change ∂∆np/∂t is proportional to ∆np and an excess minority
carrier recombination time (lifetime) τe is defined by
∂∆n p
∆n
=− p
∂t
τe
In practice, the injected excess minority carrier concentration ∆np is much greater than the
actual equilibrium minority carrier concentration npo. There are two conditions on ∆np
corresponding to weak and strong injection based on ∆np compared with the majority
carrier concentration ppo. In weak injection, ∆np << ppo, where ppo is the majority carrier
concentration. Then np ≈ ∆np and pp ≈ ppo + ∆pp ≈ ppo ≈ Na = acceptor concentration.
The rate of recombination in this case is given by,
∂∆np/∂t = −B(nppp − npoppo) ≈ −BoNa∆np
where B is the direct recombination capture coefficient. Thus, under weak injection, the
lifetime is constant and given by,
τe = 1/BNa
In strong injection, ∆np >> ppo. Then the rate of recombination becomes,
∂∆np/∂t = −Bo∆pp∆np = B(∆np)2
so that under high level injection conditions the lifetime τe is inversely proportional to the
injected carrier concentration. When a light emitting diode (LED) is modulated under
high injection levels for example, the lifetime of the minority carriers is therefore not
constant, which in turn leads to distortion of the modulated light output. See direct
recombination capture coefficient.
Minority carriers are electrons in a p-type and holes in an n-type semiconductor.
Miscibility indicates the mutual solubility of two substances in the same phase, for example,
both liquids.
Modal or intermodal dispersion is due to the spread in time of an infinitesimally thin light
pulse of single wavelength as it propagates along a fiber through various modes. Each
mode has a different propagation constant so that at the end of the fiber the modes arrive
at different times and constitute an output pulse that is broadened in time. Modal
dispersion zero in a single mode fiber that allows only one mode, the fundamental
mode, to propagate.
Mode field diameter (2wo) is the extent of the field distribution across the optical guide in the
fundamental mode. The field penetrates the cladding so that the mode field diameter
is not simply the diameter of the core.
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Mode is a distinct transverse (to the waveguide axis) electric field pattern that can propagate and
hence be guided along the waveguide.
Mode or state of lattice vibration is a distinct, independent way in which a crystal lattice can
vibrate with its own particular frequency ω and wavevector K. There are only a finite
number of vibrational modes in a crystal.
Molar quantity is an extensive property per unit mole of a substance. Molar enthalpy is the
enthalpy per unit mole, sometimes written as Hm.
Mole of a substance is that amount of the substance which contains NA number of atoms (or
molecules) where NA is Avogadro's number (6.023 × 1023). One mole of a substance
has a mass as much as its atomic (molecular) mass in grams. For example 1 mole of
copper contains 6.023 × 1023 number of copper atoms and has a mass of 63.55 grams.
Molecular beam epitaxy (MBE) is one of the most advanced epitaxial techniques available
today, offering arguably the most flexibility during growth and highest quality material.
MBE is a refined form of vacuum evaporation. The refinement comes from the nature of
the sources used and the vacuum system itself. The vacuum levels typical for this
technique are on the order of 10-11 Torr permitting molecular flow (i.e., molecules from
the source arrive at the substrate without suffering collisions with other molecules).
These conditions are commonly referred to as Ultra High Vacuum (UHV) conditions.
MBE sources provide beams of material used for deposition. These beams result in very
slow growth rates (about 1 to 3 Å/second for GaAs). Source beams originate from
Knudsen or effusion cells, which are essentially heated crucibles with a defined aperture
at their open end. The cells are filled with high purity charges of appropriate elements or
compounds and are heated to provide a flux of pure vapor of the appropriate constituent.
By blocking the aperture with a shutter the beams can be turned on and off. Given the
extremely slow growth rates, this enables atomically engineered device structures to be
fabricated (so-called nanostructures). Growth is usually performed at relatively low
temperatures (from about 580 to 630 oC for GaAs). Doping is achieved by adding
appropriate additional Knudsen cells. In general, complex materials structures can be
programmed; this is done in practice by adding appropriate Knudsen cells, and by
adjusting the flux of atoms from the given cell by adjusting its temperature, while
applying appropriate shuttering. Because of the extremely slow growth rates, film quality
is excellent, as is the capability to vary structures (e.g., thickness, composition and
doping) on the nanoscale. Moreover, layer purity is also excellent as source purity is
always strictly controlled and the environment itself is conducive to strict purity
standards. Another key feature of the MBE UHV environment is that it is ideally suited
for incorporating in situ characterization tools including, for example, techniques for realtime layer-by-layer thickness monitoring. [H.R.]
Molecular orbital wavefunction, or simply molecular orbital is a wavefunction for an
electron within a system of two or more nuclei (e.g. a molecule). A molecular orbital
defines the probability distribution of the electron within the molecule just as the atomic
orbital defines the electron's probability distribution within the atom. The molecular
orbital can take two electrons with opposite spins.
Monochromatic radiation contains waves that all have the same single frequency or
wavelength. There is no perfectly monochromatic light in nature.
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MOS is short for a metal-insulator-semiconductor structure in which the insulator is typically
the silicon oxide. It can also be a different type of dielectric for example it can be the
nitride, Si3N4.
Multimode fiber allows the propagation of light via many guides EM waves called guided
modes along the fiber. Typically it has a core diameter that is much larger than the
wavelength of light which leads to a V-number greater 2.405 and hence to many guided
modes.
Multiple quantum well (MQW) lasers have the structure of alternating ultrathin layers of
wide and narrow bandgap semiconductors. The smaller bandgap layers are the active
layers where electron confinement and lasing transition take place whereas the wider
bandgap layers are the barrier layers.
Active layer Barrier layer
E
Ec
A multiple quantum well
(MQW) structure.
Electrons are injected by the
forward current into active
layers which are quantum
wells.
Ev
Although the optical gain curve is narrower than the corresponding bulk device, the
output spectrum from a quantum well device is not necessarily a single mode. The
number of modes depends on the indiviual widths of the quantum wells. It is, of course
possible, to combine a MQW design with a distribued feedback structure to obtain a
single mode operation. Many commercially available LDs are currently MQW devices.
Multiple quantum well device is a semiconductor structure that has more than one quantum
well and that the quantum wells form a period structure.
Nanoelectronics refers to the technology for fabricating electronic devices with feature sizes
ranging from a few nanometers to the sub-micron range. The general motivation for
implementing this technology is to achieve enhanced functionality of electronic devices;
this includes (i) operating speed, (ii) memory capacity, and (iii) novel devices based on
quantum-confinement effects. Ultimately, this can lead to a “superchip”, which would
consist of a three-dimensional network of trillions of switching elements operating at
terahertz switching speeds. This will be made possible by reducing feature sizes to the
level of several nanometers. Since on this scale, the quantum-mechanical nature of
electrons determines their behavior, novel structures, devices and circuits are possible. In
such cases, electron tunneling and energy quantization are of paramount importance
and novel types of nanoelectronic devices have been developed including, for example,
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quantum dot and quantum wire based devices, resonant tunneling devices and single
electron devices. [H.R.]
Nanofabrication refers to the nanometer-scale fabrication of semiconductor structures and
devices and nanometer-scale modification of surfaces. This field is rapidly developing to
realise the benefits of nanoelectronic devices. We can distinguish between several types
of nanofabrication methods: (i) conventional lithography and patterning using electron
beams, X-rays, and ions, (ii) methods employing self-assembly, and (iii) nanometerscale fabrication of semiconductor structures and modification of surfaces using
scanning probe microscopy (SPM) techniques, such as scanning tunneling microscopy
(STM) and atomic force microscopy (AFM). [H.R.]
Nanometer (nm) is the unit of linear measurement equal to 1/1,000,000,000 (one billionth) of a
meter. It is equivalent to 10 angstroms or typically to several atom diameters. It is also
used in the measurement of the wavelength of light. [H.R.]
Nanotechnology refers to a multidisciplinary field (or set of technologies) for designing,
fabricating, and applying nanometer-scale materials, structures and devices. [H.R.]
Neutron number (N) is the number of neutrons in the nucleus.
Nitric acid (HNO3) is a corrosive oxidizing liquid prepared from sulfuric acid, nitrates and
ammonia. Nitric acid is used in etching solutions, to clean silicon wafers, and to etch
metals. [H.R.]
Nitrogen (N2) is a non-toxic nonflammable gas that is used for purging and cleaning, and as a
chemical vapor deposition (CVD) carrier gas. [H.R.]
Nitrogen trifluoride (NF3) is a toxic gas that is used as a source of fluoride in plasma
processes. These include the etching of poly-silicon, silicon nitride, tungsten silicide
and tungsten films, as well as for cleaning process chambers. [H.R.]
Nitrous oxide (N2O) is a nontoxic, nonflammable, mildly oxidizing gas that is used in
combination with silane for the chemical vapor deposition (CVD) of silicon nitride.
[H.R.]
NMOS is an enhancement type n-channel MOSFET.
Noise equivalent power (NEP) of a detector is numerically equal to the optical power
necessary to give a photocurrent equal to the noise current in the detector when the
detector bandwidth is 1 Hz. More rigorously, it is the optical power necessary per square
root of bandwidth to give a signal to noise ratio, SNR, of unity.
Nondegenerate semiconductor has electrons in the conduction band and holes in the
valence band that obey Boltzmann statistics. Put differently, the electron
concentration, n, in the conduction band is much less than the effective density of states
Nc and similarly p << Nv. It refers to a semiconductor that has not been heavily doped so
that these conditions are maintained; typically doping concentrations less than 1018 cm−
3
.
Nordheim's rule states that the resistivity of a solid solution (an isomorphous alloy) due
to impurities, ρI, is proportional to the concentration of the solute, X, and the solvent (1X).
Numerical aperture is a characteristic of an optical fiber that depends on the refractive indices
of the core and the cladding and measures light gathering ability of the core. It is the
sine of the maximum acceptance angle at which a ray of light can enter the fiber core
and propagate along the core.
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Ohmic conduction refers to electrical conduction that is governed by J = σE where σ is the
conductivity of the material. The current flow is limited by the rate of transport of
intrinsic charge carriers (e.g electrons and holes) in the material and their drift mobility
and not by the rate of carrier injection from the electrical contacts. The contacts ideally
simply replenish the electrons and holes in the material reaching the electrodes and
exiting the sample.
Ohmic contact is a contact that can supply charge carriers to a semiconductor at a rate
determined by charge transport through the semiconductor and not by the contact
properties itself. Thus the current is limited by the conductivity of the semiconductor
and not be the contact.
Optical activity refers to the rotation of the electric field E-vector of a linearly polarized light
wave as it passes through certain crystals, such as a quartz, along the optic axis. This
rotation increases continuously with the distance traveled through the crystal (about
21.7° per mm of quartz). The rotation of the plane of polarization by a substance is
called optical activity. In very simply intuitive terms, optical activity occurs in materials in
which the electron motions induced by the external electromagnetic field follows
spiraling or helical paths (orbits) 1. Electrons flowing in helical paths resemble a current
flowing in a coil and thus possess a magnetic moment. The optical field in light therefore
induces oscillating magnetic moments which can be either parallel or antiparallel to the
induced oscillating electric dipoles. Wavelets emitted from these oscillating induced
magnetic and electric dipoles interfere to constitute a forward wave that has its optical
field rotated either clockwise or counterclockwise. If θ is the angle of rotation, then θ is
proportional to the distance L propagated in the optically active medium. For an observer
receiving the wave through quartz , the rotation of the plane of polarization may be
clockwise (to the right) or counterclockwise (to the left) which are called dextrorotatory
and levorotatory forms of optical activity. The structure of quartz is such that atomic
arrangements spiral around the optic axis either in clockwise or counterclockwise sense.
Quartz thus occurs in two distinct crystalline forms, right-handed and left-handed, which
exhibit dextrorotatory and levorotatory types of optical activity respectively. Although we
used quartz as an example, there are many substances that are optically active, including
various biological substances and even some liquid solutions (e.g. corn syrup) that
contain various organic molecules with a rotatory power. The specific rotatory power is
defined as the extent of rotation per unit length. (θ/L) of distance traveled in the optically
active substance. Specific rotatory power depends on the wavelength. For example, for
quartz this is 49° at 400 nm but 17° at 650 nm.
1
The explanation of optical activity involves examining both induced magnetic and electric dipole moments
which will not be described here in detail. There are very readable qualitative explanations as mentioned under
Further Reading.
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87
Levo
E
E
Dextro
E
E
z
z
z
Quartz
L
Optic axis
An optically active material such as quartz rotates the plane of polarization of
the incident wave: The optical field E rotated to E . If we reflect the wave back
into the material, E rotates back to E.
Optical fiber amplifier is an optical amplifier operating on the principle of stimulated
emission. Typically it is a glass optical fiber whose core is doped with rare earth ions
which are optically excited from an external light source to achieve population
inversion and hence optical amplification.
Optical power is the electromagnetic wave (light) energy flowing per unit time through an area
of interest. It is also called the radiant flux. Light intensity, also known as irradiance
or radiant flux density, is the optical power flowing per unit area.
Optical semiconductor amplifier is a semiconductor laser structure that can be used as an
optical amplifier that amplifies light waves passing through its active region. Light to be
amplified is made to enter the active region of the laser semiconductor diode and the
active region is pumped by a sufficiently large diode current just as in a normal laser
diode. The wavelength of radiation to be amplified must be within the optical gain
bandwidth of the laser. Such a device would not be laser oscillator, emitting lasing
emission without an input, but an optical amplifier with input and output ports for light
entry and exit. In the traveling wave semiconductor laser amplifier the ends of the
optical cavity have antireflection (AR) coatings so that the optical cavity does not act as
an efficient optical resonator, a condition for laser-oscillations. Light, for example, from
an optical fiber, is coupled into the active region of the laser structure. As the radiation
propagates through the active layer, optically guided by this layer, it becomes amplified
by the induced stimulated emissions, and leaves the optical cavity with a higher
intensity. The Fabry-Perot laser amplifier is similar to the conventional laser oscillator,
but is operated below the threshold current for lasing oscillations; the active region has
an optical gain but not sufficient to sustain a self-lasing output. Light passing through
such an active region will be amplified by stimulated emissions but, because of the
presence of an optical resonator, there will be internal multiple reflections. These multiple
reflections lead to the gain being highest at the resonant frequencies of the cavity within
the optical gain bandwidth. Optical frequencies around the cavity resonant frequencies
will experience higher gain than those away from resonant frequencies. Although the
Fabry-Perot laser amplifier can have a higher gain than the traveling wave amplifier, it is
less stable.
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Pump current
Signal out
Signal in
Active region
AR = Antireflection
coating
AR
(a) Traveling wave amplifier
Partial mirror
Partial mirror
(b) Fabry-Perot amplifier
Simplified schematic illustrations of two types of laser amplifiers
A 1550 nm semiconductor optical amplifier using an InGaAsP chip. (Courtesy of Alcatel)
Optical waveguide is a dielectric waveguide which has a core region of higher refractive index
surrounded by a region of lower refractive index called the cladding. Electromagnetic
waves with wavelengths in the optical region propagate in the core region of guide by
total internal reflection.
Orbital is a region of space where an electron with a given energy may be found in an atom or
molecule. Two electrons with opposite spins can occupy the same orbital. Orbit which is
a well defined path for an electron cannot be used to describe the whereabouts of the
electron in an atom or molecule because the electron has a probability distribution. The
wavefunction, ψ nl ml (r,θ , φ ) is often simply referred to as an orbital which represents the
spatial distribution of the electron since | ψ nl ml (r,θ , φ ) |2 is the probability of finding the
electron per unit volume in the spatial region at (r,θ,φ).
Orbital (angular momentum) quantum number specifies the orbital angular momentum of
the electron via L = h√[l(l+1)] where l is the orbital quantum number with values
0,1,2,3,...up to n−1. These l values, 0,1,2,3, are labeled as s,p,d,f states.
Orbital wavefunction describes the spatial dependence of the electron and not its spin. It is
simply ψ(r,θ,φ) which depends on n, l and ml in which the spin dependence, ms, has been
excluded. Generally ψ(r,θ,φ) is simply called an orbital.
Oxidation is the term used to refer to the production of silicon dioxide on silicon. Typically,
silicon is exposed to either water vapor or oxygen at high temperatures to controllably
produce a layer of oxidized silicon, or silicon dioxide. [H.R.]
Paramagnetic materials have a small and positive magnetic susceptibility. In an applied
field they develop a small amount of magnetization in the direction of the applied field
so that the magnetic field in the material is slightly greater. They are attracted to higher
magnetic field.
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Partial discharge occurs when only a local region of the dielectric is exhibiting discharge so
that the discharge does not directly connect the two electrodes.
Passivation refers to the process of chemically protecting a semiconductor surface from
degradation. For example for bare gallium arsenide surfaces surface charge builds up on
exposure to air due to chemical oxidation. Chemical passivation with for example sulfur
containing solutions has been shown to be able to compensate this charge and thus avoid
deleterious fields within a device structure. Another level of passivation is physical
passivation. That is encapsulating a semiconductor surface with for example a protective
layer of silicon nitride or silicon dioxide. [H.R.]
Passive device or a component is a device that exhibits no gain and no directional function.
Resistors, capacitors and inductors are passive components.
Pauli exclusion principle excludes any two electrons from having the same set of quantum
numbers, n,l,ml,ms. There can be no two electrons occupying a given state ψ(n,l,ml,ms).
Equivalently, up to two electrons with opposite spins can occupy a given orbital,
ψ(n,l,ml).
Peltier effect is the phenomenon of heat absorption or liberation at the contact between two
dissimilar materials as a result of a dc current passing through the junction. The rate of
heat generation, Q', is proportional to the dc current, I, passing through the contact so that
Q' = ±Π I where Π is called the Peltier coefficient and the sign depends whether heat is
absorbed or released.
Period is a horizontal row in the periodic table. Li, Be, B. C, N, O, F, Ne constitute the second
period.
Permeability - The induction (B) in a material is related to the magnetic field (H) through the
relation B = µ0(H + M), where µ0 is the free space permeability and M is the
magnetization of the material. Using the relation M = χH, relating the magnetization to
the applied field, one gets B = µ0(1 + χ)H. This leads to the definition of the total
permeability µ = µ0(1 + χ) that yields the constitutive relation B = µH. In general, µ is
frequency dependent. If losses, resulting from the absorption of magnetic energy, occur
during propagation of an electromagnetic wave in a material, it is possible to extend the
definition of permeability to the complex plane. Losses are attributed to peaks in the
imaginary part of the permeability at the absorption frequencies. [C.T.]
Peroxydisulfuric acid (PDSA) is a chemical that when combined with sulfuric acid and
hydrogen peroxide is used to create a wafer cleaning solution called piranha. [H.R.]
Phase (in materials science) is a physically homogeneous portion of a materials system that has
uniform physical and chemical characteristics. It has the same composition, structure and
properties everywhere so that it is a homogeneous portion of the chemical system under
consideration. In a given chemical system, one phase will be in contact with another of
the system. For example, iced water will have solid and liquid phases in contact at 0 °C.
Each phase, ice and water, has a distinct structure.
Phase diagram is a temperature vs. composition diagram in which the existence and
coexistence of various phases are identified by regions and lines. Between the liquidus
and solidus lines, for example, the material is a heterogeneous mixture of liquid and
solid phases.
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Phase of a traveling wave is the quantity (kx−ωt) which determines the amplitude of the wave
at position x and at time t given k(2π/λ) and ω. In three dimensions it is the quantity
(k.r−ωt) where k is the wavevector and r is the position vector where the amplitude is
measured at time t.
Phase velocity is the rate at which a given phase on a traveling wave advances. It represents the
velocity of a given phase rather than the velocity at which information is carried by the
wave. Two consecutive peaks of a wave are separated by a wavelength λ and it takes a
time period 1/υ for one peak to reach the next (or time -separation of two consecutive
peaks at one location), then the phase velocity is defined as v = λ/(1/υ) = λυ.
Phonon is a quantum of energy associated with the vibrations of the atoms in the crystal,
analogous to the photon. A phonon has an energy of hΩ where Ω is the frequency of
the lattice vibration, and h = 2π/h, h = Planck's constant.
Phosphine (PH3) is a toxic, pyrophoric gas that is used as a source of phosphorus in
chemical vapor deposition (CVD), ion implantation and epitaxy. [H.R.]
Phosphoric acid (H3PO4) is a phosphorous-based oxygen acid that is used to etch silicon
nitride. [H.R.]
Phosphorus (P) is a poisonous solid that is used for preparing III-V compound
semiconductors such as indium phosphide, gallium phosphide and aluminum phosphide
by techniques such as liquid phase epitaxy (LPE) and solid source molecular beam
epitaxy (MBE). It is also used as an n-type dopant for ion implantation of silicon.
Phosphorus exhibits the property of being is self-igniting in air. [H.R.]
Photoconductive detectors have the simple metal-semiconductor-metal structures, that is two
electrodes are attached to a semiconductor that has the desired absorption coefficient
and quantum efficiency over the wavelengths of interest. Incident photons become
absorbed in the semiconductor and photogenerate electron hole pairs (EHPs). The result
is an increase in the conductivity of the semiconductor and hence an increase in the
external current which constitutes the photocurrent Iph. The actual response of the
detector depends whether the contacts to the semiconductor are ohmic or blocking (for
example Schottky junctions that do not inject carriers) and on the nature of carrier
recombination kinetics.
Light
d
n = no + n
p = po + p
V
w
Iphoto
A semiconductor slab of length , width w and
depth d is illuminated with light of wavelength
and intensity is I. Equilibrium carrier
concentrations are no and po. Under steady state
illumination these become n = no + n and p =
po + p. The change in the conductivity
is
the photoconductivity of the sample.
The photoconductivity of the sample ∆σ under uniform illumination is given by
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
91
eηIλτ ( µe + µh )
hcd
where e is the electronic charge, η is the quantum efficiency, µe and µh are the electron
and hole drift mobilities, τ is the mean recombination time (lifetime), h is Planck’s
constant, c is the speed of light and d is the thickness of the photoconductive slab. It is
assumed that all the incident radiation is absorbed; otherwise this expression must be
multiplied by [1 − exp(−αd)], where α is the absorption coefficient at the wavelength of
interest.
Photoconductive gain is occurs in a photoconductor when the external photocurrent is due to
more than one electron flow per absorbed photon. The photoconductor must have
ohmic contacts to allow carriers to enter the semiconductor. The photoconductive gain
is then simply
Rate of electron flow in external circuit
G=
Rate of electron generation by light absorption
which can be shown to be
τ µ 
G = 1 + h 
µe 
te 
where µe and µh, are the drift mobilities of the electrons and holes respectively, te is the
electron transit time, te = l/( µeE) where l is the photoconductor length and E is the
electric field and τ is the mean recombination time. The photoconductive gain can be
quite high if τ/te is kept large which means a long recombination time and a short transit
time. The transit time can be made shorter by applying a greater field but this will also
lead to an increase in the dark current and more noise. The speed of response of the
device is limited by the recombination time of the injected carriers. A long τ means a
slow device.
∆σ =
(a)
(b)
(c)
(d)
(e)
h+
e–
Photoconductor
Iph
Iph
Iph
Iph
Iph
A photoconductor with ohmic contacts (contacts not limiting carrier entry) can exhibit gain. As
the slow hole drifts through the photoconductors, many fast electrons enter and drift through the
photoconductor because, at any instant, the photoconductor must be neutral. Electrons drift
faster which means as one leaves, another must enter.
Photoconductivity is the change in the conductivity from dark to light, σlight − σdark.
Photodiode is a semiconductor diode that generates a photocurrent upon illumination with a
suitable range of wavelengths.
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Photoelectric effect is the emission of electrons from a metal upon illumination with a
frequency of light above a critical wavelength that depends on the material. It is found
that the kinetic energy of the emitted electron is independent of the light intensity but
dependent on the light frequency, υ, via KE = hυ−Φ where h is the Planck constant and
Φ is a material related constant called the work function of the metal.
Photogeneration is the excitation of an electron into the conduction band by the absorption
of a photon. If the photon is absorbed by an electron in the valence band then its
excitation to the conduction band will generate an EHP.
Photoinjection is the photogeneration of carriers in the semiconductor by illumination.
Photogeneration may be valence band to conduction band excitation in which case
electrons and holes are generated in pair.
Photolithography uses light in the lithographic process to define a pattern on the surface of
wafer.
Photon is a quantum of energy of amount hυ (where h is the Planck constant and υ the
frequency) associated with electromagnetic radiation. It also has a zero rest mass and a
momentum, p, given by the De Broglie relationship, p = h / λ where λ is the
wavelength. Even though a photon has no rest mass, it does possess a "moving mass" of
amount hυ / c2 so that it experiences gravitational attraction from other masses. Light
from a star becomes deflected as it passes by the sun.
Phototransistor is a bipolar junction transistor (BJT) that operates as a photodetectors with
a photocurrent gain. Typically the base terminal is normally open and there is a voltage
applied between the collector and emitter terminals just as in the normal operation of a
common emitter BJT. An incident photon is absorbed in the space charge layer (SCL)
between the base and collector to generate an electron hole pair (EHP). The electric field
E in the SCL separates the electron hole pair and drifts them in opposite direction. This
is the primary photocurrent and effectively constitutes a base current even though the
base terminal is open circuit (current is flowing into the base from the collector). Since
the photon generated primary photocurrent Ipho is amplified as if it were a base current
(IB), the photocurrent flowing in the external circuit is
Iph ≈ βIpho
where β is the current gain (or hFE) of the transistor. The phototransistor construction is
such that incident radiation is absorbed in the base-collector junction SCL. It is possible
to construct a heterojunction phototransistor that has different bandgap materials for the
emitter, base and collector. For example, if the emitter is InP (Eg = 1.35 eV) and the base
is an InGaAsP alloy (for example, Eg ≈ 0.85 eV) then photons with energies less than
1.35 eV but more than 0.85 will pass through the emitter and become absorbed in the
base. This means the device can be illuminated through the emitter.
Photovoltaic devices or solar cells convert the incident solar radiation energy into electrical
energy. Incident photons are absorbed to photogenerate charge carriers that pass
through an external load to do electrical work. Photovoltaic devices may be
metal/semiconductor Schottky junctions , pn junction or pin devices . For example, a
crystalline Si pn junction solar cell may have a thin n-type semiconductor layer on a thick
p-type substrate. The electrodes attached to the n-side must allow illumination to enter
the device and at the same time result in a small series resistance. They are deposited on
to the n-side to form an array of finger electrodes on the surface. The n-side is very
narrow to allow most of the photons to be absorbed within the depletion region and
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93
within the neutral p-side. These photons photogenerate electron hole pairs (EHPs) in
these regions. EHPs photogenerated in the depletion region are immediately separated by
the built-in field Eo which drifts them apart. The electron drifts and reaches the neutral n+
side whereupon it makes this region negative by an amount of charge −e. Similarly the
hole drifts and reaches the neutral p-side and thereby makes this side positive.
Consequently an open circuit voltage develops between the terminals of the device with
the p-side positive with respect to the n-side. If an external load is connected then the
excess electron in the n-side can travel around the external circuit, do work, and reach the
p-side to recombine with the excess hole there. There will be an external photocurrent. It
is important to realize that without the internal field Eo it is not possible to drift apart the
photogenerated EHPs and accumulate excess electrons on the n-side and excess holes on
the p-side. A thin antireflection coating on the surface reduces reflections and allows
more light to enter the device.
Bus electrode
for current collection
Finger electrodes
Light
n
p
o
Drift
Back
electrode
Finger
electrode
n
Depletion
region
Neutral
p-region
p
Iphotocurrent
Finger electrodes on the
surface of a solar cell reduce
the series resistance
The principle of operation of the solar cell.
Honda’s two seated Dream car is powered by photovoltaics. The Honda Dream was first to
finish 3,010 km in four days in the 1996 World Solar Challenge. (Courtesy of Photovoltaics
Special Research Centre, University of New South Wales, Sydney, Australia)
Photovoltaic effect is the generation of an emf (electromotive force) as a result of illumination.
See photovoltaic device.
Photovoltaic or solar cell I-V characteristics are the current vs. voltage characteristics of the
device under different intensities of illumination within the spectral response curve of the
device. Under illumination, the dark I-V characteristics become shifted so that there is a
short circuit current Isc and an open circuit voltage Voc; that is, a photocurrent Isc when the
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94
solar cell is shorted and a voltage Voc when it is in open circuit. Isc represents the
conventional current that would normally flow in a forward biased diode. However, the
actual photocurrent Iph is in the opposite direction to Isc, thus Isc = −Iph.
I (mA)
L
I
20
Dark
Voc
V
V
0
I
R
When a solar cell drives
a load R, R has the same
voltage as the solar cell
but the current through
it is in the opposite
direction to the
convention that current
flows from high to low
potential.
0.2
Iph
0.4
0.6
Light
–20
Twice the light
Typical I-V characteristics of a Si solar cell. The short
circuit current is -Iph and the open circuit voltage is Voc. The
I-V curves for positive current requires an external bias
voltage. Photovoltaic operation is always in the negative
current region.
The total current I through a pn junction solar cell can normally be written as,
eV  

I = − I ph + Io exp
−1
  nkT  
where V is the voltage across the solar cell, Iph is the short circuit photocurrent, k is
Boltzmann’s constant, T is temperature (K) and n is the ideality factor (1 to 2) for the
pn junction. The open circuit output voltage, Voc, of the solar cell is given by the point
where the I-V curve cuts the V-axis (I = 0). It is apparent that although it depends on the
light intensity, its value for Si solar cells typically lies in the range 0.4-0.6 V. When the
solar cell is connected to a load R, the load has the same voltage as the solar cell and
carries the same current. But the current I through R is now in the opposite direction to
the convention that current flows from high to low potential. Thus,
V
I=−
R
The actual current I′ and voltage V′ in the circuit must satisfy both the I-V characteristics
of the solar cell and that of the load. We can find I′ and V′ by solving these two
equations through a graphical solution; called a load line construction. The I-V
characteristics of the load is a straight line with a negative slope −1/R. This is called the
load line. The load line cuts the solar cell characteristic at a point P called the operating
point. At P, the load and the solar cell have the same current and voltage I′ and V′. The
current I′ and voltage V′ in the circuit are hence given by point P. The power delivered to
the load is Pout = I′ V′, which is the area of the rectangle bound by I- and V- axes and the
dashed lines in the figure. Maximum power is delivered to the load when this rectangular
area is maximized (by changing R or the intensity of illumination), when I′ = Im and V′ =
Vm. Since the maximum possible current is Iph and the maximum possible voltage is Voc,
IphVoc, represents the desirable goal in power delivery for a given solar cell. It is therefore
useful to compare the maximum power output, ImVm, with IscVoc. The fill factor FF,
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95
which is a figure of merit for the solar cell, is defined as
I V
FF = m m
IscVoc
FF is a measure of the closeness of the solar cell I-V curve to the rectangular shape (the
ideal shape). It is clearly advantageous to have FF as close to unity as possible but the
exponential pn junction properties prevent this. Typically FF values are in the range 7085% and depend on the device material and structure.
I (mA)
Voc
V
V
0
0.2
–10
Isc= –Iph
0.4
0.6
I-V for a solar cell under an
illumination of 600 Wm-2.
Slope = – 1/R
Operating Point
I
P
The Load Line for R = 30 Ω
(I-V for the load)
–20
The current I and voltage V in the circuit of (a) can be found from a load
line construction. Point P is the operating point (I , V ). The load line is for
R = 30 Ω.
Physical vapor deposition (PVD) refers to processes for depositing thin films of material
onto a substrate. PVD includes evaporation and sputtering processes. PVD is
commonly used to deposit metals on semiconductors. [H.R.]
Piezoelectric material has a non-centrosymmetric crystal structure which leads to the
generation of a polarization vector P, or charges on the crystal surfaces, upon the
application of a mechanical stress, T. When strained, a piezoelectric crystal develops an
internal field and therefore exhibits a voltage difference between two of its faces.
Equivalently, a piezoelectric crystal when strained develops an internal field and therefore
exhibits a voltage difference between two of its faces. The mechanical stress, Tj, in one
direction (along j) can generate polarization, Pi, along a different direction (along i) and
are related by Pi = dij Tj where dij is the piezoelectric coefficient.
Pigtail is a short optical fiber that is directly coupled to an optical component, for example, an
LED. A pigtailed emitter, for example, comes with this short fiber already attached to it
so that one can simply use this short fiber to couple the emitter to another component
(e.g. a long-haul fiber by splicing etc.).
A 1550 nm MQW-DFB InGaAsP laser diode pigtail-coupled to a fiber. (Courtesy of Alcatel.)
pin diode is semiconductor diode that has the structure, p+/ intrinsic /n+ with a relatively thick
intrinsic region that is depleted of free carriers. It has a much lower depletion layer than a
normal photodiode.
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96
Pinch-off voltage is the gate to source voltage needed to just pinch off the conducting channel
between the source and drain with no source to drain voltage applied. It is also the source
to drain voltage that just pinches off the channel when the gate and source shorted
beyond pinch-off, the drain current is almost constant and controlled by VGS, not by VDS.
Planarization refers to the process of smoothing or milling the surface of a wafer. [H.R.]
Plane wave is a wave that has a constant electric field and a constant magnetic field in any
given infinite plane perpendicular to the direction of propagation, k. The field in
successive planes, however, oscillates with time. The field is said to have a constant
phase anywhere on a given plane perpendicular to k.
Plasma is a gas composed of ionized species. [H.R.]
Plasma-enhanced chemical vapor deposition (PECVD) is a variation of the chemcial vapor
deposition (CVD) process where a gas plasma is used to lower the temperature required
to obtain a chemical reaction and achieve film deposition. [H.R.]
PLZT, lead lanthanum zirconate titanate, is a PZT type material with lanthanum which occupies
the Pb site.
PMOS is an enhancement type p-channel MOSFET.
pn Junction is a contact between a p-type and an n-type semiconductor. It has rectifying
properties.
Pockels effect is a change in the refractive index of a crystal due to an application of an external
electric field, other than the field of the light wave. Suppose that x,y and z are the principal
axes of a crystal with refractive indices n1, n2 and n3 along these directions. For an
optically isotropic crystals, these would be the same whereas for a uniaxial crystal n1 = n2
≠ n3. Suppose that we suitably apply a voltage across a crystal an thereby apply an
external dc field Ea along the z-axis. In Pockels effect, the field will modify the optical
indicatrix. The exact effect depends on the crystal structure. For example, a crystal like
GaAs, optically isotropic with a spherical indicatrix, becomes birefringent, and a crystal
like KDP (KH2PO4 - potassium dihydrogen phosphate) that is uniaxial becomes biaxial.
In the case of KDP, the field Ea along z rotates the principal axes by 45° about z, and
changes the principal indices. The new principal indices are now n′1 and n′2 which means
that the cross section is now an ellipse. Propagation along the z-axis under an applied
field now occurs with different refractive indices n′1 and n′2. The applied field induces
new principal axes x′, y′ and z′ for this crystal (though in this special case z′ = z). In the
case of LiNbO3 (lithium niobate), an optoelectronically important uniaxial crystal, a field
Ea along the y-direction does not significantly rotate the principal axes but rather changes
the principal refractive indices n1 and n2 (both equal to no) to n′1 and n′2 . As an
example consider a wave propagating along the z-direction (optic axis) in a LiNbO3
crystal. This wave will experience the same refractive index (n1 = n2 = no) whatever the
polarization. However, in the presence of an applied field Ea parallel to the principal y
axis, the light propagates as two orthogonally polarized waves (parallel to x and y)
experiencing different refractive indices n′1 and n′2. The applied field thus induces a
birefringence for light traveling along the z-axis. The field induced rotation of the
principal axes in this case, though present, is small and can be neglected. Before the field
Ea is applied, the refractive indices n1 and n2 are both equal to no. The Pockels effect then
gives the new refractive indices n′1 and n′2 in the presence of Ea as
and
n1′ ≈ n1 + 12 n13r22 Ea
n2′ ≈ n2 − 12 n23r22 Ea
where r22 is a constant, called a Pockels coefficient, that depends on the crystal structure
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
97
and the material. The reason for the seemingly unusual subscript notation is that there are
more than one constant and these are elements of a tensor that represents the optical
response of the crystal to an applied field along a particular direction with respect to the
principal axes (the exact theory is more mathematical than intuitive). We therefore have
to use the correct Pockels coefficients for the refractive index changes for a given crystal
and a given field direction. If the field were along z, the Pockels coefficient above would
be r13. It is clear that the control of the refractive index by an external applied field (and
hence a voltage) is a distinct advantage which enables the phase change through a
Pockels crystal to be controlled or modulated; such a phase modulator is called a
Pockels cell. In the longitudinal Pockels cell phase modulator the applied field is in the
direction of light propagation whereas in the transverse phase modulator, the applied
field is transverse to the direction of light propagation.
y
y
n2 = no
n2
x
n1 = no
z
KDP, LiNbO3
(a)
y
x
n1
Ea
z
Ea
n2
45
x
x
z
n1
KDP
LiNbO3
(c)
(b)
(a) Cross section of the optical indicatrix with no applied field, n1 = n2 = no (b) The
applied external field modifies the optical indicatrix. In a KDP crystal, it rotates the
principal axes by 45 to x and y and n1 and n2 change to n 1 and n 2 . (c) Applied field
along y in LiNbO2 modifies the indicatrix and changes n1 and n2 change to n 1 and n 2 .
Point defects are defects in a crystal that have dimensions comparable to the atomic size and
arise as a result of the presence of additional host or impurity atoms, or simply missing
atoms in the crystal lattice. Typical examples are vacancies, substitutional and
insterstitial impurities.
(a) A vacancy in the
crystal.
(b) A substitutional
impurity in the crystal.
The impurity atom is
larger than the host
atom.
(c) A substitutional
impurity in the crystal.
The impurity atom is
smaller than the host
atom.
(d) An interstitial
impurity in the crystal.
It occupies an empty
space between host
atoms.
Point defects in the crystal structure. The regions around the point defect become
distorted; the lattice becomes strained.
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98
Polarizability (α) is the ability of an atom or molecule to become polarized in the presence of
an electric field. It is induced polarization in the molecule per unit field along the field.
Polarization of an electromagnetic (EM) wave describes the behavior of the electric field vector
in the EM wave as it propagates through a medium. If the oscillations of the electric field
at all times are contained within a well-defined line then the EM wave is said to be
linearly polarized. The field vibrations and the direction of propagation, e.g. z-direction,
define a plane of polarization (plane of vibration) so that linear polarization implies a
wave that is plane-polarized. By contrast, if a beam of light has waves with the E-field in
each in a random perpendicular direction to z, then this light beam is unpolarized. A light
beam can be linearly polarized by passing the beam through a polarizer, such as a
polaroid sheet, a device that only passes electric field oscillations lying on a well defined
plane at right angles to the direction of propagation.
Plane of polarization
y
E
x
^
y
Ey
^
x
^
xE
Ex
E
^
yE
y
E
z
(a)
(b)
x
(c)
(a) A linearly polarized wave has its electric field oscillations defined along a line
perpendicular to the direction of propagation, z. The field vector E and z define a plane of
polarization. (b) The E-field oscillations are contained in the plane of polarization. (c) A
linearly polarized light at any instant can be represented by the superposition of two fields Ex
and Ey with the right magnitude and phase.
Polarization is the separation of positive and negative charges in a system so that there is a net
electric dipole moment per unit volume.
Polarization vector (P) measures the extent of polarization in a unit volume of dielectric
matter. It is the vector sum of dielectric dipoles per unit volume. If p is the average dipole
moment per molecule and n is the number of molecules per unit volume then P = np. In
a polarized dielectric matter (e.g. in an electric field), the bound surface charge density,
σp, due to polarization is equal to the normal component of P at that point, σp = Pnormal.
Polarized EM wave (polarized light) is an EM wave which has the oscillations of the electric
field in a well defined direction (but still at right angles to the direction of propagation).
In unpolarized light the field oscillations are in random directions but once polarized the
field oscillations are along a well defined direction. If this direction does not change as
the wave propagates it is said to be plane polarized.
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Poling is the application of a temporary electric field to a piezoelectric (or ferroelectric) material,
generally at an elevated temperature, to align the polarizations of various grains and
thereby develop piezoelectric behavior.
Poly-Si gate is short for a polycrystalline and highly doped Si gate.
Polymorphism or allotropy is an attribute of a material that allows it to posses more than one
crystal structure. Each crystal structure that can exist is a polymorph. Generally the
structure of the polymorph depends not only on the temperature and pressure but also on
the method of preparation of the particular solid (for example diamond can be prepared
from graphite by the application of very high pressures).
Polysilicon (Poly) is a type of silicon which is not single crystal, but consists of randomly
oriented grains. Such material is typically produced by chemical vapor deposition
(CVD) from a silicon gas source such as silane, on to silicon dioxide or silicon
nitride. [H.R.]
Poole-Frenkel effect is field enhanced thermally activated conductivity in which the field
lowers the activation energy. The field enhancement occurs because the field lowers the
potential energy barrier that controls the conductivity. For example, if electrons are
generated by the ionization of certain impurities then the field can lower the potential
energy barrier against the ionization process.
Population inversion is the phenomenon of having more atoms occupy an excited energy
level, E2, than a lower energy level, E1, so that the normal equilibrium distribution is
reversed, i.e. N(E2) > N(E1). Population inversion occurs temporarily as a result of the
excitation of a medium (pumping). If left on its own, the medium will eventually,
however long, will return to its equilibrium population distribution with more atoms at E1
than at E2. For gas atoms, this means N(E2)/N(E1) = exp[−(E2−E1)/kT].
Potential energy (PE) represents a system's ability to do work. If we move an object by a small
distance dl along a conservative force F acting on that object, then the change in the PE is
Fdl. Conservative forces are such that the energy involved in taking an object from point
A to point B does not depend on the path but only on the final and initial positions.
Typical examples are gravitational and electrostatic forces. A 100 gram apple resting on a
table top experiences a gravitational force of mg. which is about 1 Newton. When it is
lifted by to a height h = 1 m, the work done is mgh or about 1 Joule. This represents its
PE because if we were to let it go it will drop on to the table and on impact it will do work
that is mgh.
Precession is the angular motion of the axis of a spinning object (e.g. a spinning top) in the
presence of an applied field (e.g. a gravitational field) that produces a torque that depends
on the spin. The precession occurs around the direction of the applied field.
Preform is a glass rod which has an appropriate core and cladding from which an optical fiber
is drawn by a fiber drawing process at an elevated temperature.
Primary bond is a strong interatomic bond, typically greater than 1 eV/atom, that involves ionic,
covalent or metallic bonding.
Principal quantum number, n, is a quantum number with integer values 1,2,3,... which
characterizes the total energy of the electron. The energy increases with n. It determines,
with the other quantum numbers l and ml, the orbital of the electron in an atom,
ψn,l,ml,ms(ρ,θ,φ). n = 1,2,3 ,4,... are labelled as K,L,M,N,... shells within each of which there
may be subshells based on l = 0,1,2,..(n−1) and corresponding to s,p,d,... states.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
100
Principal refractive indices of a crystal, according all experiments and theories, are a set of
three refractive indices n1, n2 and n3 (along three mutually orthogonal directions in the
crystal, say x, y and z called principal axes) which are necessary to characterize light
propagation even in the most anisotropic crystal. These indices correspond to the
polarization state of the wave along these axes. Crystals that have three distinct
principal indices also have two optic axes and are called biaxial crystals. On the other
hand, uniaxial crystals have two of their principal indices the same (n1 = n2) and only
have one optic axis. Uniaxial crystals, such as quartz, that have n3 > n1 and are called
positive, and those such as calcite that have n3 < n1 are called negative uniaxial crystals.
Probe test refers to the functional testing of the electrical parameters of each die after
fabrication. It is also called wafer sort. [H.R.]
Property is a characteristic or an attribute of a system which we can measure. Pressure, volume,
temperature, mass, energy, magnetization, polarization, color are all properties of
matter. Properties such as pressure, volume and temperature can only be attributed to a
system of many particles (which we treat as a continuum). We note that heat and work
are not properties of a substance but represent energy transfers involved in producing
changes in the properties.
Pumping in lasers involves exciting atoms from their ground states to states at higher
energies.
PV Work is work done when a system (any substance) expands or contracts by in volume as a
result of an external pressure, Pext acting on the system. For example, when the gas in a
cylinder expands by dV against a piston it pushes the piston against an external pressure
of Pext and in doing so it does work by an amount PextdV. If the change in the volume is
done reversibly, i.e the pressure of the system is only infinitesimally larger than the
external pressure (expansion is therefore infinitely slowly), then P = Pext and dW = PdV.
Maximum work is done by a system only during a reversible change. Further, W = ∫PdV
is a path function in that its value for a change from state A to state B depends on the path
(processes).
Pyroelectric material is a polar dielectric (such as barium titanate) in which a temperature
change ∆T induces a proportional change ∆P in the polarization, i.e. ∆P = p ∆T where
p is the pyroelectric coefficient of the crystal.
PZT is a general acronym for lead zirconate titanate (PbZrO3-PbTiO3 or PbTi0.48Zr0.52O3)
family of crystals.
Q-factor or quality factor of an impedance is the ratio of its reactance to its resistance. The Qfactor of a capacitor is Xc / Rp where Xc=1/ωC and Rp is the equivalent parallel resistance
that represents the dielectric and conduction losses. The Q-factor of a resonant circuit
measures the circuit's peak response at the resonant frequency and also its bandwidth.
Greater is Q, higher is the peak response and narrower is the bandwidth. For a series
RLC resonant circuit, Q = ωoL/R = 1/(ωoCR ) where ωo is the resonant angular
frequency, ωo =1/√(LC). The width of the resonant response curve between half-power
points is ∆ω = ωoQ.
Quantum efficiency (QE) η of the detector, or external quantum efficiency, is defined as
η=
Number of free electron - hole pairs generated and collected
Number of incident photons
Not all the incident photons are absorbed to create free electron-hole pairs (EHPs) that
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101
can be collected and give rise to a photocurrent. The efficiency of the conversion process
of received photons to free EHPs is measured by the above quantum efficiency
definition. The measured photocurrent Iph in the external circuit is due to the flow of
electrons per second to the terminals of the photodiode. Number of electrons collected
per second is Iph/e. If Po is the incident optical power then the number of photons
arriving per second is Po/hυ. Then the QE η can also be defined by
I /e
η = ph
Po / hυ
where h is the Planck constant, e is the electronic charge and υ is the frequency of light.
Not all of the absorbed photons may photogenerate free EHPs that can be collected.
Some EHPs may disappear by recombination without contributing to the photocurrent
or become immediately trapped. Further if the semiconductor length is comparable with
the penetration depth (1/α) then not all the photons will be absorbed. The device QE is
therefore always less than unity. It depends on the absorption coefficient α of the
semiconductor at the wavelength of interest and on the structure of the device. QE can be
increased by reducing the reflections at the semiconductor surface, increasing absorption
within the depletion layer and preventing the recombination or trapping of carriers before
they are collected. The above QE is for the whole device. More specifically, it is known
as the external quantum efficiency. Internal quantum efficiency is the number of free
EHPs photogenerated per absorbed photon and is typically quite high for may devices.
The external quantum efficiency incorporates internal quantum efficiency because it
applies to the whole device.
Quantum efficiency is the number of free electron hole pairs photogenerated per absorbed
photon. Put differently, it is the number of electrons flowing in the external photocurrent
per absorbed photon per unit second.
Quantum noise or photon noise is the fluctuations in the photocurrent due to the quantum or
discrete (i.e. photon) nature of light. Incident light on a photodetector is a flux of
photons, discrete entities, which means that the photogeneration process is not a
smooth continuous process without fluctuations; photons arrive like discrete particles.
Quantum well device typically has an ultra thin, typically less than 50 nm, narrow bandgap
semiconductor, such as GaAs, sandwiched between two wider bandgap semiconductors,
such as AlGaAs which is a heterostructure device. We assume that the two
semiconductors are lattice matched in the sense that they have the same lattice
parameter a. This means that interface defects due to mismatch of crystal dimensions
between the two semiconductor crystals are minimal. Since the bandgap, Eg, changes at
the interface, there are discontinuities in Ec and Ev at the interfaces. These discontinuities,
∆Ec and ∆EV, depend on the semiconductor materials and their doping. In the case of
GaAs/AlGaAs heterostructure shown in the figure, ∆Ec is greater than ∆Ev. Very
approximately, the change from the wider Eg2 to narrower Eg1 is proportioned 60% to
∆Ec and 40% to ∆Ev. Because of the potential energy barrier, ∆Ec, conduction electrons
in the thin GaAs layer are confined in the x-direction. This confinement length d is so
small that we can treat the electron as in a one-dimensional potential energy (PE) well in
the x-direction but as if it were free in the yz plane.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
102
E
Dy
∆Ec n = 2
E
d
Dz AlGaAs
n=1
Eg2
AlGaAs z
Eg1
y
x
GaAs
Ev
QW
d
Ec
∆Ev
Bulk
E3
E2
E1
QW
Bulk
Density of states
(E
A quantum well (QW) device. (a) Schematic illustration of a quantum well (QW) structure in
which a thin layer of GaAs is sandwiched between two wider bandgap semiconductors (AlGaAs)
(b) The conduction electrons in the GaAs layer are confined (by ∆Ec) in the x-direction to a small
length d so that their energy is quantized. (c) The density of states of a two-dimensional QW. The
density of states is constant at each quantized energy level.
We can appreciate the confinement effect by considering the energy of the conduction
electron that is bound by the size of the GaAs layer which is d along x and Dy and Dz
along y and z. The energy of the conduction electron will be the same as that in a three
dimensional PE well of size d, Dy and Dz and given by
h 2 ny2
h2n2
h 2 nz2
E = Ec +
+
+
8me* d 2 8me* Dy2 8me* Dz2
where n, ny and nz are quantum numbers having the values 1,2,3,…. The reason for the Ec
in this equation is that the potential energy (PE) barriers are defined with respect to Ec.
These PE barriers are ∆Ec along x and electron affinity (energy required to take the
electron from Ec to vacuum) along y and z. But Dy and Dz are orders of magnitude
greater than d so that the minimum energy, denoted as E1, is determined by the term with
n and d, the energy associated with motion along x. The minimum energy E1 corresponds
to n = 1 and is above Ec of GaAs. The separation between the energy levels identified by
ny and nZ and associated with motion in the yz plane is so small that the electron is free to
move in the yz plane as if it were in the bulk semiconductor. We therefore have a twodimensional electron gas which is confined in the x-direction. The holes in the valence
band are confined by the potential energy barrier ∆Ev (hole energy is in the opposite
direction to electron energy) and behave similarly. The density of electronic states for
the two dimensional electron system is not the same as that for the bulk semiconductor.
For a given electron concentration n, the density of states g(E) number of quantum
states per unit energy per unit volume, is constant and does not depend on the energy.
The density of states for the confined electron and that in the bulk semiconductor are
shown schematically below. g(E) is constant at E1 until E2 where it increases as a step
and remains constant until E3 where again it increases as a step by the same amount and
at every value of En. Density of states in the valence band behaves similarly.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
E
Ec
E1
h = E1 – E 1
E1
103
In single quantum well (SQW) lasers electrons are
injected by the forward current into the thin GaAs
layer which serves as the active layer. Population
inversion between E1 and E 1 is reached even with a
small forward current which results in stimulated
emissions.
Ev
Since at E1 there is a finite and substantial density of states, the electrons in the
conduction band do not have to spread far in energy to find states. In the bulk
semiconductor, on the other hand, the density of states at Ec is zero and increases slowly
with energy (as E1/2) which means that the electrons are spread more deeply into the
conduction band in search for states. A large concentration of electrons can easily occur
at E1 whereas this is not the case in the bulk semiconductor. Similarly, the majority of
holes in the valence band will be around E′1 since there are sufficient states at this
energy. Under a forward bias electrons are injected into the conduction band of the
GaAs layer which serves as the active layer. The injected electrons readily populate the
ample number of states at E1 which means that the electron concentration at E1 increases
rapidly with the current and hence population inversion occurs quickly without the
need for a large current to bring in a great number of electrons. Stimulated transitions of
electrons from E1 to E′1 leads to a lasing emission. There are two distinct advantages.
First is that the threshold current for population inversion and hence lasing emission is
markedly reduced with respect to that for bulk semiconductor devices. For example in a
single quantum well (SQW) laser this is typically in the range 0.5 − 1 mA whereas in a
double heterostructure laser the threshold current is in the range 10 − 50 mA. Secondly,
since majority of the electrons are at and near E1 and holes are at and near E′1, the range
of emitted photon energies are very close to E1 − E′1. Consequently the spread in the
wavelength, the linewidth, in the output spectrum is substantially narrower than that in
bulk semiconductor lasers.
Quarter-wave plate is a retarder plate (made from a birefringent refracting crystal) that results
in a relative phase change of a quarter of a wave (π/4) between the ordinary and
extraordinary waves propagating inside the crystal from entry to exit. A linearly polarized
light incident with its E-field at an angle α to the optic axis leaves the crystal either as
elliptically polarized light or as a circularly polarized light (α = 45°).
Quarternary (III-V) alloys have four different elements from the III and V groups. For
example In1-xGaxAs1-yPy. is a quaternary alloy having Ga and In from group III and As
and P from group V. There are as many group III elements as there are group V
elements and formula reflects this requirement.
Quartz (SiO2) is a form of silicon dioxide. [H.R.]
Radiant sensitivity, see responsivity.
Radiationless recombination, a nonradiative transition, is that in which an electron and a hole
recombine through a recombination center such as a crystal defect or an impurity and
emit phonons (lattice).
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104
Ramo’s theorem relates the external photocurrent I(t) due to a charge q being drifted with a
velocity vd(t) by a field between two biased electrodes separated by L, that is
qv (t )
i(t ) = d
; t < ttransit
L
Consider a semiconductor material with a negligible dark conductivity that is electroded
and biased to generate a field E in the sample that is uniform and is given by V/L. This
situation is almost identical to the intrinsic region of a reverse biased pin photodiode.
Suppose that a single photon is absorbed at a position x = l from the left electrode and
instantly creates an electron hole pair. The electron and the hole drift in opposite
directions with respective drift velocities ve = µeE and vh = µhE, where µe and µh are the
electron and hole drift mobilities respectively. The transit time of a carrier is the time it
takes for a carrier to drift from its generation point to the collecting electrode. The
electron and hole transit times te and th are
L−l
l
te =
and
th =
ve
vh
Consider first only the drifting electron. Suppose that the external photocurrent due to
the motion of this electron is ie(t). The electron is acted on by the force eE of the electric
field. When it moves a distance dx, work must be done by the external circuit. In time dt,
the electron drifts a distance dx and does an amount of work eEdx which is provided by
the battery in time dt as Vie(t)dt. Thus,
Work done = eEdx = Vie(t)dt
Using E = V/L and ve = dx/dt we find the electron photocurrent
ev
ie (t ) = e ; t < te
L
It is apparent that this current continues to flow as long as the electron is drifting (has a
velocity ve) in the sample. It lasts for a duration te at the end of which the electron
reaches the battery. Thus, although the electron has been photogenerated instantaneously,
the external photocurrent is not instantaneous and has a time spread. We can apply
similar arguments to the drifting hole as well which will generate a hole photocurrent ih(t)
in the external circuit given by
ev
ih (t ) = h ; t < th
L
The total external current will be the sum of ie(t) and ih(t). If we integrate the external
current iph(t) to evaluate the collected charge Qcollected we would find,
te
th
0
0
Qcollected ∫ ie (t ) + ∫ ih (t ) = e
Thus, the collected charge is not 2e but just one electron.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
105
V
iph(t)
0
Semiconductor
E
(a)
h+
vh
e–
l
l
0
h+
(b)
Charge = e
(d)
te
ve
L
th
l
t
0
L
evh/L
eve/L
x
i(t)
e–
te
ie(t)
te
th
th
t
evh/L + eve/L
iph(t)
evh/L
t
(c)
ih(t)
t
(a) An EHP is photogenerated at x = l. The electron and the hole drift in opposite
directions with drift velocities vh and ve. (b) The electron arrives at time te = (L l)/ve
and the hole arrives at time th = l/vh. (c) As the electron and hole drift, each generates an
external photocurrent shown as ie(t) and ih(t). (d) The total photocurrent is the sum of
hole and electron photocurrents each lasting a duration th and te respectively.
Rayleigh cycle/law is a hysteresis loop for small magnetic fields, i.e., H < Hc. The initial
magnetization curve follows Rayleigh’s law: M(H) = χ0H + αRH2, where χ0 is the
susceptibility and αR is the Rayleigh coefficient. This law describes reversible motion of
the magnetization. [C.T.]
Reach-through avalanche photodiode (APD) is an avalanche photodiode device with a
structure n+ - p -π - p+, where π represents very slight p-type doping. The n+ side is thin
and it is the side that is illuminated through a window. There are three p-type layers of
different doping levels next to the n+ layer to suitably modify the field distribution across
the diode. The first is a thin p-type layer and the second is a thick lightly p-type doped
(almost intrinsic) π-layer and the third is a heavily doped p+ layer. The diode is reverse
biased to increase the fields in the depletion regions. Under zero bias the depletion
layer in the p-region (between n+p) does not normally extend across this layer. But when
a sufficient reverse bias is applied the depletion region in the p-layer widens to reachthrough to the π-layer (and hence the name reach-through). The field extends from the
exposed positively charged donors in the thin depletion layer in n+ side, all the way to the
exposed negatively charged acceptors in the thin depletion layer in p+-side. The electric
field is given by the integration of the net space charge density ρnet across the diode
subject to an applied voltage Vr across the device. The variation in the field across the
diode is such that the field lines start at positive ions and end at negative ions which exist
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
106
through the p, π and p+ layers. This means that E is maximum at the n+p junction, then
decreases slowly through the p-layer. Through the π-layer it decreases only slightly as
the net space charge density here is small. The field vanishes at the end of the narrow
depletion layer in the p+ side. The absorption of photons and hence photogeneration
takes place mainly in the long π-layer. The nearly uniform field here separates the
electron-hole pairs (EHPs) and drifts them at velocities near saturation towards the n+
and p+ sides respectively. When the drifting electrons reach the p-layer, they experience
even greater fields and therefore acquire sufficient kinetic energy (greater than the
bandgap Eg) to impact-ionize some of the Si covalent bonds and release EHPs. These
generated EHPs themselves can also be accelerated by the high fields in this region to
sufficiently large kinetic energies to further cause impact ionization and release more
EHPs which leads to an avalanche of impact ionization processes. Thus from a single
electron entering the p-layer one can generate a large number of EHPs all of which
contribute to the observed photocurrent. The photodiode possesses an internal gain
mechanism in that a single photon absorption leads to a large number of EHPs
generated. The photocurrent in the APD in the presence of avalanche multiplication
therefore corresponds to an effective quantum efficiency in excess of unity. The reason
for keeping the photogeneration within the π-region and reasonably separate from the
avalanche p-region is that avalanche multiplication is a statistical process and hence leads
to carrier generation fluctuations which leads to excess noise in the avalanche multiplied
photocurrent. This is minimized if impact ionization is restricted to the carrier with the
highest impact ionization efficiency which in Si is the electron.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
Electrode
Iph
SiO2
107
R
E
h > Eg
e–
π
n+ p
h+
net
(a)
p+
Electrode
(b)
x
E(x)
(c)
x
Absorption
region
Avalanche
region
(a) A schematic illustration of the structure of an avalanche photodiode (APD)
biased for avalanche gain. (b) The net space charge density across the photodiode.
(c) The field across the diode and the identification of absorption and multiplication
regions.
Recombination centers are defects or impurities in a crystal that facilitate the recombination
of electrons and holes, usually (but not always) via phonon emissions, that is, without
photon emission.
Recombination current flows under forward bias to replenish the carriers recombining in the
space charge (depletion) layer (SCL). Typically the recombination current is described
by I = Iro[exp(eV/2kT)−1], where Iro is a constant, e is the electronic charge, k is
Boltzmann’s constant and T is the temperature (Kelvins). The constant Iro contains the
details of the carrier recombination process in the space charge layer, for example, the
mean recombination times in the SCL in the p and n-sides.
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Recombination of an electron hole pair involves an electron in the conduction band (CB)
falling in energy down into an empty state (hole) in the valence band (VB) to occupy
it. The result is the annihilation of the electron hole pair. Recombination is direct when
the electron falls directly down into an empty state in the VB as in GaAs. Recombination
is indirect if the electron is first captured locally by a defect or an impurity, called a
recombination center, and from there it falls down into an empty state (hole) in the VB
as in Si and Ge.
Reflectance is the fraction of power in the reflected electromagnetic wave with respect to the
incident power.
Reflection coefficient is the ratio of the amplitude of the reflected EM wave to that of the
incident wave. It can be positive, negative or a complex number which then represents a
phase change.
Refraction is a change in the direction of a wave when it enters a medium with a different
refractive index. A wave that is incident at a boundary between two media with different
refractive indices experiences refraction and changes direction in passing from one to the
other medium. The angles of incidence and refraction obey Snell's law.
Refractive index n of an optical or dielectric medium is the ratio of the velocity c of an
electromagnetic (EM) wave, that is light, in vacuum to its velocity v in the medium; n =
c/v. By solving the EM wave equation (that is Maxwell’s equations) in a medium of
relative permittivity εr at the frequency of interest we can show that n is related to εr by n
= (εr)1/2. Typically n depends on the wavelength λ of the EM radiation because εr
depends on the polarization mechansim in the material and this depends on the frequency
of the electric field polarizing the medium. The relationship between n and λ is called the
dispersion relation. For example, for GaAs, from λ = 0.89 to 4.1 µm,
3.78λ2
n 2 = 7.10 + 2
λ − 0.2767
where λ is in microns (µm). The refractive index of a semiconductor material typically
decreases with increasing energy bandgap Eg.
Relative permeability µr measures the magnetic field in a medium with respect to that in
vacuum, µr = B / (µoH). Since B depends on the magnetization of the medium, µr
measures the ease with which the material to become magnetized.
Relative permittivity (εr) or the dielectric constant of a dielectric is the fractional increase in
the stored charge per unit voltage on the capacitor plates due to the presence of the
dielectric between the plates (the whole space between the plates is assumed to be filled).
Alternatively we can define it as the fractional increase in the capacitance of a capacitor
when the insulation between the plates is changed from vacuum to a dielectric material
keeping the geometry the same.
Relaxation time (τ) is a characteristic time that determines the sluggishness of the dipole
response to an applied field. It is the mean time for the dipole to loose its alignment with
the field due to its random interactions with the other molecules through molecular
collisions, lattice vibrations etc. It is an equivalent term for the mean free time between
scattering events.
Reluctance is analogous of electrical resistance in a circuit made of magnetic materials such as
transformer cores or record/read magnetic heads. A magnetic material with length L,
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
109
cross-sectional area A, and permeability µ has a reluctance R = L/µA. Reluctances
might be in series or parallel in exact analogy with electrical circuits. [C.T.]
Remanent magnetization or remanence (Mr) is the magnetization that remains in a
magnetic material after it has been fully magnetized and the magnetizing field has been
removed. It measures the ability of magnetic material to retain a portion of its
magnetization after the removal of the applied field. The corresponding magnetic field
(µoMr) is the remanent magnetic field Br.
Residual resistivity (ρR) is the contribution to the resistivity arising from scattering
processes aside from the thermal vibrations of the lattice, e.g. scattering from impurities,
grain boundaries, dislocations, point defects, vacancies, etc.
Resist is an irradiation sensitive chemical emulsion that is coated as a thin layer onto the surface
of a wafer. Its chemical solubility (or etchability) depends on irradiation (UV light, Xrays or electron beam). If the resist is sensitive to light (UV light) it is called a
photoresist.
Resistivity is a measure of the difficulty with which an electrical charge is able to move through
a given material. Resistivity measures the material's opposition to the flow of charges
through it. It is the required electric field that must be applied per unit current density
through the substance,
J = E/ρ
where ρ is the resisitivity, E is the applied field and J is the current density. Resistivity is
a specific resistance in the sense that a given sample's opposition to current flow is
considered independely of its geometry; resistance of a substance per unit length and for
unit area. It is the reciprocal of the conductivity.
Resonance, in general, is a “state” of a system in which the smallest driving oscillations can
most easily build up into large amplitude oscillations of the system. For example, a
parallel inductor-capacitor circuit is in resonance when the driving oscillator frequency, f
= 1/[2π(LC)1/2] at which the circuit oscillates naturally and consumes the minimum
energy from the driving oscillator.
Resonant frequency, in general, is the frequency of an allowed wave or oscillation within a
given structure; a natural frequency of the structure. A resonant frequency of an optical
cavity is a frequency of an allowed mode of electromagnetic oscillations within the
optical cavity. The resonant frequency depends on the cavity properties; the cavity size,
reflectances and the refractive index
Response time is the duration of time it takes for a device to produce the required output in
response to a step input.
Responsivity is the photocurrent generated by a photodiode per unit incident optical power.
It depends on the quantum efficiency and the wavelength of the incident radiation. The
responsivity R of a photodiode characterizes its performance in terms of the
photocurrent generated (Iph) per incident optical power (Po) at a given wavelength by
I
Photocurrent ( A )
R=
= ph
Incident Optical Power ( W ) Po
From the definition of quantum efficiency (QE)
e
eλ
R =η
=η
hυ
hc
where η is the quantum efficiency which depends on the light wavelength λ, h is
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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Planck’s constant, υ is the light frequency and e is the electronic charge. The
responsivity therefore clearly depends on the wavelength. R is also called the spectral
responsivity or radiant sensitivity. The R vs. λ characteristics represents the spectral
response of the photodiode and is generally provided by the manufacturer. Ideally with a
quantum efficiency of 100% (η = 1), R should increase with λ up to λg. In practice, QE
limits the responsivity to lie below the ideal photodiode line with upper and lower
wavelength limits as shown for a typical Si photodiode in the same figure. The QE of a
well designed Si photodiode in the wavelength range 700 - 900 nm can be close to 9095%.
Responsivity (A/W)
1
0.9
0.8
Ideal Photodiode
QE = 100% ( = 1)
0.7
Responsivity ( ) vs.
0.6
wavelength ( ) for an
0.5
ideal photodiode with
g
QE = 100% ( = 1) and
0.4
for a typical commercial
0.3
Si Photodiode
Si photodiode.
0.2
0.1
0
0
200 400 600 800 1000 1200
Wavelength (nm)
Reticle is a patterned mask that is placed in a UV light projection system to project the image of
the pattern onto the wafer surface for the lithographic process.
Reverse bias is the application of an external voltage to a pn junction such that the positive
terminal is connected to the n-side and negative to the p-side. The applied voltage
increases the built-in potential and hence the internal field in the space charge layer.
Reverse diode current is the diode current in the dark when the diode is reverse biased.
Under reverse bias, the hole concentration in the n-side just outside the space charge
layer (SCL) is nearly zero by the law of the junction, whereas the hole concentration in
the bulk (or near the negative terminal) is the equilibrium concentration pno, which is
small. There is therefore a small concentration gradient and hence a small hole diffusion
current towards the SCL.
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Minority Carrier
Concentration
o+
Neutral p-region
Neutral n-region
Thermally
generated
EHP
Holes
Electrons
npo
Wo
W
V
pno
x
Reverse biased pn
junction. Minority carrier
profiles and the origin of
the reverse current.
Diffusion
Drift
r
Similarly, there is a small electron diffusion current from bulk p-side to the SCL. Within
the SCL, these carriers are drifted by the field. This reverse current is basically the
Shockley equation under reverse bias and is called the reverse saturation current, Iso.
This saturation current depends on the square of the intrinsic concentration, that is ni2,
but not on the voltage. The thermal generation of electron hole pairs (EHPs) in the space
charge region can also contribute to the observed reverse current since the internal field
in this layer will separate the electron and hole and drift them towards the neutral regions.
This drift will result in an external current Igeneration due to EHP generation in the SCL.
Igeneration increases slightly with the reverse bias Vr because SCL width increases with Vr.
Igeneration is proportional to ni. The total reverse current Irev is the sum of the diffusion and
generation components. Their relative importance of these terms depends not only on the
semiconductor properties but also on the temperature since ni ~ exp(−Eg/2kT), where Eg
is the semiconductor bandgap, k is Boltzmann’s constant and T is the temperature. For
example, the reverse dark current Ireverse in a Ge pn junction (a photodiode) when
plotted as ln(Ireverse) vs. 1/T as in the figure shows two regions. Above 238 K, Ireverse is
controlled by ni2 because the slope of ln(Ireverse) vs. 1/T yields an Eg of approximately
0.63 eV, close to the expected Eg of about 0.66 eV in Ge. In this range, the reverse
current is due to minority carrier diffusion in neutral regions. Below 238 K, Ireverse is
controlled by ni because the slope of ln(Ireverse) vs. 1/T is equivalent to an Eg/2 of
approximately 0.33 eV. In this range, the reverse current is due to EHP generation in the
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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SCL via defects and impurities (recombination centers).
Photodiode reverse current (A) at Vr = 5 V
Ge Photodiode
10-4
323 K
10-6
0.63 eV
10-8
10-10
238 K
10-12
0.33 eV
10-14
10-16
0.002
Dark current, i.e. reverse diode current,
in a Ge pn junction as a function of
temperature in a ln(Ireverse) vs 1/T plot.
Above 238 K, Ireverse is controlled by ni2
and below 238 K it is controlled by ni.
The vertical axis is a logarithmic scale
with actual current values. (From D.
Scansen and S.O. Kasap, Cnd. J. Physics.
70, 1070-1075, 1992.)
0.004
0.006 0.008
1/Temperature (1/K)
Reverse osmosis (RO) is one of the primary processes used to create ultra-pure RO/Deionized (DI) Water. Reverse osmosis is a membrane process in which ions are removed
from a solution using relatively high pressure as the driving force. Such ions and other
contaminants are rejected by the RO membrane while pure water is forced through the
membrane under pressure. [H.R.]
Reverse saturation current is the reverse current that would flow in a reversed biased ideal pn
junction obeying the Shockley equation.
Reversible process is that in which the system changes from state A to state B through
equilibrium states. In other words, as the system changes from (P1,V1,T1) to (P2,V2,T2)
it is always in equilibrium; the pressure and temperature in the system are always
uniform. Such changes necessarily take place very slowly; almost infinitely slowly.
Many changes in the real world are irreversible in that during the change the pressure
and the temperature are not uniform even though in the final state they stabilize to give an
equilibrium state.
Rise time of a photodetector is the time it takes for the photocurrent to rise from the 10% to the
90% of the steady state value when the photodetector is suddenly illuminated as a step
function. Rise time of an LED or a laser diode is the time it takes for the light output to
rise from the 10% to the 90% of steady state value when the driving current is suddenly
applied as a step function.
Saturated solution is a solution which has the maximum possible amount of solute dissolved
in a given amount of solvent at a specified temperature and pressure.
Saturation magnetization is the maximum magnetization that can obtained in a
ferromagnetic crystal at a given temperature when all the magnetic moments have been
aligned in the direction of the applied field, when there is a single magnetic domain
with its magnetization M along the applied field.
Scaling describes shrinking the dimensions of devices to integrate more devices per unit area
and to increase the speed of operation.
Scanning probe based nano-fabrication relies on the strong interactions that occur between
an atomically sharp tip and a substrate. Several tip-substrate interactions can be
employed to fabricate nano-structures, including attractive and repulsive forces, confined
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113
electron currents, and electric fields. A scanning tunneling microscope (STM) can
operate in either the tunneling mode or the field-emission mode. In the former case, when
the tip is brought sufficiently close to the surface with an appropriately high positive
bias, electrons can tunnel from surface bound atoms to the tip, permitting selective
removal of surface atoms. Alternatively, in the field-emission mode with an appropriate
negative bias, tip-adsorbed atoms can be transferred to the surface. An STM can also
provide a finely focused (i.e., nano-meter size) beam of low-energy electrons, permitting
processes such as bond breaking, surface migration, and chemical reactions. [H.R.]
Scattering is a process by which the energy from a propagating electromagnetic (EM) wave is
redirected as secondary EM waves in various directions away from the original direction
of propagation. There are a number of scattering process. In Rayleigh scattering,
fluctuations in the refractive index, inhomogeneities etc. lead to the scattering of light that
decreases with the wavelength as λ4. For an EM wave propagating along an optical fiber,
scattering is a cause of attenuation along the fiber (direction of propagation). Rayleigh
scattering is responsible for the blue color of the sky as blue wavelengths are scattered
more in the atmosphere.
Schottky defect is an imperfection in an ionic crystal that occurs when a pair of ions is
missing; a pair of cation and anion vacancies.
Schottky junction is a contact between a metal and a semiconductor that has rectifying
properties. For a metal/n-type semiconductor junction, electrons on the metal side have to
overcome a potential energy barrier ΦB to enter the conduction band of the
semiconductor whereas the conduction electrons in the semiconductor have to overcome
a smaller barrier eVo to enter the metal. Forward bias decreases eVo and thereby greatly
encourages electron emissions over the barrier e(Vo−V). Under reverse bias electrons
have to overcome ΦB and the current is very small.
Schrödinger equation is a fundamental equation in nature whose solution describes the wavelike behavior of a particle. The equation cannot be derived from a more fundamental law.
Its validity is based on its ability to predict any known natural phenomena. The solution
requires as input, the potential energy function, V(x,y,z,t), of the electron and the
boundary and initial conditions. The PE function, V(x,y,z,t) describes the interaction of
the particle with its environment. Time independent Schrödinger equation describes the
wave behavior of a particle under steady state conditions, i.e. when the PE is time
independent, V(x,y,z). If E is the total energy, S2 = (d2/dx2+d2/dx2+d2/dx2),me is the
electron mass and ψ is the wavefunction of the electron then S2ψ + (2 me/h2)(E−V)ψ =
0. The solution of the time independent Schrödinger equation, gives the wavefunction
ψ(x,y,z) of the electron and its energy E. The wavefunction,ψ(x,y,z) has the interpretation
that |ψ(x,y,z)|2 is the probability of finding the electron per unit volume at point x,y,z.
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Screw dislocation occurs when one portion of a perfect crystal is twisted or skewed with
respect to another portion on one side of a line only.
A
C
D
A screw dislocation
involves shearing one
portion of a perfect
crystal with respect to
another portion on one
side of a line (AB).
Dislocation line
Secondary bond is a weak bond, typically less than 0.1 eV/atom, which is due to dipole-dipole
interactions between the atoms or molecules.
Seebeck effect is the development of a built-in potential difference across a material as a result
of a temperature gradient. If dV is the built-in potential across a temperature difference
dT, then the Seebeck coefficient S is defined by S = dV/dt . It gauges the magnitude of
the Seebeck effect. Only the net Seebeck voltage difference between different metals can
be measured. The principle of the thermocouple is based on the Seebeck effect.
Selection rules determine what values of l and ml are allowed for transitions involving the
emission and absorption of electromagnetic radiation, i.e. photons. In summary, ∆l =
±1 and ∆ml = 0, ±1. The spin of the electron, ms, remains unchanged. The transition of
the electron within an atom from one state, ψ(n,l,ml,ms), to another, ψ(n′, l′, ml′, ms′),
due to collisions with other atoms or electrons does not necessarily obey the selection
rules.
Self-assembly is a process in which atoms and molecules arrange themselves into ordered (i.e.,
organized) structures driven by thermodynamic considerations. The term self-assembly
is used for describing various processes. It often refers to a nucleation phase for
adsorbed species on a surface forming the basis for a subsequent growth process
defined by the underlying pattern. The final pattern depends on interactions between the
species themselves, and between the species and the surface. Self-assembly can also
occur on vicinal surfaces, (i.e., those formed by cleavage of a single-crystal structure at
a small angle to a high-index crystal plane). Such surfaces are comprised of an array of
terraces and steps that can provide favorable nucleation sites suitable for forming
quantum wires. In heavily lattice-mismatched epitaxial growth, after a critical amount of
material is deposited (typically on the scale of a monlayer), subsequent deposition results
in three-dimensional island formation (typically with dimensions on the order of tens of
nanometers, constituting quantum dots). The morphology of these dots depends on the
thermodynamics and kinetics of their formation, as well as on their growth by the
coarsening process. This, in turn, determines their electronic properties. Typical
examples of such strained systems are InAs/GaAs and GeSi/Si. Self-assembled
nanocrystals can also be prepared by controlled precipitation from solution. [H.R.]
Semiconductor is a nonmetallic element (e.g. Si or Ge) that contains both electrons and holes
as charge carriers in contrast to an enormous number of electrons only as in metals. A
hole is essentially a "half-broken" covalent bond which has a missing electron and
therefore behaves effectively as if positively charged. Under the action of an applied field
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
115
the hole can move by accepting an electron from a neighboring bond thereby passing on
the "hole". Electron and hole concentrations in a semiconductor are generally many
orders of magnitude less than those in metals thus leading to much smaller
conductivities.
Semiconductor laser is a solid state laser device that may have various structures to form an
optical resonator and to provide a lasing output at a particular wavelength under forward
bias.
A semiconductor laser (Courtesy of SDL, San Jose, California)
Separate absorption and multiplication (SAM) avalanche photodiode (APD) is
typically a heterostructure, e.g. InGaAs-InP, with different bandgap materials to separate
absorption and multiplication (SAM). InP has a wider bandgap than InGaAs and the p
and n type doping of InP is indicated by capital letters, P and N. The main depletion layer
is between P+-InP and N-InP layers and it is within the N-InP. This is where the field is
greatest and therefore it is in this N-InP layer where avalanche multiplication takes place.
With sufficient reverse bias the depletion layer in the n-InGaAs reaches through to the
N-InP layer. The field in the depletion layer in n-InGaAs is not as great as that in N-InP.
Although the long wavelength photons are incident onto the InP side, they are not
absorbed by InP since the photon energy is less than the bandgap energy of InP (Eg =
1.35 eV). Photons pass through the InP layer and become absorbed in the n-InGaAs
layers. The field in the n-InGaAs layer drifts the holes to the multiplication region where
impact ionization multiplies the carriers. The real device is more complicated than this
simple description. Photogenerated holes drifting from n-InGaAs to N-InP become
trapped at the interface because there is a sharp increase in the bandgap and a sharp
change ∆Ev in Ev (valence band edge) between the two semiconductors and holes
cannot easily surmount the potential energy barrier ∆Ev. This problem is overcome by
using thin layers of n-type InGaAsP with intermediate bandgaps to provide a graded
transition from InGaAs to InP. Effectively ∆Ev has been broken up into two steps. The
hole has sufficient energy to overcome the first step and enter the InGaAsP layer. It
drifts and accelerates in the InGaAsP layer to gain sufficient energy to surmount the
second step. These devices are called separate absorption, grading and multiplication
(SAGM) APDs. Both the InP layers are grown epitaxially on an InP substrate. The
substrate itself is not used directly to make the P-N junction to prevent crystal defects
(for example, dislocations) in the substrate appearing in the multiplication region and
hence deteriorating the device performance.
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Vr
Iph
Electrode
InP
R
InGaAs
InP
e–
h
h+
P+
(x)
Avalanche
region
N
n
n+
Absorption
region
Vout
Simplified schematic
diagram of a separate
absorption and
multiplication (SAM)
APD using a
heterostructure based
on InGaAs-InP. P and
N refer to p and n -type
wider-bandgap
semiconductor.
x
Shape anisotropy is the anisotropy in magnetic properties associated with the shape of the
ferromagnetic (or ferrimagnetic)substance. A crystal rod that is thin and long prefers to
have its magnetization, M, along the length (long axis) of the rod because this direction
of magnetization creates less external magnetic fields and leads to less external
magnetostatic energy compared with the case when M is along the width (short axis)
of the rod. Reversing the magnetization involves rotating M through the width of the rod
where the external magnetic field and hence magnetostatic energy are large and require
large substantial work. It is therefore difficult to rotate magnetization around from the
long axis to the short axis. A spherical magnetic particle has no shape anisotropy and the
preferred magnetization depends on the magnetocrystalline anisotropy.
Shockley diode equation relates the diode current to the diode voltage through I =
Io[exp(eV/kT) −1]. It is based on the injection and diffusion of injected minority
carriers by the application of a forward bias.
Short diode is a pn junction in which the neutral regions are shorter than the minority
carrier diffusion lengths.
Shot noise is the fluctuations in the current passing through a pn junction (or a Schottky
diode) as a consequence of the fluctuations in the number of carriers injected across the
potential energy barrier. In general it refers to fluctuations in the current through any
device due fluctuations in the emitted (or injected) carriers and arises from the discrete
nature of electronic charge. Stated differently, shot noise arises because of the discrete
nature of electrons and their random arrival time. Each time an electron arrives at an
electrode, there is a discrete charge of -e in the collected charge. It is analogous to
randomly dropping ball bearings on a drum. The balls are discrete (each the same mass)
but they arrive at random times, like shots, and the sound they make is called shot noise.
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If the current were a continuous flow of "gaseous charge" without any fluctuations then
the shot noise would be zero.
Signal to noise ratio (SNR, S/N) in the photodetector is defined as the ratio of the power in the
photogenerated current to the noise power (power in the random fluctuations) in the
detector. When the photodetector is connected to a receiving circuit, the noise power
must include that generated in the circuit as a whole:
Signal Power
SNR =
Noise Power
Silane SiH4 is a colorless, flammable and pyrophoric gas used as a silicon source in epitaxial
deposition, for low-temperature silicon dioxide chemical vapor deposition (CVD), and
for silicon nitride CVD. [H.R.]
Silica glass or fused silica glass is the non-crystalline, or amorphous, form of SiO2. It is
similar to melt silica but, due to a very high viscosity at room temperature, behaves like a
solid (glass). The crystalline form is called quartz.
Silicides are materials that result from the chemical reaction between silicon or polysilicon
with a metal. Examples of important silicides are titanium and cobalt disilicides.
Although polysilicon is well-suited to self-aligned masking technology in
microelectronics, even when highly doped it has a significant resistivity (greater than
~300 µΩ cm). Thus, with the trend to finer lines in semiconductor fabrication, this
results in a large resistive contribution to the RC time constant for the lines, providing
significant signal delay to active devices. Resistivities of refractory metal silicides, such
as cobalt and titanium silicides, can be as low as ~20 µΩ cm, and hence are suitable for
implementing much finer lines than in polysilicon, such as for the 0.1 µm process
implementation. In addition, the resistivities of these silicides can be sufficiently low as to
consider their use for interconnect technology, resulting in an overall simplification of the
integrated circuit processing technology. [H.R.]
Silicon dioxide (SiO2) is also called quartz and glass. It can be formed using thermal
oxidation of silicon. It is often used as a passivation, masking, or insulating layer.
[H.R.]
Silicon nitride (Si3N4) is typically used as a passivation, masking, or insulating layer. [H.R.]
Silicon tetrachloride (SiCl4) is a colorless, corrosive, nonflammable liquid that forms
hydrogen chloride when combined with water. It is used for epitaxial deposition of
silicon and for the formation of silicon dioxide by high-temperature chemical vapor
deposition (CVD). It is also called tetrachlorosilane. It will react to any contact with
moisture to form hydrochloric acid. [H.R.]
Silicon tetrafluoride (SiF4) is a colorless, corrosive, gas used in its pure state and in oxygen
mixtures to etch silicides, silicon, and polysilicon films. Silicon tetrafluoride
dissociates in the presence of an RF field to produce reactive fluoride ions which react
with and etch silicon films. [H.R.]
Single Mode Step Index Fiber is a step index fiber that allows only the fundamental mode
to propagate at the wavelength of interest. To allow the fundamental mode to propagate,
the fiber normally has a thing core (e.g. 5-10 µm) and a very small refractive index
different between the core and cladding (0.2-0.3%).
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Skin effect is an electromagnetic phenomenon that restricts the ac current at high frequencies to
flow near the surface of a conductor to reduce the energy stored in the magnetic field.
Slurry is a liquid carrier with a suspended abrasive component (usually aluminum oxide or
silica) that is used to mechanically lap, polish or grind a semiconductor surface. [H.R.]
Small Scale Integration (SSI) is a semiconductor fabrication technology that can create device
densities of between 2 and 100 devices on each individual die. See also Large Scale
Integration (LSI) and Very Large Scale Integration (VLSI). [H.R.]
Small signal equivalent circuit of a transistor replaces the transistor with an equivalent
circuit that consists of resistances, capacitances and dependent sources (current or
voltage). The equivalent circuit represents the transistor behavior under small signal ac
conditions. The batteries are replaced with short circuits (or their internal resistances).
Small signals imply small variations about dc values.
Snell’s law relates the angles of incidence and refraction to the refractive indices of the media.
Suppose that light is traveling in a medium with index n1 is incident on a medium of
index n2, and if the angles of incidence and refraction (transmission) are θi and θt, then
according to Snell’s law, n1sinθi = n2sinθt. See refraction.
Sodium hydroxide (NaOH) is a caustic base used as an etchant for polysilicon and silicon
nitride. [H.R.]
Soft magnetic materials characteristically have high saturation magnetizations (Bsat) but
low saturation magnetizing fields (Hsat) and low coercivities (Hc) so that they can be
magnetized and demagnetized easily. They have tall and narrow B-H hysteresis loops.
Solid solution is a crystalline material that is a homogeneous mixture of two or more
chemical species. The mixing occurs at the atomic scale as in mixing alcohol and water.
Solid solutions can be substitutional (as in Cu-Ni) or interstitial (for example C in Fe).
Solid solution is a homogeneous crystalline phase which contains two or more chemical
components.
(a) Disordered Substitutional
Solid Solution. Example: CuNi alloys ({100} planes).
(b) Ordered Substitutional
Solid Solution. Example:
Cu-Zn alloy of composition
50%Cu-50%Zn. ({110}
planes).
(c) Interstitial Solid
Solution. Example: Small
number of C atoms in FCC
Fe (austenite). ({100}
planes)
Solid solutions can be disordered substitutional, ordered substitutional and
interstitial substitutional. There is only one phase within the alloy which has the
same composition, structure and properties everywhere.
Solute is the minor chemical component of a solution; that component which is usually added in
small amounts to a solvent to form a solution.
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Solvent is the major chemical component of a solution.
Space charge limited current (SCLC) through an insulator occurs when the carrier
concentration that is injected from the electrodes exceeds the thermal equilibrium
concentration of carriers intrinsic to the insulator. The current is limited by the space
charge of the injected charge carriers which controls the electric field and hence the rate
of charge flow, the current, in the insulator. Characteristically the current density (J) vs.
electric field (E) behavior exhibits volume dependence, e.g. in the absence of traps, J =
(9/8)εoεrµ E 2 / d where d is the thickness of the sample, µ is the drift mobility of the
injected carriers and εoεr is the permittivity of the medium.
Spectrum of a optical signal is generally understood to be the “relative optical power” vs.
frequency distribution that constitutes the optical light signal. It represents all the
necessary frequencies each with the correct optical power level that is needed to
constitute the signal. The relative optical power vs. frequency spectrum is represented in
such a way that its integration over all the frequencies represents the total optical power
of the signal. Thus, “relative optical power” means optical power per unit frequency.
The spectrum can also be represented in terms of wavelength. The necessary phase
information is typically not included in spectrum discussions.
Spherical wave is described by a traveling field that emerges out from a point electromagnetic
source (EM) source and whose amplitude decays with distance r from the source. At any
point r from the source, the field at time t is given by
A
E = cos(ωt − kr )
r
where A is a constant, ω is the angular frequency and k is the propagation constant.
Spin of an electron, S, is its intrinsic angular momentum (analogous to the spin of Earth
around its own axis) which is space quantized to have two possibilities. The magnitude
of the electron's spin is constant, h √3 / 2, but its component along a magnetic field in
the z-direction is msh, where ms is the spin magnetic quantum number, +1/2 or −1/2
Spontaneous emission is the phenomenon by which a photon is emitted when an electron in a
high energy state, ψ(n,l,ml,ms) with an energy E2, spontaneously oscillates down to a
lower energy state, ψ(n',l',ml',ms') with energy E1 that is not occupied. The photon
energy, hυ = (E2−E1). Since the emitted photon has an angular momentum, the
orbital quantum number, l, of the electron must change, i.e. ∆l = l'− l = ±1.
Sputter etch refers to the use of ion bombardment to remove a film from the surface a wafer.
[H.R.]
Sputtering is a technique for depositing a metal layer unto a wafer by bombarding a target
material (such as aluminum or gold) with an argon plasma. [H.R.]
SRD is an automated wafer cleaning tool. The name derives from its functions; Spin, Rinse and
Dry. [H.R.]
State function is any property, e.g the internal energy U of a system that depends on the state
of the system, P,V,T and not on how that state was reached, that is the path to reach that
state. Thus U = U(P,V,T) and in a cyclic change which brings the system back to its
original state ∫ dU = 0.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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State is a possible wavefunction for the electron that defines its spatial (orbital) and spin
properties e.g. ψ(n,l,ml,ms) is a state of the electron. From the Schrödinger equation,
each state corresponds to a certain electron energy E. We thus speak of a state with
energy E as state of energy E, or even an energy state. Generally there may be more than
one state ψ, with the same energy E.
Stefan's Law is a phenomenoligical description of the energy radiated per unit second from a
surface. When a surface is heated to a temperature T then it radiates net energy at a rate
given by Pradiated = εσA(T4 - To4) where σ is Stefan's constant (= 5.67 × 10−8 W m-2 K-4),
ε is the emissivity of the surface, A is the surface area and To is the ambient temperature.
Step index fiber has a central core of constant refractive index and a surrounding layer of
cladding of smaller refractive index. There is a step decrease in the refractive index from
the core to the cladding.
Stepper is short for stepper and repeater which is an optical based system that projects the
pattern on a reticle (mask) onto a small area on the surface of the wafer. This projected
image forms the processing pattern for one chip. The wafer is stepped in the x and y
directions to repeat the imaging of other chips.
Stimulated emission is the phenomenon by which an incoming photon of energy hυ = E2−E1
interacts with an electron in a high energy state, ψ(n, l, ml , ms), at E2, and induces it to
oscillate down to a lower energy state, ψ(n',l',ml',ms'), at E1, that is not occupied. The
photon that is emitted by stimulation has the same energy and phase as the incoming
photon and, further, it is in the same direction. Consequently, stimulated emission results
in two coherent photons, with the same energy, traveling in the same direction. The
stimulated emission process must obey the selection rule just as spontaneous
emission; ∆l = l' − l = ±1.
Stochiometric compounds are those which have an integer ratio of atoms as in CaF2 where
two fluorine atoms bond with one Ca atom.
Strain is a measure of the deformation a material exhibits under an applied stress. It is
expressed in normalized units. Under an applied tensile stress, strain (ε) is the change in
the length per unit original length, ∆L/Lo. When a shear stress is applied, the resulting
deformation involves a shear angle. Shear strain is defined as the tangent of the shear
angle that is developed by the application of the shearing force.
Stress is force per unit area, F / A. When the applied force is perpendicular to the area it leads
either to a tensile or compressive stress, σ = F / A. If the applied force is tangential to the
area then it leads to a shear stress, τ = F / A.
Substrate is a single mechanical support which carries active and passive devices. For example
in the integrated circuit technology, typically, many integrated circuits are fabricated on
a single silicon crystal wafer which serves as the substrate.
Sulfur hexafluoride (SF6) is a colorless, odorless, nontoxic, nonflammable, gas used for dry
plasma etching prior to chemical vapor deposition (CVD). These processes include
oxide etching, nitride etching, and wafer cleaning. SF6, is itself inert, but disassociates in
the presence of an RF field to form reactive flouride ions, which are then used to etch
tungsten and tungsten silicide films. [H.R.]
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
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Sulfuric acid (H2SO4) is a poisonous, corrosive liquid used to remove photoresist and clean
wafers. Concentrated sulphuric acid can cause severe burns. [H.R.]
Superconductivity is a phenomenon in which a substance loses all resistance to current flow
(acquires zero resistivity) and also exhibits Meissner effect (becomes a perfect
diamagnet).
Superconductors see Type 1 and Type 2 Superconductors (under Type).
Surface density of states refers to the number of surface states at a given energy, per unit
energy range, per unit volume of the material. [H.R.]
Surface emitting LEDs (SLED) has its emitted radiation emerging from an area in the plane
of the recombination layer .The simplest method of coupling the radiation from a surface
emitting LED into an optical fiber is to etch a well in the planar LED structure and lower
the fiber into the well as close as possible to the active region where emission occurs.
This type of structure is called a Burrus type device (after its originator). An epoxy resin
is used to bond the fiber and provide refractive index matching between the glass fiber
and the LED material to capture as much of the light rays as possible. Note that in the
double heterostructure LED used in this way, the photons emitted from the active region
(e.g. p-GaAs) do not get absorbed by the neighboring layer (AlGaAs) which has a wider
bandgap. Another method is to use a truncated spherical lens (a microlens) with a high
refractive index (n = 1.9 - 2) to focus the light into the fiber. The lens is bonded to the
LED with a refractive index matching cement and, in addition, the fiber can be bonded to
the lens with a similar cement.
Fiber (multimode)
Fiber
Epoxy resin
Electrode
Microlens (Ti2O3:SiO2 glass)
Etched well
Double heterostructure
SiO2 (insulator)
Electrode
Light is coupled from a surface
A microlens focuses diverging light from a
emitting LED into a multimode fiber
surface emitting LED into a multimode optical
using an index matching epoxy. The
fiber.
fiber is bonded to the LED structure.
Surface states are electronic states originating from surface-related phenomena - these include,
surface relaxation and reconstruction processes, as well as states formed as a result of
chemical processes on surfaces. The latter includes surface oxidation, and the
interaction of surfaces with adsorbed species. The surface state related energy bands
would not exist in the absence of these phenomena, resulting in the only a bulk band
structure. It should be noted that a so-called ideal surface, in which atoms assume their
bulk relationships, can still result in a surface band structure owing to the severing of
bonds at the surface resulting in a redistribution of charge, distinct from that of the bulk.
The occupation of surface bands is responsible for a surface charge, and this, in turn,
results in a near surface field. The insensitivity of Schottky barrier heights to the metal
work function, for certain combinations of metals deposited on semiconductor surfaces,
has been attributed to a pinning of the Fermi energy within such surface states. [H.R.]
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
122
Surface tension γ represents the energy required to increase the surface of a body by some unit
area keeping the total number of atoms the same. An atom on the surface of a liquid or a
solid has less bonds than an atom within the bulk of the substance. Thus, if we were to
increase the surface area of the body, e.g. changing it from a sphere to a cube which has
higher surface area, we need to work because we would have less bonds per atom
(effectively we have broken bonds). If energy dE is required to increase the surface area
by dA then γ = dE/dA. A hypothetical line on the surface of a liquid or a body
experiences a force per unit length that is equal in magnitude to the surface tension.
Surface tension in crystal depends on the crystal structure and the surface plane
(because the energy difference per atom on the surface and within the bulk depends on
the arrangements of atoms on the crystal surface and in the crystal bulk).
Surface tracking is an external dielectric breakdown that occurs over the surface of the
insulation.
Surroundings is the that part of the universe with which the system interacts. In other words,
it is that part of the universe with which the system is in contact and with which the
system can exchange energy through work and heat. Sometime the term environment is
used for surroundings.
System is that part of the world separated from the rest by definite boundaries. The world
outside is called the surroundings. If the boundaries do not allow any changes in the
system due to changes in the surroundings then the system is isolated.
Temperature coefficient of resistivity (TCR) (α0) is defined as the fractional change in the
electrical resistivity of a material per unit increase in the temperature at some reference
temperature T0,
1  dρ 
α0 =
ρ 0  dT T = T0
where ρ0 is the restivity and dρ/dT is the gradient, both at the reference temperature T0. If
ρ of a material follows a linear dependence on the absolute temperature T of the form ρ
= AT + B, where A and B are constants, then ρ(T) is given by
ρ(T) = ρ0[1 + α0(T − T0)]
Note that α0 depends on the reference temperature T0. If α1 is TCR at the reference
temperature T1, then α1 and a0 are related by
α0
α1 =
1 + α 0 (T1 − T0 )
Ternary (III-V) alloys have three different elements from the III and V groups. For example
GaAs and InAs are III-V compounds individually, but they can be alloyed to produce a
ternary alloy, In1-xGaxAs. There are as many group III elements as there are group V
elements.
Ternary semiconducting alloy has three different elements in its composition, for example,
AlxGa1-xAs has three elements Al, Ga, As. This AlxGa1-xAs alloy is composed of III (Al
and Ga) and V (As) groups only and the molar amounts from each group is the same;
and hence it is a III-V ternary alloy. The bandgap Eg of the ternary alloys AlxGa1-xAs
follows the empirical expression,
Eg(eV) = 1.424 + 1.266x + 0.266x2.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
Eg (eV)
Quaternary alloys
with indirect bandgap
2.6
2.4
Direct bandgap
Indirect bandgap
GaP
2.2
2
Quaternary alloys
with direct bandgap
1.8
1.6
1.4
GaAs
InP
1.2
1
0.8
0.6
In1-xGaxAs
In0.535Ga0.465As
X
0.4
InAs
0.2
0.54 0.55 0.56 0.57 0.58 0.59 0.6
Lattice constant, a (nm)
0.61 0.62
123
Bandgap energy Eg and lattice
constant a for various III-V
alloys of GaP, GaAs, InP and
InAs. A line represents a
ternary alloy formed with
compounds from the end
points of the line. Solid lines
are for direct bandgap alloys
whereas dashed lines for
indirect bandgap alloys.
Regions between lines
represent quaternary alloys.
The line from X to InP
represents quaternary alloys
In1-xGaxAs1-yPy made from
In0.535Ga0.465As and InP
which are lattice matched to
InP.
Tetrafluoromethane (halocarbon 14) is a colorless, odorless, nonflammable, gas combined
with oxygen for dry plasma etching of oxide, nitride, polysilicon and some silicides
prior to chemical vapor deposition (CVD). [H.R.]
Tetrahedron is a regular solid geometry that has 4 identical equilateral triangular faces, 6 sides
of equal length and 4 equivalent vertices.
Thermal breakdown is a breakdown process that involves thermal runaway which leads to a
runaway current or discharge between the electrodes. If the heat generated by dielectric
loss, due to εr'', or Joule heating, due to finite σ, cannot be removed sufficiently rapidly
then the temperature of the dielectric rises which increases the conductivity and the
dielectric loss. The increases in εr '' and σ lead to more heat generation and a further
rise in the temperature so that a thermal runaway ensues followed by either a large
shorting current or local thermal decomposition of the insulation accompanied by a
partial discharge in this region.
Thermal conductivity (κ) is a property of a material that quantifies the ease with which heat
flows along a material from higher to lower temperature regions. Since heat flow is due a
temperature gradient, κ is the rate of heat flow across a unit area per unit temperature
gradient.
Thermal equilibrium carrier concentrations are those electron and hole concentrations that
are solely determined by the statistics of the carriers and the density of states in the
band. Thermal equilibrium concentration obey the mass action law, np = ni2.
Thermal generation current is the current that flows in a reverse biased pn junction as a
result of the thermal generation of electron hole pairs in the depletion layer which
become separated and swept across by the built-in field.
Thermal oxidation is the process of creating silicon dioxide when silicon reacts with oxygen
at or near 1000°C. [H.R.]
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
124
Thermal resistance (θ ) is a measure of the difficulty with which heat conduction takes place
along a sample. It is defined as the temperature drop per unit heat flow , θ = ∆T/Q’. It
depends on both the material and its geometry. If the heat losses from the surfaces are
negligible, θ = L/κA where L is the length of the sample (along heat flow) and A is the
cross sectional area.
Thermal strain is the fractional change in the length of a body due to a change in the
temperature when the body is not constrained (not prevented from thermal expansion or
contraction). If l is the thermal expansion coefficient, Lo is the original length of the body
and ∆L is the change in the length, then the thermal strain εth = ∆L/Lo = l ∆T where ∆T is
the temperature change.
Thermal stress is the stress induced in a body as a result of the body being unable to thermally
expand or contract due to a temperature change by virtue of being constrained. The
change in the temperature does not lead to the normal free expansion or contraction and
there is a mechanical strain induced in the body.
Thermal velocity (vth) of an electron in the conduction band is its mean (or effective) speed
in the semiconductor as it moves around in the crystal. For a nondegenerate
semiconductor, it can simply be obtained from 1/2me*vth2 = 3/2kT.
Thermalization is a process in which an excited electron in the conduction band (CB) loses
the excess energy as it is collides with lattice vibrations, and falls close to Ec, that is, until
its average energy is (3/2)kT above Ec.
Ec+
CB
Large h
h
Thermalization
Ec
Eg
Eg
Ev
3kT
2
Optical absorption generates electron hole
pairs. Energetic electrons must loose their
excess energy to lattice vibrations until
their average energy is 3/2kT in the CB.
(CB = Conduction Band, VB = Valence
Band, Eg = Bandgap energy)
VB
Thermally activated conductivity means that the conductivity increases in an exponential
fashion with temperature as in σ = σoexp(Eσ/kT) where Eσ is the activation energy.
Thermionic emission is the emission of electrons from the surface of a heated metal. When a
metal is heated, the proportion of electrons having grater energy than the work function
(Φ) plus Fermi energy (EF) increase due to the tailing of the Fermi-Dirac function to
higher energies. Consequently, some of the electrons can be emitted over this potential
barrier into vacuum and become free. The emission probability depends exponentially on
the temperature. If the emitted electrons are collected and the metal replenished with
electrons, as in the vacuum tube, then the thermionic current density is described by the
Richardson-Dushman equation
Thompson effect is the phenomenon of heat generation or absorption, other than joule heating
(ρJ2), that occurs when a current, J, is passed through a conductor that has a temperature
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
125
gradient along it. It should be emphasized that the heat, ∆QTh, generated or absorbed, is
that other than the joule heating ρJ2, and it is due to temperature difference ∆T across the
conductor. The heat absorbed or released, ∆QTh, due to the presence of a current density,
J, and the temperature gradient, ∆T, is called the Thompson heat and is proportional to
both J and ∆T. The Thompson coefficient, µT, gauges the magnitude of the Thompson
heat, ∆QTh via ∆QTh=µTJ∆T. Thompson effect occurs in a homogeneous material and not
across a junction of two different material as for the Peltier effect.
Threshold current Ith of a laser diode is the minimum current that is needed for achieving a
lasing emission from the device. At this current value, the optical gain in the active
region is the threshold gain. Lasing radiation is only obtained when the optical gain in
the medium can overcome the photon losses from the cavity, which requires the diode
current I to exceed a threshold value Ith. Below Ith, the light from the device is due to
spontaneous emission and not stimulated emission. The light output is then
composed of incoherent photons that are emitted randomly and the device behaves like
an LED. Threshold current is strongly temperature dependent.
Optical Power
Optical Power
LED
Optical Power
Laser
Optical Power
Laser
Stimulated
emission
Spontaneous
emission
I
0
Ith
Typical output optical power vs. diode current (I) characteristics and the
corresponding output spectrum of a laser diode.
Threshold gain is the critical optical gain gth that an active medium in an optical resonator must
have to achieve steady state (self-sustained) lasing radiation as output from this
resonator; this threshold gain just overcomes the losses in the active medium and also the
losses from the optical cavity and the reflectors. When the optical gain of the medium is
equal to the threshold gain gth the device becomes a self-sustained laser oscillator. If γ is
the loss coefficient of the medium, L is the length of the optical cavity, R1 and R2 are the
reflectances of the end-reflectors of the cavity, then the optical gain of the medium for
lasing oscillations (i.e. for continuous wave lasing emission from the device),
1  1 
gth = γ +
ln

2 L  R1R2 
Threshold population inversion is the is that population inversion N2 − N1 that
corresponds to the threshold optical gain (gth).
Threshold voltage is the gate voltage needed to establish a conducting channel between the
source and drain of an enhancement MOST.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
126
Torr is a unit for the measurement of pressure exerted by 1 mm of mercury, equal to 1/760th of
standard atmospheric pressure. [H.R.]
Total Internal Reflection (TIR) is the total reflection of a wave traveling in a medium when it
is incident at a boundary with another medium of lower refractive index. The angle of
incidence must be greater than the critical angle (θc).
Transconductance, or mutual transconductance g, is defined as the change in the output
current of an active device per unit change in the input voltage when the output voltage is
kept constant. Consider a metal-oxide-semiconductor (MOS) FET or a JFET. Suppose
iD is the output current, vDS is the voltage between the output terminals, and vGS is the
voltage between the input terminals, then
 ∂iD 
g=
∂vGS 
v DS = constant
D
iD
G
S
Input vGS
vDS Output
Definition of transconductance
based on a common source
MOSFET device
Transducer is a device that converts electrical energy into another form of usable energy or vice
versa, e.g. piezoelectric transducers convert electrical energy to mechanical energy and
vice versa.
Transistor is a three terminal solid state device in which a current flowing between two
electrodes is controlled by the voltage between the third and one of the other terminals or
by a current flowing into the third terminal.
Transmission coefficient is the ratio of the amplitude of the transmitted wave to that of the
incident wave when the incident wave traveling in a medium meets a boundary with a
different medium (different refractive index).
Transmittance is the fraction of transmitted intensity when a wave traveling in a medium is
incident at boundary with a different medium (different refractive index).
Trichlorosilane (TCS) or SiHCl3 is a flammable corrosive liquid used as a silicon source in
epitaxial processes and in the production of polycrystalline silicon. Trichlorosilane is a
chlorine-containing material and will react to any contact with moisture to form
hydrochloric acid. [H.R.]
Tungsten hexafluoride WF6 is a toxic, corrosive nonflammable liquid used in tungsten silicide
chemical vapor deposition (CVD) to create a conductive film. [H.R.]
Tunneling of an electron is its penetration through a potential energy barrier by virtue of its
wave-like behavior. In classical mechanics, if the energy of the electron, E, is less than the
PE barrier Vo, then it is impossible for the electron to cross the barrier. In quantum
mechanics there is a distinct probability that the electron will make it through the barrier
to appear on the other side. The probability of tunneling depends very strongly on the
height of the PE barrier and its width.
Type I superconductors have a single critical field (Bc) above which the superconducting
behavior is totally lost.
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Type II superconductors have a lower (Bc1) and an upper (Bc2) critical field. Below Bc1 the
substance is in the superconducting phase with Meissner effect; all magnetic flux is
excluded from the interior. Between Bc1 and Bc2 magnetic flux lines pierce through local
filamentary regions of the superconductor which behave normally. Above Bc2, the
superconductor reverts to normal behavior.
Ultraviolet (UV) radiation is an electromagnetic wave with wavelength typically in the range
400 nm − 4 nm, shorter than violet light but longer than X-rays. When the wavelength is
in the 400 − 300 nm range it is called near UV and in the 300-200 nm range it called far
UV. Ultraviolet radiation with a wavelength shorter than 200 nm is known as extreme
or vacuum UV.
Uncertainty principle states that the uncertainty, ∆x, in the position of a particle and the
uncertainty, ∆px, in its momentum in the x-direction obey (∆x)(∆px) > h. This is a
consequence of the wave nature of matter and has nothing to do with the precision of
measurement. If ∆E is the uncertainty in the energy of a particle during a time, ∆t, then
according to the uncertainty principle, (∆E)(∆t) > h. To measure the energy of a particle
without any uncertainty means that we will need an infinitely long time, ∆t → ∞.
Unit cell is the most convenient small cell in the crystal structure that carries the properties of
the crystal. The repetition of the unit cell in three dimensions, generates the whole crystal
structure.
Universe is the system and its surroundings.
V-number or normalized frequency is a dimensionless quantity that is a characteristic of a
dielectric waveguide which determines the nature of propagation of electromagnetic (EM)
waves along the guide. For a step index fiber it is defined by V = (2πa/λ) [n12−n22]1/2
where a is the core radius, λ is the free space wavelength of the radiation to be guided
and n1 and n2 are the refractive indices of the core and cladding respectively.
Vacancy is a point defect in a crystal where a normally occupied lattice site has a missing
atom.
Vacuum level is the energy level where the PE of the electron and the KE of the electron are
both zero. It defines the energy level where the electron is just free from the solid.
Valence band (VB) is a band of energies for the electrons in bonds in a semiconductor. The
valence band is made of all those states (wavefunctions) that constitute the bonding
between the atoms in the crystal. At absolute zero of temperature the valence band is full
of all the bonding electrons of the atoms. When an electron is excited to the conduction
band, then this leaves behind an empty state which is called a hole. It carries positive
charge and behaves as it were a "free" positively charged entity with an effective mass of
mh*. It moves around the VB by having a neighboring electron tunnel into the
unoccupied state.
Valence electrons are those electrons in the outer shell of an atom. As they are the farthest
away from the nucleus they are the first electrons involved in atom-to-atom interactions.
Varshni equation describes the change in the energy bandgap Eg of a semiconductor with
temperature T in terms of
AT 2
E g = E go +
B+T
where Ego is the bandgap at T = 0 K, and A and B are material-specific constants . For
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
128
example, for GaAs, Ego = 1.519 eV, A = 5.405×10-4 eV K-1, B = 204 K, so that at T = 300
K, Eg = 1.42 eV. We can find the temperature coefficient of bandgap Eg′ by
differentiating the Varshni equation,
dE
AT (T + 2 B)
E g′ = g = −
(B + T )2
dT
which for GaAs, using the values above, gives Eg′ = −0.45 meV K-1.
Velocity v is the rate of change of an object's position x, that is v = dx/dt. The greater the rate of
change, the faster the object is moving. An object moving a constant velocity experiences
no net force in any direction.
Very Large Scale Integration (VLSI) is the integration of 106-107 devices into a single Si
chip to implement very complex circuits (for example, microprocessor chips, memories
etc.)
Vibrating Sample Magnetometer (VSM) is an apparatus that measures the magnetic
properties of materials. When a material is placed within a uniform magnetic field and
made to undergo sinusoidal motion (i.e. mechanically vibrated), there is some magnetic
flux change. This induces a voltage in the pick-up coils, which is proportional to the
magnetic moment of the sample. [C.T.]
Viscosity is a measure of the resistance of a material against flow under an applied shear stress.
It is the reciprocal of the fluidity of a material. If under an applied shear stress, the
substance tends to flow easily, then it is said to be fluid, or exhibit little viscosity. When a
shear stress τ = F/A is applied to a liquid-like material, atomic layers flow with respect to
each other resulting in permanent deformation which we call viscous flow. Within the
material, the atomic layers move with different velocities with respect to the bottom layer,
which we take as reference. There is therefore a velocity gradient in the material. In time
∆t, the permanent displacement is ∆x = v∆t where v is the flow velocity. Viscosity is then
defined as shear stress required to generate a unity velocity gradient, i.e.
dv
τ =η
dy
Viscosity is measured in Pa s (Pascal × second). If an applied shear stress generates a
uniform flow velocity gradient, the fluid is called Newtonian; otherwise it is called nonNewtonian. Viscosity of glasses exhibits a strong temperature dependence, typically
following an Arrhenius behavior, η ∝ exp(∆Hη/RT) where ∆Hη is the activation energy
(in J mol-1), R is the gas constant and T is the temperature.
Material
Water
Viscosity (Pa s) 10-3
Olive oil
10-1
Borosilicate glass
103 at 1245 °C, 107 at 820 °C, 1013 at 435 °C.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
Surface area, A
Shearing Force, F
y
x=v t
y
Liquid-like
material
F
Time, t = t
Flow
Velocity, v
129
Under a shear stress F/A,
the atomic layers move
with different velocities
with respect to the
bottom layer. There is
therefore a velocity
gradient in the material.
In time t, the permanent
displacement is x = v t
where v is the flow
velocity.
Wafer is a semiconductor substrate, usually about 1/40" thick and anywhere from 75 mm (3")
to 300 mm (12") in diameter. During manufacturing, a wafer may contain several
hundred devices. Each individual device on a wafer is called a die. [H.R.]
Water Reverse Osmosis/De-ionized (RO/DI) Water is water which has had organic and
inorganic contaminants removed by reverse osmosis, deionization and mechancial
filtration. The goal of RO/DI water production is pure H2O, with all of the solids,
minerals and contaminants removed. Since H2O by itself does not conduct electricity, the
cleanliness of RO/DI Water is measured by its resistivity. The fewer contaminants, the
higher the resistivity. [H.R.]
Wave equation is a general partial differential equation in classical physics, of the form v2d2u /
dx2 − d2u / dt2 = 0 whose solution describes the space and time dependence of the
displacement, u(x,t), from equilibrium or zero, given the boundary conditions. The
parameter v in the wave equation is the propagation velocity of the wave. In the case of
electromagnetic waves in vacuum, the wave equation describes the variation of the electric
(or magnetic) field E(x,t) with space and time, c2d2E / dx2 − d2E /dt2 = 0 where c is the
speed of light.
Wave is a periodically occurring disturbance, such as the displacements of atoms from
equilibrium positions in a solid carrying sound waves, or a periodic variation in a
measurable quantity, such as the electric field E(x,t) in a medium or space. In a traveling
wave, energy is transferred from one location to another by the oscillations.. For
example, Ey(x,t)=Eyosin(kx−ωt), where k = 2π / λ and w = 2πυ, is a traveling wave in the x
direction. The electric field in the y-direction varies periodically along the x with a period
λ called the wavelength and with time with a period 1 / υ where υ is the frequency. The
wave propagates along the x - direction with a velocity of propagation, c. In a longitudinal
wave, the displacement is in the direction of propagation as in the propagation of a sound
wave, whereas in a transverse wave, the displacement is at right angles to the direction of
propagation as in an electromagnetic wave. Electromagnetic waves are transverse waves
in which the electric and magnetic fields Ey(x,t) and Hz(x,t) are at right angles to each
other and also the direction of propagation, x. A traveling wave in the electric field must
be accompanied by a similar traveling wave in the magnetic field Hz(x,t)=Hzosin(kx - ωt).
Typical wave-like properties are interference and diffraction.
Wave number or propagation constant is defined as 2π/λ. It is the phase shift in the wave over
a distance of unit length.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
130
Wavefront is a surface where all the point have the same phase. A wavefront on a plane wave
is an infinite plane perpendicular to the direction of propagation.
Wavefunction, Ψ(x,y,z,t), is a probability based function that is used to describe the wave-like
properties of a particle. It is obtained by solving the Schrödinger equation which in
turn requires the knowledge of the PE of the particle and the boundary and initial
conditions. |Ψ(x,y,z,t)|2 is the probability per unit volume of finding the electron at (x,y,z)
at time t. Put differently, |Ψ(x,y,z,t)|2dxdydz is the probability of finding the electron in
the small volume dxdydz at (x,y,z) at time t.. Under steady state conditions, the
wavefunction can be separated into space dependent, ψ(x,y,z), and time dependent
components as Ψ(x,y,z,t) = ψ(x,y,z)exp(−jEt/h) where E is the energy of the particle and h
= h/(2π.) The spatial part, ψ(x,y,z) satisfies the time independent Schrödinger equation.
Waveguide condition specifies the condition which an EM wave must satisfy to be
propagated and hence be guided through a waveguide given the V-number of the
waveguide. Each EM wave satisfying the waveguide condition is a mode of the
waveguide as it can be propagated.
Waveguide dispersion, as separate from materials dispersion, is dispersion that arises
because of the wavelength dependence of the V-number which determines the
propagation constant inside the guide. As the radiation fed into the core has a finite range
of wavelengths, ∆λ not equal to 0, the V-number is not constant which leads to
fundamental modes with different wavelengths which propagate at different velocities.
Wavevector is a vector denoted as k that describes the direction of propagation of a wave and
has the magnitude of the wave number, k = 2π/λ where λ is the wavelength.
Wet Bench is a special workstation used when handling acid, base and caustic solutions. Wet
benches incorporate personnel protection guards, spill containment and isolated waste
and treated exhaust systems. [H.R.]
Wire Bonding refers to the attachment of aluminum or gold leads (via thermal compression or
ultrasonic welding) to a die before it is packaged. [H.R.]
Work function, Φ is the minimum energy needed to free an electron from the metal at absolute
zero of temperature. It is the energy separation of the Fermi level from the vacuum
level. Work function, in general, is the energy required to remove an electron from the
solid to the vacuum level.
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
Electron outside
the metal
Electron Energy
Vacuum
Level
7.2 eV
Empty
states
Electron inside
the metal
4.7 eV
EF0
EF0
EB
Full of
electrons
0
131
Typical electron energy band
diagram for a metal (Li). All
the valence electrons are in an
energy band which they only
partially fill. The top of the
band is the vacuum level where
the electron is free from the
solid (potential energy = 0).
EF0 is the Fermi energy at 0 K.
EB is the bottom of the
conduction band. is the work
function.
Work, PV, see PV work.
X-rays are electromagnetic radiation of wavelength typically in the range 10 pm - 1 nm, which is
shorter than the ultraviolet light. X-rays photons have high energies.
Yield is the ratio of the number of functional die to the total number of die produced. [H.R.]
Young's Modulus see Elastic modulus.
Zener breakdown is the enormous increase in the reverse current in a pn junction when the
applied voltage is sufficient to cause the tunneling of electrons from the valence band
in the p-side to the conduction band in the n-side. Zener breakdown occurs in pn
junctions that are heavily doped on both sides so that the depletion layer width is narrow.
Zero-point energy is the minimum energy of a harmonic oscillator, 1/2hω. Even at zero Kelvin,
an oscillator in quantum mechanics will have a finite amount of energy which is its zeropoint energy. Heisenberg’s uncertainty principle does not allow a harmonic oscillator to
have zero energy because that would mean no uncertainty in the momentum and
consequently an infinite uncertainty in space (∆px∆x > h).
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
Physical Constants
c
Speed of light in vacuum
2.9979 × 108 m s-1
h
Planck’s constant
6.6261 × 10-34 J s
h
h = h/2
1.0546 × 10-34 J s
e
Electronic charge
1.60218 × 10-19 C
εo
Absolute permittivity
8.8542 × 10-12 F m-1
kB
Boltzmann’s constant (kB = R/NA)
1.3807 × 10-23 J K-1
kBT/e
Thermal voltage at 300 K
0.02585 V
me
Mass of the electron in free space
9.10939 × 10-31 kg
µo
Absolute permeability
4π × 10-7 H m-1
NA
Avogadro’s number
6.0221×1023 mol-1
R
Gas constant (Nak)
8.31457 J mol-1 K-1
Conversions
1 eV = 1.60218 × 10-19 J
1 Å = 10-10 m = 0.1 nm
132
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
133
PERIODIC TABLE
GROUP
2
1
H
Metals
PERIOD
1.0079
He
Nonmetals
4.0026
3
4
5
6
7
8
9
10
Li
Be
B
C
N
O
F
Ne
6.941
9.012
10.811
12.011
14.007
15.999
18.998
20.180
11
12
13
14
15
16
17
18
Na
Mg
Al
Si
P
S
Cl
Ar
22.99
24.305
26.982
28.086
30.974
32.066
35.453
39.948
d Transition Elements
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
39.098
40.078
44.955
47.88
50.941
51.996
54.938
55.847
58.933
58.69
63.546
65.39
69.723
72.610
74.921
78.960
79.904
83.80
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
85.468
87.620
88.906
91.224
92.906
95.940
(97.907)
101.07
102.906
106.42
107.87
112.41
114.82
118.71
121.75
127.60
126.90
131.29
55
56
57
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
Cs
Ba
La*
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
132.91
137.33
138.91
178.49
180.95
183.85
190.20
192.22
196.97
200.59
204.38
207.20
208.98
(208.99)
(209.99)
(222.02)
87
88
89
104
105
106
186.21
Fr
Ra
Ac**
Unq
Unp
Uns
(223.02)
(226.03)
(227.03)
(261.11)
(262.11)
(262.12)
195.08
34
Gas
Atomic number
Se
Liquid
78.96
Atomic mass (g mol-1)
f Transition Elements
58
59
60
61
62
63
64
65
66
67
68
69
70
71
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
140.12
*Lanthanides
(Rare Earths)
140.91
144.24
(144.92)
150.36
151.97
157.25
158.93
162.50
164.94
167.26
168.93
173.04
174.97
90
91
92
93
94
95
96
97
98
99
100
101
102
103
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
232.04
(231.04)
(238.05)
(237.05)
(244.06)
(247.07)
(247.07)
(242.06)
(252.08)
(257.10)
(258.10)
(259.10)
(260.11)
**Actinides
(243.06)
Useful Information
h
eV
109
1023
106
103
1021
10-3
1
1018
1012
1015
f
Hz
10-6
Visible
400 nm
780 nm
Violet
Red
109
10-9
106
Radio waves
Microwaves
Infrared
UV
X-Rays
Gamma rays
fm
nm
pm
m
mm
km
m
Wavelength ranges and colors as usually specified for LEDs
Color
Blue
Emerald
green
Green
Yellow
Amber
Orange
RedOrange
Red
Deep red
Infrared
λ (nm)
λ < 500
530-564
565-579
580-587
588-594
595-606
607-615
616 - 632
633-700
λ >700
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
134
Some Useful Formulae
Complex Numbers
j = (−1)1/2
j2 = −1
exp(jθ) = cosθ + jsinθ
Z = a + jb = rejθ
r = (a 2 + b 2)1/2
tanθ = b/a
Z* = a − jb = re−jθ
Re(Z) = a
Im(Z) = b
2
Magnitude = | Z |2 = ZZ* = a2 + b2
cosθ =
[
1 jθ
e + e − jθ
2
]
Argument = θ = arctan(b/a)
sin θ =
[
1 jθ
e − e − jθ
2j
]
Trigonometry
sin(π/2 ± θ) = cosθ
sin2θ + cos2θ = 1
sin2θ = 2 sinθ cosθ
cos2θ = 1 − 2sin2θ = 2cos2θ − 1
sin(A + B) = sinAcosB + cosAsinB
cos(A + B) = cosAcosB − sinAsinB
sinA + sinB = 2sin[1/2(A + B)]cos[1/2(A − B)]
cosA + cosB = 2cos[1/2(A + B)]cos[1/2(A − B)]
Expansions
1 2 1 3
x + x +K
2!
3!
n(n − 1) 2 n(n − 1)(n − 3) 3
(1 + x )n = 1 + nx +
x +
x +K
2!
3!
sinx ≈ x
tanx ≈ x
Small x(1 + x)n ≈ 1 + nx
ex = 1 + x +
Small ∆x in x = xo + ∆x,
df
f ( x ) ≈ f ( xo ) + ∆x  
 dx  x o
cosx ≈ 1
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
135
Selected LED semiconductor materials
Optical communication channels are at 850 nm (local network) and at 1.3 and 1.55 µm (long
distance). D = direct, I = Indirect bandgap. DH = Double heterostructure. ηexternal is typical and
may vary substantially depending on the device structure.
Semiconductor
Substrate
D or I
λ (nm)
ηexternal (%) Comment
GaAs
GaAs
D
870 - 900
10
Infrared LEDs
AlxGa1-x As
GaAs
D
640 - 870
5 - 20
Red to IR LEDs. DH
In1-xGaxAsyP1-y
(y ≈ 2.20x, 0 < x < 0.47)
InP
D
1 - 1.6
µm
> 10
LEDs in communications
InGaN alloys
GaN or SiC
Saphire
D
430 - 460
2
Blue LED
500 - 530
3
Green LED
SiC
Si; SiC
I
460 - 470
0.02
Blue LED. Low efficiency
In0.49Alx Ga0.51-x P
GaAs
D
590 - 630
1 - 10
Amber, green red LEDs
GaAs1-yPy (y < 0.45)
GaAs
D
630 - 870
<1
Red - IR
GaAs1-yPy (y > 0.45)
(N or Zn, O doping)
GaP
I
560 - 700
<1
Red, orange, yellow LEDs
GaP (Zn-O)
GaP
I
700
2-3
Red LED
GaP (N)
GaP
I
565
<1
Green LED
(0< x < 0.4)
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
136
Properties of Selected Semiconductors at 300 K
εr (0) and εr (∞) represent the relative permittivity at dc (low frequency) and at optical (high)
frequencies. εr (∞) excludes ionic polarization but includes electronic polarization. Effective
mass related to conductivity (a) is different than that related to the density of states (b).
Property
Ge
Si
GaAs
In0.53Ga0.47As
Density g cm
Eg (eV)
ni (cm-3)
5.33
0.66
2.4×1013
2.33
1.12
1.45×1010
5.32
1.42
1.8×106
6.15
0.75
Nc (cm-3)
1.04×1019
2.8×1019
4.7×1017
5.4×1017
Nv (cm-3)
6×1018
1.02×1019
7×1018
1.2×1019
εr (0); εr (∞)
16
11.9
13.1; 10.6
me*/me
0.26a
1.08b
0.38a
0.56b
1350
0.07a,b
µe (cm2 V-1 s-1)
0.12a
0.56b
0.23a
0.40b
3900
µh (cm2 V-1 s-1)
1900
450
-3
m h*/m e
InP
4.81
1.35
1.2×107
12.5; 9.61
12.5; 9.61
0.40a
0.50b
8500
13800
4600
400
400
150
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
137
Selected Semiconductors
Crystal structure, lattice parameter a, bandgap energy Eg at 300 K, type of bandgap (D = Direct
and I = Indirect), change in Eg per unit temperature change (dEg/dT), bandgap wavelength λg and
refractive index n close to λg. (A = Amorphous, D = Diamond, W= Wurtzite, ZB = Zinc blende)
Semiconductors
Group IV
Ge
Si
a-Si:H
SiC
III-V Compounds
AlAs
AlP
AlSb
GaAs
GaAs 0.88Sb0.12
GaN
GaP
GaSb
In0.53Ga0.47As on InP
In0.58Ga 0.42As 0.9P 0.1 on
InP
In0.72Ga 0.28As 0.62P 0.38 on
InP
InP
InAs
InSb
II-VI Compounds
ZnSe
ZnTe
Crystal a
nm
D
D
0.5658
0.5431
A
ZB
ZB
ZB
ZB
0.5661
0.5451
0.6135
0.5653
ZB
Eg
eV
Typ
e
dEg/dT
meV K-1
λg
(µm)
n
around
λg
0.66
1.12
1.71.8
2.9
I
I
−0.37
−0.23
1.87
1.11
0.73
4
3.45
0.42
3.1
2.16
2.45
1.58
1.42
1.15
3.44
I
I
I
D
D
D
−0.5
−0.35
−0.3
−0.45
0.57
0.52
0.75
0.87
1.08
0.36
3.2
3
3.7
3.6
2.24
0.73
0.75
0.80
I
D
D
D
−0.54
−0.35
0.55
1.7
1.65
1.55
3.4
4
I
−0.45
ZB
0.3190
a
0.5190
c
0.5451
0.6096
0.5869
0.5870
ZB
0.5870
0.95
D
ZB
0.5869
0.6058
0.6479
1.35
0.35
0.18
D
D
D
−0.46
−0.28
−0.3
0.91
3.5
7
3.4-3.5
3.8
4.2
0.5668
0.6101
2.7
2.25
D
D
−0.72
0.46
0.55
2.3
2.7
W
ZB
ZB
ZB
ZB
ZB
ZB
ZB
1.3
Illustrated Dictionary of Electronic Materials and Devices: Concise Student Edition
138
Safa Kasap is currently a Professor of Electronic Materials and Devices in the
Electrical Engineering Department at the University of Saskatchewan, Canada.
He obtained his PhD (1983) degree from Imperial College of Science,
Technology and Medicine, University of London, specializing in amorphous
semiconductors and optoelectronics. In 1996 he was awarded the DSc
(Engineering) degree from London University for his research contributions to
materials science in electrical engineering. He is a Fellow of the Institution of
Electrical Engineers, the Institute of Physics and the Institute of Materials. His
research interests are in amorphous semiconductors, noise in electronic
devices, photoconductors, photodetectors, X-ray image detectors, laser
induced transient photoconductivity and related topics, with more than one
hundred refereed journal publications in these areas. He is the author of
McGraw-Hill’s Principles of Electronic Materials and Devices, Second Edition,
which is now used as a standard textbook in electronic materials in many major
universities world wide. His second textbook, Optoelectronics and Photonics:
Principles and Practices has been recently published by Prentice Hall
(http://Photonics.Usask.Ca).
Harry Ruda received the Ph.D. degree from Massachusetts Institute of
Technology, Cambridge, Massachusetts, USA, in 1982, for work on growth and
characterization of HgCdTe for infrared detectors. Following these studies, he
accepted an IBM postdoctoral fellowship to work on defect calculations in GaAs
and transport in low dimensional GaAlAs-based quantum heterostructures. In
1984 he joined 3M where his work focused on theoretical optical and transport
properties of wide bandgap II-VI semiconductors, principally ZnSe-based. In
1989, Dr. Ruda joined the University of Toronto and now holds the position of
Full Professor. He currently is also the Energenius Advanced Nanotechnology
chair holder, and Director of the Energenius Centre for Advanced
Nanotechnology as well as the Photonics Materials Research Centre at the
University of Toronto.
WARNING
All material in this publication is copyrighted. It is unlawful
to duplicate any part of this publication.
© The authors reserve all rights. No part of this publication
may be reproduced, stored in a retrieval system, or
transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise, without
the prior written permission of the authors.
© 2000 S.O. Kasap and H. Ruda
“Al Asuli writing in Bukhara some 900 years ago divided his
pharmacopoeia into two parts, 'Diseases of the rich' and
'Diseases of the the poor'."
Abdus Salam (1926-1997; Nobel Laureate, 1979)
v.2.0 Date: 10 March 2001
Email the author to report your corrections: Kasap@Engr.Usask.Ca