Introduction
• Electronics is defined as the science of the motion of charges
in a gas, vacuum, or semiconductor.
• Today, electronics generally involves transistors and transistor
circuits
• Microelectronics refers to integrated circuit (IC) technology,
which can produce a circuit with multimillions of components
on a single piece of semiconductor material.
History of Semiconductors
1821: Thomas Seebeck discovered semiconductor
properties of PbS
1833: Michael Faraday reported on conductivity
temperature dependence of semiconductors
1875: Werner von Siemens invented a selenium
photometer
1878: Alexander Graham Bell used this device for
wireless optical communications
1907 Round demonstrated the first LED (using SiC)
1940 Russell Ohl discovered a p-n junction diode
History of Semiconductors
• Russell Ohl – Inventor of a p-n
junction (1940)
• In 1939, vacuum tubes were state
of the art in radio equipment.
Most scientists agreed tubes were
the future for radio and
telephones everywhere.
• Russell Ohl didn't agree. He kept
right
on
studying
crystals,
occasionally having to fight Bell
Labs administration to let him do
it.
History of Semiconductors
1947: Bardeen, Brattain,
and Shockley discovered a
Bipolar Junction transistor
First Integrated Circuit is Invented by Jack Kilby
: 1958
First Transistor, 1947
The Nobel Prize in Physics 1956
Intel’s 1.7 Billion Transistor Chip 2004
Brief History
• In December 1947, the first transistor was demonstrated at
Bell Telephone Laboratories by William Shockley, John Bardeen
and Walter Brattain.
• From then until 1959, the transistor was available only as a
discrete device, so the fabrication of circuits required that the
transistor terminals be soldered directly to the terminals of
other components.
• In September 1958, Jack Kilby of Texas Instruments
demonstrated the first integrated circuit fabricated in
germanium. At about the same time, Robert Noyce of Fairchild
Semiconductor introduced the integrated circuit in silicon.
Brief History
• 1954, Chapin, Fuller, and Pearson developed a solar cell.
• 1958, John Kilby, invented the Integrated Circuit (IC).
• 1958, Leo Esaki discovered a tunnel diode (Esaki diode).
• 1960, Kahng and Atalla demonstrated the first MOSFET.
• 1962, three groups headed by Hall, Nathan, and Quist
demonstrated a semiconductor laser.
• 1963, Gunn discovered microwave oscillations in GaAs and InP
(Ridley-Watkins-Hilsum-Gunn effect).
• 1963, Wanlass and Sah introduced CMOS technology
Brief History
• The development of the IC continued at a rapid rate through
the 1960s, using primarily bipolar transistor technology.
• Since then, the metal-oxide-semiconductor field-effect
transistor (MOSFET) and MOS integrated circuit technology
have emerged as a dominant force, especially in digital
integrated circuits.
• Device size continues to shrink and the number of devices
fabricated on a single chip continues to increase at a rapid rate.
• Today, an IC can contain arithmetic, logic, and memory
functions on a single semiconductor chip.
• The primary example of this type of integrated circuit is the
microprocessor.
Passive and Active Devices
•
In a passive electrical device, the time average power
delivered to the device over an infinite time period is always
greater than or equal to zero.
• Resistors, capacitors, and inductors, are examples of passive
devices.
• Active devices, such as dc power supplies, batteries, and ac
signal generators, are capable of supplying particular types of
power.
• Transistors are also considered to be active devices in that
they are capable of supplying more signal power to a load
than they receive.
Electronic Circuits
Schematic of an electronic circuit with two input signals: the dc power supply
input, and the signal input
Atomic Structure
An atom is composed of :
• Nucleus (which contains positively charged protons and
neutral neutrons)
• Electrons (which are negatively charged and that orbit the
nucleus)
Valence Electrons
• Electrons are distributed in various shells at different
distances from nucleus
• Electron energy increases as shell radius increases.
• Electrons in the outermost shell are called valence
electrons
• Elements in the period table are grouped according to the
number of valence electrons
• The valence electrons are shared between atoms, forming
what are called covalent bonds
At room temperature, some of the covalent bonds are broken by thermal ionization.
Each broken bond gives rise to a free electron and a hole, both of which become
available for current conduction.
Valence Electrons
a portion of the periodic table
Semiconductor Materials
Elemental
Semiconductors
1. Si Silicon
2. Ge Germanium
Compound
Semiconductors
1. GaAs Gallium arsenide
2. GaP Gallium phosphide
3. AlP Aluminum phosphide
4. AlAs Aluminum arsenide
5. InP Indium phosphide
Elemental/Compound Semiconductors
• Silicon (Si) and Germanium (Ge) are in group IV, and are
elemental semiconductors
• Galium arsenide (GaAs) is a group III-V compound
semiconductors
Silicon Crystal
• At 0°K, each electron is in its lowest possible energy state, and
each covalent bounding position is filled.
• If a small electric field is applied, the electrons will not move
silicon is an insulator
Silicon Atom Diagram at 0°K
Two-dimensional representation of single crystal silicon
At T = 0 K; all valence electrons are bound to the silicon atoms
by covalent bonding
Silicon Atom Diagram at Ambiant Temp
The breaking of covalent bond for T>0°K creating an electron
in the conduction band and a positively charged “empty
state”
Intrinsic Silicon
•
If the temperature increases, the valence electrons will gain
some thermal energy, and breaks free from the covalent bond
• It leaves a positively charged hole
• In order to break from the covalent bond, a valence electron
must gain a minimun energy Eg: Bandgap energy
Energy band
• The energy Eν is the maximum
energy of the valence energy
band.
• The energy Ec is the minimum
energy of the conduction
energy band.
• The bandgap energy Eg is the
difference between Ec and Eν
• The region between these two
energies
is
called
the
forbidden bandgap.
• Electrons cannot exist within
the forbidden bandgap.
Energy band diagram
a) Vertical scale is electron energy &
horizontal scale is distance
through
the
semiconductor,
although these scales are
normally not explicitly shown.
b)The generation process of
creating an electron in the
conduction band and the
positively charged “empty state”
in the valence band
Energy band diagram
a) Vertical scale is electron energy &
horizontal scale is distance
through
the
semiconductor,
although these scales are
normally not explicitly shown.
b)The generation process of
creating an electron in the
conduction band and the
positively charged “empty state”
in the valence band
Energy gap
The energy gap decreases with the increase in temperature
and is given by
EG( T) = EG0-T
where  = a constant, (depends on material nature)
 = 3.60 X 10-4 for silicon ;
 = 2.23 X 10-4 for germanium ;
For germanium
EG0 = 0.785eV; at 0°K
For silicon
EG0 = 1.21eV; at 0°K
For germanium,
EG(T) = 0.785 - 2.23 X 10-4T; &
At room temperature (300°K), EG = 0.72 ev.
For silicon,
EG(T) = 1.21 - 3.60 X 10-4T; &
At room temperature (300°K), EG= 1.1 ev.
Energy-band structure of (a) an insulator, (b) a semiconductor, and (c) a metal.
Insulators/Conductors
• Materials that have large bandgap energies (in the range of 3
to 6 electron-volts (eV)) are insulators, because at room
temperature, essentially no free electron exists in the material
• Materials that contain very large number of free electrons at
room temperature are conductors
• In a metal, the conduction band is partially filled. These
electron can move easily in the material and conduct heat and
electricity (Conductors).
Semiconductors
• Most electronic devices are fabricated by using
semiconductor materials along with conductors and
insulators.
• Silicon is by far the most common semiconductor material
used for semiconductor devices and integrated circuits.
• Other semiconductor materials are used for specialized
applications.
Semiconductors
• In a semi-conductor at 0 k the conduction band is empty and
valance band is full. The band-gap is small enough that at
room temperature some electrons move to the conduction
band and material conduct electricity.
• In a semiconductor, the bandgap energy is in the order of 1
eV. The net flow of free electrons causes a current.
• In a semiconductor, two types of charged particles contribute
to the current: the negatively charged electrons and the
positively charged holes
An electron–volt is the energy of an electron that has been accelerated
through a potential difference of 1 volt, and 1 eV = 1.6 × 10−19 joules.
Semiconductor
In semiconductors, two types of charged particles contribute to
the current:
• the negatively charged free electron
• the positively charged hole.
• Two charge carrying particles (free electrons and holes) are
formed along with a new electron-hole pair.
• µn = mobility of the free electron (-ve charge carrying particle)
• µp = mobility of the hole (+ve charge carrying particle)
• Carriers
A free electron is negative charge and a hole is positive
charge. Both of them can move in the crystal structure.
They can conduct electric circuit.
• Recombination
Some free electrons filling the holes results in the
disappearance of free electrons and holes.
• Thermal equilibrium
At a certain temperature, the recombination rate is equal
to the ionization rate. So the concentration of the carriers
is able to be calculated.
• In a pure semiconductor: no. of holes = no. of electrons i.e.
n=p
• The concentration of electrons and holes directly influence
the magnitde of the current
• In an intrinsic semiconductor (a single crystal semiconductor)
the densities of holes and electrons are equal.
Carrier concentration for n type
Thermal equilibrium equation
nn 0  pn 0  ni
2
Electric neutral equation
nn 0  pn 0  N D
Carrier concentration for p type
Thermal equilibrium equation
p p 0  n p 0  ni
2
Electric neutral equation
p p0  n p0  N A
Because the majority is much great than the minority, we can get
the approximate equations shown below:
nno  N D

2

ni
for n type
 pn 0 
ND

 p p0  N A

2

ni
for p type
n p 0 
NA

• Carrier concentration in thermal equilibrium
n  p  ni
3  EG kT
ni  BT e
2
• At room temperature(T=300K)
ni  1.5  1010 carriers/cm3
B: constant related to specific
semiconductor material
Eg: Bandgap energy (eV)
T: Temperature (°K)
K: Boltzman Constant in eV/°K
Semiconductor Constants
• ni has a strong function of temperature.
• The high the temperature is, the dramatically great the
carrier concentration is.
• At room temperature only one of every billion atoms is
ionized.
• Silicon’s conductivity is between that of conductors and
insulators.
• Actually the characteristic of intrinsic silicon approaches
to insulators.
• Electron density in the conduction band.
• NC= 2.86 X 1019cm-3 for silicon and 4.7 X 1017cm-3 for
gallium arsenide.
• NV= 2.66 X 1019cm-3 for silicon and 7 X 1018cm-3 for
gallium arsenide
Fermi function
Where n is in cm-3and N(E) is density of states in (cm3-eV)
N(E) = γ(E – Ec)1/2
The probability that an electron occupies and electronic state
with energy E is given by Fermi-Dirac distribution.
Fermi function f(E) is :
f(E) = 1/(1+e(E-Ef)/kT)
Fermi distribution function F(E) versus (E–EF) for various
temperatures.
Mass Action Law
n = p : number of electrons in CB = number of holes in VB
This is due to the fact that when an electron makes a transition
to the Conduction Band, it leaves a hole behind in Valance Band,
having a bipolar (two carrier) conduction and the number of
holes and electrons are equal.
n.p = ni2
This equation is called as mass-action law.
Intrinsic semiconductor. (a) Schematic band diagram. (b) Density of states. (c) Fermi
distribution function. (d) Carrier concentration.
n-Type semiconductor. (a) Schematic band diagram.
(b) Density of states. (c) Fermi distribution function (d) Carrier concentration. Note
that np= ni2.
Extrinsic Semiconductor / Doping
• Doped semiconductors are materials in which carriers of
one kind predominate.
• Only two types of doped semiconductors are available.
• Conductivity of doped semiconductor is much greater
than the one of intrinsic semiconductor.
• The pn junction is formed by doped semiconductor.
Extrinsic Semiconductor / Doping
• The electron or hole concentration can be greatly increased
by adding controlled amounts of certain impurities
• For silicon, it is desirable to use impurities from the group III
and V.
• The phosphorus (group V) atom is called donor impurity
because it donates an electron that is free to move
• The boron (group III) has accepted a valence electron (or
donated a hole), it is therefore called acceptor impurity
• An N-type semiconductor can be created by adding
phosphorus or arsenic
N-Type Semiconductor
Each dopant atom donates a free electron
and is thus called a donor.
The doped semiconductor becomes n type.
A silicon crystal doped by a pentavalent element.
A two-dimensional representation of the silicon crystal showing
the movement of the positively charged “empty state”
• In the figure, it appear as
if a positive charge is
moving through the
semiconductor
• This positively charged
imaginary “particle” is
called a hole.
P-Type Semiconductor
A silicon crystal doped with a trivalent
impurity.
Each dopant atom gives rise to a hole,
and the semiconductor becomes p type.
Conductivity of Semiconductor
Total current density J with in the intrinsic semiconductor
is given by
J = Jn + Jp
= qnµnE + qpµpE
= (nµn + pµp)qE
= σE
σ is the conductivity of a semiconductor
The resistivity (ρ) of a semiconductor is the reciprocal of
conductivity, i.e., ρ = 1/σ.
Conductivity of Semiconductor
• For pure (intrinsic) semiconductor, n = p = ni (intrinsic carrier
concentration).
• Conductivity of an intrinsic semiconductor is
σi = niq(µn + µp).
Conductivity of N-and P-type semiconductors:
• For N-type semiconductors, as n>>p, then the conductivity,
σ = q n µn
• For P-type semiconductors, as p>>n, then the conductivity,
σ = q p µp
Drift & Diffusion
There are two mechanisms by which holes and free
electrons move through a silicon crystal.
Drift--- The carrier motion is generated by the electrical
field across a piece of silicon. This motion will produce
drift current.
Diffusion--- The carrier motion is generated by the
different concentration of carrier in a piece of silicon. The
diffused motion, usually carriers diffuse from high
concentration to low concentration, will give rise to
diffusion current.
Drift velocity and Current
• Drift
Drift velocities

vp drift   p E


vn drift    n E
where
q
q
n
p
n  m ,  p  m
Drift current densities
J n  drift  (qn)  (  n E )  qn n E
J p  drift  qp   p E
Where µn , µp are the constants called mobility of holes and
electrons respectively.
• Total drift current density
J drift  q（n n＋p p ) E
• Resistivity
  1 q ( n ＋ p  )
n
p
• Resistivities for doped semiconductor
1
For n type
 qN D  n
1
  q(n  p )  
n
p
For p type
 1 qN 
A p

* Resistivities are inversely proportional to the concentration of
doped impurities.
• Temperature coefficient(TC)
TC for resistivity of doped semiconductor is positive due to
negative TC of mobility
• Resistivity for intrinsic semiconductor
  1 q (n  p )  1 qn (    )
n
p
i
n
p
* Resistivity is inversely proportional to the carrier concentration
of intrinsic semiconductor.
• Temperature coefficient(TC)
TC for resistivity of intrinsic semiconductor is negative due to
positive TC of .
• Diffusion
A bar of intrinsic silicon (a) in which the hole concentration profile shown
in (b) has been created along the x-axis by some unspecified mechanism.
Cont…
I
diff
n
I
diff
p
I diff
dn
 qADnn  qADn
dx
dp
 qAD p p  qAD p
dx
 I ndiff  I pdiff  qADnn  D p p 
 I T  I diff  I drift
Diffusion currents only flow when there is a concentration
difference for either the electrons or holes (or both).
Einstein Relationship
Einstein relationship exists between the carrier diffusivity and
mobility:
Dn
Dp
kT

 VT 
n  p
q
Where VT is Thermal voltage.
At room temperature， V
T
 25mv
Diffusion length (L)
• The average distance that on excess charge carrier can diffuse
during its life time is called the diffusion length L
L  D
• Where D is the diffusion coefficient that may be related to the
drift mobility, µ, through the Einstein relation as
D   (kT / q)
Diffusion length
• Lp is the average distance a hole will move before
recombining.
• Ln is the average distance an electron will move before
recombining.
Ln 
Dn n
Lp 
D p p
Carrier life time
• The carrier life time is defined as the time for which, on
average, a charge carrier will exist before recombination
with a carrier of opposite charge.
• It depends on the temperature and impurity concentration
in the semiconductor material.
Carrier life time
• The mean life times n , p of electrons and hole
concentrations indicate the time required for the excessive
electron and hole concentrations to return to their
equilibrium values.
dn n 0  n

dt
n
dp
p0  p

dt
p
Continuity Equation
Relating to the conservation of charge.
Rate of hole build up = increase of hole concentration in the
volume - the recombination rate
The equation of conservation of charge, or the continuity
equation,
p  p0
dp
d p
dp

 Dp 2   p
dt
p
dx
dx
2
Where Ɛ is the electric field intensity within the volume.
• Considering holes in the n-type material, the subscript n is
added to P and p0.
• Also, since p is a function of both t and x, partial
derivatives should be used. Making these changes, finally
equation is,
pn
pn  pno
 pn
pn

 Dp
 p
2
t
p
x
x
2