Electronics Review A
EETS8304/TC715N
SMU/NTU
Scheduled Lecture Jan. 20, 2004
Electronic Materials
(print slides only, no notes pages)
Page 1
© 1997-2004, R.Levine
Linear vs. Non-linear
• Electronic telecommunication uses electromagnetic fields
in space and inside materials.
• Many “linear” electronic devices are important
– Resistors (described by Ohm’s “Law”), Inductors,
Transformers, Capacitors, transmission wires and cables
• Linear equations describe linear phenomena
– Example: v=R • i, where R is a constant (resistance measured
using the unit of Ohms) note 1
– voltage is proportional to electric current
• or electric charge, the time integral of current (for a
capacitor q= i•dt); therefore q=C•v
• or time rate-of-change of current (for an inductor
v=L• di/dt)
Note 1: The “resistance” of thermal insulation for use in walls or ceilings of buildings is
also denoted “R,” but in that case it is the ratio of heat flow (analogous to current
flow) to temperature difference (analogous to voltage). In North America, English
units are used: BTU/min/sq.ft and degrees Fahrenheit.
Page 2
© 1997-2004, R.Levine
Linear Systems
• Linear systems have Interesting, important, but
limited capabilities
– Transmit electromagnetic waveforms from place to
place via wires or radio
• Usually accompanied by an undesired reduction (called
loss or attenuation) in signal power level
– Modify the amplitude and the wave shape of certain
waveforms in linear filters
• This can be viewed as the result of selectively distinct
attenuation and time delay of different frequency
components of a waveform
– Filters separate one radio frequency signal from many
others at distinct frequencies in the radio frequency
spectrum
• Important for frequency division multiplexing (FDM)
Page 3
© 1997-2004, R.Levine
Non-Linear Systems
• Many traditional electrical devices are non-linear
– Examples: relays, switches. incandescent and fluorescent
lamps have non-linear voltage-current relationship
• Electronic power amplifiers are non-linear, although
some have a limited approximately linear range of
operation
– Examples: diodes, transistors, vacuum tubes have limited
range approximately linear “regions” of operation, ranges of
voltage and/or current, although they are grossly non-linear
overall
• Digital electronics intentionally exploits the nonlinear properties of these devices
– The practical advantages of semiconductors (reliability, high
component density, low power consumption) make them the
devices of choice for almost all applications
Page 4
© 1997-2004, R.Levine
Junctions of Semiconductors
• Most important electronic semiconductor devices are made
by joining
– a. two different types of semiconductors,
– b. a semiconductor and a conductor, or
– c. a semiconductor and an insulator
• The electrical properties of current flowing across the
junction are very non-linear (as in diodes and junction
transistors)
– Even current flowing parallel to the junction in only one
material can have its flow area modified by electrical voltage
across the junction (basis of field effect transistors)
• Incidentally, joining two conductors (like copper and iron)
does not produce a junction with non-linear properties
– However, metal-metal junctions are useful thermo-electric
generator devices; another story not described in this course.
Page 5
© 1997-2004, R.Levine
Semiconductors and Digital Electronics
• Electrons do most of the interesting things in the
physics of materials. Their activity produces:
– electrical conductivity
– most of the “flow” of heat (thermal conduction)
– mechanical properties like hardness, ductility, etc.
• The negative electric charge of electrons pulls together the
otherwise mutually-repelling positive nuclear charge of
atoms to make up molecules, liquids and solids
• Protons and Neutrons, the other components of
atoms, “just sit there” in the nucleus
– Actually there is lots of internal nuclear activity
– But nuclear internal structure has little effect on most
electrical, chemical and mechanical properties
Page 6
© 1997-2004, R.Levine
Common Atomic Misconceptions:
• Electrons are not little point objects like
tiny baseballs!
• They are amorphous, “cloud” like, without
predetermined shape
• Their “shape” or “form” in any atomic size
situation is the result of forces acting on
the electrons from
– (positive charge) protons (in nucleus)
– other (negative charge) electrons nearby
Page 7
© 1997-2004, R.Levine
Bohr Model of the Atom
•
•
Famous, but historically superseded by later and better models
Still used today in the legal seal of the US Department of Energy
and the Richardson, Texas public school system, etc. etc.
Nucleus consists of
protons (positive charge)
and neutrons (electrically
neutral)
Point object electrons whirling
around the nucleus in specific
circular or elliptical orbits.
This frequently shown
picture is known to be
wrong in several ways.
Neils Bohr, Danish physicist, invented this theoretical model ca. 1905.
Page 8
© 1997-2004, R.Levine
Known to be Wrong
• Bohr got around some self-contradictory
problems of “classical” (non-quantum)
physics by assuming certain
unexplainable and unexplained things:
– Why don’t whirling electrons radiate light
energy continuously and thus fall into the
nucleus?
– Why do atoms cling together to make
molecules or solids (solids are giant molecules
with billions of atoms or more)
• Later theories (particularly Schrödinger’s wave theory) give
a better explanation. Erwin Schrödinger, Austrian physicist,
invented wave (quantum) mechanics in 1926. (His family
name is also written Schroedinger.)
Page 9
© 1997-2004, R.Levine
Energy = h • frequency
• The energy (in joules or watt•seconds) of an
electromagnetic wave (light, radio waves, infrared, etc.) is related to its frequency f (in
cycles/second or hertz -- Hz) by this formula:
E = h • f (the Greek letter  (pronounced nu) is used
rather than f in some documents)
• where h = 6.625 • 10-34 joule•seconds (Planck’s
constant)
• This is known from photo-electric emission of
electrons from a metal when illuminated by light,
and other experiments. Higher frequency light
causes emission of electrons having more
energy.
Page 10
© 1997-2004, R.Levine
Frequency and Energy
•
•
On a scale of frequency and energy, we show the range of ionizing
radiation starting just below visible light frequency range (energetic
enough to give an electron sufficient energy to leave an atom)
In general, frequencies below the ionizing energy threshold can cause
warming to the human body, but are not capable of initiating any chemical
activity. Most fears of bodily harm due to low intensity non-ionizing
communication radio waves are not fully substantiated by accurate
experiments...
106 Hz
1 MHz
109
1 GHz
Cellular and
SMR Radio
AM Broadcasting
Band (car radio)
TV and FM
Broadcasting
(VHF and UHF)
1012
1015
1 PetaHz
1 TeraHz
IR
1018
Ionizing radiation frequency range
UV
Visible Light
X-Rays
Gamma Rays
PCS Radio
Band (1.9 GHz)
On this logarithmic scale each mark represents a value 10 times the value to its left.
Page 11
© 1997-2004, R.Levine
Spectroscope
• Identifies Frequencies/Wavelengths Present in Light
Diffraction grating, a front
surface mirror with tiny
parallel grooves.
Some lenses used to focus
the image are not shown
here
Greatly enlarged view of
grooved surface
Light obstacle
with slit. Width
of slit is actually
very narrow.
Light source such as
hydrogen gas in a sealed
glass tube with electric
sparks.
Page 12
Images of the slit are formed on
photographic film.
© 1997-2004, R.Levine
Spectrogram of Atomic
Radiation
•
•
Measured position of each line can be used to calculate the
wavelength of light making up that spectral line
Then frequency f can also be calculated from f=c/wavelength,
where c=3•108meter/second, the speed of light
– Illustration shows lines in color on film on black background. Actual
spectroscope films are usually black and white, typically the
“negative” of this picture, with dark lines on a clear background.
Page 13
© 1997-2004, R.Levine
Bohr Orbits
•
Bohr’s atom was like a little “solar system” of planets
–
•
Working backwards from known data, Bohr made each orbit of a size which produced
the observed frequencies of light when an electron moved from one orbit to another
–
•
Each negative electron held in an orbit by electric attraction to the positive nucleus
Each stable orbit has angular momentum that is an integral multiple (1,2,3, etc.) of the
minimum angular momentum h/2p
Bohr assumed (without proof) that these special orbits were somehow “stable” (non
radiating)
–
–
But radiation does occur in Bohr’s theory when an electron moves from one orbit to another
This theory was convenient but contradicted the known fact that an electric charge radiated
energy when it accelerated (such as rotating in a circular path)...
Non-radiating high energy EH orbit
Non-radiating low energy EL orbit
Radiated light
frequency f,
where h•f= EH- EL
Page 14
© 1997-2004, R.Levine
Assumed Mechanism
• Each spectrum line indicates a different distinct frequency
component of the visible light radiation
– Line spectrum arises from sparks in hydrogen gas
– Continuous spectrum (not distinct lines) arises from merely
heating a solid object until it is “red hot” or “white hot”
• Bohr assumed each distinct line frequency was related to
the difference between two internal energy levels
• In Bohr’s theory, radiation of energy only occurred when an
electron moved from a larger diameter, high energy orbit to
a smaller, lower energy orbit. The difference in energy was
related to the frequency by this formula:
EH - EL = h • f
• Conversely, when an atom absorbs energy from light falling
on the atom, an electron moves from a low energy orbit to a
high energy orbit.
Page 15
© 1997-2004, R.Levine
Partly Good, Partly Bad
• Bohr could calculate the correct energy levels for a hydrogen
atom by assuming that only certain rotational speeds were
allowed (angular momentum= n • h/2p, for n=1,2,etc.)
• But not for a hydrogen molecule H2
– This theory could not explain how the 2 electrons and the 2 positive
nuclei could stay near each other and not fly apart in an H2
molecule
• There was a vague idea that the negative charge electron, while
it was in between the two positive nuclei, could attract both of
them and hold them together
– But when it moved away from the inter-atomic position in its normal
rotations around the nuclei, the nuclei would repel each other and
push apart!
• The theory said it couldn’t happen, but most of the hydrogen
atoms in a tank of room temp. hydrogen gas are in H2
molecules!
• The problem is partly due to treating the electrons as point-like
objects.
Page 16
© 1997-2004, R.Levine
Wave Theory
• In 1926, Erwin Schrödinger derived a wave
equation which related the local
wavelength of a “matter wave” to the
kinetic (motion-related) energy of the
matter
• It accurately predicted the shape and
radiation frequencies of the atom
• It also ultimately accurately explained how
atoms bond into molecules and solids
Page 17
© 1997-2004, R.Levine
“Angular” Molecules
• Certain tri-atomic molecules are known to have an
“angular” (not straight line) form
– From their electrical properties (dielectric constant) we know
their molecular shape is not a straight line
• From symmetry we might expect a straight-line form
• Examples are water (H2O) or hydrogen sulfide (H2S)
All experiments
indicate this
molecular
form.
Not this
“straight line”
form.
Page 18
© 1997-2004, R.Levine
Wave Properties
•
•
Schrödinger was a mathematical physicist who had already
studied wave equations describing waves flowing in flat circular
objects (like a drumhead) and on the surface of an inflated balloon
He was aware of standing wave patterns which caused high
concentrations of vibration in some areas, and little or none in
other areas.
– This suggested that if the flow or circulation of matter around a
spherical surface was described by a wave-like motion, then the
material (the high amplitude portions of the oscillating wave) was
mainly gathered at certain places on the spherical surface
– Somewhat like atmospheric clouds existing at some latitudes and
longitudes over the earth, but with no clouds over other parts of the
earth
– If these “clouds” indicated where the electronic charge was mostly
gathered, then the negative electron charge in those areas would stay
in between two positive charge nuclei of two atoms (the big central
one, oxygen, and the little nearby one, hydrogen) and attract both
nuclei, thus holding the molecule together.
Page 19
© 1997-2004, R.Levine
Electron “Clouds”
• There are 2 main electron clouds visible on this sphere, and
a third cloud, not visible, on the back as well.
– Result of a circulating wave with three wavelengths fitting
around the equator of the sphere
Electron cloud areas
are the places where the
other molecules will form
molecular bonds, due to the
mutual attraction of the negative
charge electron cloud(s) and the
positive charge nuclei of the
atom shown here and the other
atoms which will attach.
Page 20
© 1997-2004, R.Levine
A Better Theory
• Schrödinger’s wave theory of quantum
mechanics is the most accepted and accurate
theory in modern physics
– It accurately predicts the physical, mechanical,
chemical, and electrical properties of atoms, molecules
and solids
• Schrödinger’s original theory only described
lower (non-relativistic) energy values.
• Extensions of the original theory for higher
energies (in conformance with Einstein’s theory
of relativity) give accurate predictions of atomic,
nuclear and sub-atomic phenomena.
Page 21
© 1997-2004, R.Levine
Main Properties
• Electrons and other fundamental “particles” are
not particle-like at all (some say “wavicle”)
• The electron is described by a wave equation
(similar to the analysis method used for radio
waves)
• The quantity analogous to local radio wave power
is the local density of electron material or of
electric charge density
– This local material density varies from one place to
another in a way we can predict from knowing the
attractive and repulsive forces acting on the wave
material
• An electron wave with higher energy has a higher
oscillatory frequency and a shorter wavelength
Page 22
© 1997-2004, R.Levine
Atom Structure
• Electron waves can circulate around a nucleus in an
approximately spherical “shell” (also called an “orbital”)
– It is amorphous and cloud-like, with matter spread over a
range of radius values, not a shell with distinct inner and outer
surfaces like an eggshell
• The diameter of the most dense portion of the shell is
related to the energy (and thus the frequency and
wavelength) of the electron
– An integral number (1,2,3, etc.) of wavelengths can fit into the
equator circumference
• As the wave circulates, it repeatedly has high density areas in the
same physical place (same “longitude”)
– Only shells with the proper diameter for an integral number of
wavelengths are stable
• Many different energy levels (and thus many different shell
diameters) are theoretically possible
Page 23
© 1997-2004, R.Levine
Filling the Energy Levels
•
•
•
•
In a multi-electron atom, the form of the outer (higher energy)
electron shells can be calculated very accurately by including the
effect of both the positive nucleus and the inner, smaller electron
shells as well
When we examine a number of different chemical elements with
different atomic number (number of electrons, or number of
protons in the nucleus) we find a sequence of different energy
levels for which the outermost shell has a similar form of electron
clouds
This is the reason for the similarity of chemical and other
properties of elements in a column in the Mendeleyev Periodic
Table of the Elements.
Arranging the elements in atomic number order, we find that the
various theoretically permissible electron shells are “filled” with
electrons in the order beginning with the shell of lowest electron
energy for the first element, atomic hydrogen, and then the two
lowest energy shells for the next element helium (having 2
electrons), then the three lowest energy shells for lithium, and so
on…
Page 24
© 1997-2004, R.Levine
Atomic Light Radiation/Absorption
• Light is radiated when an electron changes its configuration
from a higher energy shell to a lower energy shell. The
transition is not instantaneous, but involves a gradual
(millisecond time interval) reshaping of the electron cloud
• During this interval, the electric charge oscillates back and
forth between the initial and final cloud shapes at a
frequency f=(EH-EL)/h. The radiation from this oscillating
charge is similar to radiation from a large size antenna
• Radiative energy transition from individual atoms occur
unpredictably at random instants of time
• Atoms can also absorb energy from an oscillating
electromagnetic field and thus reconfigure the electron
charge into a higher energy shell shape
– Later this same electron may radiate an electromagnetic wave
and migrate to a lower energy level. In some cases, the same
frequency which was absorbed is re-radiated and the electron
returns to its original energy level.
Page 25
© 1997-2004, R.Levine
Lasers and Masers
•
•
A Laser (Light Amplification by Stimulated Emission of Radiation)
operates by exciting electrons to higher energy levels:
First we cause absorption of energy and transition of electrons to
higher energy levels
– This can occur due to accelerating atoms by means of an electric field
(as in a fluorescent light tube), or by illumination with a higher
frequency light
•
•
When electrons fall back in energy to lower energy levels, they
emit radiation
In a Laser, the radiating electrons are contained in a “box” with
parallel reflecting walls. The walls are intentionally spaced apart
by an integral number of wavelengths of the desired light. This
causes the radiation from many atoms to occur at the same light
frequency.
– Some energy gets out from one side of the “box” through either a
small hole in one reflector, or by making one reflector partially
transparent
Partly reflecting
“mirror”
Fully reflecting
“mirror”
Page 26
© 1997-2004, R.Levine
Interesting Side Note: Spin
• The two lowest energy electron shells have an almost
identical shape. Of the two, one shell is “filled” first with an
electron which has an intrinsic magnetic direction which is
opposite to the intrinsic magnetic field caused by the
nucleus. The next shell has an electron with the opposite
magnetic direction.
– The intrinsic “spin” magnetism of the electron was discovered
in the 1920s by the Dutch-American physicists Samuel
Goudsmit and George Uhlenbeck. It is believed to be due to
some internal circulation of the electron matter, in addition to
its wave flow around the equator of the shell.
– The wave flow around the equator of the atom also produces
atomic orbital magnetic effects. Some shells have no net
orbital circulation, which is explained as the result of two
equal and opposite counter-rotating orbital waves.
– The magnetism of the nucleus is due to the fundamental
internal spin of the proton.
Page 27
© 1997-2004, R.Levine
Atomic Magnetic Properties
•
Therefore, most atoms with odd atomic numbers (1,3,5…) have a
very slight overall atomic magnetism due to one electron spin
(and some orbital magnetism in some elements), while most even
atomic number (2,4,6…) atoms have no net electron spin
magnetism, and thus approximately zero resulting atomic
magnetism
– However, due to the effect of inner shell electrons, in a few elements
(iron with even atomic number 26 being the most significant of this
type), the energy levels of several shells with the same direction of
electron spin magnetism are all lower than their counterpart shells
with the opposite direction of electron spin.
– Therefore these materials have a very high total magnetism (at least
twice as high as any odd atomic number element), since there are 2
electrons with their spin in the same direction, and neither one has a
matching electron with spin in the opposite direction.
– When we can arrange almost all the atoms in such a solid with the
same direction of magnetism, we obtain a permanent magnet
Page 28
© 1997-2004, R.Levine
Further Electron Shells
• When we examine the case of a 2-atom molecule (like H2)
compared to a corresponding single atom
– We find twice as many theoretically permitted electron shells
– The shells are not approximately spherical but instead they are
approximately shaped like two hollow spheres touching each other.
– For each shell predicted by the wave equation in a single atom, there
are now two slightly different shell forms (this is in addition to the two
electron spins, thus 4 altogether)
• One of these shells correspond to a form with more electron charge in
between the two nuclei
• The other corresponds to a form with more electron charge outside of the
two nuclei and less in the middle region between the two nuclei.
– When we examine a 3-atom molecule, we find 3 distinct shell forms
compared to 1 for a single atom
– When we examine a very large n-atom molecule (like a long carbon
chain which occurs in gasoline or oil) we find a “splitting” of each
one-atom energy level into n energy levels, each one corresponding to
a somewhat different electron shell form
Page 29
© 1997-2004, R.Levine
Solid State
• A solid piece of an element (like a lump of copper or sulfur)
is actually an n-atom molecule in which each atom (except
the ones on the surface) has a molecular bond (one or more
electron clouds) pulling it toward the atoms that surround
it!
• In a cubic centimeter of solid aluminum, there are about
1022 atoms
– Avogadro’s number, the number of atoms in one grammolecular-mass of a material, is about 1023
– the mass of a cm3 of Al is 2.7 grams and the atomic “weight” of
Al is about 27)
• Therefore, there are about 1022 distinct theoretically
possible electron energy levels in this piece of Aluminum
for each electron in each atom, each one corresponding to
a different wave shell. These energy levels are so close to
each other that they form almost a continuous “band” of
energy levels
Page 30
© 1997-2004, R.Levine
Electron Waves in Solids
•
Some of the lower energy wave shells are clustered closely
around each nucleus
– These are called valence electrons and they mainly help to hold the
solid together mechanically by providing electrostatic attraction to the
nearest positive atomic nuclei
•
Some of the higher energy wave shells are spread out almost
evenly throughout all the space inside the piece of Aluminum,
rather than all clustered in the vicinity of one atom:
– These are called conduction electrons. These are the electrons which
carry electric charge from place to place, providing electrical
conductivity
– they also carry thermal energy (heat) from place to place, providing
thermal conductivity
• Note that for all metal conductors, the ratio of the electrical resistance (in
Ohm•meters) of a metal to its thermal resistance* (measured in units
watt/meter/Kelvin degree) is a constant (called the Wiedemann-Franz
constant). This is due to the fact that the same primary mechanism (electron
wave movement) transports both electricity and heat in a metal
Page 31
© 1997-2004, R.Levine
Energy Bands
• In a solid with many many atoms, the number of
energy levels is so great and they are so closely
spaced, that we describe them as a “band” of
energy values
• In a solid material, a change in energy level of an
electron corresponds to a change in the
oscillating frequency of the associated
Schrödinger wave, and a consequent change in
wavelength
• In some materials, interesting things occur when
the wavelength of the electron wave is exactly
equal to the distance between atomic nuclei, or
exactly 1/2 of this distance, or 1/3, and so forth…
Page 32
© 1997-2004, R.Levine
Speed, Wavelength, Frequency
• For a simple oscillatory wave, these three
properties are related by this formula:
wave speed = wavelength/cycle time
• cycle time is also called a period. Frequency f is
1/period, so
wave speed = wavelength • frequency
• wave speed =  • f
– using the Greek letter (lambda) for
wavelength.
– Frequency is also sometimes represented by
the lower case Greek letter Nu () in physics
books.
Page 33
© 1997-2004, R.Levine
Speed, Wavelength, Frequency
• Low energy, low frequency electrons have longer
wavelength.
– Their electric charge permeates in between the atomic nuclei
and helps to hold the solid together. So-called valence
electrons.
• High energy, high frequency electrons have shorter
wavelength.
– Their electric charge is more localized, and moves around
constantly due to thermal motion (except at absolute zero
temperature)
– The motion of the localized blob of electric charge can be
analyzed approximately, but with reasonable accuracy, when
we treat it like a point object
– Electrons in this higher energy level band are described as
conduction electrons
• In conductors (most metals and some other materials) there
is no distinct dividing point in energy between these two
categories
Page 34
© 1997-2004, R.Levine
Energy Gap
•
•
Certain materials (e.g. sulfur, some crystal structures of carbon,
some mixtures and alloys, etc.) have a “forbidden” range of
energy levels which separates the valence and conduction bands
This is due to a cumulative internal reflection of the electron
waves by each atomic core or nucleus in the solid in a certain
range of wavelengths
– This depends on the spacing between the rows of atoms in the solid
vis-à-vis the electron wavelength
•
•
•
Electron waves above this frequency (energy) or below this
frequency (energy) are not reflected, and will “flow” through
The particular reflected waves will not propagate through the
solid. They are “forbidden” to enter, and such waves of this
wavelength bounce back when we try to shoot them into the solid
This reflection occurs for a particular energy level and a small
range of energy levels above and below it, producing a distinct
“gap” in the almost continuous range of energy levels in the solid.
Page 35
© 1997-2004, R.Levine
Davisson-Germer
• In the 1920s, Davisson and Germer, two scientists at Bell
Laboratories, discovered the effect named for them (and
got the Nobel Prize!!):
Accelerator electrode
• They fired electrons from an “electron gun” in a vacuum
chamber at various metal and non-metal surfaces
– The electron gun was similar to an electron source used in a
TV picture tube. Electrons are thermally emitted from a hot
filament, and then accelerated by being pulled toward a
positive voltage electrode with a hole in it. Many electrons fly
through the hole to the test target surface. The energy of the
electrons is controlled by changing the positive voltage of the
electrode
• As they changed the electron energy, they found reflection
of the electron beam from the target surface at some middle
range of energy (the “energy gap”), and absorption of the
beam at other (lower and higher) ranges of energy (the
valence band or the conduction band).
Page 36
© 1997-2004, R.Levine
Optical Wave Analogies
• Certain types of sunglasses or photographic lenses are
coated with a thin “anti-reflective” coating of optical
material. The coating produces reflections from both its
front and back surface
• The thickness of the material is designed so that the
reflected waves align in phase for a specific part of the
visible light frequency range
– For example, the short wavelength part of the visible spectrum
may be “bounced back” and will not penetrate this special
coating. Hence so-called “blue blocker” sunglasses!
– Longer and shorter wavelengths will pass through
• When you look at a thin layer of oil floating on water (an “oil
slick”), you see areas of reflected colors. This is the result
of a combined reflection from the upper and lower surface
of the very thin oil layer. The combination of the two surface
reflections produces only certain colors (wavelengths) of
reflected light.
Page 37
© 1997-2004, R.Levine
Energy Gap
• Many materials have a significant energy
separation between the valence electron
energy levels and the conduction electron
energy levels
• Unless a valence electron can get
significantly more energy in some way, it
stays in the lower valence energy band
• A material with all its electrons in the
valence band is not a good electric
conductor (no moveable conduction
electrons)
Page 38
© 1997-2004, R.Levine
Directional Properties
• Since the electrical conductivity properties depend on the
relationship of the spacing between the atoms to the electron
wavelength…
• The direction of the electron wave motion (and resulting electric
current flow) relative to the rows of atoms is important.
• In a material with a cubic arrangement of atoms, with nearest
rows a distance d apart, we are concerned with the relationship
of the electron wavelength to the distance d when the waves
propagate parallel to the main cubic axes
• When the wave propagates at 45 degrees to the main cubic axis,
the spacing between apparent nearest rows of atoms is 2•d or
1.414•d, and also half that for some of the atoms.
1.0
Page 39
© 1997-2004, R.Levine
Different Spacing
•
•
The distance between rows of atoms are called Bragg spacing
after the British physicist Lawrence Bragg
consider atoms arranged at corners of consecutive cubes:
wave direction b
wave direction a
d
1.41d
0.7d
Page 40
© 1997-2004, R.Levine
Non-isotropic Material
• Some materials have a normally non-isotropic crystal
structure in the pure single-crystal form
– Isotropic means “the same in all directions”
• Most solids consist of small regions (grains) with different
crystal orientation, rather than one large crystal. Large
single crystals (e.g. table salt, quartz) have a distinctive
external shape related to the crystal structure.
• Some materials can form more than one crystal structure
depending on the temperature and pressure, or the
conditions existing when they are cooled from a melted or
fluid state
– Water ice is a material with several crystal forms
– Atom arrangements formed under low pressure have
hexagonal crystal structures
– Thus snowflakes and some ice flakes have hexagonal shapes
– Atom arrangements formed under high pressure are not
hexagonal
Page 41
© 1997-2004, R.Levine
Carbon has two major crystal structures:
1. Diamond has a highly symmetrical crystal structure, with
each atom having four equidistant nearest atoms
– Diamond is very mechanically hard, and this property is
independent of direction
– Diamond is a semiconductor (explanation later)
– Silicon and Germanium have the same diamond-like crystal
structure
2. Graphite (used for writing pencil “lead” and as a dry
lubricant), with each atom having two close neighbors and
two more distant neighbors
– Graphite crystal structure has carbon atoms arranges in
“sheets” of approximately hexagonal atom positions, with these
sheets separated from adjacent sheets by a greater distance
– Graphite is mechanically softer in one direction than the other. It
breaks apart or crumbles into sheets in one direction, but the
sheets are very hard to break apart into smaller sheets.
– Graphite is an electrical conductor
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Grain Structure
• Many samples of material appear to be structurally
homogeneous on a large scale
• When we examine the surface with a microscope, we see that
the material is composed of small grains of material with
slightly different appearance (called polycrystalline):
– Typically different reflected color or luster in each grain
– In metals, each grain is a uniform crystal of the same metal, but the
major axes of the atom rows are in different directions
– When melted metal cools, it normally forms small grains of
material with uniform rows and columns of atoms inside each
grain, but different orientation of these rows in adjacent grains
– To make a large “perfect crystal” of metal, it is necessary to rapidly
“freeze” it from the melted liquid by suddenly cooling it all the way
through
• Many of the physical properties of metals and alloys thus
depend on heating and re-freezing
– for example, hardening or “tempering” steel alloy by heating and
then suddenly cooling it -- plunging the hot metal into cold water
or oil
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Large Single Crystals
•
Large single perfect crystals have interesting mechanical and
electrical properties, but they tend to reform naturally into smaller
grains of different crystal axis orientation
–
Even when we make a large single crystal of metal this way, when we leave it
standing at room temperature for several months, microscopic examination shows
that it is naturally forming small grains of different atomic row orientation,
particularly at places of high mechanical stress (like the inside corner of an Lshaped piece under tension)
• Because all these small grains have different atomic row
orientation, a large sample of polycrystalline material may
show the same electrical properties in all different directions
of current flow
– This is true even if the material has a single-crystal structure
(arrangement of atoms) which is not completely isotropic
– For example, graphite used in writing pencils is intentionally
made up of small particles produced by grinding up natural
graphite, and then compacting it together with an adhesive
binder. This material appears to be electrically homogeneous in
its conductivity properties.
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Two Important Categories
• Solid materials fall into two important categories:
1. Those with an electron energy gap
– Insulators (both electrical and thermal, in general)
– Semiconductors are a sub-class of Insulators, as we will
see
2. Those with no energy gap
– Conductors (both electrical and thermal conductors)
• Note: there are a few peculiar non-metal materials
(for example, Beryllium Oxide) which are
moderately good thermal conductors and yet are
electrical insulators.
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Best Metal Conductors (in order)
• Silver: resistivity 16 n•m (nano-Ohm-meters)
– too costly for most applications. Sometimes used as a surface
plating over copper or brass for certain purposes (electrical or
decorative)
• Copper: resistivity 17 n•m
– widely used in pure or alloy form (Brass, etc.); forms a surface
oxide which is a relatively low resistance semiconductor
• Gold: resistivity 24 n•m
– not the best conductor, but it does not form surface oxides or
otherwise corrode, so it is often used as a protective metal
surface plating on copper or brass for connectors, etc.
• Aluminum: resistivity 28 n•m
– inexpensive and lighter than copper, but forms a surface oxide
which is a high resistance (insulator). Bad mechanical joints in
aluminum wire (from loose holding screws, etc.) permit
oxidation, local heating, and in some cases this heat initiates
fires in combustible materials.
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Why Distinguish Insulators from
Semiconductors?
• When we examine the room temperature specific
resistivity* of many materials, we find:
• all metals have relatively low resistivity, and
• many insulators (glass, sulfur, most plastics, etc.)
have very high resistivity (many millions of times
bigger than the resistivity of metals)
• Some materials appear to have resistivity
somewhat larger than the metals, but much lower
than the standard insulators at room temperature
– Historically we call these materials (silicon, germanium,
etc.) semi-conductors
* Resistivity is measured in ohm•meters, and is the resistance measured between two
opposite faces of a 1 meter cube sample. For practical purposes, The ohm•centimeter
unit is often used also.
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Historical Name is Physically Misleading
• However, this classification into three categories
is misleading
• Insulators and semiconductors have the same
basic internal electrical property:
– An energy gap between valence and conduction
electron energy bands.
• An insulator has a much larger energy gap
(difference in energy between the highest and
lowest energy levels at the gap top and bottom on
the energy scale)
– Therefore almost no moveable conduction band
electrons are present at room temperature.
• A semiconductor has a much smaller energy gap
– Therefore more movable conduction band electrons are
present at room temperature
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Other Distinctions
• The electrical resistance of a conductor
increases with increasing temperature
– The change is approximately a uniform
percentage increase
– Typically a percent or so increase for each few
degrees Celsius.
• The electrical resistance of an insulator or
semiconductor decreases with increasing
temperature
– The change is approximately exponential
– The resistivity decreases by a factor of about
50% for each 10 deg Celsius temperature
increase
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Resistance vs. Temperature
• One mechanism causes increased electrical
resistance at high temperature, but its effect is
“hidden” in semi-conductors:
– Increased scattering of electron waves to the sides, away
from their directed motion in an electric current
– This scattering is worse at higher temperatures because the
atomic cores in the solid material vibrate more due to their
own thermal energy of motion
– This occurs in conductors, in which the number of movable
conduction electrons is fixed, and causes a relatively small
percent increase in resistivity as temperature increases
– This also occurs in insulators and semiconductors, but it is
hardly noticeable in combination with a much larger countereffect, namely the increase in the number of moveable
conduction band electrons
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Temperature Effects
• Temperature is an expression of the manner in
which the microscopic kinetic (motion related)
energy is distributed among various electrons,
atoms and molecules (the participants) in a
material.
– If all the energy levels of all participants are the same, the
material has zero temperature
• This is called the “ground state.” When all the electrons of
certain conductors are in the ground state, a conductor
becomes a “superconductor” and has no electrical
resistance whatever.
– At the other extreme, if electrons all have different energy
levels, the temperature is very high. Electrical resistance
of a conductor is then higher.
– At high temperatures, many of the electrons have a high
energy level.
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Number of Conduction Electrons
• The number of electrons having a high enough energy to
place them in the conduction band of an insulator or
semiconductor
– Increases exponentially with increasing temperature
– Is so small at room temperature for good insulators that even
after it doubles for each 10 degree Celsius increase in
temperature, it is still too small to produce any significant
current
– Is a moderate number at room temperature in classic
semiconductors
• The quantitative distinction between insulators and
semiconductors depends on the temperature at which the
measurement of their resistance is made
– At a high enough temperature, a material called an
insulator at room temperature may have enough
conduction electrons to qualify as a semiconductor
• Unless it melts first at a lower temperature, of course!
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Resistance vs. Temperature
Resistivity in ohm•meter
Typical semiconductor
Theoretical semiconductor with no wave scattering
due to thermal vibration of atom nuclei in the solid.
Typical electric conductor (metal)
Temperature
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Temperature Relationships
• Temperature is itself a measurement of the range
of energies of various electrons (and other
fundamental particles) in a material
– At very low temperatures, all the electrons have the
lowest possible energy
– At higher temperatures, some electrons have higher
energies, and the range of energies, from the lowest to
the highest, is increased
• Electrons increase their energy by means of:
– Interactions (such as collisions) with other electrons
– Interactions with the atomic nuclei in the solid
– Interactions with electromagnetic waves (light, infrared,
etc.). This occurs particularly in situations where
semiconductors are used as optical detectors.
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Changing Energy Bands
• When an electron “moves” from the valence band
to the conduction band, it does so by changing its
wavelength and the shape or form of the electron
charge cloud
– Instead of being spread out over most of the space over
many rows of atoms, the electric charge clusters
together into a relatively small lump
– When this occurs, it is somewhat like suddenly creating
an electron at a particular place
• All of its electric charge was really already there (but
spread out over many atoms) before this
• Now that it is more local, it can move along and contribute
to the electric current
• This particularly happens in electrical diodes and junction
transistors, as we will show
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Important Structure
• We will find that an important semiconductor
structure occurs at the junction between
– two different types of semiconductors having different
average internal electron energy
– or a metal-to-semiconductor junction
• Two layers of electric charge build up at the
junction
– Some extra electrons produce a net negative charge on
one side of the junction
– a region with less than the normal number of electrons on
the opposite side of the junction. This, in combination with
the positive charge of the atomic nuclei, thus produces a
layer of net positive charge
• These are called “depletion layers” and they are
important in the operation of diodes and transistors
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