This document discusses electric and magnetic fields, and how they arise from interacting electric charges and currents. It defines the electric field E as the force F experienced by a test charge q, divided by q. Similarly, the magnetic field B is defined as the force F experienced by a current-carrying wire, divided by the product of the current i and wire length l. The document then discusses linear and non-linear circuit elements, semiconductors, and Niels Bohr's early atomic model, noting that while insightful, Bohr's model made assumptions that were later disproven.

1. © 1997-2005, R.LevinePage 1
Electronics Review
EETS8320
SMU
Session 4, Fall 2005
(print slides only, no notes pages)

2. © 1997-2005, R.LevinePage 2
Electric and Magnetic Fields
• When electric charges or currents (moving electric
charges) interact at a distance, there are forces
acting on the charges and currents.
– These forces have a direction and a magnitude.
– We can in principle measure the force(s) at a point, acting
on a test charge or a test current. Force can be measured
with a mechanical spring, for example.
• We theorize that there is “something happening
there” at the point where we measure the force.
– That “something” is called an “electric field” or a “magnetic
field”
– These fields have a direction at each point in space, as can
be seen from the directional characteristics of the force
produced by a field.

3. © 1997-2005, R.LevinePage 3
Electric Field
• The electric field E is the ratio of the force F
(acting on a test electric charge) to the
amount q of test charge
• Magnitude: E=F/q or F=q•E
• Unit: newton/coulomb (or volt/meter)
• Direction: Force F is parallel to electric field E.
Notes: A newton is the International metric unit of force,
approximately equal to 0.2248 pounds of force.
A coulomb is the amount of electric charge produced by
one ampere flowing for one second.
A volt is the ratio of one joule (one watt•second) of
energy divided by one coulomb of electric charge

4. © 1997-2005, R.LevinePage 4
Magnetic Field
• The magnetic field is the ratio of the force (acting on a test electric
current-carrying wire of length l), to the product of λ with the amount i
of test current.
• Magnitude B=F/(i•λ) or F= i•λ×B
• Unit: newton/(ampere•meter) (or volt•sec/meter2
)
• Direction: Perpendicular to the field direction and the current direction.
Can be expressed by “right hand rule” or “cross product” vector
notation.
Note: a volt•second is also called a weber.
The product of a volt of voltage, with an ampere of current, is an amount
of power called a watt. Power is the time rate at which energy flows or
“moves.”
The unit of energy is the result of one watt of power “flowing” for one
second. This is called a watt•second or a joule (rhymes with “foul.”)

5. © 1997-2005, R.LevinePage 5
Directions
q
E
F
i•λ
B
F
Force on charge is parallel
to electric field.
Force on current element
is perependicular to both
current element and
magnetic field.

6. © 1997-2005, R.LevinePage 6
Distributed vs. Lumped Circuit Elements
• Analysis and/or measurement of fields in space are necessary for
understanding or designing:
– Transmission lines (twisted pair, co-axial cable, fiber optics, etc.)
– Antennas and reflection and refraction of radio waves at a distance
– Analysis of components having size/dimensions larger than about 1/6 wavelength
of the electro-magnetic waves flowing in and around it. (Typically at high sine wave
frequencies).
– Devices and cases above are often called “distributed” components or spaces.
Analysis involves time and also three dimensions (x,y,z) of space in general as
independent variables.
• In most other cases, it is far simpler for human calculations to approximately
characterize each component by stating the relationship of current and
voltage at its “terminals” (the electrodes where current enters and leaves).
These are called “lumped” components and analysis involves only time as an
independent variable.
• Often engineers approximate a real components by a combination of several
lumped ideal devices. Example: a real coil or inductor is represented via an
ideal zero resistance coil of wire in series with an ideal “equivalent resistor.”

7. © 1997-2005, R.LevinePage 7
Voltage and Current
• Voltage difference between two points is also called Tension in
non-English documents.
– A volt is the ratio of energy change per unit of electric charge.
– Voltage difference at the terminals of a component is equal to the sum
of many smaller voltage changes. Consider a current path through the
component from one termnal to the other. Imagine this path “cut up”
into n short lengths, like slicing a sausage. Consider a short length λk of
the kth
piece, and Ek is the local value of the electric field parallel to the
λk segment there. The product vk=Ek•λk, is the voltage change of this kth
piece. The sum of all the little voltages, v1 + v2 +v3 +…+ vn. computes the
total terminal voltage.
• Current is the time rate of electric charge flow (coulomb/second)
• Some lumped components can be described by a graph or list or
table or formula giving the voltage for each value of current. (These
component types have “amnesia” and don’t have any dependence
on past historical values of voltage or current.)
• Other types of components require a description of the relationship
between the time rate of change of current or voltage.

8. © 1997-2005, R.LevinePage 8
Linear vs. Non-linear
• Considering “amnesic” components, the current-voltage graph
(or input-output voltage graph) may be either a straight line or a
curved line. A straight line relationship indicates a “linear”
component.
• 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.

9. © 1997-2005, R.LevinePage 9
Linear Systems
• Linear systems have Interesting, important, but
limited capabilities
– Transmit electromagnetic waveforms from place to place via
wires, cables, optical fiber, or radio
• Usually accompanied by an undesired reduction (called loss or
attenuation) in signal power level
– These transmission media typically modify the amplitude
and the wave shape of certain waveforms
• 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)

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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 non-linear overall
• Digital electronics intentionally exploits the non-linear
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

11. © 1997-2005, R.LevinePage 11
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 discussed in this course.

12. © 1997-2005, R.LevinePage 12
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
– Exotic high energy particles (like cosmic “rays”) have some
significance (for example their bad effects if they penetrate a
memory chip) but they are also outside the scope of this
course.

13. © 1997-2005, R.LevinePage 13
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

14. © 1997-2005, R.LevinePage 14
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 (symbolic of
Lithium) is known to be
wrong in several ways.
Niels Bohr, Danish physicist, invented this theoretical model ca. 1913.

15. © 1997-2005, R.LevinePage 15
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.
*also written Schroedinger

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Energy = h • frequency
• The energy Ê (in joules or watt•seconds) of an
electromagnetic wave (light, radio waves, infra-red,
etc.) is related to its frequency f (in cycles/second or
hertz -- Hz) by this formula:
Ê = h•f (the Greek letter ν (pronounced nu) is used
rather than f in some documents)
• where h = 6.625•10-34
joule•seconds (Planck’s
constant) (alternate unit: watt•s2
)
• 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.

17. © 1997-2005, R.LevinePage 17
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...
1 MHz
106
Hz 109
1012
1015
1018
On this logarithmic scale each mark represents a value 10 times the value to its left.
1 GHz 1 TeraHz 1 PetaHz
AM Broadcasting
Band (car radio)
TV and FM
Broadcasting
(VHF and UHF)
Cellular and
SMR Radio
PCS Radio
Band (1.9 GHz)
Ionizing radiation frequency range
Visible Light X-Rays
IR UV
Gamma Rays

18. © 1997-2005, R.LevinePage 18
Spectroscope
Light source such as
hydrogen gas in a sealed
glass tube with electric
sparks.
Greatly enlarged view of
grooved surface
Diffraction grating, a front
surface mirror with tiny
parallel grooves.
Some lenses used to focus
the image are not shown
here
Images of the slit are formed on
photographic film.
Light obstacle
with slit. Width
of slit is actually
very narrow.
• Identifies Frequencies/Wavelengths Present in Light

19. © 1997-2005, R.LevinePage 19
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•108
meter/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.

20. © 1997-2005, R.LevinePage 20
Bohr Orbits
• Bohr’s atom was like a little “solar system” of planets
– Each negative electron held in an orbit by electric attraction to the positive nucleus
• 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 stable orbit has angular momentum that is an integral multiple (1,2,3, etc.) of the minimum
angular momentum h/2π
• 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 Ê H orbit
Non-radiating low energy EL orbit
Radiated light
frequency f,
where h•f= Ê H- Ê L

21. © 1997-2005, R.LevinePage 21
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:
Ê H - Ê L = 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.

22. © 1997-2005, R.LevinePage 22
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/2π, for n=1,2,etc.)
Note: Planck’s constant h is both a unit of energy·time product (joule•sec) or alternatively a unit of angular momentum (kg•m2
/s)
• But not for a hydrogen molecule H2
– Bohr’s 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!
• Bohr’s 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.

23. © 1997-2005, R.LevinePage 23
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

24. © 1997-2005, R.LevinePage 24
“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.

25. © 1997-2005, R.LevinePage 25
Wave Properties
• Erwin 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.

26. © 1997-2005, R.LevinePage 26
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.

27. © 1997-2005, R.LevinePage 27
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.

28. © 1997-2005, R.LevinePage 28
Main Properties
• Electrons and other fundamental “particles” are not
particle-like at all (some say “wave-icle”)
• 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

29. © 1997-2005, R.LevinePage 29
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

30. © 1997-2005, R.LevinePage 30
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…

31. © 1997-2005, R.LevinePage 31
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)
oscillatory 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
f=(Ê H- Ê L)/h.
• The radiation from this oscillating charge is similar to radiation from a
large size radio 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.

32. © 1997-2005, R.LevinePage 32
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
Fully reflecting
“mirror”
Partly reflecting
“mirror”

33. © 1997-2005, R.LevinePage 33
Interesting Side Note: Spin
• The two lowest energy electron shells have an almost identical
shape. Of the two, one shell is occupied or “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 its orbital 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.

34. © 1997-2005, R.LevinePage 34
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

35. © 1997-2005, R.LevinePage 35
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

36. © 1997-2005, R.LevinePage 36
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 gram-molecular-
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

37. © 1997-2005, R.LevinePage 37
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 when measured at the same temperature
(this constant is 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

38. © 1997-2005, R.LevinePage 38
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…

39. © 1997-2005, R.LevinePage 39
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 = λ • f
– using the Greek letter λ (lambda) symbol for
wavelength.
– Frequency is also sometimes represented by the
lower case Greek letter Nu (ν) in physics books.

40. © 1997-2005, R.LevinePage 40
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 described by a combination of higher energy
waves 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
of valence and conduction electrons.

41. © 1997-2005, R.LevinePage 41
Energy Gap
• Certain materials (e.g. sulfur, some crystal structures of carbon, silicon,
germanium, 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.

42. © 1997-2005, R.LevinePage 42
Davisson-Germer
• In the 1920s, Davisson and Germer, two scientists at Bell
Laboratories, discovered the effect named for them (and got the
Nobel Prize!!):
• 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 accelerator electrode
• As they changed the electron energy, D. & G. 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).
Accelerator electrode

43. © 1997-2005, R.LevinePage 43
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.

44. © 1997-2005, R.LevinePage 44
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)

45. © 1997-2005, R.LevinePage 45
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.
1.01.414

46. © 1997-2005, R.LevinePage 46
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 a
wave direction b
d
1.41d
0.7d

47. © 1997-2005, R.LevinePage 47
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
– H2O atom arrangements formed under high pressure are not
hexagonal

48. © 1997-2005, R.LevinePage 48
Carbon has two major crystal structures:
1. Diamond has a highly symmetrical crystal structure, with each
atom having four equidistant nearest atoms
– Diamond is mechanically very 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

49. © 1997-2005, R.LevinePage 49
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 materials):
– 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

50. © 1997-2005, R.LevinePage 50
Large Single Crystals
• Large single perfect crystals have interesting mechanical and electrical
properties, but they tend to reform naturally over time into smaller grains
of different crystal axis orientationer
– 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 L-shaped 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.

51. © 1997-2005, R.LevinePage 51
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.

52. © 1997-2005, R.LevinePage 52
Best Metal Conductors (in order)
• Silver: resistivity 16 nΩ•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 nΩ•m
– widely used in pure or alloy form (Brass, etc.); forms a surface
oxide which is a relatively low resistance semiconductor
• Gold: resistivity 24 nΩ•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 nΩ•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 nearby
combustible materials.

53. © 1997-2005, R.LevinePage 53
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.

54. © 1997-2005, R.LevinePage 54
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

55. © 1997-2005, R.LevinePage 55
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

56. © 1997-2005, R.LevinePage 56
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 counter-effect,
namely the increase in the number of moveable conduction band
electrons

57. © 1997-2005, R.LevinePage 57
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.

58. © 1997-2005, R.LevinePage 58
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!

59. © 1997-2005, R.LevinePage 59
Resistance vs. Temperature
Typical
semiconductor
Temperature
Typical electric conductor (metal)
Theoretical semiconductor with no wave scattering
due to thermal vibration of atom nuclei in the solid.
Resistivity in ohm•meter

60. © 1997-2005, R.LevinePage 60
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.

61. © 1997-2005, R.LevinePage 61
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

62. © 1997-2005, R.LevinePage 62
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

63. © 1997-2005, R.LevinePage 63
Junctions
• When two materials are in contact
– In general, some electrons transfers from one material to the
other
– Materials with a higher atomic number have more positive charge
on the atomic nuclei in the atoms, and thus they attract negative-
charged electrons with greater force. Electrons move into that
material from the other.
• In a mixture of atoms (an alloy or an almost pure material “doped*”
with a small amount of a second material) the average positive atomic
charge is used, based on a large number of atoms
– Materials are classified in reference books according to their
“electro-negativity” or “contact potential” or “ionization potential”
measured in volts
• This affects other situations when electrons leave or enter a
piece of material
– Electrodes in electric batteries (flashlight or electric torch, automobile,
etc.)
– Photoelectric emission of electrons from metals (“electric eye”)
*“Doping” is alloying using very small amounts of minor materials

64. © 1997-2005, R.LevinePage 64
“Static” Electricity Example
• When you rub two dissimilar objects together and
then separate them quickly:
– hard rubbing removes any contamination on the
surface, permitting good contact
– electrons transfer to the material with higher
“average” atomic number, producing negative net
movable electric charge
– The other material is left with a deficit of electrons
and a net positive charge
• Also occurs when you:
– quickly break solid objects (e.g., a sugar cube or
mint candy) into pieces
– pull adhesive tape from a roll

65. © 1997-2005, R.LevinePage 65
Safe to Try This at Home!
• Take roll of “Scotch®” brand or similar sticky tape:
– Wait in a darkened room until the pupils of your
eyes accommodate to the darkness
– Rapidly pull about 50 cm (20 inches) of tape off
the roll while looking at the point where the
adhesive side separates from the layer below it
– You will see a line of electric sparks...Due to
electrons which cling to one of the separated
materials, and then jump back through the air
– Safe “experiment” to do with/for children!
• don’t bump into anything in the dark!
• don’t waste too much tape!
pull
Pencil used
as axle

66. © 1997-2005, R.LevinePage 66
Static Electric Effects
• When you brush your hair, rub your shoes on a carpet, rub a
glass rod with fur, etc. etc., you produce so-called “tribo-
electricity” (electricity due to rubbing)
– If you separate the two dissimilar touching objects quickly,
each object becomes oppositely electrically charged (some
extra electrons stay with one object).
– Best done in dry, low atmospheric humidity conditions
(winter months, dry climate area, etc.)
• High humidity (water vapor in air) causes surface
condensation, producing an electrically conductive
surface condition, which allows electric charge to move
to other areas and thus neutralize a local charged area
• Anti-static sprays for clothing, etc., produce an
electrically conductive surface
• Good conductors (like metals) don’t retain charge at one spot,
but spread it over the surface of the entire object

67. © 1997-2005, R.LevinePage 67
Semiconductors and
Insulators
• In a good insulator, surface charge stays put for a
very long time
• Semiconductor spot surface charge very slowly
moves (diffuses) away
– slow movement is due to thermal diffusion (random motion
due to thermal energy) of electrons
– electrons are always in some random motion, which we
perceive as motion (kinetic) energy of “heat”
– Somewhat like a “neat” pile of leaves eventually spreading
out over the whole lawn due to random motions due to
changing wind directions, etc.

68. © 1997-2005, R.LevinePage 68
Controlled Charge Layers
• The operation of “active” semi-conductor devices
depends on producing and controlling layers of
electric charge
• These usually occur at the interface between two
kinds of semi-conductor materials, or between a
semi-conductor and a metal conductor
• A “favorite” semiconductor is silicon (Si), which is
abundantly available (purified from beach sand SiO2,
for example) and on which we intentionally form an
excellent surface protective layer of SiO2 on
integrated circuits, transistors, etc.
• Other semiconductors are germanium (Ge) which is
scarcer, and gallium arsenide (GaAs) 50-50% alloy

69. © 1997-2005, R.LevinePage 69
Purified Semiconductors
• To produce a controlled result, semiconductors are first highly purified
– Typically only one “impure” atom in 100,000,000 silicon atoms!
• A thick silicon rod is “zone refined”
– Melted and then cooled slowly, starting from one end, to form a very pure solid
• This “zone refining” process is similar to freezing pure water ice out of salty
ocean water
– Icebergs near the earth’s poles consist of pure water (no salt)
– “silicon ice” (solid) which is slowly frozen from melted silicon is very pure
• The impurities are mostly trapped in the end of the rod which solidifies last
• That end is cut off and used for other purposes where the silicon does not
need to be so pure
– Example: making “Varistors” for telephone sets (discussed in another
session)
• Purified silicon (or a Group III-V alloy) is then “doped” to produce a slight (1
part in 106
) fraction of nuclei with either higher or lower electric charge than
the average nuclear charge

70. © 1997-2005, R.LevinePage 70
Materials Used
• Most semiconductor materials are in Group 4(a) of the
Mendeleyev Periodic Table of the elements
– Doping materials are taken from Groups 3a and 5a
• Similar atomic size and electron bonding
• Fits into the crystal structure of the solid semiconductor
• In some cases a 50-50 mixture (alloy) of materials
from Groups 3a and 5a is the base material
– Called III-V (Roman numerals 3-5) materials
– Gallium Arsenide (GaAs) is used extensively because of
higher electron mobility (electron waves move further-- on
average --before interacting with nuclei). Consequently
transistors have better high frequency or fast switching
performance
– Doping achieved by using slightly more/less than 50% of the
Group 3 or 5 material

71. © 1997-2005, R.LevinePage 71
Part of Periodic Table
Yellow-highlighted names are elements used in practical room-
temperature semiconductor devices.
• Chemical abbreviation names are underlined.
• C and Sn have multiple crystal structures, only one of which
(diamond structure) is a semiconductor
• Elements in groups 3, 5 are used as dopants
• Germanium is used only rarely for special applications.
Group 3a Group 4a Group 5a
Boron Carbon Nitrogen
Aluminum Silicon Phosphorus
Gallium Germanium Arsenic (As)
Indium Tin (Sn) Antimony (Sb)

72. © 1997-2005, R.LevinePage 72
Alloying or Doping
• When Group 5 material is added, the average atomic number is higher.
This is called N (negative) type material
– The average nuclear positive charge per unit volume is greater than
“intrinsic” (pure) silicon, and there are also more electrons as well
• Of course, a piece of material as a whole is electrically neutral
– When Group 3 material is added, the average atomic number is lower. This
is called P (positive) type material
– The average nuclear positive charge per unit volume is less than “intrinsic”
(pure) silicon
• A semiconductor diode is made by joining two pieces of silicon:
P and N material respectively, and also outer electrodes
– By welding two pieces in historically early transistors
– Depositing built-up layers from vapor in a vacuum chamber
– Implanting ions from the surface using an electric “ion gun” in a
vacuum chamber to produce doping in layers

73. © 1997-2005, R.LevinePage 73
PN Junction Diode
P N
Anode Cathode
P-type N-type
Graph shows net electric charge
density vs. distance right or left
of junction
Electrically
neutral
region
Electrically
neutral
region
Region of extra electrons,
represented by green color.
Region of missing or
“depleted” electrons,
represented by red color.
}
So-called “depletion layers”
Electrode
Graphic
Symbol
+
-

74. © 1997-2005, R.LevinePage 74
When P and N Pieces First Touch...
• (Touching surfaces must be microscopically
clean in this example...)
• First, electrons spill over from the border side
of the N material into the P material, because
they are attracted by the greater nuclear
positive electric charge of the P material
• This leaves a layer just inside of the left
surface of the N material (red color) which
has less electrons per unit volume than the
neutral parts of the N piece

75. © 1997-2005, R.LevinePage 75
Depletion Layers
• The width of these two layers increases until they reach an
equilibrium condition in which just enough electrons are on the
left side to repel any more electrons spilling over.
• If we could mechanically break the P and N pieces suddenly
apart at this time, we would leave some negative charge
trapped on the P side, and a net positive charge trapped on the
N side. (The charge may jump back creating a spark!)
• Because this is a semiconductor instead of a good conductor,
these layers* stay in place at the two sides of the interface. (In a
metal, the extra electrons would move quickly away from the
interface and go all over the surface of piece of metal.)
• This double layer of two opposite net electric charges (+ and -)
is also called a “dipole” layer or “sandwich”
*Called depletion layers, although only one of them is actually
“depleted” below the normal number of electrons.

76. © 1997-2005, R.LevinePage 76
Current-Voltage Measurement
• The Diode is a “non-linear” electrical device. This setup (shown
schematically) measures current, i, at various voltage v values
V
A
+
-
Ammeter, measures
current
Ideal voltmeter measures diode’s voltage, but no current
flows through the voltmeter. Real voltmeters allow very
small current flow. Anode (top) of diode symbol is the
conventional positive voltage terminal.
Adjustable or variable voltage source,
can produce both positive and negative
voltages.
i

77. © 1997-2005, R.LevinePage 77
Typical Diode i-v Curve
• Several distinct regions of operation
A
B
C
D
Vz 1 2 v (volts)
i
(mA)
Note: a section of negative
voltage axis is not shown. Origin of graph,
v=0, i=0
1
Region Description
A-B Approximately linear increase in
current vs. voltage.
B-C Accurate theoretical formula:
i = Io (e qv/kT
-1)
where Io is temperature dependent,
but is typically ~10 µA at room
temperature. Also kT/q ≅ 0.2 volts
at room temperature.
C-D Zener or avalanche breakdown
region. Approximately constant
voltage. Vz can be 3 to 600 V,
depending on design of diode.
mA=milliamperes
of current;
1 mA=0.001 A.
B is approx. boundary
between exponential
and linear parts.

78. © 1997-2005, R.LevinePage 78
Forward Current Regions
• In region A-B, the voltage across the depletion layer is very small,
and we mainly see the ordinary electrical resistance of the two
neutral parts of the diode, resistance Rf.
– The depletion layer is very thin.
• In region B-C, the depletion layer gets thicker or thinner, adding or
removing electrons at their outer edges, when the voltage changes.
• When the applied voltage is positive, the depletion layer is very
narrow, and most electrons can go across the junction (right to left
flow of electrons makes a positive current left-to-right, since positive
current flow is opposite negative electron flow*)
• The number of electrons which have enough energy to get across the
depletion layer is dependent on temperature (more about this later)
• The theoretical prediction of this formula (stated without proof), based on
electron thermal energy level, is very accurate in this region
* Blame Benjamin Franklin for using negative numbers for one kind of static electricity. If he knew then that
electric current is mainly from electrons, he would have made the opposite choice, I’m sure! Before
Franklin’s suggestion “positive” electricity was classified as vitreous (from rubbing glass) and “negative”
electricity was classified as resinous (from rubbing amber). Franklin realized that they were two polarities of
the same qualitative type, instead of two qualitatively different things.

79. © 1997-2005, R.LevinePage 79
Two-segment Approximation
• In some situations, a two segment straight line approximation can be
reasonably accurate for some mathematical analysis purposes
1 2
v (volts)
i
(mA)
mA=milliAmperes
of current;
1 mA= 0.001 A
Origin of graph,
v=0, i=0
Forward region is described
as a resistance Rf.
Special
case is Rf=0 ohms.
Reverse current is described
as zero. No description of
breakdown voltage region
in this example.

80. © 1997-2005, R.LevinePage 80
Reverse Current
• Reverse Current
– The depletion layer is very wide when reverse voltage is high.
Very few electrons get into the depletion layer from the neutral
parts of the diode. Only electrons “produced” inside the
depletion layer will move through it. These electrons are
“produced” by giving more energy to valence band electrons so
that they become conduction band electrons (a change of
electron wavelength). Two methods for giving electrons more
energy:
• Higher temperature
• Shine light (infra-red, visible, ultra-violet) on the junction
– The reverse “leakage” current (from origin to point C) is almost
constant over most of the negative voltage range. Reverse
current depends on the number of electrons per second which
“appear” in the depletion layer, and not upon the voltage.
Mainly temperature dependent.

81. © 1997-2005, R.LevinePage 81
Breakdown Current
• In region C-D, the diode has a sudden increase in current. This
is called the “avalanche breakdown” or “Zener” region (named
for physicist Clarence Zener)
• In this region, the high electric field in the middle of the depletion
layers accelerates electrons produced there (by action of heat
or light) so much that they can “dislodge” other electrons from
the valence band (into the conduction band)
• When one energetic electron can “dislodge” two or more such
electrons, we start a “chain reaction” in which these electrons
can produce even more conduction electrons.
• This is like a geological avalanche, in which the first boulders
rolling down a hill dislodge other boulders and so forth...

82. © 1997-2005, R.LevinePage 82
Depletion Layer Thickness
• Depletion layer becomes narrow when positive voltage is
applied to the diode
– Then more electrons spill over from N to P part of diode.
• Depletion layer becomes thicker when negative voltage is
applied to the diode
• Thickness of depletion layer is main thing which controls how
many electrons can cross the depletion layer “barrier”
distance right or left
of junction
Vertical axis is
net electric charge
density
Zero volts on
diode (blue)
Positive voltage
on diode (red)
Negative voltage on
diode (green)

83. © 1997-2005, R.LevinePage 83
• The average number of electrons at each level of
internal energy in a solid is given by the Fermi
formula (stated here without proof). Non-integer
values of n(Ê) indicate average of various integers.
Electron Energy
Êf (the Fermi energy level)
Ê
n(Ê)
1
0
Very low temperature (blue)
Medium temperature (green)
Very high temperature (red)
Êb, a typical “barrier” energy
Shaded area on graph indicates
energy levels with electrons at medium
temperature. Gap surrounding Êf is due
to the band gap in a semiconductor.
1
n(Ê) = e ((
Ê-
Êf
)/kT)
+1

84. © 1997-2005, R.LevinePage 84
There are Either 1 or 0 Electrons at a Specific
Energy Level (Pauli’s Exclusion Principle)
• Because of electron “spin” (intrinsic
magnetism and angular momentum) there
are two wave arrangements at almost the
same energy level
• Some documents describe the maximum
number of electrons at each level as 2
• Some documents describe each level with
different spin separately, and give the
maximum number of electrons per level as 1

85. © 1997-2005, R.LevinePage 85
How Many Electrons Pass Over the Barrier?
• The depletion layers in the diode act as an adjustable energy
level barrier to control electron flow across the two parts of the
depletion layer
– Positive applied battery voltage lowers the energy barrier, and
negative voltage raises the energy barrier
• The amount of current flow is related to the number of electrons
which have enough (thermal) energy to naturally get past the
barrier
– This is shown on the previous graph by the shaded area under a
curve from the barrier energy, Êb, upward
– Such a typical area is shaded under part of the medium
temperature (green) curve
– You can see that the corresponding area would be greater under
the high temperature curve, although it is not marked
• For a positive voltage, the barrier is lowered so much that
almost all the conduction electrons can pass through
– Only the ordinary “ohmic” resistance of the neutral parts limits the
current when very high positive voltage is used!

86. © 1997-2005, R.LevinePage 86
Reverse Current• When the energy barrier is very high (large negative voltage) almost
no electrons have enough thermal energy to pass over the two parts
of the depletion layer
• But the electric field in the junction, between the two parts of the
depletion layer, is very strong:
– electrons in the left depletion layer repel any electron at the junction, pushing it to
the right
– the right (positive) depletion region pulls any electrons at the junction to the right
• We have all the forces to move electrons an produce a large negative
current…. except that there are almost no conduction electrons located at the
junction!
• If a conduction electron is produced or created in the middle of the junction, it
will immediately be moved by the strong electric field
• A few electrons “appear” in the junction each second because they have
enough thermal energy to change from the valence to the conduction band
just at the junction! (consider case without light on the junction)
• Thus the reverse current is dependent on the number of thermally produced conduction
electrons, and not on the reverse voltage. It changes only due to temperature, not due to
voltage changes.

87. © 1997-2005, R.LevinePage 87
Avalanche (Zener) Breakdown
• Zener breakdown occurs due to high electric field in the junction
• High reverse electric fields are produced by:
– Heavily doped P and N materials to fabricate diode
– High negative voltage
• They produce a larger charge density in the depletion layer,
even at low reverse voltage
• Diodes made specifically to “break down” at low reverse
voltages are called Zener diodes. They also are designed and
made with cooling fins, etc. to keep them from melting under
high voltage and high current (high power)
• Current is then limited only by the ohmic resistance (usually an
external resistor designed to be used with the diode)
• Zener diodes are mostly used to produce an accurate reference
voltage for measurement devices or analog-digital converters,
etc.

88. © 1997-2005, R.LevinePage 88
Semiconductor Applications
• One important use for diodes is to convert alternating current into direct
(unidirectional) current in power supply circuits.
• Diodes are also useful in some logic devices, and we can make some
types of digital logic circuits using only diodes and resistors
• Transistors are more interesting and have more applications than
diodes.
• Two types of transistors are widely used:
– Bipolar Junction transistors1
(BJTs), which are physically like two
junction diodes back-to-back
– Field Effect Transistors (FETs), consisting of a singlelarge area
junction diode, in which we use the voltage on a control (gate)
electrode to modify the available current flow area outside the
depletion layer for transverse current flow in the other part of the
diode. This category includes metal oxide silicon (MOS) FETs
Note 1: The name “transistor” is a contraction of the two terms trans-
resistor. Name due to John R. Pierce, Bell Laboratories scientist.

89. © 1997-2005, R.LevinePage 89
Transistor Properties
• Transistors can “amplify” electrical signals
– In the normal amplification state, transistors actually control
the flow of electric power, from a battery or other power
source, usually in proportion to the input power from the
signal
– The British name for the vacuum tube (the historical
predecessor of the transistor) was a “valve,” which is a very
good description of what a transistor does in the amplifying
state
– It controls power flow from the power supply like a water
valve controls water flow
• Transistors have 3 electrical terminals, and thus a
separate input and output “port”
– More convenient for processing analog or digital signals

90. © 1997-2005, R.LevinePage 90
Junction Transistor
N
P
N
Collector
Emitter
Base
C
B
E
Graphic
symbol
In the usual amplifying configuration,
the base is more positive than the emitter,
and the collector is at an even more positive
voltage. The E-B junction is thus ON and the
C-B junction is OFF (reverse biased). The thick
arrow represents the magnitude of electron flow.
Most of the electrons that pass from the Emitter
to the Base are collected by the Collector.
NPN unit is shown.
PNP units also
are made, and use
opposite voltage
polarities from NPN.
The graphic symbol
for a PNP transistor
has the opposite arrow
point direction.

91. © 1997-2005, R.LevinePage 91
Transistor Amplification
• The voltage across the Emitter-Base junction controls
the Emitter current
• A large, and almost constant, fraction (called α) of the
emitter current is “collected” by the collector
– The ratio iC/iE is traditionally called α (alpha). It depends
mainly on the geometry of the transistor. Since the neutral
region in the base is very narrow, most of the emitter-base
electrons go into the base-collector junction, where the high
electric field propels them out the collector electrode. A small
fraction (1-α) leaves via the base electrode. Typical value for
α is 0.99
– The ratio beta β = α/(1-α) is the ratio of the collector current
to base current. Typical value for β is 99. The transistor
therefore “amplifies” the base current by approximately 100
and produces a larger current at the collector.

92. © 1997-2005, R.LevinePage 92
One Computational Model
• This simplified circuit model for a junction transistor
uses a current-controlled current source
– The base current is viewed computationally as the thing
which controls the collector current
B
C
E
iC
iE= iB • (1+β)
iB
β•iB (A current-controlled current source.)
• This model only describes behavior when the collector
junction is in reverse voltage state and emitter junction is in
forward voltage state, typically for amplification purposes.

93. © 1997-2005, R.LevinePage 93
Field Effect Transistor
Source
Electrode
Drain Electrode
Gate
Electrode
P-gate, N-channel unit
shown.
}
S
D
G
Graphic
Symbol
Notice the “blob” in the
N-side depletion layer due
to electric field interaction
with Drain electrode.
The arrow indicates
direction of electron
flow. Narrowing
of arrow suggests
current “strangling”
effect from negative
gate voltage, which
narrows the
neutral N channel.
Depletion layers.
The words “source”
and “drain” are based
on the concept of
positive charge flow.

94. © 1997-2005, R.LevinePage 94
Two FET Analysis Models
1. Variable resistor between Source and Drain
– Resistance increases when Gate voltage is more negative
– Physically a good model
• Represents the narrowing of the N-channel
• But computationally non-linear, leads to products of
independent variables like current and voltage
2. Current source between Source and Drain, controlled
by gate voltage
– Not as accurate physically for signals with large voltage
ranges
– But computationally leads to linear equations, which are
easier to solve

95. © 1997-2005, R.LevinePage 95
Model 2
• This circuit model uses a voltage-controlled current
source
– The gate voltage is viewed computationally as the thing
which controls the source-drain current
Gate
Source
Drain
iS-D+ vG -
g•vG
The parameter g is the so-
called trans-conductance of
the FET. It is the ratio of a change in
iS-D to the causative change in vG.
Note that there is no current path
in this model between the gate and
other parts of the FET. This is due
to assuming that the reverse current
of the gate-body junction is zero. In
fact it is typically a few microamperes.

96. © 1997-2005, R.LevinePage 96
Metal Oxide Silicon (MOS) Transistor
Source
Electrode
Drain Electrode
Gate
Electrode
(metal)
Also called insulated gate FET
(IGFET). A layer of SiO2 (equi-
valent to beach sand, shown in
blue on the drawing) electric
insulation here is actually much
thinner than the illustration. No
P-type layer! This still produces
a positive (red) depletion layer
in the N-type part and channel
width is controlled by the gate
voltage. No steady (dc) gate
current flows for either positive
or negative gate voltage.

97. © 1997-2005, R.LevinePage 97
Multiple Gate Transistor - I
Source
Electrode
Drain Electrode
Gate
Electrode 1
Multiple gate electrodes are
used to implement digital
logic functions (to be discussed
more in a later lecture). This
form with side-by-side gates
allows some source-drain current
to flow when either gate 1 OR
gate 2 has a positive voltage. This
implements the inclusive OR
logical function with a minimum
number of components, particularly
when implemented in an integrated
circuit.
Gate
Electrode 2

98. © 1997-2005, R.LevinePage 98
Multiple Gate Transistor - II
Source
Electrode
Drain Electrode
Gate
Electrode 1
Current from source to drain
flows only when both gate 1
AND gate 2 are positive. Note
that there are two places where
negative gate voltage could
pinch off the channel. This
implements the digital logic
AND function.
All of these configurations can
be implemented in integrated
circuits, although these pictures
show source and drain electrodes
on the edges.
Gate
Electrode 2

99. © 1997-2005, R.LevinePage 99
Generic Amplifier
• All these 3-electrode transistor types can be used to build an amplifier
• Digitally interesting things happen in the two extreme output voltage regions of
operation, aside from use of such devices for amplifying sound or radio signals
• More details on the operation of the amplifier in the next lecture.
output voltage point
+
-
input
voltage
source
Generic “ground” or “earth”
graphic symbol. Actually represents
the frame or cabinet in most modern
equipment.
Fixed voltage power
supply, shown here
as a battery symbol.
Often the power supply
device and the wire from
power source to ground
is omitted from drawings.
RL , “load” resistor (or
Loudspeaker, etc.)
Generic “cathode”:
(drain or emitter)
Generic control
electrode: (gate
or base)
Generic “anode”:
(source or collector) Vpower
←This box is replaced
by a particular transis-
tor in a real amplifier.

100. © 1997-2005, R.LevinePage 100
Radiation and Semiconductor
Junctions
• Several important interactions between absorption
and radiation of light and electromagnetic waves
occur in semiconductor junctions
• These interactions relate to:
– Temperature dependence of Io (“leakage current”)
– Photo-voltaic cells (“electric eyes”)
– Light Emitting Diodes
– Laser Diodes
• Important to systems reliability and use of diodes in
optical systems

101. © 1997-2005, R.LevinePage 101
Temperature Dependence of Io
• The term Io in the formula for diode current:
i = Io (e (qv/kT)
-1), is itself temperature dependent
• There is a very high electric field at the very center of
the junction, but usually almost no conduction
electrons are present
– High electric field is due to a combination of excess electron
repulsion and net positive depletion layer attraction, which
both act in the same direction on any moveable electron
which may exist at the junction center
– A conduction electron can be “created” (electron-hole “pair”
production) in that location when a valence electron absorbs
enough energy so that it reconfigures its wave function as a
conduction electron there.

102. © 1997-2005, R.LevinePage 102
Conduction Electron Production
• Energy could come from:
– Thermal kinetic energy
• Interaction with thermal vibration of nuclear cores of atoms
• More thermal energy transfer at higher temperature, leads to
greater Io reverse “leakage” current, exponentially increasing with
temperature
– Direct electron absorption of radiation
• Infra-red, visible or ultraviolet light, or x-rays, cosmic rays, etc.
• Frequency of radiation must be high enough so E=h•f is greater
than energy gap (where h is Planck’s constant). Radio frequency
radiation is usually too low
– Due to “avalanche” chain reaction
• Secondary effect of thermally created conduction electrons at
Zener breakdown voltage
• Direct electron-electron interactions create even more conduction
electrons via “chain reaction”

103. © 1997-2005, R.LevinePage 103
Diode PhotoElectric Devices
• These effects allow reverse-voltage diode to
generate current due to radiation
– Photo-voltaic direct power conversion from sunlight
• Io proportional to incident light intensity
– opto-electric detector for fiber optic system receiver
• Avalanche diode is sensitive to very low radiation, due to
“multiplication” of current by the avalanche effect
• Similar phenomena of electron avalanche was used in
historical vacuum tube technology. Electron-multiplier
photocells were used to detect very low levels of light and
in the early Farnsworth “image dissector” TV camera

104. © 1997-2005, R.LevinePage 104
Undesired Radiation Effects
• Devices which use semiconductor junctions
(transistors, etc.) for digital logic and memory
purposes are adversely affected by low-level ionizing
background radiation, cosmic rays, etc.
• Computer memory chips appeared to have random
infrequent but mysterious data errors until this cause
was identified in the 1970s
• Radiation-induced current pulses cause OFF
transistors to suddenly go ON
• Integrated circuit packaging must shield the silicon
chip from external radiation, and must not itself
contain radioactive isotopes
• High purity levels required in plastic encapsulation as
well as interior silicon!

105. © 1997-2005, R.LevinePage 105
Light Emission During Forward
Current Flow
• When an electron crosses the junction from N to P
side, its energy changes due to difference in interior
average atomic number of the atom cores
• The electron “cloud” experiences oscillations during
the transition from higher to the lower energy level
– The frequency f of this oscillation is given by Ê2-Ê1=h•f
– Some diodes are made with opaque enclosures so emitted
light is not noticeable. Light may also be in the Infra-red
spectrum and not perceptible to the human eye! However,
radiation is produced by forward current in a diode.

106. © 1997-2005, R.LevinePage 106
Light Emitting Diodes (LEDs)
• Greater difference in energy levels in the P and N
sides of the diode (due to high dopant amounts)
produce greater energy change, higher frequency
light, shorter wavelength
• Earliest light emitting diodes produced infra-red or
visible red light
– LEDs in yellow, green and recently blue visible light colors
are now available
• LEDs are used extensively as indicator lamps, and as
picture elements in color matrix displays for lap-top
computers, etc.
• LEDs are used as electro-optic converters for multi-
mode and graded index fiber optics

107. © 1997-2005, R.LevinePage 107
Laser Diodes (LDs)
• Fabrication of light emitting junction surrounded by
partially reflecting surfaces which produce a standing
wave electromagnetic field, thus causing intense
emission of approximately mono-chromatic light
(LASER=light amplification by stimulated emission of
radiation)
• More efficient light output than LED
• Narrower, monochromatic, focused beam
– Couples better into small core of single mode optical fiber than
LED
– Less chromatic dispersion (pulse time-spreading) in the fiber,
so higher data bit rate is permitted
– Used also for reading/writing reflective spots on CD-ROM disks