Electronics Review

1
Electronics Review

• EETS8320
• SMU
• Session 4, Fall 2005
• (print slides only, no notes pages)

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
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 EF/q or FqE
• 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
  wattsecond) of energy divided by one coulomb of
  electric charge

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 ? with the amount
  i of test current.
• Magnitude BF/(i?) or F i??B
• Unit newton/(amperemeter) (or voltsec/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 voltsecond 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
  wattsecond or a joule (rhymes with foul.)

5
Directions
F
Force on charge is parallel to electric field.
E
q
Force on current element is perependicular to
both current element and magnetic field.
F
B
i?
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
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
  ?k of the kth piece, and Ek is the local value of
  the electric field parallel to the ?k segment
  there. The product vkEk?k, 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 dont 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
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 Ohms Law), Inductors,
  Transformers, Capacitors, transmission wires and
  cables
• Linear equations describe linear phenomena
• Example vR 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? idt) therefore qCv
• or time rate-of-change of current (for an
  inductor vL 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
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)

10
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
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
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
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
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
Known to be Wrong

• Bohr got around some self-contradictory problems
  of classical (non-quantum) physics by assuming
  certain unexplainable and unexplained things
• Why dont 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 Schrödingers wave
  theory) give a better explanation. Erwin
  Schrödinger, Austrian physicist, invented wave
  (quantum) mechanics in 1926.
• also written Schroedinger

16
Energy h frequency

• The energy Ê (in joules or wattseconds) 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 hf (the Greek letter ? (pronounced nu) is
  used rather than f in some documents)
• where h 6.62510-34 jouleseconds (Plancks
  constant) (alternate unit watts2)
• 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
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
109
1012
1015
1018
1 MHz
1 GHz
Ionizing radiation frequency range
1 PetaHz
1 TeraHz
Cellular and SMR Radio
IR
UV
Visible Light
Gamma Rays
X-Rays
TV and FM Broadcasting (VHF and UHF)
AM Broadcasting Band (car radio)
PCS Radio Band (1.9 GHz)
On this logarithmic scale each mark represents a
value 10 times the value to its left.
18
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.
Images of the slit are formed on photographic
film.
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
  fc/wavelength, where c3108meter/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
Bohr Orbits

• Bohrs 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/2p
• Bohr assumed (without proof) that these special
  orbits were somehow stable (non radiating)
• But radiation does occur in Bohrs 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 hf Ê H- Ê L
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 Bohrs 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
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
  nh/2p, for n1,2,etc.)
• Note Plancks constant h is both a unit of
  energytime product (joulesec) or alternatively
  a unit of angular momentum (kgm2/s)
• But not for a hydrogen molecule H2
• Bohrs 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!
• Bohrs theory said it couldnt 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
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
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
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
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
A Better Theory

• Schrödingers 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
• Schrödingers original theory only described
  lower (non-relativistic) energy values.
• Extensions of the original theory for higher
  energies (in conformance with Einsteins theory
  of relativity) give accurate predictions of
  atomic, nuclear and sub-atomic phenomena.

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
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
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
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
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
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
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
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
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
• Avogadros 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
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 Ohmmeters) 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
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
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) symbol for
  wavelength.
• Frequency is also sometimes represented by the
  lower case Greek letter Nu (?) in physics books.

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
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
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
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
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
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 ?2d or 1.414d, and
  also half that for some of the atoms.

1.414
1.0
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 b
wave direction a
1.41d
d
0.7d
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
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
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
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
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
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 nearby combustible
  materials.

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 ohmmeters, and is
  the resistance measured between two opposite
  faces of a 1 meter cube sample. For practical
  purposes, the ohmcentimeter unit is often used
  also.

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
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
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
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
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
Resistance vs. Temperature
Resistivity in ohmmeter

• Typical semiconductor

Theoretical semiconductor with no wave
scattering due to thermal vibration of atom
nuclei in the solid.
Typical electric conductor (metal)
Temperature
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
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
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
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
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
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!
• dont bump into anything in the dark!
• dont waste too much tape!

pull
Pencil used as axle
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) dont retain charge
  at one spot, but spread it over the surface of
  the entire object

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
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
Purified Semiconductors

• To produce a controlled result, semiconductors
  are first highly p