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© 1997-2005, R.Levine Page 1 Electronics Review EETS8320 SMU Session 4, Fall 2005 (print slides only, no notes pages)
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© 1997-2005, R.LevinePage 1
Electronics Review
EETS8320
SMU
Session 4, Fall 2005(print slides only, no notes pages)
© 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.
© 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
© 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.”)
© 1997-2005, R.LevinePage 5
Directions
q E
F
i•λB
F
Force on charge is parallelto electric field.
Force on current elementis perependicular to bothcurrent element and magnetic field.
© 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.”
© 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.
© 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.
© 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)
© 1997-2005, R.LevinePage 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
© 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.
© 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.
© 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
© 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 ofprotons (positive charge)and neutrons (electricallyneutral)
Point object electrons whirlingaround the nucleus in specific circular or elliptical orbits.
This frequently shownPicture (symbolic ofLithium) is known to bewrong in several ways.
Niels Bohr, Danish physicist, invented this theoretical model ca. 1913.
© 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
© 1997-2005, R.LevinePage 16
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.
© 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 BroadcastingBand (car radio)
TV and FM Broadcasting(VHF and UHF)
Cellular andSMR Radio
PCS RadioBand (1.9 GHz)
Ionizing radiation frequency range
Visible Light X-Rays
IR UVGamma Rays
© 1997-2005, R.LevinePage 18
Spectroscope
Light source such ashydrogen gas in a sealed glass tube with electricsparks.
Greatly enlarged view of grooved surface
Diffraction grating, a frontsurface mirror with tinyparallel grooves.Some lenses used to focus the image are not shownhere
Images of the slit are formed on photographic film.
Light obstaclewith slit. Widthof slit is actuallyvery narrow.
• Identifies Frequencies/Wavelengths Present in Light
© 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•108meter/second, the speed of light
– Illustration shows lines in color on film on black background. Actual spectroscope films are usually black and white, typically the “negative” of this picture, with dark lines on a clear background.
© 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 orbitNon-radiating low energy EL orbit
Radiated light frequency f,
where h•f= Ê H- Ê L
© 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.
© 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.
© 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
© 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 experimentsindicate thismolecularform.
Not this “straight line”form.
© 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.
© 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 areasare the places where the other molecules will formmolecular bonds, due to themutual attraction of the negative charge electron cloud(s) and thepositive charge nuclei of theatom shown here and the otheratoms which will attach.
© 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.
© 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
© 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
© 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…
© 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.
© 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”
© 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.
© 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
© 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
© 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
© 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
© 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…
© 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, sowave 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.
© 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.
© 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.
© 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
© 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.
© 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)
© 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
© 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
d1.41d
0.7d
© 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
© 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
© 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
© 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.
© 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.
© 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.
© 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.
© 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
© 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
© 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
© 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.
© 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!
© 1997-2005, R.LevinePage 59
Resistance vs. Temperature
Typical semiconductor
Temperature
Typical electric conductor (metal)
Theoretical semiconductor with no wave scatteringdue to thermal vibration of atom nuclei in the solid.
Resistivity in ohm•meter
© 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.
© 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
© 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
© 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
© 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
© 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 usedas axle
© 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
© 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.
© 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
© 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
© 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
© 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 5aBoron Carbon Nitrogen
Aluminum Silicon Phosphorus
Gallium Germanium Arsenic (As)Indium Tin (Sn) Antimony (Sb)
© 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
© 1997-2005, R.LevinePage 73
PN Junction Diode
P NAnode Cathode
P-type N-type
Graph shows net electric chargedensity vs. distance right or left of junction
Electricallyneutralregion
Electricallyneutralregion
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
+
-
© 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
© 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.
© 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, measurescurrent
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 negativevoltages.
i
© 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 negativevoltage axis is not shown. Origin of graph,
v=0, i=0
1
Region Description
A-B Approximately linear increase incurrent vs. voltage.
B-C Accurate theoretical formula:
i = Io (e qv/kT -1)where Io is temperature dependent,but is typically ~10 µA at roomtemperature. Also kT/q ≅ 0.2 voltsat room temperature.
C-D Zener or avalanche breakdownregion. Approximately constantvoltage. Vz can be 3 to 600 V,depending on design of diode.
mA=milliamperesof current;1 mA=0.001 A.
B is approx. boundarybetween exponentialand linear parts.
© 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.
© 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 2v (volts)
i(mA)
mA=milliAmperesof current;1 mA= 0.001 A
Origin of graph,v=0, i=0
Forward region is describedas a resistance Rf.
Special case is Rf=0 ohms.
Reverse current is described as zero. No description ofbreakdown voltage regionin this example.
© 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.
© 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...
© 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 isnet electric chargedensity
Zero volts ondiode (blue)
Positive voltageon diode (red)
Negative voltage ondiode (green)
© 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” energyShaded area on graph indicatesenergy levels with electrons at mediumtemperature. Gap surrounding Êf is dueto the band gap in a semiconductor.
1
n(Ê) = e ((Ê-Êf)/kT) +1
© 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
© 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!
© 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.
© 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.
© 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.
© 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
© 1997-2005, R.LevinePage 90
Junction Transistor
N
P
N
Collector
Emitter
Base
C
B
E
Graphicsymbol
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 thickarrow represents the magnitude of electron flow.Most of the electrons that pass from the Emitterto the Base are collected by the Collector.
NPN unit is shown.PNP units alsoare made, and useopposite voltagepolarities from NPN.The graphic symbolfor a PNP transistorhas the opposite arrowpoint direction.
© 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.
© 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.
© 1997-2005, R.LevinePage 93
Field Effect Transistor
SourceElectrode
Drain Electrode
GateElectrode
P-gate, N-channel unit shown.
S
D
GGraphicSymbol
Notice the “blob” in theN-side depletion layer dueto electric field interactionwith Drain electrode.
The arrow indicatesdirection of electronflow. Narrowingof arrow suggestscurrent “strangling”effect from negativegate voltage, whichnarrows the neutral N channel.
Depletion layers.
The words “source”and “drain” are basedon the concept of positive charge flow.
© 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
© 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 ofthe FET. It is the ratio of a change iniS-D to the causative change in vG.
Note that there is no current pathin this model between the gate and other parts of the FET. This is dueto assuming that the reverse currentof the gate-body junction is zero. Infact it is typically a few microamperes.
© 1997-2005, R.LevinePage 96
Metal Oxide Silicon (MOS) Transistor
SourceElectrode
Drain Electrode
GateElectrode(metal)
Also called insulated gate FET(IGFET). A layer of SiO2 (equi-valent to beach sand, shown inblue on the drawing) electricinsulation 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 channelwidth is controlled by the gatevoltage. No steady (dc) gate current flows for either positiveor negative gate voltage.
© 1997-2005, R.LevinePage 97
Multiple Gate Transistor - I
SourceElectrode
Drain Electrode
GateElectrode 1
Multiple gate electrodes areused to implement digitallogic functions (to be discussedmore in a later lecture). This form with side-by-side gatesallows some source-drain current to flow when either gate 1 ORgate 2 has a positive voltage. This implements the inclusive OR logical function with a minimumnumber of components, particularlywhen implemented in an integratedcircuit.
GateElectrode 2
© 1997-2005, R.LevinePage 98
Multiple Gate Transistor - II
SourceElectrode
Drain Electrode
GateElectrode 1
Current from source to drain flows only when both gate 1AND gate 2 are positive. Notethat there are two places wherenegative gate voltage couldpinch off the channel. Thisimplements the digital logic AND function.
All of these configurations canbe implemented in integratedcircuits, although these picturesshow source and drain electrodeson the edges.
GateElectrode 2
© 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
+ -
inputvoltagesource
Generic “ground” or “earth”graphic symbol. Actually representsthe frame or cabinet in most modernequipment.
Fixed voltage powersupply, shown hereas a battery symbol.Often the power supplydevice and the wire frompower source to ground is omitted from drawings.
RL , “load” resistor (orLoudspeaker, etc.)
Generic “cathode”:(drain or emitter)
Generic control electrode: (gateor base)
Generic “anode”:(source or collector) Vpower
←This box is replacedby a particular transis-tor in a real amplifier.
© 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
© 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.
© 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”
© 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
© 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!
© 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.
© 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
© 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
