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1. EETS7320 SMU Session 4, Fall 2007 (print slides only, no notes pages)‏ Electronics Review

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: E=F/q or F=q•E • Unit: newton/coulomb (or volt/meter)‏ • Direction: Force F is parallel to electric field E. Notes: A newton is the International metric unit of force, approximately equal to 0.2248 pounds of force. A coulomb is the amount of electric charge produced by one ampere flowing for one second. A volt is the ratio of one joule (one watt•second) of energy divided by one coulomb of electric charge

4. 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 B=F/(i•) or F= i•B • Unit: newton/(ampere•meter) (or volt•sec/meter2)‏ • Direction: Perpendicular to the field direction and the current direction. Can be expressed by “right hand rule” or “cross product” vector notation. Note: a volt•second is also called a weber. The product of a volt of voltage, with an ampere of current, is an amount of power called a watt. Power is the time rate at which energy flows or “moves.” The unit of energy is the result of one watt of power “flowing” for one second. This is called a watt•second or a joule (rhymes with “foul.”)‏

5. 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 vk=Ek•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 don’t have any dependence on past historical values of voltage or current.)‏ • Other types of components require a description of the relationship between the time rate of change of current or voltage.

8. Linear vs. Non-linear • Considering “amnesic” components, the current-voltage graph (or input-output voltage graph) may be either a straight line or a curved line. A straight line relationship indicates a “linear” component. • Many “linear” electronic devices are important • Resistors (described by Ohm’s “Law”), Inductors, Transformers, Capacitors, transmission wires and cables • Linear equations describe linear phenomena • Example: v=R • i, where R is a constant (resistance measured using the unit of Ohms) note 1 • voltage is proportional to electric current • or electric charge, the time integral of current (for a capacitor q= i•dt); therefore q=C•v • or time rate-of-change of current (for an inductor: v=L• di/dt)‏ Note 1: The “resistance” of thermal insulation for use in walls or ceilings of buildings is also denoted “R,” but in that case it is the ratio of heat flow (analogous to current flow) to temperature difference (analogous to voltage). In North America, English units are used: BTU/min/sq.ft and degrees Fahrenheit.

9. 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 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. ErwinSchrödinger, Austrian physicist, invented wave (quantum) mechanics in 1926. *also written Schroedinger

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  (pronounced nu) is used rather than f in some documents)‏ • where h = 6.625•10-34 joule•seconds (Planck’s constant) (alternate unit: watt•s2)‏ • This is known from photo-electric emission of electrons from a metal when illuminated by light, and other experiments. Higher frequency light causes emission of electrons having more energy.

17. Frequency and Energy 106 Hz 109 1012 1015 1018 1 MHz 1 GHz Ionizing radiation frequency range 1 PetaHz 1 TeraHz • 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... 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 Diffraction grating, a front surface mirror with tiny parallel grooves. Some lenses used to focus the image are not shown here • Identifies Frequencies/Wavelengths Present in Light 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 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.

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/2 • 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 ÊH orbit Non-radiating low energy EL orbit Radiated light frequency f, where h•f= ÊH- ÊL

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: ÊH - ÊL = 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= n•h/2, forn=1,2,etc.)‏ Note: Planck’s constant h is both a unit of energy·time product (joule•sec) or alternatively a unit of angular momentum (kg•m2/s)‏ • But not for a hydrogen molecule H2 • Bohr’s theory could not explain how the 2 electrons and the 2 positive nuclei could stay near each other and not fly apart in an H2 molecule • There was a vague idea that the negative charge electron, while it was in between the two positive nuclei, could attract both of them and hold them together • But when it moved away from the inter-atomic position in its normal rotations around the nuclei, the nuclei would repel each other and push apart! • Bohr’s theory said it couldn’t happen, but most of the hydrogen atoms in a tank of room temp. hydrogen gas are in H2 molecules! • The problem is partly due to treating the electrons as point-like objects.

23. 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 • Schrödinger’s wave theory of quantum mechanics is the most accepted and accurate theory in modern physics • It accurately predicts the physical, mechanical, chemical, and electrical properties of atoms, molecules and solids • Schrödinger’s original theory only described lower (non-relativistic) energy values. • Extensions of the original theory for higher energies (in conformance with Einstein’s theory of relativity) give accurate predictions of atomic, nuclear and sub-atomic phenomena.

28. 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=(ÊH- ÊL)/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 • Avogadro’s number, the number of atoms in one gram-molecular-mass of a material, is about 1023 • the mass of a cm3 of Al is 2.7 grams and the atomic “weight” of Al is about 27)‏ • Therefore, there are about 1022 distinct theoretically possible electron energy levels in this piece of Aluminum for each electron in each atom, each one corresponding to a different wave shell. These energy levels are so close to each other that they form almost a continuous “band” of energy levels

37. Electron Waves in Solids • Some of the lower energy wave shells are clustered closely around each nucleus • These are called valence electrons and they mainly help to hold the solid together mechanically by providing electrostatic attraction to the nearest positive atomic nuclei • Some of the higher energy wave shells are spread out almost evenly throughout all the space inside the piece of Aluminum, rather than all clustered in the vicinity of one atom: • These are called conduction electrons. These are the electrons which carry electric charge from place to place, providing electrical conductivity • they also carry thermal energy (heat) from place to place, providing thermal conductivity • Note that for all metal conductors, the ratio of the electrical resistance (in Ohm•meters) of a metal to its thermal resistance* (measured in units watt/meter/Kelvin degree) is a constant when measured at the same temperature (this constant is called the Wiedemann-Franz constant). This is due to the fact that the same primary mechanism (electron wave movement) transports both electricity and heat in a metal

38. 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 Accelerator electrode • 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).

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 2•d or 1.414•d, 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.