# ELECTRICAL CONDUCTION

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1 Chapter 12: Electrical Properties Learning Objectives... How are electrical conductance and resistance characterized? What are the physical phenomena that distinguish conductors, semiconductors, and insulators? For metals, how is conductivity affected by imperfections, deformation, and temperature? For semiconductors, how is conductivity i affected by imperfections, i impurities i i (doping) and Temperature? 1 Relevant Reading for this Lecture... Pages Ohm's Law: voltage drop (volts) ELECTRICAL CONDUCTION V = I R current (amps) Cross sectional Area Resistivity, and Conductivity, : A (cross sect. area) resistance (Ohms) e - V I L V L I A these terms are independent of sample geometry or shape this equation is another form of Ohm's Law (recall normalization with ) RA resistivity (Ohm m) L Resistance: 2 R L A L A conductivity (Ohm m) 1 neqe e I More about this later 1

2 Electrical Properties Which will have the greater resistance? D R 1 D 2 D 2 2 2D R 2 2D 2 D R Analogous to flow of water in a pipe Resistance depends on sample geometry and size. 3 Chapter 12-3 Electrical Conductivity: Comparison (at room temperature!) Material (Ohm m) 1 Metals Silver 6.8 x 10 7 Copper 6.0 x 10 7 Aluminum 3.8 x 10 7 Iron 1.0 x 10 7 conductors Material (Ohm m) 1 Ceramics Soda-lime glass Concrete Alumina (Al 2 O 3 ) Semiconductors Silicon 4.0 x 10-4 Polymers Polystyrene Germanium 2.2 x 10 0 Polyethylene GaAs 1.0 x 10-6 semiconductors < insulators 4 2

3 EX: CONDUCTIVITY PROBLEM 100m Cu wire - e - I = 2.5A + V What is the minimum diameter (D) of the Cu wire so that V < 1.5V? 100m L V < 1.5V R A I 2.5A D x 10 (Ohm m) 4 Solve to get D > 1.88 mm 5 Pauli Exclusion Principle gives rise to energy s Figure 12.2 in Callister Quantum Mechanics states that no two electrons can occupy the same state Electrons not accompanying the same state 6 ublications/apsnews/ /images/Wolfga ng_pauli_1.jpg Energy level diagram for a hypothetical Nɑ 4 molecule. The four shared, outer orbital electrons are split into four slightly different energy levels (the Pauli exclusion principle). 3

4 Metals are good conductors since their valence is only partially. Adapted from Fig. 12.3, Callister & Rethwisch 4e. 7 Know this! Metal e.g., Cu Metal e.g., Mg Insulator Semiconductor >2eV <2eV Adapted from Fig. 12.4, Callister & Rethwisch 4e. E f = Fermi energy. This is the boundary between the and un energy levels. For electrons to conduct, they must move to where there are un energy levels. 4

5 CONDUCTION & ELECTRON TRANSPORT Metals: Thermal energy puts many electrons into a higher energy state. Energy States: the cases at right for metals show that nearby energy states are accessible by thermal fluctuations ti 9 Only those e that can get into the empty energy levels can conduct - Energy empty partly valence net e - flow GAP Cu is like this. states + Fermi My level highest state neqe e n e = # of e per m 3 q e = Charge of e e = e mobility Energy AboutMe/GIFs/Fermi_2.jpg Mg is like this. states s empty valence ENERGY STATES: INSULATORS AND SEMICONDUCTORS Insulators: Higher energy states are not accessible due to gap. gp Energy sta ates empty GAP valence Engineered material: Gaps are tunable more to come Semiconductors: Higher energy states separated by a smaller gap. Energy? es stat empty GAP valence 10 wide gap (> 2 ev) narrow gap (< 2 ev) 5

6 Insulators: A parallel plate capacitor involves an insulator, or dielectric, between two metal electrodes. The charge density buildup at the capacitor surface is related to the dielectric constant of the material E, Electric field strength (V/m) A D oke l Capacitance 11 charge C = C = Q/V C= A/l voltage Q V A C l D, charge density (C/m 2 ) k, dielectric constant (material property) o electric permittivity in vacuum, constant, 8.9x10 12 C/(Vm) ok electric permittivity Note your text uses r for k Dielectric Constants & Strength Dielectric constant r 60 Hz 1 MHz Ceramics Titanate ceramics ,000 Mica Soda-lime glass Porcelain Dielectric strength (V/mil)* Polymers Polystyrene Polyethylene * in = 1 mil 12 6

7 Resistivity, 13 METALS: RESISTIVITY VS T, IMPURITIES Imperfections increase resistivity grain boundaries dislocations These act to scatter electrons so that they impurity atoms take a less direct path, thus. vacancies Ohm-m) ( Cu at%ni Cu at%ni deformed Cu at%ni Cu at%ni Pure Cu T ( C) Adapted from Fig. 18.8, Callister 6e. (Fig adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw Hill Book Company, New York, 1970.) o[ 1 a( T Trt)] a is temperature coefficient of resistivity, o is intrinsic (no impurity) resistivity Resistivity increases with: temperature wt% impurity %Cold Work Why???? Variation in electrical resistivity with composition for various copper alloys with small levels of elemental additions (at T = 20 C). Ac 1 i c i A composition independent constant c i concentration of impurities 14 7

8 PURE SEMICONDUCTORS: CONDUCTIVITY VS T 15 Data for Pure Silicon: increases with T opposite to metals electrical l conductivity, it (Ohm-m) p 10-1 pure (undoped) T(K) Adapted from Fig , Callister 5e. (Fig adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.) Energy? states empty GAP material Si Ge GaP CdS valence Selected values from Table 18.2, Callister 6e. electrons can cross gap at higher T gap (ev) CONDUCTION IN TERMS OF ELECTRON AND HOLE MIGRATION Light (shown), heat, some input of energy is required to excite e from valence to conduction leaving a positively charged hole behind. Conduction can be either by negative carriers, electrons (n type) and/or positive carriers, holes (p type). Electrical Conductivity given by: # holes/m 3 n q p q Electrons move towards electron mobility hole mobility (+) potential and holes move to ( ) potential # electrons/m 3 charge of e e h 16 8

9 In class problem What fraction of the conductivity of intrinsic silicon at room temperature is due to (a) electrons and (b) holes? n q p q e h neqe e n e = # of e per m 3 q e = Charge of e e = e mobility Here n = p From Table 12.3, =0.736 From Table 12.3, = Eg 2 oe kt Arrhenius equation; Why 2? Produce two charge carriers electron and hole 18 Determining the activation energy for conduction e Eg 1 2k T o Eg 1 ln ln o 2k T y B mx 9

10 INTRINSIC VS EXTRINSIC CONDUCTION Intrinsic semiconductors: # of thermally generated electrons = # of holes (broken bonds) Extrinsic semiconductors: Impurities are added to the semiconductor that contribute additional electrons or holes. Doping = intentional impurities Si is the primary material in semiconductors Large gap (1.1 ev); allows Si to operate at warmer temperatures (150 o C) Can form a native oxide, SiO 2, for insulating barriers (important in fabrication) Si can be made into large (12 inch dia.), high purity, single crystal ingots. Doping of Si Si has 4 outer shell electrons (group IV) n type: Phosphorous, arsenic (group V), donate extra electron p type: boron (group III) for Si 19 n type 4 valence electrons of As allow it to bond like Si, but the fifth electron is left orbiting As site the energy to release the fifth electron into the CB is small ne e 20 10

11 p type Boron has only 3 valance electrons. When it substitutes for a Si atoms, one of its bonds has a missing electron (hole) Hole tunnels around, and can be liberated by thermal vibration of Si atoms, from the B site into the VB. pe h 21 p type n type? type? type 22 11

12 Why the increase? Why 2? Produce two charge carriers electron and hole Arrhenius plot of electrical conductivity for an n type semiconductor over a wide temperature range. At low temperatures (high 1/T), the material is extrinsic. At high temperatures (low 1/T), the material is intrinsic. In between is the exhaustion range, in which all extra electrons have been promoted to the why? 23 In class problem Calculate the conductivity for the saturation range of silica doped with 10 ppb boron. The calculated density of B atoms/m 3 is also the density of electron holes in this p type semiconductor at saturation. 10/10 9 Hence solve for n = 10 8 n = 10 8 X 6.02x10 23 atoms B g B X 2.33x10 6 g/m 3 Si = 1.30 x10 21 amu B Density of Si Using this equation σ=nqµh and the data from Table 12.3: (q is the magnitude of electron charge which equals 0.16 x C) σ = nqµ h = (1.30 x m 3 )(0.16 x C) (0.05 m 2 /V s) 24 = 10.4 Ω 1 m 1 12

13 Compound Semiconductors 25 Group III V and II V compounds nominally have the Zinc Blend structure and areintrinsic semiconductors. Can be doped, like Si, to change conduction (extrinsic) MX Compounds: Group III 3+ valence, Group V 5+ valence avg. of 4+ valence per atom // Group II 2+ valence, Group VI 6+ valence avg. 4+ valence per atom Applications: Solar cells Light emitting diodes (occurs with electron hole recombination) Higher operation speeds, etc. IC DEVICES: P N RECTIFYING JUNCTION Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current). Results: No applied potential: no net current flow. Forward bias: carriers flow through p type and n type regions; holes and electrons recombine at p n junction; current flows. Reverse bias: carriers flow away from p n junction; carrier conc. greatly reduced at junction; little current flow. p-type n-type p-type + - n-type p-type n-type

14 P N Rectifying Junction 27 Light Emitting Diode (LED) 28 Band gap determines wavelength (color) of light emitted d/0695/0695_fig4.jpg 14

15 Compare three light bulbs. Conventional incandescent (tungsten filament) Bulb is hot to the touch, most of the electricity is lost as heat. Short life (few months?) Compact fluorescent (CFL s) Bulb is warm, but not hot, less heat loss Longer life (many months 2 years) LED s Extremely efficient, i little or no conversion of electricity it to heat. Very long life decades. Many LED s made in the 70 s & 80 s are still working! 29 The Transistor Invented by Shockley, Bardeen, and Brattain in Nobel prize in A three terminal device that acts like a simple on off switch (logic control). The basis of Integrated Circuits (IC) technology Computers, cell phones, automotive control, etc. Circa 1948 today When voltage (potential) is applied to the gate, current flows between the source and the drain. On/off switch logic switch, go/no go ~ tens of nanometers (1000X smaller than diameter of your hair) 30 15

16 31 SUMMARY Electrical conductivity and resistivity are: material parameters, i.e. properties. independent of geometry. Electrical resistance is: a geometry and material dependent parameter. Conductors, semiconductors, and insulators... each is different, depending on whether there are accessible energy states for conducting electrons. For metals, conductivity is increased by reducing deformation reducing imperfections decreasing temperature. For pure semiconductors, conductivity is increased by increasing temperature doping (e.g., adding B to Si (p type) or P to Si (n type). Transistors are logic based devices Metals: Influence of Temperature and Impurities on Resistivity Presence of imperfections increases resistivity -- grain boundaries -- dislocations -- impurity atoms These act to scatter electrons so that they -- vacancies take a less direct path. Re esistivity, (10-8 Ohm-m) d i t T ( C) Resistivity increases with: -- temperature -- wt% impurity -- %CW = thermal + impurity 32 Adapted from Fig. 12.8, Callister & Rethwisch 4e. (Fig adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw-Hill Book Company, New York, 1970.) + deformation 32 16

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