CHAPTER 18: Electrical properties ISSUES TO ADDRESS... 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, T, and deformation? For semiconductors, how is conductivity affected by impurities (doping) and T? Chapter 18 1
Scanning electron microscope images of an IC: Al Si (doped) View of an integrated circuit 45μm (d) A dot map showing location of Si (a semiconductor): Si shows up as light regions. (a) (b) 0.5mm A dot map showing location of Al (a conductor): Al shows up as light regions. (c) Fig. (d) from Fig. 18.25, Callister 6e. (Fig. 18.25 is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.) Fig. (a), (b), (c) from Fig. 18.0, Callister 6e. Chapter 18 2
Ohm's Law: voltage drop (volts) A (cross sect. area) ΔV = I R current (amps) e ΔV I Resistivity, ρ and Conductivity, σ: geometryindependent forms of Ohm's Law Resistance: Electrical conduction E: electric field intensity ΔV L = I A ρ R = ρl A = L Aσ L resistance (Ohms) resistivity (Ohmm) J: current density conductivity σ= I ρ Chapter 18 3
Conductivity: comparison Room T values (Ohmm) 1 METALS conductors CERAMICS Silver 6.8 x 10 7 Sodalime glass 10 10 Copper 6.0 x 10 7 Concrete 10 9 Iron 1.0 x 10 7 Aluminum oxide <10 13 SEMICONDUCTORS POLYMERS Silicon 4 x 10 4 Polystyrene <10 14 Germanium 2 x 10 0 Polyethylene 10 15 10 17 GaAs 10 6 semiconductors insulators Selected values from Tables 18.1, 18.2, and 18.3, Callister 6e. Chapter 18 4
Ex: Conductivity problem Question 18.2, p. 649, Callister 6e: Cu wire 100m e I = 2.5A + ΔV What is the minimum diameter (D) of the wire so that ΔV < 1.5V? 100m < 1.5V R = L Aσ = ΔV I πd 2 4 Solve to get D > 1.88 mm 2.5A 7 1 6.07 x 10 (Ohmm) Chapter 18 5
Electron mobility Under acceleration from external electric field Average distance traveled by electrons = mean free path, d. The drift velocity, v e is the average speed of the electrons. v d = d/t The mobility is defined as μ e = v d /Ε (expressed in m 2 /V.s) Conductivity expression In general, for an electronic carrier σ = n e μ e n, the number of carriers per unit volume, or density of carriers (#carriers/m 3 ). e, the electron charge, (1.6x10 19 Coulombs) μ e, the electron mobility, (m 2 /V.s) Chapter 18
Energy Band model d p Energy gap or gap s Equilibrium interatomic spacing Interatomic spacing Chapter 18
Energy structures Valence and Conduction s Energy empty partly filled valence filled GAP filled states filled valence filled states GAP filled states GAP filled states Metals Al, Na, Cu Metals Mg, Zn Semiconductor Si, Ge, GaAs Insulator Diamond Chapter 18
Conduction & electron transport Metals: Thermal energy puts many electrons into a higher energy state. Energy States: the cases below for metals show that nearby energy states are accessible by thermal fluctuations. Fermi energy = energy corresponding to top most filled state at 0K Energy empty partly filled valence filled net e flow GAP E f filled states + Energy filled states E f Chapter 18 6
Energy states: insulators and semiconductors Insulators: Higher energy states not accessible due to gap. Energy Conduction GAP Semiconductors: Higher energy states separated by a smaller gap. Energy? Conduction GAP filled states filled valence filled filled states filled valence filled Chapter 18 7
Imperfections increase resistivity grain boundaries dislocations impurity atoms vacancies Resistivity, ρ (10 8 Ohmm) Metals: resistivity vs T, impurities 6 5 4 3 2 1 0 Cu + 3.32 at%ni Cu + 2.16 at%ni deformed Cu + 1.12 at%ni Cu + 1.12 at%ni 200 100 0 These act to scatter electrons so that they take a less direct path. Pure Cu T ( C) Adapted from Fig. 18.8, Callister 6e. (Fig. 18.8 adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGrawHill Book Company, New York, 1970.) Resistivity increases with: temperature wt% impurity %CW ρ = ρ thermal +ρ thermal +ρ def Chapter 18 8
Question: Estimate the electrical conductivity of a CuNi alloy Yield strength (MPa) that has a yield strength of 125MPa. 180 160 140 120 100 21 wt%ni 80 60 0 10 20 30 40 50 wt. %Ni, (Concentration C) Adapted from Fig. 7.14(b), Callister 6e. Ex: Estimating conductivity Resistivity, ρ (10 8 Ohmm) 50 40 30 20 10 0 ρ=30x10 8 Ohm m σ= 1 ρ = 3.3x106 (Ohm m) 1 0 10 20 30 40 50 wt. %Ni, (Concentration C) Adapted from Fig. 18.9, Callister 6e. Chapter 18 9
Energies Electrical energy Voltage gradient or electric field 1.25x10 6 volts/cm ~ 2.5 ev Thermal energy Average thermal energy = kt At RT (~300 K) = 0.86 x 300 = 0.026 ev At 2000 C, kt = measily 0.2 ev Light energy 1millions Volts! + + 8 mm Visible light photon energy quanta whooping 1.7 to 3.1 ev! Shining light of a given wavelength on a crystal transfer more electrons across the gap than through thermal excitation or electric field!!!. Obviously Light carries lots of energy!!!! Chapter 18
Conduction in terms of electron and hole migration Concept of electrons and holes: valence electron Si atom electron hole pair creation electron hole pair migration + + no applied electric field applied electric field Electrical Conductivity given by: # holes/m 3 applied electric field Adapted from Fig. 18.10, Callister 6e. σ=neμ e + peμ h # electrons/m 3 electron mobility hole mobility Chapter 18 11
Intrinsic vs extrinsic conduction Intrinsic: # electrons = # holes (n = p) case for pure Si Extrinsic: n p occurs when impurities are added with a different # valence electrons than the host (e.g., Si atoms) Ntype Extrinsic: (n >> p) Ptype Extrinsic: (p >> n) Phosphorus atom 4+ 4+ 4+ 4+ σ neμ e 4+ 5+ 4+ 4+ 4+ 3+ 4+ 4+ σ peμ h 4+ 4+ 4+ no applied electric field 4+ hole conduction electron valence electron Si atom Boron atom 4+ 4+ 4+ 4+ 4+ 4+ 4+ no applied electric field 4+ Chapter 18 12
Examples of elemental and compound H Li Na K Rb Cs Fr Be Mg Ca Sr Ba Ra material Si Ge GaP CdS semiconductors Ti Cr Fe Ni Zn Ga Ge As 0.7 Sn 0.1 Pb Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, GaAs 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. gap (ev) 1.11 0.67 2.25 2.40 Si Ge Group IV Sn column IVA C 5.5 Si 1.1 ZnSe CdTe Group IIVI HgTe O F 4.0 Cl Br I At He Ne Ar Kr Xe Rn GaP Group IIIV CdS Chapter 18 11
Pure semiconductors: conductivity vs T Data for Pure Silicon: σ increases with T opposite to metals electrical conductivity, (Ohmm) 1 10 4 10 3 10 2 10 1 10 0 10 1 pure (undoped) 10 2 50 100 1000 T(K) Adapted from Fig. 19.15, Callister 5e. (Fig. 19.15 adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.) σ σ undoped e E gap /2k B T Energy? filled states empty GAP filled valence filled material Si Ge GaP CdS Selected values from Table 18.2, Callister 6e. electrons can cross gap at higher T gap (ev) 1.11 0.67 2.25 2.40 Chapter 18 10
electrical conductivity, σ (Ohmm) 1 10 4 10 3 10 2 10 1 10 0 10 1 doped semicon: conductivity vs T Data for Doped Silicon: σ increases doping reason: imperfection sites lower the activation energy to produce mobile electrons. 0.0052at%B doped 0.0013at%B pure (undoped) 10 2 50 100 1000 T(K) Adapted from Fig. 19.15, Callister 5e. (Fig. 19.15 adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.) Comparison: intrinsic vs extrinsic conduction... extrinsic doping level: 10 21 /m 3 of a ntype donor impurity (such as P). for T < 100K: "freezeout" thermal energy insufficient to excite electrons. for 150K < T < 450K: "extrinsic" for T >> 450K: "intrinsic" conduction electron concentration (10 21 /m 3 ) 3 2 1 0 0 freezeout doped undoped 200 extrinsic 400 in trinsic 600 Adapted from Fig. 18.16, Callister 6e. (Fig. 18.16 from S.M. Sze, Semiconductor Devices, Physics, and Technology, Bell Telephone Laboratories, Inc., 1985.) T(K) Chapter 18 13
Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current. Processing: diffuse P into one side of a Bdoped crystal. Results: No applied potential: no net current flow. Forward bias: carrier flow through ptype and ntype regions; holes and electrons recombine at pn junction; current flows. PN rectifying junction ptype + + + ++ ntype ptype + ntype + + + + + Reverse bias: carrier flow away from pn junction; carrier conc. greatly reduced at junction; little current flow. ptype ntype + + + + + + Chapter 18 14
Extrinsic Intrinsic temperature behavior Intrinsic behavior Slope = E g /2k B E g ln σ Donor exhaustion or acceptor saturation range E a ptype: slope = E a /k B Extrinsic behavior ntype: slope = (E g E d )/k B E d 1/T (K 1 ) Chapter 18
Ntype Silicon solar cell, E g = 1.1 ev Ptype hν = Electron + hole Incident light creates electronhole pairs, which are moved as shown producing electricity On contact electrons and holes neutralize each other in A thin layer recombination zone Electron + hole = hν In radiative recombination* Charge separation creates electric field + Positively charged layer Negatively charged layer Positively charged layer Negatively charged layer * In some materials, such as GaAs, GaN light is given off Chapter 18
Emitter n type Transistors Thin Base ptype + + + ++ Collector n type n + Forward bias + ptype + + ++ Reverse bias n + Input signal Output signal Recombination Chapter 18
Bipolar junction transistor Voltage output Voltage input, V E + + pbase nemitter ncollector Silicon Chapter 18
SUMMARY Electrical conductivity and resistivity are: material parameters. geometry independent. Electrical resistance is: a geometry and material dependent parameter. Conductors, semiconductors, and insulators... different in whether there are accessible energy states for conductance 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 (ptype) or P to Si (ntype). Chapter 18 15
Chapter 18
ANNOUNCEMENTS Reading: Chapter 18 113 Core Problems: Chapter 18: 7, 12, 29, Selfhelp Problems: Design Example 18.1 Chapter 18 0