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1 Chapter 12: Electrical Properties School of Mechanical Engineering Choi, Hae-Jin Materials Science - Prof. Choi, Hae-Jin Chapter 12-1 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, temperature, and deformation? For semiconductors, how is conductivity affected by impurities (doping) and temperature? Chapter

2 Electrical Conduction Ohm's Law: voltage drop (volts = J/C) C = Coulomb V = I R resistance (Ohms) current (amps = C/s) Resistivity, : -- a material property that is independent of sample size and geometry surface area RA ρ of current flow current flow path length Conductivity, 1 Chapter 12-3 Electrical Properties Which will have the greater resistance? D 2D 2 R D 2 D 2 2 R 2 2D 2 D R Analogous to flow of water in a pipe Resistance depends on sample geometry and size. Chapter

3 Definitions Further definitions J = <= another way to state Ohm s law current I J current density like a flux surface area A electric field potential = V/ J = (V/ ) Electron flux conductivity voltage gradient Chapter 12-5 Conductivity: Comparison Room temperature values (Ohm-m) -1 = ( -m) -1 METALS conductors Silver 6.8 x 10 7 Copper 6.0 x 10 7 Iron 1.0 x 10 7 CERAMICS -10 Soda-lime glass Concrete 10-9 Aluminum oxide <10-13 SEMICONDUCTORS Silicon 4 x 10-4 Germanium 2 x 10 0 GaAs 10-6 semiconductors Selected values from Tables 12.1, 12.3, and 12.4, Callister & Rethwisch 3e. POLYMERS Polystyrene <10-14 Polyethylene insulators Chapter

4 Example: Conductivity Problem What is the minimum diameter (D) of the wire so that V < 1.5 V? Cu wire 100 m - I = 2.5 A + V 2 D 4 Solve to get 100 m V R A I D > 1.87 mm < 1.5 V 2.5 A 6.07 x 10 7 (Ohm-m) -1 Chapter 12-7 Electron Energy Band Structures Adapted from Fig. 12.2, Callister & Rethwisch 3e. Chapter

5 Band Structure Representation Adapted from Fig. 12.3, Callister & Rethwisch 3e. Chapter 12-9 Conduction & Electron Transport Metals (Conductors): -- for metals empty energy states are adjacent to states. -- thermal energy excites electrons into empty higher energy states. -- two types of structures for metals - partially - empty that overlaps Partially Overlapping s Energy Energy empty GAP empty partly states s state es Chapter

6 Energy Band Structures: Insulators & Semiconductors Insulators: -- wide gap (> 2 ev) -- few electrons excited across gap Energy empty conduction GAP Semiconductors: -- narrow gap (< 2 ev) -- more electrons excited across gap Energy? empty conduction GAP states s valence states s valence Chapter Metals: Influence of Temp. and Impurities on Resistivity Presence of imperfections increases resistivity -- grain boundaries -- dislocations -- impurity atoms -- vacancies Re esistivity, (10-8 Ohm-m) d These act to scatter electrons so that they take a less direct path. T ( C) Adapted from Fig. 12.8, Callister & Rethwisch 3e. (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.) i t Resistivity increases with: -- temperature -- wt% impurity -- %CW = thermal + impurity + deformation Chapter

7 Estimating Conductivity Question: -- Estimate the electrical conductivity of a Cu-Ni alloy Yield strength (MP Pa) that has a yield strength of 125 MPa wt% Ni 80 Resistivity, (10-8 Ohm-m m) Adapted from Fig. 12.9, Callister & Rethwisch 3e wt% Ni, (Concentration C) wt% Ni, (Concentration ti C) Adapted from Fig. 8.16(b), Callister & Rethwisch 3e x 10 Ohm m From step 1: x 10 (Ohm m) C Ni = 21 wt% Ni Chapter Charge Carriers in Insulators and Semiconductors Adapted from Fig (b), Callister & Rethwisch 3e. Two types of electronic charge carriers: Free Electron negative charge in conduction Hole positive charge vacant electron state in the valence Move at different speeds - drift velocities Chapter

8 Intrinsic Semiconductors Pure material semiconductors: e.g., silicon & germanium Group IVA materials Compound semiconductors III-V compounds Ex: GaAs & InSb II-VI compounds Ex: CdS & ZnTe The wider the electronegativity difference between the elements the wider the energy gap. Chapter Intrinsic Semiconduction 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 applied applied electric field electric field electric field Electrical Conductivity given by: # holes/m 3 n e # electrons/m3 electron mobility e p e h hole mobility Adapted from Fig , Callister & Rethwisch 3e. Chapter

9 Number of Charge Carriers Intrinsic Conductivity n e e p e h for intrinsic semiconductor n = p = n i = n i e ( e + h ) Ex: GaAs n i e 10 6 ( m) (1.6x10 C)( m /V s) e h For GaAs n i = 4.8 x m -3 For Si n i = 1.3 x m -3 Chapter Intrinsic Semiconductors: Conductivity vs T Data for Pure Silicon: -- increases with T -- opposite to metals n i e e h n i e E gap / kt material Si Ge GaP CdS gap (ev) Selected values from Table 12.3, Callister & Rethwisch 3e. Chapter

10 Intrinsic vs Extrinsic Conduction Intrinsic: -- case for pure Si -- # electrons = # holes (n = p) Extrinsic: -- electrical behavior is determined by presence of impurities that introduce excess electrons or holes -- n p n-type Extrinsic: (n >> p) p-type Extrinsic: (p >> n) n e e Adapted from Figs (a) & 12.14(a), Callister & Rethwisch 3e. Phosphorus atom 5+ no applied electric field hole conduction electron valence electron Si atom Boron atom 3+ h no applied electric field p e Chapter Extrinsic Semiconductors: Conductivity vs. Temperature Data for Doped Silicon: -- increases doping -- reason: imperfection sites lower the activation energy to produce mobile electrons. Comparison: intrinsic vs extrinsic conduction extrinsic doping level: /m 3 of a n-type donor impurity (such as P). -- for T < 100 K: "freeze-out, thermal energy insufficient to excite electrons. -- for 150 K < T < 450 K: "extrinsic" -- for T >> 450 K: "intrinsic" Conduction electron concentration (10 21 /m 3 ) c freeze-out 200 doped undoped extrinsic 400 intrinsic 600 Adapted from Fig , Callister & Rethwisch 3e. (Fig from S.M. Sze, Semiconductor Devices, Physics, and Technology, Bell Telephone Laboratories, Inc., 1985.) T (K) Chapter

11 p-n Rectifying Junction 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 B-doped crystal. -- 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. + p-type n-type p-type n-type Adapted from Fig , Callister & Rethwisch 3e. -- Reverse bias: carriers flow away from p-n junction; junction region depleted of carriers; little current flow. + p-type n-type Chapter Properties of Rectifying Junction Fig , Callister & Rethwisch 3e. Fig , Callister & Rethwisch 3e. Chapter

12 Junction Transistor Fig , Callister & Rethwisch 3e. Chapter MOSFET Transistor Integrated Circuit Device Fig , Callister & Rethwisch 3e. MOSFET (metal oxide semiconductor field effect transistor) Integrated circuits - state of the art ca. 50 nm line width ~ 1,000,000,000 components on chip chips formed one layer at a time Chapter

13 Ferroelectric Ceramics Experience spontaneous polarization BaTiO 3 -- ferroelectric below its Curie temperature (120ºC) Fig , Callister & Rethwisch 3e. Chapter Piezoelectric Materials Piezoelectricity application of stress induces voltage application of voltage induces dimensional change stress-free with applied stress Adapted from Fig , Callister & Rethwisch 3e. (Fig from Van Vlack, Lawrence H., Elements of Materials Science and Engineering, 1989, p.482, Adapted by permission of Pearson Education, Inc., Upper Saddle River, New Jersey.) Chapter

14 Summary Electrical conductivity and resistivity are: -- material parameters -- geometry independent Conductors, semiconductors, and insulators differ in range of conductivity values -- differ in availability of electron excitation states For metals, resistivity is increased by -- increasing temperature -- addition of imperfections -- plastic deformation For pure semiconductors, conductivity it is increased by -- increasing temperature -- doping [e.g., adding B to Si (p-type) or P to Si (n-type)] Other electrical characteristics -- ferroelectricity -- piezoelectricity Chapter

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