L293031ElecCond145s10

L293031ElecCond145s10 - Lectures 29-31 spring 2010 ENGR 145...

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Unformatted text preview: Lectures 29-31, spring 2010 ENGR 145, Chemistry of Materials Case Western Reserve University Reading assignment : C&R §12.1-12.13, 12.16-12.20; OGC §22.5-22.7; OGC pp. 939-940 Learning objectives: • Know what acts as charge carriers in • metals • semiconductors • insulators • Know how carrier concentration in metals and semiconductors depends on temperature and composition • Understand how carrier mobility in metals and semiconductors depends on composition, temperature, and microstructure • Know under what conditions ceramics and polymers can exhibit appreciable electrical conductivity • Understand the Wiedemann-Franz relationship, and to what category of materials it applies Lectures 29-31: Electrical Conductivity 1 Lectures 29-31, spring 2010 ENGR 145, Chemistry of Materials Case Western Reserve University Charge & Heat Transport • Fourier’s law of cooling: • Ohm’s law: • : current density (charge flux) • : electrical conductivity • : electric field = (voltage gradient) q A = −κ dT dx J = σ E energy area i time charge area i time J σ E dV dx OGC eq. 22.4; C&R eq. 12.5 2 Lectures 29-31, spring 2010 ENGR 145, Chemistry of Materials Case Western Reserve University • Current density, conductivity, electric field: • resistance of material: • voltage drop across material: • current through material: • Ohm’s law: Electrical Conduction: “Macroscopic” View [C&R §12.2; OGC §22.5] V IR = R = ρ A = σ A I = JA V = E C&R Figure 12.1 J = σ E ρ : electrical resistivity σ : electrical conductivity 3 Lectures 29-31, spring 2010 ENGR 145, Chemistry of Materials Case Western Reserve University Electrical Conduction: “Microscopic” View [C&R §12.2] σ = nq e | z | µ • σ : electrical conductivity • n : concentration of charge carriers • q e : charge on an electron • z : oxid ʼ n # of charge carriers • μ : mobility of charge carriers — a constant (±1, ±2, …) • This expression holds for all substances • Electrical conductivity varies by >22 orders of magnitude in ordinary materials • If material has more than one type of charge carrier: , because of differences in n and μ σ tot = ne | z | μ all carrier types ∑ |z| = 1 for electrons and holes, 2 for O 2– ions, … [ Ω –1 m –1 ]=Cm –1 V –1 s –1 [m –3 ] [C] [m 2 V –1 s –1 ] 4 Lectures 29-31, spring 2010 ENGR 145, Chemistry of Materials Case Western Reserve University Review: Energy Bands in Metals [OGC 21.3] OGC Figure 21.19 • Two column-I atoms (e.g. Na): • Bonding states (flled) • Antibonding states (empty) … as in H 2 • More atoms more closely spaced states • Many atoms: • “Bands” o¡ electron states • Virtually continuous energy levels • Li, Na, K, Cu, Ag, Au: valence orbital in ¡ree atom is hal¡-flled band in solid is hal¡-flled 5 Lectures 29-31, spring 2010 ENGR 145, Chemistry of Materials Case Western Reserve University C&R Figure 12.4, modifed Metals: e.g. Na, Cu Review: Energy Bands in Metals [C&R §12.5] 6 Lectures 29-31, spring 2010...
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This note was uploaded on 01/30/2011 for the course EMSE 103 taught by Professor Ggh during the Spring '10 term at Case Western.

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L293031ElecCond145s10 - Lectures 29-31 spring 2010 ENGR 145...

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