Summary d

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Unformatted text preview: Summary EF Metal band overlap Insulator or semiconductor 5.3 Electrons in External fields Effective mass: dv 1 = F dt m ∗ 1 ∂E 1 ∗ = m ij h ∂k i k j (band curvature) F: external force m*: describes forces arising from periodic crystal potential Parabolic shape (e.g., at zone boundaries) ⇒ m* = const. S- 9 1 Summary Holes Charge: +e Effective mass: - me ⇒ mp > 0 for holes in valence band, because me < 0 dv 1 = ∗ q( dt m ⇒ vp = -ve same sign in current: j = qnv Change in Fermi distribution in applied field or temperature gradient ∂f + v grad r f 123 44 ∂t # 0 in T − gradient ∂f & + k grad k f = ∂t collisions Boltzmann equation f ( k ) − f 0 (k ) ∂f =− Relaxation approximation: ∂t τ (k ) collisions ⇒ exponential decay of perturbation Collisions bring distribution back to equilibrium: f - f0 = [f(t=0)-f0]e-t/τ S- 0 2 Summary Linearization: grad f ≈ grad f0 Electrical conductivity & F = −e( = h k , friction term due to collisions ⇒ stationary shift of free electron Fermi sphere e f ( k ) ≈ f 0 ( k + τ ( k )( ) h4 123 4 δk e j = σ( = 4π 3 ∫ v( k ) f ( k ) d 3 k Brillouin zone analogous to j=env ⇒ e 2τ ( E F ) n σ= ∗ m n(T) = const for metals Only electrons near Fermi surface can gain energy in field. Matthiesen rule: const. el. resistivity ρ = ρdefects + ρphonons(T) S- 1 2 Summary Influence of temperature gradient Additional current: { ′ j = L11 ( + L12 (− gradT ) =σ 1 ↑ ( + grad r EF e Metals: ( ′ ≈ ( Heat flow: { ′ jQ = L21 ( + L22 ( − gradT ) λ Seebeck effect: T2 Thermovoltage U = ∫ ( K A − K B )dT T1 ( = Kgrad T ↑ absolute thermopower Peltier effect: inversion of Seebec jQ=Πj...
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This note was uploaded on 01/19/2010 for the course MATERIALS M504 taught by Professor Adelung during the Spring '02 term at Uni Kiel.

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