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lecture_18_07c

# lecture_18_07c - 3-dim Fermi level In 3-d Fermi energy is...

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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 1 3-dim Fermi level In 3-d Fermi energy is altered - e - s now fill a spherical well (real potentials?) E Fermi ( T = 0 K ) = h 2 c 2 8 m e c 2 3 N pV 2/3 Examples: N/V(cm 3 ) E F (eV) Al 18.1 × 10 22 11.7 Cu 8.47 × 10 22 7.04 K 1.40 × 10 22 2.11 E F (0K)>>kT(300K) (or 0.026eV)

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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 2 Density of states At T = 0K p ( E ) = 3 N 2 E F - 3/ 2 E 1/2 for E E F and 0 otherwise. p ( E ) dE = N and E ave = 0 E F Ep ( E ) dE 0 E F / N = 3 5 E F At finite T have Fermi- Dirac factor 1 e E - E F kT +1 also p(E) E F E T=0 kT=E F / 50 Only small fraction of e’s (~ kT/2E F ) above E F can move to other states in response to Electric field. Only v just above v from E F can drift
05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 3 Drift velocity v f(v) With E field v=v Fermi +v drift Few e - s are free to move Collision time is “coherence length”/v drift QM -> very long length

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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 4 Electrical & Thermal properties-metals Classical free electron theory - Ohm’s Law But fails: magnitude of ρ (resistivity) or σ (conductivity) 2200 ρ classical (T)~v ave (T)~√T but ρ msd (T)~T & ρ msd ~ ρ class /10 QM electron gas: v ave ~independent of T (for kT<<E fermi ) 2200 ρ depends on wave-like e - s propagating in lattice Why conductors and insulators?
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lecture_18_07c - 3-dim Fermi level In 3-d Fermi energy is...

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