Occupation statistics Handout

Occupation statistics Handout - University of California,...

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University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Occupation statistics Handout.fm Semiconductor Statistical Mechanics (Read Kittel Ch. 8) Conduction band occupation density: f(E) - occupation probability - Fermi-Dirac function: g(E) - density of states / unit volume. For an isotropic, parabolic band, generalize free-electron theory: where . Define dimensionless variables: “Fermi-Dirac integrals” (tabulated in Semiconductor Statistics , J.S. Blakemore, Pergamon, 1962) nf E () gE E d E c = 1 2 π 2 -------- 2 m e * h _ 2 --------- ⎝⎠ ⎜⎟ ⎛⎞ 32 EE c 12 = n 1 2 π 2 2 m e * h _ 2 ε ε d 1 ε E F E c + kT [] exp + ------------------------------------------------------------------ 0 = ε c η ε ----- η c E c μ E F ------ == = n 1 2 π 2 2 m e * h _ 2 ---------------- η η d 1 ημ η c + exp + ------------------------------------------------ 0 = N c F μη c F n x 2 π z n z d 1 zx exp + ---------------------------------- 0
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- 83 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor “effective density of states”: Recall the discussion of degenerate / non-degenerate Fermi-gas. N C is density for the degenerate case. Some numbers: For Si, (“density of states” mass); at 300K . For GaAs, ; at 300K at 4K Anisotropic bands density of states mass: ν = degeneracy factor - # of equivalent CB valleys = 6 in Si = 1 in GaAs Maxwell-Boltzmann approximation If is well inside band-gap (non-degenerate case): , then the Fermi func- tion Boltzmann factor for This expression can be interpreted as if there are N c states all located at band edge. m e * 1.18 m o = N c 2.8 19 × 10 cm 3 = m e 0.067 m o = N c 4.3 17 × 10 3 = 6.6 14 × 10 3 = E F E c E F kT » F n x () 2 π ------- z n e xz z d 0 e x = n 1 2 -- =
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- 84 - University of California, Berkeley
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Occupation statistics Handout - University of California,...

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