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L25_Phonon Scattering III

L25_Phonon Scattering III - ECE-656 Fall 2009 Lecture 25...

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ECE-656: Fall 2009 Lecture 25: Phonon Scattering III Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA 1 Lundstrom ECE-656 F09 2 outline 1) Review 2) POP and IV scattering 3) Scattering in common semiconductors 4) Electron-electron scattering 5) Summary
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Lundstrom ECE-656 F09 3 electron-phonon scattering S p , p ( ) = 2 π H p , p 2 δ E E   ω ( ) (weak scattering) H p , p 2 = 1 Ω K β 2 2 ρ ω N ω + 1 2 1 2 δ p , p ± β N ω = 1 e ω k B T 1 Isotropic: no β dependence in the matrix element. Elastic: approximately elastic when ω << E p ( ) p p β α E = E ± ω β p = p ± β Lundstrom ECE-656 F09 4 ADP scattering S p , p ( ) 2 π H p , p 2 δ E E ( ) (ABS + EMS) H p , p 2 = 1 Ω K β 2 2 ρ ω N ω + 1 2 1 2 δ p , p ± β N ω = 1 e ω k B T 1 k B T ω K β 2 = β 2 D A 2 1 τ = 2 π D A 2 k B T c l D 3 D E ( ) 2 1 τ = 1 τ m (isotropic) (Nearly elastic at room temperature) E 1 τ 1 τ E
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Lundstrom ECE-656 F09 5 ODP scattering S p , p ( ) 2 π H p , p 2 δ E E ± ω 0 ( ) H p , p 2 = 1 Ω K β 2 2 ρ ω N 0 + 1 2 1 2 δ p , p ± β N 0 = 1 e ω k B T 1 < N 0 + 1 1 τ = 1 τ m (isotropic) (inelastic at RT and below) 1 τ = 2 π D O 2 2 ρω 0 N 0 + 1 2 1 2 D 3 D E ± ω 0 ( ) 2 1 τ abs 1 τ ems K β 2 = D 0 2 E 1 τ ω 0 (EMS ABS Lundstrom ECE-656 F09 6 outline 1) Review 2) POP and IV scattering 3) Scattering in common semiconductors 4) Electron-electron scattering 5) Summary
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1 τ > 1 τ m > 1 τ E 1 τ = 1 τ abs + 1 τ ems = q 2 ω 0 2 κ 0 κ 1 2 πκ 0 ε 0 2 E m * N 0 sinh 1 E ω 0 + N 0 + 1 ( ) sinh 1 E ω 0 1 See Lundstrom, pp. 84 – 86 for momentum and energy relaxation rates. 7 POP scattering S p , p ( ) 2 π H p , p 2 δ E E ± ω 0 ( ) H p , p 2 = 1 Ω K β 2 2 ρ ω N 0 + 1 2 1 2 δ p , p ± β N 0 = 1 e ω 0 k B T 1 < N 0 + 1 (inelastic at RT and below) K β 2 = ρ q 2 ω 0 2 β 2 κ 0 ε 0 κ 0 κ 1 (favors small angle scattering) Lundstrom ECE-656 F09 8 POP scattering E 1 τ ω 0 ABS + EMS ABS 10 13 10 12 1 τ 1 τ m possibility of “polar runaway” ω 0
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