Electron phonon scattering Handout

# Electron phonon scattering Handout - University of...

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University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Electron phonon scattering Handout.fm Electron-phonon scattering (Finish Lundstrom Chapter 2) Deformation potentials The mechanism of electron-phonon coupling is treated as a perturbation of the band ener- gies due to the lattice vibration. Equilibrium atomic positions: Lattice vibrations cause perturbations about equilibrium: . Energy bands shift locally due to perturbation. In a linear approximation: are constants known as deformation potentials. Lattice vibration waves lead to sinusoidal variations δ E. These mix Bloch waves for the electrons which leads to scattering. We will use δ E as a perturbation and then apply Fermi’s Golden Rule to get the scattering rates. Energy and momentum conservation We consider inelastic scattering where an electron makes a transition from momentum p to p ¢ involving emission or absorption of a phonon q : Energy conservation: + sign phonon absorption - sign phonon emission Assuming spherical, parabolic bands, and intra -valley scattering (i.e. both initial and final electron states are within the same parabolic band): (1) Momentum conservation tells us that: R 1 ° R 2 ° R 3 ° ,,, R ° R δ + E c δ D c R δ a ------ = E v δ D v R δ a = D c D v ,

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- 116 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor take (2) compare (1) & (2) to obtain: simplifying: (3) where . (3) sets min, max values for phonon wave vectors via Intravalley acoustic phonon scattering . : sound velocity Typically, and (300K). So, p ' ph _ q ± = p 2 h _ 2 q 2 2 h _ pq θ cos ± + = 2 m h _ ω ± h _ 2 q 2 2 h _ θ cos ± = h _ q 2 p θ ω qv e ------- ± cos + = v e p m ------ = 1 θ cos 1 ≤≤ ω π/ a q optical acoustic ω s = v s h _ q 2 p θ v s v e ---- ± cos + = q max : θπ absorption = θ 0 emission = v s 10 5
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Electron phonon scattering Handout - University of...

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