Electron-phonon interaction in a crystalline lattice
Acoustic phonon scattering limits electron mobility in semiconductors. The scattering rate Γ ∝ D²T·n(ω,T)/ε_k where D is the deformation potential, T is temperature, and n(ω,T) = 1/(exp(ℏω/k_BT)−1) is the Bose-Einstein phonon occupation. At high T the rate scales linearly: Γ ∝ k_BT, giving mobility μ ∝ T⁻³/² for parabolic bands (Bardeen-Shockley, 1950).