Week 15: Emission is easier than absorption

Emission is easier than absorption (Datta Part B, Ch. 21, Eqs. 21.16–21.18)

A scatterer that exchanges one quantum ℏω with the electron has rates ∝ N_ω for absorption and ∝ N_ω+1 for emission. Left: the rate arrows from one level. Middle: N_ω(T) and the ratio (N_ω+1)/N_ω = e^ℏω/kT. Right: a ladder of levels spaced by ℏω, started in a non-equilibrium distribution, relaxes to the Boltzmann distribution only because the two rates differ.

Phonon energy ℏω (meV) Temperature T (K) Initial distribution Rates

N_ω (Bose–Einstein)–

emission / absorption–

ℏω / kT–

mean level ⟨k⟩ (now / equilibrium)–