Inelastic scattering

An inelastic scattering mechanism, like phonon scattering, makes an electron emit/absorb energy of ℏω_q. The number of unique energy values representable by the discrete k-values is determined by the number of unique sum of squares:

S = n21 + n22 + n23,n1,2,3 ∈ [0,K - 1]. (B.1)

The resulting energy grid is non-uniform, but remains approximately uniform for energies under ~ 0.8eV (for Δk = -π-
100

nm^-1). At higher energies the grid becomes more non-uniform and coarser.

The energy gained/lost through phonon absorption/emission (ℏω_g) in general will not exactly correspond to an interval in the discretized energy grid and therefore will be rounded up/down. The approximation introduced by this rounding is below 1meV for most points in the energy grid. However, at higher energy values, where the energy grid is coarser, the energy gained/lost by optical phonon can be under- or overestimated.

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