Carrier Scattering - Phonon Scattering

Phonon Scattering

We now consider carrier scattering with lattice deformations termed phonons. Consider the volumetric displacement such a propagating wave produces, which consequently results in a time-dependent strain, where a simple plane wave is used to describe the phonon propagation, . Displacement of atoms away from their equilibrium positions generally causes a change in the electronic band structure (Figure 5) where, for scattering, we are concerned with electrons in the conduction band with energy ~E_CB,
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The empirical parameter, Z_DP, is termed the deformation potential and describes electron-phonon coupling strength. Multiplying by the phonon population (Bose-Einstein distribution, N_q) gives the total deformation potential,

(the reason for the root will be apparent below). Here, the + corresponds to phonon emission and – for phonon absorption during the scattering event. A note, because for transverse phonons, only interactions with longitudinal phonons are non-zero. Therefore, the complete interaction matrix is

where the Kronecker delta enforces momentum conservation and arises from assuming the electronic wavefunctions (final state, ) are plane waves as well.