### 5.5 Optical Deformation Potential Scattering

In contrast to the case of acoustic vibrations where the perturbation Hamiltonian is proportional to
the derivative of the atomic displacement, the perturbation Hamiltonian for the optical modes is
assumed to be proportional to the atomic displacement. Due to the quite flat dispersion
curve, the energy associated with optical phonons is assumed to be constant. In this case,
the phonon occupation number N_{op} is independent on the phonon wave vector. Since the
scattering arises from the band edge variation induced by optical phonons, we can rely on the
considerations done for deformation potential scattering for acoustic phonons. Assuming an isotropic
deformation potential, the coupling coefficient of its interaction potential can be written
as

| (5.28) |

The scattering rate caused by optical phonons is given by (see Appendix B.3)

| (5.29) |