Boltzmann collision kernels and velocity saturation in semiconductors

For different models of the electron-phonon interaction, the asymptotic behaviour of the moments of the stationary homogeneous solution of the linear Boltzmann equation is determined in the limit of a high external field. For Hilbert-Schmidt kernels of a finite rank, a result recently proven for kernels of rank one is found generally valid; as a consequence velocity saturation is excluded for these collision models. For a class of singular collision kernels in contrast, velocity saturation is generally obtained.