Moments of the electron distribution in semiconductors for large electric fields

For a general class of collision operators, we perform an asymptotic analysis of the moments of the stationary homogeneous solution of the linear Boltzmann equation in the limit of a large external field. We consider collision operatrs with separable kernels, which are also known as “relaxation time approximations”. It turns out that the behaviour of the moments is determined by the inverse function N−1 of the integral over the collision frequency; the nth moment behaves like the nth lower of N−1 (E) as the field E tends to infinity. As a consequence, velocity saturation is excluded.