Orders of approximation in transport theory for electrons or holes in a scattering medium

In the framework of the path integral method, a transport quantity for free electrons (or holes) either in gases or in semiconductors in the presence of a static and uniform electrical field E, can be expressed as a sum of terms, each containing as a factor a properly indexed function vsub(j)(a)=Vsub(j)(eE/m) which can be reduced to a rapidly convergent series of integrals over the thermal electron speed v. In a wide variety of cases, the integrals can be solved by series expansion, and Vsub(j)(a) turns out to be given by a rapidly converging series of (W2/)<<1, where W is the drift velocity. This ratio for elastic collisions can reach an asymptotic value (for high E fields) of the order epsilon2=m/M where m and M are the masses of the electron and of a scattering centre respectively. (Auth.)