Asymptotic Solution of the Boltzmann Equation for Hot Carriers

The steady‐state Boltzmann equation for hot carriers is solved asymptotically for the case of predominate inelastic scattering by nonpolar optical phonons in the limit of high carrier energies. This solution has a simple analytic shape and permits one to define a temperature T and an anisotropy parameter η for the hot carriers. The analytic relation between T, η, the lattice temperature TL, and the applied field strength E is demonstrated. In the high‐energy limit the applicability of conventional approaches, which are based on a Legendre polynomial expansion, is discussed by comparison with the asymptotic solution.