Use of the Fokker–Planck equation in high-field transport problems

The Fokker–Planck drift-diffusion equation is often used to describe Brownian motion of a particle in thermal equilibrium with the surrounding medium. The present paper shows that the equation has the ability to describe charged particle transport far from equilibrium, such as occurs in the presence of a high electric field in a neutral gas or a semiconducting solid. These transport problems are usually tackled by means of the Boltzmann transport equation, but the Fokker–Planck approach is mathematically simpler, and gives insight into the statistics of energy-exchange processes and their thermalization capacity.