Simplifying Semiclassical Electron Transport in Highly Inhomogeneous Fields

The Boltzmann transport equation describes the dynamics of electrons via the time evolution of a 6-D scalar field. This semiclassical description is valid in any device where the external field is relatively constant over the decoherence length. Near equilibrium, the electron distribution can be characterized by a local chemical potential and the lattice temperature, leading to a simplified electron state described by a 3-D scalar field. When external fields are large, this approximation breaks down as the electrons are accelerated far away from a lattice temperature thermal equilibrium. If the external field is quasi-homogeneous, the local field or average kinetic energy can be used to characterize the shape of the distribution function, leading to an electron state described by one or two 3-D scalar fields. However, if the external field is not quasi-homogeneous, there is currently no significant simplification of the Boltzmann transport equation that is widely accepted as being theoretically sound.