The influence of abrupt electric field variations on the distribution function of hot electrons

Some analytical models of quiescent hot electron distributions are extended to the transient conditions, in order to describe the response of hot electrons to step changes in the magnitude of the electric field. These models apply to semiconductors having one or several equivalent energy minima in the conduction band, and isotropic lattice scattering due to low-energy acoustic phonons (elastic in-valley scattering) and to high energy single-level acoustic phonons (inelastic inter-valley scattering) or dispersionless optical phonons (inelastic in-valley scattering). Step changes in the field magnitude are considered with respect to the time and space (one-dimensional) variables, separately. In both cases, the spherically-symmetrical term ?_O of the electron distribution function may be expressed using a Laguerre polynomial expansion in the energy variable. For a positive step change in field magnitude, transient electron drift velocities in excess of the steady-state “scattering-limited” values are found in both silicon and germanium.