QUANTUM-THEORY OF IMPACT IONIZATION IN COHERENT HIGH-FIELD SEMICONDUCTOR TRANSPORT

Generation of carriers in semiconductors by impact ionization is studi ed under the influence of a constant, arbitrarily high electric field. Using the density-matrix approach a system of equations for the coher ent dynamics of electrons and holes in the presence of impact ionizati on and Auger recombination is derived, which extends the semiconductor Bloch equations by the inclusion of impact-ionization density-correla tion functions as additional dynamic variables. From these equations w e recover the pure (Zener) and the photon-induced (Franz-Keldysh) carr ier tunneling rate and derive an expression for the field-assisted imp act-ionization scattering rate. Different levels of approximation of t he kinetic equations are discussed. It is shown that in contrast to th e semiclassical treatment in the presence of an electric field, a fixe d impact-ionization threshold does no longer exist, and the impact-ion ization scattering rate is drastically enhanced around the semiclassic al threshold by the intracollisional held effect. The close connection of field-assisted impact ionization to the Franz-Keldysh effect is em phasized.