W. Quade et al., QUANTUM-THEORY OF IMPACT IONIZATION IN COHERENT HIGH-FIELD SEMICONDUCTOR TRANSPORT, Physical review. B, Condensed matter, 50(11), 1994, pp. 7398-7412
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.