The transport-time to state-lifetime ratio in semiconductor quantum-well alloys: a multiple scattering analysis

A theoretical study is made of how the transport-time to state-lifetime ratio (tau(t)/tau(S)) varies as a function of sheet carrier density in semiconductor quantum-well alloys at low temperature. Various sources of ionized impurity scattering are considered, in addition to alloy scattering, using a self-consistent multiple-scattering theory proposed originally by Gold and Gotze. To begin, we present the theory of Gold and Gotze in its most transparent form. We then examine electron transport in In1-xGaxAs quantum wells and hole transport in Si1-xGex quantum wells. The interplay between alloy scattering and ionized impurity scattering leads to interesting behaviour, and to a significant reduction in the value of tau(t)/tau(S) as compared to systems where alloy scattering is not a factor. Multiple-scattering effects become progressively more important as the sheet carrier density decreases, and indications are given as to when lowest-order transport theory ceases to be adequate.