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 rat io (tau(t)/tau(S)) varies as a function of sheet carrier density in semicon ductor quantum-well alloys at low temperature. Various sources of ionized i mpurity 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 trans parent 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 effect s become progressively more important as the sheet carrier density decrease s, and indications are given as to when lowest-order transport theory cease s to be adequate.