Electron scattering in semiconductor alloys

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Abstract
Suitability of the Born approximation and the Boltzmann equation is demonstrated for the scattering of free-carrier electrons by random-alloy atomic potentials in semiconductor alloys. Composition dependences of alloy-scattering potential strengths are hypothesized and electron scattering rates are derived. ‘‘Order parameters’’ are derived from scattering theory and compared to those derived previously from statistical and thermodynamic arguments by Warren and Cowley. The treatment is generalized to include ternary, quaternary, and lattice-matched alloys which, in general, show more complicated order-parameter dependencies than the previously known x(1−x) dependence for ternary zincblende alloys. Electron-momentum relaxation-rate expressions are given, including nonparabolic Kane bands and admixed wave functions appropriate to small energy-gap semiconductors. Electron drift mobility, as determined by alloy scattering, is derived in the effective-mass limit which shows that any short-range alloy potential yields the experimentally observed 1/(m*5T)1/2 dependence reported in the literature. An effective-charge model for alloy scattering is compared to experiments on AlxGa1−xAs. The magnitude of the effective charge on isolated Al atoms in GaAs is found to be 0.145 electron charges.