FREE-CARRIER TRANSPORT IN SUPERLATTICES - SMOOTH TRANSITION BETWEEN THE QUASI 2-DIMENSIONAL AND UNIFORM 3-DIMENSIONAL LIMITS

Presented here is a comprehensive, single-particle formalism for free-carrier transport in semiconductor superlattices with cylindrically symmetric energy dispersion. The spatial nonuniformity of the carrier population is accounted for by employing a scattering potential that is weighted by the wave-function distribution function. In the limit of large barrier-to-well thickness ratios, one regains the quasi-two-dimensional (2D) expressions derived previously. In the opposite limit of thin barriers and hence a nearly uniform wave-function distribution, transport in the superlattice becomes analogous to that in a 3D semiconductor with an anisotropic effective mass. Anisotropic relaxation times are obtained for acoustic-phonon, nonpolar-optical-phonon, polar-optical-phonon, and ionized-impurity scattering. Arbitrary energy dispersion relations are assumed, so that complex, numerically derived band structures may be straightforwardly incorporated. For the example of a HgTe-CdTe superlattice with weak hole dispersion but relatively strong electron dispersion in the growth direction, superlattice mobilities obtained using the present formalism are compared in detail with results for the quasi-2D and isotropic 3D limits.