Inter-quantum-well diffusion in semiconductor superlattices

The diffusion of a minority carrier in the growth direction in a semiconductor superlattice is studied theoretically. Both coherent band diffusion and incoherent well-to-well tunneling processes are considered in an ordered superlattice. The formalism is employed to calculate the diffusion length of a heavy hole in ${\mathrm{In}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs superlattices by accounting for scattering by acoustic and polar optical phonons and using the Kronig-Penney model in the temperature range 70–300 K. It is found that the diffusion takes place mainly via activation to broad-subband states above the barriers in superlattices with thick barriers (e.g., ∼115 Å). For superlattices with thinner barriers (e.g., ∼50 Å), we find a crossover from over-barrier diffusion at high temperatures to tunneling diffusion through low-lying narrow-subband states at low temperatures. For even thinner barriers (e.g., ≤40 Å) tunneling diffusion prevails at all temperatures. For a light hole, the crossover is found to occur in superlattices with much thicker barriers (e.g., ∼115 Å). The relevance of these results to recent data is discussed. Finally, the effect of the disorder-induced localization is discussed.