Folding effects in GaAs-AlAs superlattices.

Abstract

Folding effects are important in the electronic structure of GaAs-AlAs superlattices because of the indirect-gap character of the bulk AlAs. Conduction-band states at the center of the Brillouin zone of superlattices grown along the [001] direction originate from both \ensuremath{\Gamma} states of bulk GaAs and X states of bulk AlAs. The only way to properly describe such effects is to use tight-binding Hamiltonians. We introduce a simple perturbative approach to compute the eigenvalues, eigenstates, and optical transition probabilities in superlattices. The method is applied to several GaAs-AlAs superlattices. Our results show that transition probabilities between X-like conduction-band states in AlAs and \ensuremath{\Gamma}-like valence-band states in GaAs are very small because of spatial separation. These transitions are reinforced when a spike of AlAs is introduced in the center of the GaAs region. Our results indicate that in this case folding effects must be optically observable. Finally, we apply our method to study sawtooth superlattices made of ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As with x varying in the superlattice period. In this case, folding effects increase the asymmetry between conduction- and valence-band states which must be reflected in a large transient photovoltaic effect.