Exciton binding energies and the valence-band offset in mixed type-I-type-II strained-layer superlattices.

Abstract

Strained CdTe-${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zn}}_{\mathit{x}}$Te superlattices are of mixed type: electrons and heavy holes are confined to the CdTe layers (type I) while light holes are confined to the ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zn}}_{\mathit{x}}$Te layers (type II). In this paper we calculate the exciton binding energy (EBE) as a function of superlattice period for both type-I (spatially direct) and type-II (spatially indirect) excitons. For the heavy-hole (type-I) exciton the binding energy is larger than the bulk value, and varies only slowly with the period down to small periods, where the exciton acquires a three-dimensional character and our calculation breaks down. For the light-hole (type-II) exciton the binding energy at large period is much smaller, due to the spatial separation of electron and hole. As the period decreases, the binding energy increases steadily to reach its bulk value for vanishingly small period. Given the EBE's, we can fit the already published data on the exciton transition energies with a single adjustable parameter, the ``average valence-band offset'' (averaged over the heavy and light holes). This is the algebraic sum of the chemical-offset and the hydrostatic-strain contribution, and is found to be (2\ifmmode\pm\else\textpm\fi{}4)% of the difference in band gap between the barrier and well. This value lies in the range predicted theoretically.