Abstract
An investigation is made into the effect of valence-band coupling on Wannier excitons in GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum wells with well widths ranging from 30 to 200 A\r{}. The results of our calculation show that the effect is twofold. On the one hand, hole-subband nonparabolicity due to mixing of the heavy- (HH) and light-hole (LH) states causes an increase in the binding energies ${E}^{\mathrm{ex}}$, of both ground- and excited-state excitons; on the other hand, the different orbital behaviors of the spinor components of the excitonic wave function result in a decreased ${E}^{\mathrm{ex}}$ of s-state excitons and an increased ${E}^{\mathrm{ex}}$ of p- and d-state excitons. The former effect dominates in narrower wells and the latter effect dominates in wider wells. The two-band model is a good approximation for calculating ${E}^{\mathrm{ex}}$(HH1), but can cause a significant error in calculating ${E}^{\mathrm{ex}}$(LH1) in wider wells because of the stronger coupling between exciton states from different subbands.
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