Well-width dependence of the optical anisotropies in (001) and (110) semiconductor quantum wells: The effect of spin-orbit split-off bands

We have investigated both theoretically and experimentally the well-width dependence of the polarization anisotropies of the interband transitions in semiconductor quantum wells (QW’s). In our theoretical study, we adopted the six-band Luttinger-Kohn model in which the spin-orbit split-off (SO) bands are included. The polarization-dependent optical-matrix elements at the Brillouin-zone center in (001) and (110) QW’s were calculated as a function of the well width using the exact solutions of coupled effective-mass equations. The calculated results are shown for GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As and ${\mathrm{Ga}}_{0.5}$${\mathrm{In}}_{0.5}$P/(${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${)}_{0.5}$${\mathrm{In}}_{0.5}$P (001)-oriented QW’s as well as GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As (110)-oriented QW’s. In the (001) QW’s, the inclusion of the SO bands into the calculation led to a decrease in the TM/TE ratio of the optical-matrix element for the light-hole transition with decreasing well width. In the ${\mathrm{Ga}}_{0.5}$${\mathrm{In}}_{0.5}$P/(${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${)}_{0.5}$${\mathrm{In}}_{0.5}$P system, which has a smaller spin-orbit splitting energy, the decrease in the TM/TE ratio was shown to be more remarkable to show reversal between the TM and TE strength when the hole confinement energy is large.

In the (110) QW’s, the effect of coupling to the SO bands was revealed to appear not only for the light-hole transition but also for the heavy-hole transition. The calculated results for (110) GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As QW’s illustrated that the anisotropy regarding the polarization direction in the (110) QW plane increases with decreasing well width according to the increase in coupling to the SO bands. In order to investigate experimentally the well-width dependence of the in-plane optical anisotropy in (110) QW’s, polarized photoluminescence measurements were performed at 77 K on (110) GaAs/${\mathrm{Al}}_{0.2}$${\mathrm{Ga}}_{0.8}$As QW structures having various well widths. The in-plane anisotropy of heavy-hole excitonic emission was observed to be almost unchanged for well widths wider than 9 nm, while it was observed to increase for narrower well widths with decreasing well width. The degree of linear polarization observed in the photoluminescence measurements showed good agreement with the calculated results.