Near-band-gap reflectance anisotropy in orderedGa0.5In0.5P

Abstract

We present a theory that models the reflectance difference spectrum of bulk, spontaneously ordered ${\mathrm{Ga}}_{0.5}$ ${\mathrm{In}}_{0.5}$P. Near the band gap ${\mathrm{E}}_0$ this spectrum exhibits a sharp, negative feature at ${\mathrm{E}}_0$ and a broad positive feature that peaks near ${\mathrm{E}}_0$+${\mathrm{\Delta }}_{\mathrm{S}}$. The zero crossing between these two peaks occurs near ${\mathrm{E}}_0$+${\mathrm{\Delta }}_{\mathrm{C}}$. For the sample studied in this paper, the spin-orbit splitting ${\mathrm{\Delta }}_{\mathrm{s}}$ and the crystal-field splitting ${\mathrm{\Delta }}_{\mathrm{C}}$ are 120 and 25 meV, respectively. Two previous calculations, which assume constant transition-matrix elements, were able to produce a negative peak at ${\mathrm{E}}_0$, but not the positive feature. In this paper, the reflectance difference spectrum near the band gap is calculated using an 8-band k⋅p model and an explicit treatment of the momentum or k dependence of the transition-matrix elements. The new calculation produces both the negative peak at ${\mathrm{E}}_0$ and the positive feature that peaks near ${\mathrm{E}}_0$+${\mathrm{\Delta }}_{\mathrm{S}}$. The positive feature is attributed to the strong k dependence of the matrix element anisotropy. A strong coupling, enhanced by ordering, between three valence bands is essential. A problem associated with the analytical expression for the dielectric function ɛ used in previous calculations is discussed.