Conduction- and valence-band effective masses in spontaneously orderedGaInP2

An eight-band k⋅p model is developed for zinc-blende semiconductor alloys that exhibit spontaneous CuPt ordering. Energy dispersions and effective masses are calculated analytically for the conduction band and valence band as a function of the degree of ordering. All the effective-mass tensors are found to be diagonal and the energy dispersions are ellipsoidal to terms quadratic in the wave vector when the axis of quantization (the z direction) is chosen along the ordering direction. The change of effective masses is found to satisfy a sum rule when ordering is weak. Numerical results are given for the ordered ${\mathrm{GaInP}}_2$ alloy. We find that, as the order parameter increases, along the ordering direction, ${\mathit{m}}_{\mathrm{\parallel }}$ is unchanged for the heavy-hole band, increases for the light-hole band, and decreases for the spin-orbit split-off band. In the plane perpendicular to the ordering direction, ${\mathit{m}}_{\mathrm{\perp }}$ for the heavy- and light-hole bands decreases, whereas it increases for the split-off band. For the conduction band, both ${\mathit{m}}_{\mathrm{\parallel }}$ and ${\mathit{m}}_{\mathrm{\perp }}$ decrease.