Near-band-gap CuPt-order-induced birefringence in Al 0.48 Ga 0.52 InP 2

The order-induced birefringence in the near-band-gap spectral range (0.75 to 2.5 eV), and its dependence on the degree of ordering \ensuremath{\eta} is reported for ${\mathrm{Al}}_{0.48}{\mathrm{Ga}}_{0.52}{\mathrm{InP}}_{2}.$ Transmission and reflection generalized variable angle spectroscopic ellipsometry, dark-field spectroscopy, and cross-polarized reflectance difference spectroscopy (CRDS) are used to determine precisely the room-temperature dielectric functions for polarization parallel and perpendicular to the ordering direction of a series of spontaneously CuPt-ordered samples grown by metal-organic vapor-phase epitaxy. The CRDS technique is introduced as an approach to sense extremely weak anisotropy at oblique angles of incidence. The observed order birefringence is treated as ``chemical-stress'' induced piezobirefringence. The dielectric function model for piezobirefringence in zinc-blende compounds, and selection rules for the transitions from the ${\ensuremath{\Gamma}}_{4,5v},{\ensuremath{\Gamma}}_{6(1)v},{\ensuremath{\Gamma}}_{6(2)v}$ valence band states to the ${\ensuremath{\Gamma}}_{6c}$ conduction band states, allow excellent modeling of the order birefringence in the near-band-gap spectral region. Thus, explicit treatment of the transition-matrix k dependence, as recently suggested for ordered ${\mathrm{GaInP}}_{2}$ or ${\mathrm{GaInAs}}_{2},$ can be avoided. The transition energies, strengths, and broadening parameters for the three zone-center transitions are obtained from analysis of the sample dielectric function tensor. All parameters in the quasicubic perturbation model can be fitted. We find, in excellent agreement with recent theoretical predictions, that the spin-orbit splitting parameter of 76 meV is nearly ordering independent, and that the ratio of the crystal-field splitting to the band-gap reduction for the perfectly ordered alloy amounts to 0.62. The band gap of the disordered compound is extrapolated to 2.195 eV.