Optical properties of ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x{\mathrm{As}}_y{\mathrm{P}}_{1-y}$ from 1.5 to 6.0 eV determined by spectroscopic ellipsometry

We report high-precision pseudodielectric function spectra ellipsometrically measured from 1.5 to 6.0 eV of ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x{\mathrm{As}}_y{\mathrm{P}}_{1-y}$ alloys lattice-matched to InP. Analysis of third derivatives numerically calculated from these data yields critical-point energies, broadening parameters, phases, and amplitudes for the valence—conduction-band critical points $E_1$, $E_1+{\Delta }_1$, $E_0^{\prime }$, and $E_0^{\prime }+{\Delta }_0^{\prime }$. An observed inversion of the relative strengths of the $E_1$ and $E_1+{\Delta }_1$ transitions as a function of composition is attributed to the $k$-linear interaction. The phases indicate strong Coulomb interactions for $E_1$ and $E_0^{\prime }$, without the ambiguities present in the interpretation of electroreflectance spectra. The composition dependence of critical-point energies yields the following bowing parameters for $E_1$, $E_1+{\Delta }_1$, ${\Delta }_1$, and $E_0^{\prime }$: 0.33±0.05, 0.26±0.04, -0.07±0.02, and -0.01±0.05 eV, respectively. We discuss our results with the use of the models of Van Vechten and others for the nonlinear variation of energy gaps and spin-orbit splittings with composition. The $E_0^{\prime }$ structure may contain contributions from both $\Gamma$ and $\Delta$, as observed in Ge and GaAs. We reassign the feature previously attributed to $E_2$ in InP to $E_0^{\prime }+{\Delta }_0^{\prime }$, where ${\Delta }_0^{\prime }$ is the spin-orbit splitting of the second conduction band at $k=0\mathrm{}$. Our improved methods of analysis allow spectroscopic ellipsometry to be used as a valuable supplement to modulation spectroscopy for the study of interband transitions in solids.