Flatband Electroreflectance of Gallium Arsenide. II. Comparison of Theory and Experiment

Abstract

An analysis of previously reported electroreflectance (ER) data is presented. One-electron Franz-Keldysh-Aspnes (FKA) line shapes were compared to each ER structure observed in the 1.2-5.3-eV photon energy range. In addition, an excitonic theory of ER was compared to the direct edge data. We found it most useful to analyze the GaAs ER data by fitting FKA line shapes, considering the matrix elements thus obtained as exciton enhanced. The FKA fits determined the $E_0$ gap energy to be 1.427 ± 0.003 eV at 0°C; the spin-orbit splitting at $\Gamma$, ${\Delta }_0=0.336\mathrm{}\pm 0.013$ eV. The interference between light- and heavy-hole transitions at $E_0$ was seen and the following quantities determined: light-hole reduced mass ${\mu }_{\mathrm{lh}}=(0.030\mathrm{}\pm 0.005)m_e$, heavy-hole reduced mass ${\mu }_{\mathrm{hh}}=(0.062\mathrm{}\pm 0.015)m_e$, and dipole matrix elements $C_{0\mathrm{lh}}=(1.16\mathrm{}\pm 0.2)\frac{\hslash }{a_0}$, $C_{0\mathrm{hh}}=(0.6\mathrm{}\pm 0.1)\frac{\hslash }{a_0}$, and $C_{0\mathrm{soh}}=(0.66\mathrm{}\pm 0.1)\frac{\hslash }{a_0}$. At the next-higher-energy structures, $E_1$, $E_1+{\Delta }_1$, it was found that the two-dimensional FKA theory best represented the line shapes. The $E_1$ energy was found to be 2.884 ± 0.012 eV. at 0°C, and the spin-orbit splitting ${\Delta }_1=0.227\mathrm{}\pm 0.010$ eV. The reduced mass transverse to the [111] direction in $\overrightarrow{\mathrm{k}}$ space was determined to be ${\mu }_t^{2\mathrm{D}}=0.053\mathrm{}{m}_e$. Two structures in the 4.0-5.3-eV photon energy range were analyzed but remain poorly understood. A one-dimensional critical-point model is shown to be consistent with the highest-energy structure $E_{}^{\prime }{}_0{}^{}$, but the structure is so broad that it can also be fit by other one-electron models.