Electroreflectance of GaAs and GaP to 27 eV using synchrotron radiation

Abstract

Electroreflectrance (ER) spectra of GaAs and GaP, taken with the Schottky-barrier method, exhibit to 27 eV the strong structural enchancement and high resolution characteristic of similar measurements below 6 eV. Above 20 eV, a new set of critical points is observed between the flat valence bands derived from the Ga $3d$ core levels and the local extrema of the ${\mathrm{sp}}^{3}$ conduction bands. The attained resolution, of the order of 100 meV, enables us to resolve clearly the spin-orbit splitting of 0.45 eV of the $3d$-derived valence bands. The following critical-point energies have been determined in GaAs and GaP, respectively. ${\mathrm{sp}}^{3}$ valence conduction: ${{E}_{1}}^{\ensuremath{'}}$, 6.63 \ifmmode\pm\else\textpm\fi{} 0.05 eV, and 6.80 \ifmmode\pm\else\textpm\fi{} 0.05 eV; ${{E}_{1}}^{\ensuremath{'}}+{{\ensuremath{\Delta}}_{1}}^{\ensuremath{'}}$, 6.97 \ifmmode\pm\else\textpm\fi{} 0.05 eV (GaAs only); ${{E}_{0}}^{\ensuremath{'}\ensuremath{'}}({\ensuremath{\Gamma}}_{15}^{v}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{12}^{c})$, 10.53 eV, and 9.38 \ifmmode\pm\else\textpm\fi{} 0.1 eV; ${{E}_{0}}^{\ensuremath{'}\ensuremath{'}\ensuremath{'}}({\ensuremath{\Gamma}}_{15}^{v}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{1}^{c})$, 8.33 \ifmmode\pm\else\textpm\fi{} 0.1 eV, and 10.27 \ifmmode\pm\else\textpm\fi{} 0.1 eV, ${{E}_{1}}^{\ensuremath{'}\ensuremath{'}}$, 9.5 \ifmmode\pm\else\textpm\fi{} 0.2 eV, and 10.7 \ifmmode\pm\else\textpm\fi{} 0.2 eV. ${E}_{5}$, ${E}_{6}$, and ${E}_{7}$ structures are observed at 15.1, 16.7, and 17.9 eV in GaAs, and at 14.7, 16.1, and 18.6 eV in GaP. Relative values of $3d$ core to ${\mathrm{sp}}^{3}$ conduction-band matrix elements are estimated for several states and show that the lowest $3d$ core-level ER structures arise from transitions terminating at the ${X}_{1}^{c}$ conduction-band minimum. We calculate an exciton or core-hole interaction shift of 150 meV for GaP and 200 meV for GaAs, which indicates that core-hole effects are probably small for these materials. Spectral features with initial structure less than 100 meV in width are observed above 20 eV, showing that broadening effects are much smaller in this energy range than previously believed.