Line shape and symmetry analysis of core-level electroreflectance spectra of GaP

Abstract

No dependence of electroreflectance line shapes upon polarization direction or crystal orientation is found for any core-level electroreflectance structure from the $\mathrm{Ga} 3{d}^{v}$ core levels to the conduction bands in GaP. Matrix-element effects that are responsible for anisotropy in $s{p}^{3}$ valence-conduction-band electroreflectance spectra appear to be too weak to be detected in core-level spectra. The result may be general. The field-induced modulation line shape, $\ensuremath{\Delta}{\ensuremath{\epsilon}}_{1}$, for the $\mathrm{Ga} 3{d}_{\frac{3}{2},\frac{5}{2}}^{v}\ensuremath{-}{X}_{6}^{c}$ critical points is obtained from the dependence of the spectra and the generalized Seraphin coefficients upon angle of incidence. The line shape is further analyzed to obtain the $\ensuremath{\Delta}{\ensuremath{\epsilon}}_{1}$ spectrum for $\mathrm{Ga} 3{d}_{\frac{5}{2}}^{v}\ensuremath{-}{X}_{6}^{c}$ alone. This procedure yields a spin-orbit splitting ${\ensuremath{\Delta}}_{3d}=0.43\ifmmode\pm\else\textpm\fi{}0.02$ eV. A weighting of 0.65 \ifmmode\pm\else\textpm\fi{} 0.05 is also obtained for the $j=\frac{3}{2}$ band relative to the $j=\frac{5}{2}$ band. This is in good agreement with the 4:6 ratio expected on $d$-band occupancy, showing that the matrix elements are also independent of $j$. The line shape of $\ensuremath{\Delta}{\ensuremath{\epsilon}}_{1}$ is in good agreement with that predicted by the lifetime-broadened, Coulomb-enhanced Franz-Keldysh theory given by Blossey. The line shape shows a broadening of 160 meV for this transition, and a momentum matrix element about 1/3 as large as that characteristic of $s{p}^{3}$ valence-conduction-band transitions.