Deformation potentials of the fundamental exciton spectrum of InP

Abstract

Wavelength-modulated reflectivity spectra are performed on the direct exciton spectrum of InP under uniaxialstress conditions. Working at liquid-helium temperature, both the fundamental (${E}_{0}$) and spin-orbit split-off transition (${E}_{0}+{\ensuremath{\Delta}}_{0}$) are investigated. For unstressed crystals, at 5 K the $1s$ excitons are found at 1418.2 \ifmmode\pm\else\textpm\fi{} 0.5 and 1526.3 \ifmmode\pm\else\textpm\fi{} 0.5 meV, respectively. The spin-orbit splitting energy (${\ensuremath{\Delta}}_{0}$) is found to be 108 \ifmmode\pm\else\textpm\fi{} 1 meV. Next the stress dependence in configurations $X$ parallel to the [001], [111], and [110] crystallographic axes are investigated. An inability to apply stress magnitudes larger than 3 kbar necessitates analyzing the data with a simple model of orbital-strain interaction which neglects the stress-dependent spin-orbit interaction. Three deformation potentials are deduced: A fully symmetric, interband, deformation potential ${C}_{1}+{a}_{1}=\ensuremath{-}8.0\ifmmode\pm\else\textpm\fi{}0.4$ eV, which gives hydrostatic pressure coefficient $\frac{d{E}_{0}}{\mathrm{dP}}=11.1\ifmmode\pm\else\textpm\fi{}0.6$ meV/kbar and two shear deformation potentials, $b=\ensuremath{-}2.0\ifmmode\pm\else\textpm\fi{}0.2$ eV and $d=\ensuremath{-}5.0\ifmmode\pm\else\textpm\fi{}0.5$ eV. The first one, associated with pure ${\ensuremath{\Gamma}}_{12}(2{e}_{\mathrm{zz}}\ensuremath{-}{e}_{\mathrm{xx}}\ensuremath{-}{e}_{\mathrm{yy}})$ components of the strain tensor, gives the stress-induced splitting of the valence band under [001] compression while the second, associated with ${\ensuremath{\Gamma}}_{15}$ components, corresponds to pure [111] stress. The ratio of experimental splittings in both configurations is related to the anisotropic behavior of the valence band. For InP it is found to be about 0.7.