Volume Dependence of the Spin-Orbit Splitting in Representative Semiconductors from High-Pressure Electroreflectivity Measurements and Relativistic Orthogonalized-Plane-Wave Calculations

Abstract

By means of electroreflectivity measurments at room temperature and at 77 \ifmmode^\circ\else\textdegree\fi{}K performed at pressures up to 10 kbar, we have experimentally determined the volume dependence of the ${\ensuremath{\Delta}}_{0}$ and ${\ensuremath{\Delta}}_{1}$ spin-orbit splittings in CdTe and the ${\ensuremath{\Delta}}_{0}$ spin-orbit splitting in germanium. The volume dependence of the ${\ensuremath{\Delta}}_{0}$ and ${\ensuremath{\Delta}}_{1}$ (at $L$) spin-orbit splitting has also been obtained for Ge, GaAs, and CdTe from a relativistic orthogonalized-plane-wave (OPW) calculation. Our experimental and theoretical results are in agreement and indicate that the volume dependence of the spin-orbit splitting is considerably smaller than would be expected if the valence-electron density in the core region increased in proportion to the decrease in the crystal volume. These results are interpreted as an indication that the valence-electron density in the core region is little affected by the crystal volume and may be relatively unchanged from that of the free atom. The plausibility of the conclusion and some consequences are discussed. In some cases a reversible change in the electroreflectivity line shape as the pressure is cycled can give rise to erroneous results if the change in line shape is not taken into account. It is shown that all of our experimental results are consistent when reasonable corrections are made for the change in line shape, and it is suggested that such effects may not be accounted for in the experimental results of Bendorius and Shileika on GaAs which disagree with our calculated results.