Temperature dependence of the dielectric function and the interband critical-point parameters of GaP

Abstract

We have used spectroscopic ellipsometry to measure the dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}) of GaP from 10 to 640 K in the 1.6--5.6-eV photon-energy region. By performing a line-shape analysis of the observed structures, the interband critical-point (CP) parameters (strength, threshold energy, broadening, and excitonic phase angle) and their temperature dependence have been determined. Special emphasis is put on the ${\mathrm{E}}_{0}^{\ensuremath{'}}$, ${\mathrm{E}}_{0}^{\ensuremath{'}}$+${\mathrm{\ensuremath{\Delta}}}_{0}^{\ensuremath{'}}$, and ${\mathrm{E}}_{2}$ CP's. We determine the spin-orbit splitting of ${\mathrm{\ensuremath{\Gamma}}}_{15}^{\mathrm{c}}$ to be ${\mathrm{\ensuremath{\Delta}}}_{0}^{\ensuremath{'}}$=160\ifmmode\pm\else\textpm\fi{}10 meV. The observed decrease in energy of the CP's (after correction for the effect of thermal expansion) and the corresponding increase in broadening with increasing temperature agree reasonable well with results of a calculation that takes into account the Debye-Waller and self-energy terms of the deformation-potential-type electron-phonon interaction. New local empirical pseudopotential form factors were fitted to the available band-structure data and used in the electron-phonon calculations.