Deformation potentials of the direct and indirect absorption edges of GaP

Abstract

We present uniaxial-stress experiments performed on the direct and indirect exciton spectrum of GaP. Two direct transitions (${E}_{0}$ and ${E}_{0}+{\ensuremath{\Delta}}_{0}$) and three indirect phonon-assisted transitions (LA, TA, and TO phonon modes) have been investigated at 77 and 4.2\ifmmode^\circ\else\textdegree\fi{}K, respectively. Very-high-stress conditions have been achieved in this work ($X=19$kbar) which correspond to an axial deformation $\frac{\ensuremath{\delta}l}{l}=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, reaching the elastic limit of the material. We have been able to determine all linear and nonlinear deformation potentials that describe the stress dependence of the topmost valence bands (${\ensuremath{\Gamma}}_{7}$ and ${\ensuremath{\Gamma}}_{8}$) and of the lowest minima of the conduction band (${\ensuremath{\Gamma}}_{6}$ and ${X}_{6}$). The stress splitting of the valence band is produced by (i) the orbital-strain interaction, which is described by two deformation potentials ${b}_{1}$ and ${d}_{1}$, and (ii) the stress-dependent spin-orbit interaction which is described by two extra parameters ${b}_{2}$ and ${d}_{2}$. We find $b={b}_{1}+2$ ${b}_{2}=\ensuremath{-}(1.5\ifmmode\pm\else\textpm\fi{}0.2)$ eV, ${b}_{2}=+(0.2\ifmmode\pm\else\textpm\fi{}0.2)$ eV, $d={d}_{1}+2$ ${d}_{2}=\ensuremath{-}(4.6\ifmmode\pm\else\textpm\fi{}0.2)$ eV, and ${d}_{2}=+(0.3\ifmmode\pm\else\textpm\fi{}0.2)$ eV. The effect of hydrostatic deformation is again interpreted in terms of two deformation potentials ${a}_{1}$ (orbital-strain interaction) and ${a}_{2}$ (strain-dependent spin-orbit interaction). They combine with two hydrostatic deformation potentials for the conduction band ${C}_{1} (\mathrm{at} k=0)$ and ${E}_{1} [\mathrm{at} k=(\frac{2\ensuremath{\pi}}{a})(0,0,1)]$ to give the net pressure coefficients. We find ${C}_{1}+{a}_{1}+{a}_{2}=\ensuremath{-}(9.9\ifmmode\pm\else\textpm\fi{}0.3)$ eV, ${E}_{1}+{a}_{1}+{a}_{2}=+(2.3\ifmmode\pm\else\textpm\fi{}0.5)$ eV, and ${a}_{2}=\ensuremath{-}(0.4\ifmmode\pm\else\textpm\fi{}0.3)$ eV. The shear deformation potential ${E}_{2}$ of the indirect minimum of the conduction band has been obtained from the same series of measurements. We find ${E}_{2}=+(6.3+0.9)$ eV. Lastly, the stress-induced coupling between the lowest minimum of the conduction band (${X}_{6}$) and the next higher minimum (${X}_{7}$) has been observed, and is described by a single deformation potential ${E}_{3}$. We find $|{E}_{3}|=13\ifmmode\pm\else\textpm\fi{}1.5$ eV.