Deformation potentials of the direct and indirect absorption edges of GaP

We present uniaxial-stress experiments performed on the direct and indirect exciton spectrum of GaP. Two direct transitions ($E_0$ and $E_0+{\Delta }_0$) and three indirect phonon-assisted transitions (LA, TA, and TO phonon modes) have been investigated at 77 and 4.2°K, respectively. Very-high-stress conditions have been achieved in this work ($X=19\mathrm{}$kbar) which correspond to an axial deformation $\frac{\delta l}{l}=2\mathrm{}\times {10}^{-2\mathrm{}}$, 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 (${\Gamma }_7$ and ${\Gamma }_8$) and of the lowest minima of the conduction band (${\Gamma }_6$ 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 $b=b_1+2\mathrm{}$ $b_2=-(1.5\mathrm{}\pm 0.2)$ eV, $b_2=+(0.2\mathrm{}\pm 0.2)$ eV, $d=d_1+2\mathrm{}$ $d_2=-(4.6\mathrm{}\pm 0.2)$ eV, and $d_2=+(0.3\mathrm{}\pm 0.2)$ 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 $E_1 [\mathrm{at} k=(\frac{2\pi }{a}\left)\mathrm{}\right(0,0,1\left)\right]$ to give the net pressure coefficients. We find $C_1+a_1+a_2=-(9.9\mathrm{}\pm 0.3)$ eV, $E_1+a_1+a_2=+(2.3\mathrm{}\pm 0.5)$ eV, and $a_2=-(0.4\mathrm{}\pm 0.3)$ 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 $E_2=+(6.3+0.9)\mathrm{}$ 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 $\left|E_3\right|=13\mathrm{}\pm 1.5$ eV.