Effects of Uniaxial Stress on the Indirect Exciton Spectrum of Silicon

We have measured the stress dependence of the indirect exciton spectrum of silicon at 77°K, for static uniaxial compression along the [111], [001], and [110] directions with light polarized parallel and perpendicular to the stress direction, using wavelength modulation. The high stresses reached in this work ($X=1.8\mathrm{}\times {10}^{10}$ dyn ${\mathrm{cm}}^{-2\mathrm{}}$) have enabled us to accurately study the behavior of the ${\Gamma }_{{25}^{\prime }}$ valence-band maxima and the ${\Delta }_1$ conduction-band minima under stress. The stress splitting of the valence bands 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, described by $b_2$ and $d_2$. We find that $b=b_1+2\mathrm{}{b}_2=-(2.10\mathrm{}\pm 0.10)$ eV, $b_2=-(0.1\mathrm{}\pm 0.15)$ eV, $d=d_1+2\mathrm{}{d}_2=-(4.85\mathrm{}\pm 0.15)$ eV, and $d_2=-(0.05\mathrm{}\pm 0.25)$ eV. The same measurements yield a value for the shear deformation potential of the ${\Delta }_1$ conduction-band minimum ${\mathcal{E}}_2=-(8.6\mathrm{}\pm 0.4)$ eV. The effect of hydrostatic deformation is interpreted in terms of two deformation potentials: ${\mathcal{E}}_1+a_1$ (orbital-strain interaction) and $a_2$ (stress-dependent spin-orbit interaction). We obtain ${\mathcal{E}}_1+a_1=+(1.5\mathrm{}\pm 0.3)$ eV and $a_2=0\mathrm{}$. The hydrostatic coefficient of the indirect gap obtained from ${\mathcal{E}}_1+a_1$ agrees with hydrostatic pressure measurements. In addition the stress-induced coupling between ${\Delta }_1$ minima and the neighboring ${\Delta }_{2^{\prime }}$ conduction band, described by the deformation potential $\left|{\mathcal{E}}_2^{*}\right|=(8\mathrm{}\pm 3)$ eV, has been observed. Interpretation of the stress dependence of the intensities on the basis of one (${\Gamma }_{15,c}$ or ${\Delta }_{5,v}$) or two (${\Gamma }_{15,c}$ and ${\Delta }_{5,v}$) intermediate states gives the first conclusive evidence of a contribution of ${\Delta }_{5,v}\to {\Delta }_{1,c}$ virtual transitions to the indirect adsorption edge of this material.