Effects of Uniaxial Stress on the Indirect Exciton Spectrum of Silicon

Abstract

We have measured the stress dependence of the indirect exciton spectrum of silicon at 77\ifmmode^\circ\else\textdegree\fi{}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 ($X=1.8\ifmmode\times\else\texttimes\fi{}{10}^{10}$ dyn ${\mathrm{cm}}^{\ensuremath{-}2}$) have enabled us to accurately study the behavior of the ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}$ valence-band maxima and the ${\ensuremath{\Delta}}_{1}$ 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 $b={b}_{1}+2{b}_{2}=\ensuremath{-}(2.10\ifmmode\pm\else\textpm\fi{}0.10)$ eV, ${b}_{2}=\ensuremath{-}(0.1\ifmmode\pm\else\textpm\fi{}0.15)$ eV, $d={d}_{1}+2{d}_{2}=\ensuremath{-}(4.85\ifmmode\pm\else\textpm\fi{}0.15)$ eV, and ${d}_{2}=\ensuremath{-}(0.05\ifmmode\pm\else\textpm\fi{}0.25)$ eV. The same measurements yield a value for the shear deformation potential of the ${\ensuremath{\Delta}}_{1}$ conduction-band minimum ${\mathcal{E}}_{2}=\ensuremath{-}(8.6\ifmmode\pm\else\textpm\fi{}0.4)$ 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 ${\mathcal{E}}_{1}+{a}_{1}=+(1.5\ifmmode\pm\else\textpm\fi{}0.3)$ eV and ${a}_{2}=0$. 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 ${\ensuremath{\Delta}}_{1}$ minima and the neighboring ${\ensuremath{\Delta}}_{{2}^{\ensuremath{'}}}$ conduction band, described by the deformation potential $|{\mathcal{E}}_{2}^{*}|=(8\ifmmode\pm\else\textpm\fi{}3)$ eV, has been observed. Interpretation of the stress dependence of the intensities on the basis of one (${\ensuremath{\Gamma}}_{15,c}$ or ${\ensuremath{\Delta}}_{5,v}$) or two (${\ensuremath{\Gamma}}_{15,c}$ and ${\ensuremath{\Delta}}_{5,v}$) intermediate states gives the first conclusive evidence of a contribution of ${\ensuremath{\Delta}}_{5,v}\ensuremath{\rightarrow}{\ensuremath{\Delta}}_{1,c}$ virtual transitions to the indirect adsorption edge of this material.