Valley-Orbit Splitting of the Indirect Free Exciton in Silicon

Abstract

Fine structure has been observed in the indirect edge absorption and luminescence spectra of hyperpure silicon. It is shown that this structure is due to a splitting in the energy states of the free indirect exciton rather than to transitions involving additional phonons. Two free-exciton states are observed, separated by 1.8\ifmmode\pm\else\textpm\fi{}0.2 meV. The intensity ratio of the two luminescence components associated with these exciton states indicates that thermal equilibrium is achieved between them at \ensuremath{\sim}5.5\ifmmode^\circ\else\textdegree\fi{}K but not at \ensuremath{\sim}2.5\ifmmode^\circ\else\textdegree\fi{}K. This fact, together with the magnitude of the splitting, suggests that these two states do not arise from spin-spin interaction in the free exciton or from a splitting of the degenerate hole states because of coupling to the anisotropic electrons at ${\ensuremath{\Delta}}_{1}$. Instead, these experimental results, together with the intensity ratio of the two free-exciton absorption components, indicate that the splitting occurs because the binding energy of the 1s envelope state of the free exciton is significantly larger (\ensuremath{\sim}11.5 meV) when it contains a symmetric linear combination of conduction-band states; i.e., the observed splitting is due to the valley-orbit interaction. A further weakly bound free-exciton state observed in absorption is attributed to an excited envelope state.