Cyclotron Resonance in Uniaxially Stressed Silicon. II. Nature of the Covalent Bond

Abstract

An energy band of a diamond lattice at $X(\mathrm{k}=(\frac{2\ensuremath{\pi}}{a})(1, 0, 0))$ on the zone boundary is two-fold degenerate because of the presence of glide-reflection symmetries. The degeneracy of the conduction band ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{{2}^{\ensuremath{'}}}$ at $X$ in silicon was lifted by applying a compressive uniaxial stress along the [011] direction, the effect of which has been observed by measuring a shift of the cyclotron resonance line for the [100] electrons. An expression for the line shift has been obtained in terms of a perturbation series. By evaluating the series using the orthogonal-plane-wave (OPW) results of Kleinman and Phillips, the ${\ensuremath{\Delta}}_{1}\ensuremath{-}{\ensuremath{\Delta}}_{{2}^{\ensuremath{'}}}$ band mixing ratio $\frac{{\ensuremath{\Xi}}_{{u}^{\ensuremath{'}}}}{\ensuremath{\Delta}E}$ is determined to be $\frac{{\ensuremath{\Xi}}_{{u}^{\ensuremath{'}}}}{\ensuremath{\Delta}E}=11.4\ifmmode\pm\else\textpm\fi{}1.1$. This result when combined with OPW estimate for $\ensuremath{\Delta}E$, the energy separation between ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{{2}^{\ensuremath{'}}}$ at the conduction band edge, yields the value ${\ensuremath{\Xi}}_{{u}^{\ensuremath{'}}}\ensuremath{\approx}5.7$ eV for the deformation potential responsible for the band splitting at $X$. The lifting of the special degeneracy of the ${X}_{1}$ states is interpreted from the viewpoint of the tetrahedral covalent bond responding to an applied mechanical force. The sign of the cyclotron-resonance line shift indicates that two nonbonding orbitals of a valence electron connecting two neighboring Si atoms are hybridized to make the energy of the bonding orbital lower than that of the antibonding orbital when the bond is compressed. Also from the experimental work, the following values of the electron effective masses have been determined: $\frac{{m}_{\ensuremath{\perp}}}{m}=0.1905\ifmmode\pm\else\textpm\fi{}0.0001$, $\frac{{m}_{\mathrm{II}}}{m}=0.9163\ifmmode\pm\else\textpm\fi{}0.0004$.