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

An energy band of a diamond lattice at X(k=(2πa)(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 Δ₁ and Δ_2^' 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 Δ₁-Δ_2^' band mixing ratio Ξ_u^'ΔE is determined to be Ξ_u^'ΔE=11.4±1.1. This result when combined with OPW estimate for ΔE, the energy separation between Δ₁ and Δ_2^' at the conduction band edge, yields the value Ξ_u^'≈5.7 eV for the deformation potential responsible for the band splitting at X. The lifting of the special degeneracy of the X₁ 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: m_⊥m=0.1905±0.0001, mIIm=0.9163±0.0004.