Strain-induced valence-subband splitting in III-V semiconductors

A 〈001〉 axial strain introduces an additional term, known as the ${\mathit{C}}_4$ matrix element, into the valence-band Hamiltonian of III-V semiconductors, proportional to the axial strain and to ${\mathit{k}}_{\mathrm{\perp }}$, the wave-vector component perpendicular to the strain axis. This matrix element has been ignored in all previous valence-subband calculations. We use the empirical pseudopotential method and the tight-binding method to calculate the magnitude of ${\mathit{C}}_4$ in the III-V and selected II-VI semiconductors. The calculated values are smaller than but comparable to the experimentally determined value in InSb. We then present envelope-function calculations which show how the ${\mathit{C}}_4$ term may particularly affect the valence-subband structure of quantum wells under biaxial tension (e.g., Ga-rich ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As on InP), splitting the degeneracy of the highest valence subband, and shifting the valence-band maximum from the Brillouin-zone center. The strain-induced band splittings are an order of magnitude larger than those in unstrained bulk material and may be measurable in wells with moderate strain (lattice mismatch ≊1%). Finally, we discuss the influence of the ${\mathit{C}}_4$ term on optical, transport, and cyclotron-resonance data.