Analytic model for the valence-band structure of a strained quantum well

An analytic model is proposed for the valence-subband structure in a compressively strained quantum well which includes the effects of a finite barrier potential, valence-band anisotropy, and subband nonparabolicity. The solutions obtained for the zone-center effective mass and nonparabolicity factor are valid for both compressive and tensile strain, but the model gives a good approximation to the true band structure only in the case of compressive strain, where the nonparabolicity effects are relatively weak. For moderate compressive strain, the model provides a very fast, accurate representation of the subband structure within a few kT of the valence-band edge, which will be very useful in optoelectronic device design and simulation. The most important limitation to the model is its neglect of the strain-induced coupling to the spin-orbit split-off band, which becomes significant for large strain. Calculations performed on ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs quantum wells predict that both the effective mass and nonparabolicity decrease with increasing quantum-well width or compressive strain.