Effect of interdiffusion on the subbands in an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs single-quantum-well structure

The subband energies and wave functions in an interdiffusion-induced ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs single-quantum-well structure are calculated. The confinement profile of this interdiffused quantum well is nonlinear and is modeled here by an error function. The spatially dependent electron effective mass is taken into consideration using a nonparabolic band model derived from a fourth-order expansion in k with the coefficients determined using a 14-band calculation. The valence subband mixing between the heavy and light holes is also considered using an effective Hamiltonian approach. The results show that subband properties of the nonsquare quantum well differ from the conventional square quantum well. The subband-edge energy initially increases and then decreases with interdiffusion; this effect is explained by the evolution of the nonsquare quantum-well shape in terms of a crossover point, which is defined as the confinement profile intersection at the well barrier interface of the as-grown and interdiffused quantum wells. A depth-dependent quantum-well width is discussed and a cutoff scheme is introduced to quantify the division between bound and unbound states. An enhancement of interband transition is predicted for the off-diagonal selection rule at the initial stages of interdiffusion, and a reduced confinement of the wave functions is also observed. The effect of valence-band mixing remains strong, in general, with increasing interdiffusion and an almost parabolic band is restored at the latter stages of interdiffusion. An enhancement of the lowest energy light-hole negative mass is also obtained with interdiffusion. The nonmonotonic behavior of the subband-edge energies suggests that when only the lowest interband energy is used to characterize the interdiffusion process, errors are likely to occur.