Tight-binding calculation of electronic states in a triangular symmetrical quantum well

We study a ssV-shaped symmetrically graded quantum well, which has been investigated optically. The well width is 125 Å and the Al concentration x varies linearly from x=0.36 at the barriers to x=0 (pure GaAs) in the middle of the well. In the present paper, numerical calculations of the well electronic states are made within the framework of the surface Green function matching method and the ${\mathit{sp}}_3$ ${\mathit{s}}^{\mathrm{*}}$ empirical tight-binding model within virtual-crystal approximation. An algorithm developed recently by the authors is applied to treat graded composition heterostructures. The e1-hh1, e2-hh2, and e1-lh1 calculated transition energies are in fair agreement with experiment. The dependence of the transition energies on the well width and on the Al concentration is studied. A comparison with the rectangular quantum well is made. The transition energies decrease when the well width increases and are always higher than the same energies of the rectangular quantum well. All the transitions are better resolved energetically for the triangular quantum well. The energies of the transitions under study increase when the Al concentration x increases, but this dependence is much stronger for the triangular quantum well. Spatial distributions of spectral strengths of the well states are also obtained.