Diagonal representation for the transfer-matrix method for obtaining electronic energy levels in layered semiconductor heterostructures

We develop a multiband k⋅P transfer-matrix algorithm by defining a ‘‘diagonal representation’’ that provides a unified way of calculating energy levels and wave functions for superlattices as well as for quantum wells with arbitrarily shaped band-edge profiles. Numerical results of transfer-matrix calculations are presented for specific heterostructures. We show that, contrary to expectations, the various versions of the boundary conditions used in the literature lead to results for the subband energies that agree with one another reasonably well for the wide-band-gap materials.