Efficient technique for calculating the bound and virtual energy spectrum of semiconductor structures

A novel technique for determining the energies of bound and resonant states of semiconductor structures is presented. The new method is based upon R-matrix propagation techniques (known to be numerically stable) and avoids direct integration of the Schrödinger equation. The new method is recursive in nature, numerically stable, and can be applied easily to any one-dimensional potential. We show that the new technique yields the well-known analytic results describing the energy spectrum of a single quantum well. Further examples illustrate application of the R-matrix technique to determine the bound state and resonant energy spectrum of multiple quantum well structures in the presence or absence of an applied bias.