TUNNELING CALCULATIONS FOR SYSTEMS WITH SINGULAR COUPLING MATRICES - RESULTS FOR A SIMPLE-MODEL

The tight-binding approach has become one of the most common and usefu l methods for incorporating band-structure effects into the calculatio n of the tunneling resonances of resonant tunneling diodes, the energy levels oi quantum wells,and other heterostructure properties. For sev eral years now, numerical stabilization methods have;allowed the use o f light-binding models for even very long structures (similar to 3000 Angstrom). These methods still, however, suffer from a common deficien cy: the reliance on a transfer-matrix calculation to determine the bou ndary conditions, The difficulty is rooted in the fact that the mere g eneration of a transfer matrix requires a matrix inversion which may n ot always be possible. Recently, we have shown how to obtain the compl ex band structure in the case of singular coupling matrices, for which a transfer matrix does not exist. Here we study a simple model, delib erately constructed in such a way that a transfer matrix does not exis t, and demonstrate that its funneling properties are exactly what one anticipates from the bulk bands.