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 useful methods for incorporating band-structure effects into the calculation of the tunneling resonances of resonant tunneling diodes, the energy levels of quantum wells, and other heterostructure properties. For several years now, numerical stabilization methods have allowed the use of tight-binding models for even very long structures (∼3000 Å). These methods still, however, suffer from a common deficiency: the reliance on a transfer-matrix calculation to determine the boundary conditions. The difficulty is rooted in the fact that the mere generation of a transfer matrix requires a matrix inversion which may not always be possible. Recently, we have shown how to obtain the complex band structure in the case of singular coupling matrices, for which a transfer matrix does not exist. Here we study a simple model, deliberately constructed in such a way that a transfer matrix does not exist, and demonstrate that its tunneling properties are exactly what one anticipates from the bulk bands. © 1996 The American Physical Society.