Airy's functions implementation of the transfer-matrix method for resonant tunneling in variably spaced finite superlattices

We improve the Airy's function version of the transfer-matrix method by presenting it in a form which is free of the common problems: numerical inefficiency for low-applied voltages and an inability to compute the energies of some quasi-bound states. In particular, we show that the transfer-function method can be used to study the negative-energy resonances which do not affect the tunneling transmission coefficient. Since this approach is based on the exact solution of Schrodinger's equation within the effective-mass approximation, it can be used to verify other computational methods used in the theory of resonant tunneling. After mathematical errors present in some of the earlier applications of the Airy's functions method are removed, an excellent agreement is reached between the transmission coefficient, energies of the bound and quasi-bound states, and I-V characteristics of the finite superlattices computed by different techniques. The proposed version of the transfer-matrix method is used to investigate the effective-barrier symmetry in electrically biased double-barrier structures.