AIRYS 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 b y presenting it in a form which is free of the common problems: numeri cal inefficiency for low-applied voltages and an inability to compute the energies of some quasibound states. In particular, we show that th e transfer-function method can be used to study the negative-energy re sonances which do not affect the tunneling transmission coefficient. S ince this approach is based on the exact solution of Schrodinger's equ ation within the effective-mass approximation, it can be used to verif y other computational methods used in the theory of resonant tunneling , After mathematical errors present in some of the earlier application s of the Airy's functions method are removed, an excellent agreement i s reached between the transmission coefficient, energies of the bound and quasi-bound states, and I-V characteristics of the finite superlat tices computed by different techniques, The proposed version of the tr ansfer-matrix method is used to investigate the effective-barrier symm etry in electrically biased double-barrier structures.