Theoretical analysis of resonant tunneling through finite superlattices

A theoretical study has been carried out with a view to understanding the resonant tunneling phenomena in superlattice structures. For a general potential distribution, the resonance condition is derived and the relationship is found between the resonance levels and the subbands in an infinite superlattice. Especially, the relationship is studied between the resonance characteristics of a unit superlattice section with an arbitrary potential distribution and those of an n-period superlattice made of n stages of unit superlattices. It is found that the discriminating function of the n-period superlattice is given by a Chebyshev polynomial of that of the unit section. Hence, if any potential distribution (including an asymmetric one) is repeated at least twice, a resonance level can always be generated in each subband (with a zero bias voltage). A method based on this fact is presented for generating a resonance at an arbitrary energy level in an n-period superlattice. Further, by way of these discussions, it is pointed out that there exist higher-order resonances. An example for this phenomenon is presented.