Modelling of complicated nanometre resonant tunnelling devices with quantum dots

Abstract

The semiclassical expression for the transmission probability of a complicated multidimensional resonant tunnelling structure is obtained. This expression generalizes the well known Breit-Wigner formula and allows an analytical study of various structures containing electrodes and quantum dots. It is proved that the resonant conductance of a structure with N quantum dots cannot exceed N (in units of 2e²/h). It is also shown that the resonant conductance of an arbitrary structure containing a quantum dot with nondegenerate level connected in series with all others cannot exceed unity. The results obtained are applied to the analytical calculation of devices with a few quantum dots and chain and closed chain devices. The effect of the disappearance of the resonant peak corresponding to a well defined level is demonstrated. For a large number of identical dots in some examples considered, the conductance has a double-peak form in the individual energy band. This result is shown to have a clear physical meaning.