Resonant tunneling through low dimensional quantum structures

Abstract

Tunneling mechanism in zero- and one-dimensional quantum structures is studied. Several new results, peculiar to low dimensions, are predicted. We find that subband mixing and multichannel tunneling induce the appearance of new tunneling channels with unusual interference patterns, and allow for longer lifetime of the resonances at higher energies in various channels. It is shown that in low dimensions, there exists a critical size of the structure below which the resonance nature of the tunneling process is diminished. In zero and one dimensions, there exists a critical magnitude of the confinement potential, below which there are no resonances in the transmission function for any size of the well. Negative differential resistance and other phenomena related to the resonance characters of the tunneling will not appear in this case. We also develop a generalized transfer matrix method that takes into account subband mixing; this formalism can be used to describe any transport problem in low dimensions.

Tunnelling spectroscopy of low-dimensional states

“…In order to explain the fine structure of the current-voltage characteristics [107], further theoretical investigations of these tunnelling processes yielded a strong coupling between the 1D subbands in the contact region and the 0D states inside the quantum dots. However, sometimes the effect of the constriction geometry on quasi one-dimensional transport [108] cannot be neglected, and thus much effort has been made to investigate the influence of the dimensionality of the involved states with [109] magnetic fields and without magnetic fields [110,111].…”

Subband mixing in resonant magnetotunneling through double-barrier semiconductor nanostructures

“…For more general cases, one should keep in mind that a pair of numbers is packed in a single index in order to simplify the notation. The transfer-matrix method 18,27,39,40 can be easily generalized to the multichannel magnetotransport. This can be done by looking at the total wave function of the electron in the region i as a linear combination of the eigenfunctions ⌿ nk i with amplitude coefficients denoted by C n,k i .…”

“…The resonant tunneling in quantum dots becomes a multichannel process where the electrons can tunnel through different subbands in different regions, which may be coupled due to mixing at the interfaces. Sa'ar et al 27 also developed a generalized transfer-matrix method to describe vertical transport in 0D in the presence of subband mixing at zero magnetic field. Tarucha and Hirayama 9 used a magnetic field to study subband mixing and claimed to observe the effects of mixing of 2D emitter subbands with 1D subbands in the double-barrier region.…”