Tunnelling spectroscopy of low-dimensional states

Abstract

In this review a survey of tunnelling processes between barrier-separated two-dimensional (2D) systems and systems of different dimensionality is given. Tunnelling between barrier-separated 2D systems can be studied on very different samples such as triple-barrier structures, double-barrier structures with a two-dimensional emitter, double-barrier structures under hydrostatic pressure, double heterostructures, coupled quantum wells and also coupled 2D electron - hole systems. Pure 2D - 2D tunnelling processes with individual contacts on both 2D systems, however, are only reported on double heterostructures and coupled quantum wells. Using a transfer Hamiltonian formalism, it is shown that all resonances in the tunnelling current have their origin in density of states effects, transmission coefficients or the overlap integrals between the initial and final states. 2D subband energies, background impurity concentrations, the effective mass and also non-parabolicity effects can be determined quantitatively in terms of the transfer Hamiltonian formalism. By nanofabrication, tunnelling processes between 2D systems and states of lower dimensionality (1D, 0D) can also be investigated. Here, the tunnelling processes are mainly influenced by the overlap integral between the initial and final states. The corresponding resonance positions in the tunnelling current strongly depend on the shape of the confining potential and, moreover, the current - voltage characteristics turn out to be the Fourier transform of the 1D (0D) wavefunction of the final state. A brief survey of 1D - 1D and 1D - 0D tunnelling experiments is also given.