A theoretical study of the tunnelling spectroscopy of an electron waveguide

Abstract

A theoretical study on the tunnelling spectroscopy of an electron waveguide observed by Eugster and del Alamo (1991) is presented. A narrow electron waveguide coupled with another much wider one, with a thin barrier between them, is taken as a theoretical model for the leaky electron waveguide used in the experiments of Eugster and del Alamo, and the transport properties of electrons are studied comprehensively through the wavefunction of the system. The results demonstrate that the conductance for the current tunnelling out of the barrier oscillates strongly with the width of the narrow electron waveguide in line with the conductance steps for the current flowing through the narrow waveguide, and the results are in good agreement with that given by experiments. A semiclassical explanation of the electron behaviour in such a leaky electron waveguide is also proposed in the present paper. A comparison between the results from the semiclassical and quantum mechanical views shows that the semiclassical view can reveal some basic physical ideas in such systems. The results also confirm that the oscillations of the tunnelling current can be considered as a spectroscopy of one-dimensional electron density of states (1D DOS) in the electron waveguide as proposed by Eugster and del Alamo.