An exact calculation of the voltage‐dependent tunnelling current in simple one‐dimensional models: comparison with the Bardeen perturbation approach

SUMMARY In this paper we present an exact calculation of the tunnelling current for two different one‐dimensional barrier potentials. The purpose is twofold: First, we demonstrate the feasibility of applying the new method of C. Noguera as a direct analytical tool for solving tunnelling problems in the case of independent electrons. In this approach, the tunnelling current is expressed in terms of the logarithmic derivative of the Green's function which must be evaluated at the cutting surface. This can be done analytically in the one‐dimensional case. Secondly, we compare these results with the corresponding tunnelling current obtained using the Bardeen perturbation method, valid only in the large barrier limit. In particular, we investigate the use of the Bardeen approach in describing tunnelling spectroscopy. The dynamic conductance d I/ d V , as a function of bias and barrier width, is compared in both cases.