QUANTUM SIZE EFFECT IN NORMAL-METAL TUNNELING

We present a theoretical analysis of quantum size effects in normal-metal tunneling. We show that, under certain conditions, the potential barrier in the insulator of a metal-insulator-metal junction can be represented to a first approximation by a trapezoidal barrier. For this case the tunneling current can be calculated numerically for any realistic metal potentials. In the present paper we applied the theory to obtain the tunneling current, through an insulating film, between a thin-film metal and an extended one, using the simplest possible model for this junction. The extended metal is replaced by a constant potential, and the thin-film metal by an array of functions within a square well. The latter potential gives an energy-band structure for the thin film which has the correct qualitative characteristics over the region of k space and energy that contribute to the tunneling current. The parameters of the model were chosen to approximate, as far as possible the conditions in the experiments of Jaklevic and Lambe. We show that Al2O3, the insulator used in these experiments, is most probably adequately represented by a rectangular barrier. The use of this barrier, in conjunction with our model for the thin-film metal, leads to results in very good qualitative agreement with the experimental data. © 1979 The American Physical Society.