A simple theory to determine the attenuation amplitudes of quantum oscillations

Tunneling currents through ultrathin SiO₂ films have been observed to have small oscillatory components at high electric fields. In this article, a relation between the well known reflection coefficient and transmission coefficient of electron tunneling through a barrier and the amplitude of Fowler-Nordheim tunneling current oscillations is obtained based on the principle of quantum mechanics. A simple relation describing the factors affecting the amplitude of quantum oscillations is obtained based on the reflection coefficient and the transmission coefficient. It is found that the simple relation agrees well with the numerical results based on numerical calculations. A linear relation between the logarithmic attenuation of the oscillation amplitude and variable parameters such as barrier height, oxide thickness and the kinetic energy of incident electrons is observed. The results show that the oscillation amplitude attenuation can be accurately and simply described by this analytical solution.