Theory of Optimizing the Tunneling Probability Through a Potential Barrier by Acoustically Augmented Phonons

Abstract

In this research, the optimization of the tunneling probability through a potential barrier by superimposing ultra high frequency (UHF) acoustic wave over the source of the incoming particle wave function was examined theoretically and was shown to result in acoustically augmented phonons (AAP). The graph of the tunneling probability against the kinetic energy fraction [(E/V0)= x] of the particle shows a line of inflection at a non-dimensionalized critical height yc ≈ 3.12879, where yc is universal tunneling constant (UTC). As the barrier height (y) is increased further (y > yc), the reflection increases, and the tunneling probability sharply declines, in general. The lowest possible value of y is guided by the inherent particle kinetic energy, the superimposed wave number n and the material parameter β. The’ gradient of the increase in probability’ rises with a drop in the wave number n and is larger at higher values of y. A higher ratio (E/V0) coupled with a permissible-smaller wave number (n) of the applied UHF acoustic wave, leads to a higher tunneling probability. For increasing values of the UHF wave numbers and decreasing x-values, the potential barrier becomes increasingly opaque to tunneling. The higher the value of y is, the higher the tunneling opacity of the potential barrier becomes. The tunneling probability is highest (=0.98673) at y = 4, x = 0.9, when the orders of β and k are comparable.