WKB approximation based formula for tunneling probability through a multi-layer potential barrier

Abstract

In this work, we present a theoretical derivation of the analytical formula for tunneling probability through an n-layer barrier basing on the Wentzel-Kramers-Brillouin (WKB) and the effective mass approximations. The accuracy of the derived formula is analysed by comparison with the transfer matrix method (TMM). The effect of the electric charge distribution in a stack on the tunnel current is considered.