Tunneling escape time from a semiconductor quantum well in an electric field

Abstract

We calculate the tunneling escape times of quasibound states in a quantum well under applied electric field. We refine the quasiclassical Wentzel–Kramers–Brillouin approximation for a multilayer heterostructure and find a simple analytical expression for the lifetime, which takes into account different effective masses and different dielectric constants inside the heterostructure layers. We compare the quasiclassical lifetime formula with exact numerical solutions of the (complex) Schrödinger equation. For the underbarrier action Sab≥ℏ/3, good agreement between the two approaches is demonstrated. Also, by analytical expansion of the Schrödinger equation we prove the quasiclassical formula for lifetime as an asymptotic limit of the exact solution.