Angular Tunneling Effect

TL;DR

This paper explores how electrons tunnel through a potential barrier at various angles, applying boundary conditions, continuity, and Snell's law to analyze the angular dependence of tunneling probability.

Contribution

It introduces a detailed analysis of angular tunneling effects using boundary conditions and Snell's law, extending traditional tunneling models to include angular dependence.

Findings

Tunneling probability varies with angle { heta}.

Angular dependence follows Snell's law.

Boundary conditions determine tunneling outcomes.

Abstract

We investigate the tunneling of an electron with momentum p in the direction of V potential and under an angle {\theta} to the normal potential. Using the boundary conditions, the conditions of continuity and Snell's law, we obtain tunneling for various angles.