Numerical Simulation of One-Dimensional Barrier Penetration

Barrier penetration plays an important role in the semiconductor field. Relying on the one-dimensional square barrier, the basic characteristics of barrier penetration of free particles, including the wave function, probability density, transmission coefficient and reflection coefficient, are studied by theoretical derivation and numerical calculation, and compared with those reported in the previous publication. The results show that there are transmission and reflection phenomena in barrier penetration. The value of transmission coefficient T and reflection coefficient R is less than 1, and the sum of T and R is equal to 1. With the change of particle energy E, barrier energy (or barrier height) U0 and barrier width a, T and R present the form of logarithmic or exponential function in general. The visualization results and those reported in the previous publication have very good consistency.