Derivation of tunneling probabilities for arbitrarily graded potential barriers using modified Airy functions

Research paper by Kyu-Tae Lee, Eun Joo Jung, Chul Han Kim, Chang-Min Kim

Indexed on: 08 Jan '11Published on: 08 Jan '11Published in: Optical and Quantum Electronics


General expressions of tunneling probability for arbitrarily graded potential barriers are rigorously derived using the modified Airy functions. Three types of graded potential barriers for which exact solutions exist are taken as examples for comparison’s purpose. Results obtained by the proposed method are confirmed to be in fairly good agreement with exact ones, demonstrating the usefulness of the modified Airy functions method.