Optical and Quantum Electronics

, Volume 42, Issue 2, pp 129–141 | Cite as

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

  • Kyu-Tae Lee
  • Eun Joo Jung
  • Chul Han Kim
  • Chang-Min Kim


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.


Tunneling probability Graded potential barrier WKB method Modified Airy functions 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Kyu-Tae Lee
    • 1
  • Eun Joo Jung
    • 2
  • Chul Han Kim
    • 1
  • Chang-Min Kim
    • 1
  1. 1.School of Electrical and Computer EngineeringUniversity of SeoulSeoulKorea
  2. 2.Nano-Photonics Research CenterKorea Photonics Technology InstituteGwangjuKorea

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