Support Options

Submit a Support Ticket


Quantum Mechanics: Tunneling

By Dragica Vasileska1, Gerhard Klimeck2

1. Arizona State University 2. Purdue University

View Series

Slides/Notes podcast

Licensed according to this deed.



Published on


In quantum mechanics, quantum tunnelling is a micro nanoscopic phenomenon in which a particle violates the principles of classical mechanics by penetrating a potential barrier or impedance higher than the kinetic energy of the particle. A barrier, in terms of quantum tunnelling, may be a form of energy state analogous to a "hill" or incline in classical mechanics, which classically suggests that passage through or over such a barrier would be impossible without sufficient energy. The two remarkable applications of tunneling are:

  • (a)Resonant tunneling diodes, which are used as switching units in fast electronic circuits.
  • (b) Scanning tunneling microscope (STM), based on the penetration of electrons near the surface of a solid sample through the barrier at the surface. These electrons form a "cloud" of probability outside the sample. Although the probability of detecting one of these electrons decays exponentially with distance (from the surface), one can induce and measure a current of these electrons and attain a magnification factor of 100 million - large enough to permit resolution of a few hundredths the size of an atom. Gerd Binning and Heinrich Rohrer won the Noble Prize in Physics in 1986 for the invention of the STM.

To better understand the tunneling phenomena below we provide relevant reading material and access to the piece-wise constant potential barrier tool that contains examples for calculation of the tunneling coefficient in quite a variety of structures:

Sponsored by


Cite this work

Researchers should cite this work as follows:

  • Dragica Vasileska; Gerhard Klimeck (2008), "Quantum Mechanics: Tunneling,"

    BibTex | EndNote


In This Series

  1. Reading Material: Tunneling

    08 Jul 2008 | Teaching Materials | Contributor(s): Dragica Vasileska

  2. Piece-Wise Constant Potential Barriers Tool

    30 Jun 2008 | Tools | Contributor(s): Xufeng Wang, Samarth Agarwal, Gerhard Klimeck, Dragica Vasileska, Mathieu Luisier, Jean Michel D Sellier

    Transmission and the reflection coefficient of a five, seven, nine, eleven and 2n-segment piece-wise constant potential energy profile, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.