Quantum Tunneling in Gradual Potentials


  • Cristian Gabriel Herbert Galarza Faculty of Sciences, Autonomous University of Baja California. PO Box 1880, 22800 Ensenada, Mexico. https://orcid.org/0000-0003-3141-855X
  • Rogelio Orozco Duarte Faculty of Sciences, Autonomous University of Baja California. PO Box 1880, 22800 Ensenada, Mexico. https://orcid.org/0000-0003-2193-3005
  • Roberto Romo Martínez Faculty of Sciences, Autonomous University of Baja California. PO Box 1880, 22800 Ensenada, Mexico. https://orcid.org/0000-0002-9278-1013




Tunnel effect, Quantum tunneling, Smooth barriers.


One of the paradigmatic phenomena of quantum mechanics is undoubtedly the so-called tunnel effect, which manifests itself as the possibility of particles on the nanometer scale to traverse potential barriers. This phenomenon, although unintuitive, is so real that it plays a prominent role in current technology and constitutes the key mechanism of electronic transport in novel concepts of nanoelectronic devices. In this work, maps of electron density are used to illustrate the spatial and energetic distribution of electrons that propagates through gradual potential barriers, visualizing the wave nature of the electrons and the tunneling phenomenon. In particular, the effect of using gradual barriers rather than rectangular barriers is discussed.


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Maps of the DLE for a potential of a rectangular barrier of (a) height V = 20 eV, width b = 1.0 nm, and (b) height V = 4 eV and width b = 5.0 nm. Both barriers have the same area (20 eV nm) and are shown superimposed on the graphs (dashed light lines). A contour value 0.98 (solid black lines) (c) is indicated on each map. Transmission coefficient for the barrier of case (b).



How to Cite

Herbert Galarza, C. G., Orozco Duarte, R., & Romo Martínez, R. (2019). Quantum Tunneling in Gradual Potentials. REVISTA DE CIENCIAS TECNOLÓGICAS, 2(2), 50–57. https://doi.org/10.37636/recit.v225057



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