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Some solutions of the 3D Laplace equation in a layer with oscillating boundary describing an array of nanotubes and an application to cold field emission. I. Regular array

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Abstract

The aim of this paper is to construct solutions of the Dirichlet problem for the 3D Laplace equation in a layer with highly oscillating boundary. The boundary simulates the surface of a nanotube array, and the solutions are applied to compute the cold field electron emission. We suggest a family of exact solutions that solve the problem for a boundary with appropriate geometry. These solutions, along with the Fowler-Nordheim formula, allow one to present explicit asymptotic formulas for the electric field and the emission current. In this part of the paper, we consider the main mathematical aspects, restricting ourselves to the analysis of properties of the potential created by a single tube and a regular array of tubes. In the next part, we shall consider some cases corresponding to nonregular arrays of tubes and concrete physical examples.

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Authors and Affiliations

  1. Humboldt University, Berlin, Germany

    J. Brüning

  2. Institute for Problems in Mechanics, RAS, Moscow, Russia

    S. Yu. Dobrokhotov & D. S. Minenkov

  3. Moscow Institute of Physics and Technology, Moscow, Russia

    S. Yu. Dobrokhotov & D. S. Minenkov

Authors
  1. J. Brüning
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  2. S. Yu. Dobrokhotov
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  3. D. S. Minenkov
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Correspondence to J. Brüning.

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Brüning, J., Dobrokhotov, S.Y. & Minenkov, D.S. Some solutions of the 3D Laplace equation in a layer with oscillating boundary describing an array of nanotubes and an application to cold field emission. I. Regular array. Russ. J. Math. Phys. 18, 400–409 (2011). https://doi.org/10.1134/S1061920811040029

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  • DOI: https://doi.org/10.1134/S1061920811040029

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