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Journal of Applied Physics / Volume 108 / Issue 12 / ARTICLES / Plasmas and Electrical Discharges

J. Appl. Phys. 108, 123301 (2010); http://dx.doi.org/10.1063/1.3520672 (6 pages)

Modeling electron flow produced by a three-dimensional spatially periodic field emitter

A. Rokhlenko and J. L. Lebowitz

Department of Mathematics, Rutgers University Piscataway, New Jersey 08854-8019, USA

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(Received 9 August 2010; accepted 27 October 2010; published online 17 December 2010)

We study the space charge limited field emission from an emitter whose surface has a simple periodic structure with bumps. The shape of each bump is represented by a smooth function and the emission is governed by the Fowler–Nordheim–Schottky law. A mathematical scheme for modeling the potential and current structure by a set of elementary functions is developed and implemented numerically with the help of a special least square procedure. Our results show that such emitters are more efficient than emitters with long ridges only in weak electric fields. In stronger fields the latter give larger currents and they should be more durable. The emission by an individual bump in our periodic structure is compared also with that of a single emitter bump of the same shape, they appear to be quite close.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MODELING THE POTENTIAL
  3. SOLUTION
  4. RESULTS AND COMPARISON WITH 2D EMITTER
  5. SINGLE BUMP FIELD EMISSION
  6. CONCLUSION

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KEYWORDS and PACS

Keywords

field emitter arrays, least squares approximations, space charge

PACS

  • 85.45.Db

    Field emitters and arrays, cold electron emitters

  • 85.45.Bz

    Vacuum microelectronic device characterization, design, and modeling

  • 79.70.+q

    Field emission, ionization, evaporation, and desorption

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3520672

PUBLICATION DATA

ISSN

0021-8979 (print)  
1089-7550 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

    R. J. Umstattd and J. W. Luginsland, Phys. Rev. Lett. 87, 145002 (2001).

    W. P. Dyke and J. Trolan, Phys. Rev. 89, 799 (1953), Y. Feng and J. P. Verboncoeur, Phys. Plasmas 12, 103301 (2005)PHPAEN000012000010103301000001.

    A. Rokhlenko and J. L. Lebowitz, J. Appl. Phys. 107, 103301 (2010)JAPIAU000107000010103301000001.

    A. Rokhlenko and J. L. Lebowitz, Phys. Rev. Lett. 91, 085002 (2003), Phys. Plasmas 11, 4559 (2004)PHPAEN000011000010004559000001.

    E. L. Murphy and R. H. Good, Phys. Rev. 102, 1464 (1956), R. G. Forbes, Appl. Phys. Lett. 89, 113122 (2006)APPLAB000089000011113122000001.

    R. G. Forbes, J. Appl. Phys. 104, 084303 (2008)JAPIAU000104000008084303000001.

    A. Rokhlenko, K. L. Jensen, and J. L. Lebowitz, J. Appl. Phys. 107, 014904 (2010)JAPIAU000107000001014904000001.


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