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Some comments on models for field enhancement.

Richard G Forbes1, C J Edgcombe, U Valdrè

  • 1University of Surrey, School of Electronics, Computing & Maths, Surrey GU2 7XH, Guildford, UK. r.forbes@surrey.ac.uk

Ultramicroscopy
|January 22, 2003
PubMed
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Simple models for apex field-enhancement factor (gamma(a)) overpredict results for tall protrusions. This study reexamines these models and compares them with numerical simulations and analytical results, revealing discrepancies and offering rationalizations.

Area of Science:

  • Physics
  • Materials Science
  • Electrical Engineering

Background:

  • Estimating the apex field-enhancement factor (gamma(a)) is crucial for understanding electric field distributions around pointed structures.
  • Commonly used simple physical models, like the 'floating sphere' and 'hemisphere on a post', provide analytical expressions for gamma(a).

Purpose of the Study:

  • To reexamine the validity of simple physical models for estimating the apex field-enhancement factor (gamma(a)) for pointed protrusions.
  • To compare the predictions of simple models with recent numerical simulations and exact analytical results.

Main Methods:

  • Reexamination of the theoretical basis of simple physical models for field enhancement.
  • Comparison of simple formulae with numerical simulation results for the 'hemisphere on a post' model.

Related Experiment Videos

  • Comparison with the exact analytical result for the 'hemi-ellipsoid on a plane' model.

    • Main Results:

    • Simple formulae for gamma(a) significantly overpredict values when the height-to-radius ratio (h/rho) is large.
    • Discrepancies between simple models, numerical simulations, and analytical results are identified and rationalized.
    • The security of commonly used simple formulae is questioned for certain geometric configurations.

    Conclusions:

    • Simple models for apex field enhancement are less reliable than often assumed, particularly for elongated structures.
    • Numerical simulations and exact analytical solutions provide more accurate estimations of gamma(a) for complex geometries.
    • Further investigation is needed to refine models for accurate field enhancement prediction in practical applications.