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The pre-exponential voltage-exponent as a sensitive test parameter for field emission theories.

R G Forbes1, E O Popov2, A G Kolosko2

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|May 7, 2021
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Summary

Comparing theoretical and experimental k-values in field electron emission (FE) provides a sensitive tool for validating FE theories. This method aids in selecting between competing theories by analyzing current-voltage data.

Keywords:
empirical field emission equationfield electron emissionfield electron emission theory–experiment comparisonsleast-residual methodlocal-gradient methodpre-exponential voltage exponent

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Area of Science:

  • Physics
  • Materials Science
  • Surface Science

Background:

  • Field electron emission (FE) follows an empirical equation: I_m = CV_m^k exp[-B/V_m].
  • Extracting the exponent k is crucial for understanding FE behavior.
  • k-values can be derived from simulations or high-quality experimental current-voltage (I-V) measurements.

Purpose of the Study:

  • To establish a method for comparing theoretically derived and experimentally derived k-values in FE.
  • To demonstrate the utility of k-value comparison for validating FE theories and distinguishing between them.
  • To summarize existing knowledge and methods for k-value extraction.

Main Methods:

  • Discussion of existing methods for extracting k-values from experimental and simulated I-V data.
  • Introduction of a modernized 'least residual' method for k-value extraction.
  • Reporting of exploratory simulations to test the k-value extraction methodology.

Main Results:

  • The comparison of theoretical and experimental k-values serves as a sensitive tool for FE theory assessment.
  • Extracted k-values reliably match independently known analytical results.
  • Extracted k-values are sensitive to specific emission theories and assumed emitter shapes.

Conclusions:

  • Comparing theoretical and experimental k-values offers a robust approach for validating FE theories.
  • Future research should focus on disentangling the influence of emission theory and emitter shape on k-values.
  • This methodology can help investigate various scientific issues in field electron emission.