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Improved approach to Fowler–Nordheim plot analysis

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10.1116/1.4765080

### Abstract

This article introduces an improved approach to Fowler–Nordheim (FN) plot analysis, based on a new type of intercept correction factor. This factor is more cleanly defined than the factor previously used. General enabling theory is given that applies to any type of FN plot of data that can be fitted using a FN-type equation. Practical use is limited to emission situations where slope correction factors can be reliably predicted. By making a series of well-defined assumptions and approximations, it is shown how the general formulas reduce to provide an improved theory of orthodox FN-plot data analysis. This applies to situations where the circuit current is fully controlled by the emitter characteristics, and tunneling can be treated as taking place through a Schottky–Nordheim (SN) barrier. For orthodox emission, good working formulas make numerical evaluation of the slope correction factor and the new intercept correction factor quick and straightforward. A numerical illustration, using simulated emission data, shows how to use this improved approach to derive values for parameters in the full FN-type equation for the SN barrier. Good self-consistency is demonstrated. The general enabling formulas also pave the way for research aimed at developing analogous data-analysis procedures for nonorthodox emission situations.

© 2013 American Vacuum Society

Received 03 August 2012
Accepted 08 October 2012
Published online 09 November 2012

Acknowledgments: Andreas Fischer thanks the Alexander von Humboldt foundation for a Feodor Lynen fellowship and Mu'tah University for hospitality.

Article outline:

I. INTRODUCTION

II. BACKGROUND THEORY

A. Auxiliary parameter *c* _{X}

B. Orthodox emission

C. Scaled barrier field *f* and the parameter η

III. SLOPE CORRECTION FACTOR

A. Basic theory

B. Extraction of value of auxiliary constant *c* _{X}

C. Extraction of *f*-values in orthodox emission situations

IV. 2012 INTERCEPT CORRECTION FACTOR

V. ILLUSTRATION OF ORTHODOX EXTRACTION PROCEDURE

A. Introduction

B. Analysis of the slope

C. Analysis of the intercept

D. Comments

VI. DISCUSSION

A. Comparison of new and old types of intercept correction factor

B. Related methods

C. Nonlinear curve fitting

D. Other plotting methods

E. Future development

F. Summary and conclusions

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2012-11-09

2014-04-20

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