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Simple good approximations for the special elliptic functions in standard Fowler-Nordheim tunneling theory for a Schottky-Nordheim barrier

Forbes, RG (2006) Simple good approximations for the special elliptic functions in standard Fowler-Nordheim tunneling theory for a Schottky-Nordheim barrier APPLIED PHYSICS LETTERS, 89 (11). ? - ?. ISSN 0003-6951

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Abstract

The discovery is reported of simple, good approximate formulas for special elliptic functions that appear in the standard theory of Fowler-Nordheim (FN) [Proc. R. Soc. London, Ser. A 119, 173 (1914)] tunneling through an image-rounded Schottky-Nordheim [W. Schottky, Z. Phys. 15, 872 (1923); L. W. Nordheim, Proc. R. Soc. London, Ser. A 121, 626 (1928)] barrier and in the standard FN equation. The FN-exponent correction factor v can be written as v(y)approximate to 1-y(2)+(1/3)y(2) ln y, where y is the Nordheim parameter. This formula has a respectable mathematical basis, predicts exact values of v(y) to within 0.33% in 0 <= y <= 1, and can be rewritten to give (after nearly 80 years) a simple, reliable algebraic formula for the explicit dependence of v on barrier field. Significant consequences are expected.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Physics, Applied, Physics, FIELD-EMISSION, ELECTRON-EMISSION, METALS, VALUES
Related URLs:
Divisions: Faculty of Engineering and Physical Sciences > Electronic Engineering > Advanced Technology Institute > Nano-Electronics Centre
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:05
Last Modified: 23 Sep 2013 18:25
URI: http://epubs.surrey.ac.uk/id/eprint/31

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