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Comparison of approximations for the principal Schottky–Nordheim barrier function , and comments on Fowler–Nordheim plots
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10.1116/1.3363858
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Affiliations:
1 Advanced Technology Institute, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom
2 Department of Mathematics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom
a) Electronic mail: r.forbes@ieee.org
J. Vac. Sci. Technol. B 28, C2A33 (2010)
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## Figures

FIG. 1.

Graphical comparison of various approximations for the principal Schottky–Nordheim barrier function , over the range , classified according the maximum magnitude of error involved: (a) ; (b) ; (c) . In all cases, the vertical axis represents the absolute difference between the approximate result and the exact result.

FIG. 2.

(Color online) Schematic illustrating how, in the tangent method, a formula relating the quantities and is derived. The symbol denotes the term . The line is the tangent (taken at point ) to the theoretical curve . (For clarity, the curvature of is much exaggerated). Point marks the voltage at which the correction factor in the chosen FN-type equation becomes zero. At this voltage, the height of the tunneling barrier and the exponent in the chosen FN-type equation become zero, and the value of predicted by the FN-type equation is . Line represents the theoretical calculation of (i.e., for ), using the chosen FN-type equation.

## Tables

TABLE I.

To show, for the formulas listed, the maximum magnitudes of the absolute errors (Abs) and relative errors (Rel) in the ranges of indicated.

TABLE III.

Values of the Schottky–Nordheim barrier functions (for definitions, see Ref. 4), tabulated as functions of or . [“nd” is not usefully defined for .]

TABLE II.

Comparison of the Charbonnier and Martin (CM) and Spindt et al. (SBHW) approximations with the corresponding exact results for the substitution method as used in FN-plot theory. The correction factor implied for the chord method (for ) is .

/content/avs/journal/jvstb/28/2/10.1116/1.3363858
2010-03-31
2014-04-17

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