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首页> 外文期刊>Journal of Vacuum Science & Technology >Comparison of approximations for the principal Schottky-Nordheim barrier function v(f), and comments on Fowler-Nordheim plots
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Comparison of approximations for the principal Schottky-Nordheim barrier function v(f), and comments on Fowler-Nordheim plots

机译：主肖特基-诺德海姆障碍函数v（f）的近似值比较以及对福勒-诺德海姆图的评论

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摘要

The Fowler-Nordheim-type (FN-type) equation developed by Murphy and Good [Phys. Rev. 102, 1464 (1956)] contains in its exponent a correction function v, best called the "principal Schottky-Nordheim (SN) barrier function." In the last 50 years a large number of different approximations have been developed for v. This article reformulates these approximations to be functions of the scaled barrier field/rather than the Nordheim parameter y, and then compares them with the approximations u(f)≈1-f+(1/6)f ln f and u(f)≈1-f+0.1715f ln f recently reported. It is confirmed, as expected, that these new formulas outperform older approximations of equivalent complexity when the comparison is made over the range 0 ≤f≤1. However, particularly with the first formula, some older approximations are superior over limited ranges of f because they have been designed to perform well over these limited ranges. The article also presents an updated and fuller account of the theory of FN-plot analysis and an updated tabulation of values of the SN-barrier functions (also called field emission elliptic functions). Both updates use f (rather than y) as the main auxiliary variable. The limitations of the existing FN-plot theory are clarified; this reinforces the case for the development of higher quality measurements of current-voltage characteristics and of new methods of data analysis that may be able to supersede the use of FN plots.
机译：墨菲和古德[Phys。 Rev. 102，1464（1956）]在其指数中包含一个校正函数v，最好称为“主要肖特基-诺德海姆（SN）势垒函数”。在过去的50年中，已经为v开发了许多不同的近似值。本文将这些近似值重新构造为缩放的势垒场/而不是Nordheim参数y的函数，然后将它们与近似值u（f）进行比较最近报道了1-f +（1/6）f ln f和u（f）≈1-f+ 0.1715f ln f。可以预料的是，在0≤f≤1范围内进行比较时，这些新公式的性能优于旧的等效复杂度近似值。但是，特别是对于第一个公式，某些较旧的近似值在f的有限范围内优越，因为它们已被设计为在这些有限范围内表现良好。本文还介绍了FN图分析的理论的更新和更完整的说明，以及SN屏障函数（也称为场发射椭圆函数）的值的列表。这两个更新都使用f（而不是y）作为主要辅助变量。阐明了现有FN图理论的局限性；这加强了开发更高质量的电流-电压特性测量和开发新的数据分析方法的可能性，这些新方法可能能够取代FN图的使用。

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  • 来源
    《Journal of Vacuum Science & Technology》 |2010年第2期|C2A33-C2A42|共10页
  • 作者

    Richard G. Forbes; Jonathan H. B. Deane;

  • 作者单位

    Advanced Technology Institute, Faculty of Engineering and Physical Sciences, University of Surrey,Guildford, Surrey GU2 7XH, United Kingdom;

    Department of Mathematics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford,Surrey GU2 7XH, United Kingdom;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);
  • 原文格式 PDF
  • 正文语种 eng
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