Theory and Modelling of Field-Induced Electron Emission
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Theory and Modelling of Field-Induced Electron Emission Richard G. Forbes University of Surrey, School of Electronic Engineering, Guildford, Surrey GU2 7XH, UK
ABSTRACT This paper addresses issues in the theory of field-induced electron emission. First, it summarises our present understanding of the theory of Fowler-Nordheim (FN) plots, and shows the relationship between a recent precise (in standard FN theory) approach to the interpretation of the FN-plot intercept and older approximate approaches. Second, it comments on the interpretation of FN plots taken from semiconductor field emitters. Third, it summarises the main points of a recent hypothesis about the mechanism of field-induced emission from carbonbased films and other electrically nanostructured heterogeneous (ENH) materials. Weaknesses in previous hypotheses are noted. It is hypothesised that thin films of all ENH materials, when deposited on a conducting substrate, will emit electrons in appropriate circumstances. Such films emit electrons at low macroscopic fields because they contain conducting nanostructure inside them: this structure generates sufficient geometrical field enhancement near the film/vacuum interface that more-or-less normal Fowler-Nordheim emission can occur. In connection with experiments on amorphous carbon films carried out by a group in Fribourg, it is shown that nanostructure of the size measured by scanning probe techniques should be able to generate field enhancement of the size measured in field electron spectroscopy experiments. This result provides a quantitative corroboration of other work suggesting that emission from amorphous carbon films is primarily due to geometrical field enhancement by nanostructures inside the film. Some counter-arguments to the internal-field-enhancement hypothesis are considered and disposed of. Some advantages of ENH materials as broad-area field emission electron sources are noted; these include control of material design.
INTRODUCTION Development of the theory of field-induced electron emission requires progress on five fronts. (1) Consolidation of the standard theory of Fowler-Nordheim (FN) emission, and of a general theory of FN-plot interpretation. (2) Consolidation and development of theory that addresses the various weaknesses of the standard theory (see later). (3) Development of an improved theory of field emission from semiconductors. (4) Application of existing theory to problems of modelling and interpretation of experimental data. (5) Scientific exploration of unsolved problems in deciding the mechanism of field-induced emission from complex materials.
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This paper aims to deal with the first issue above and also with one issue of type (5), namely the mechanism of field-induced emission from carbon-based films. The latter is the subject of a review [1]: the present paper will outline its main arguments. THE THEORY OF FOWLER-NORDHEIM PLOTS The theory here applies to emission from a single free-electron metallic band, but can be modified to apply to other materials. Fowler-No
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