Simulation of the Influence of Interface Charge on Electron Emission
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Simulation Of The Influence Of Interface Charge On Electron Emission Kevin L. Jensen and Jonathan L. Shaw Code 6840, ESTD, Naval Research Laboratory Washington, DC 20375-5347 USA ABSTRACT Several materials are promising candidates for electron sources. For diamond, a tunneling interface at the back contact limits injecting charge into the conduction band, but a purely geometric model of internal field emission is inadequate to explain experimental data. The presence of a defect, modeled by a coulomb charge, within the tunneling barrier region significantly enhances transmission and, in concert with a geometrical model, may better account for observed current levels. Charge has been suggested to play a similar role in the SiO2 covering on a single tip silicon field emitter to explain experimental data. The tunneling theory in both cases is similar. In the present work, a general method for estimating electron transport and energy distributions through potential profiles, which describe both semiconductor interfaces and field emission potential barriers when a charged particle modifies the tunneling barrier, is developed. While the model is intended for treating a metal-semiconductor interface, it is cast here in terms of in a thin SiO2 coating over a silicon field emitter tip to enable qualitative comparisons with experimental data. Tunneling probabilities are found by numerically solving Schrödinger’s Equation for a piece-wise linear potential using an Airy Function approach. A qualitative comparison to experimental energy distribution findings is possible by utilizing an analytical model of the field emitter tip from which current-voltage relations may be found. INTRODUCTION Microfabricated diamond structures are under investigation for high power microwave amplifiers and electronic devices [1]. Emission measurements from insulating diamond on pand n-doped Si substrates suggest that the substrate-diamond interface plays a dominant role in the electron emission of a diamond film [2]. A WKB analysis of the interface barrier using a geometric model of interface roughness and parameters ascertained from experimental data underestimated observed current levels by more than order of magnitude for realistic parameters [3]. If transmission into the conduction band of diamond were due to geometrical field enhancement (internal field emission model) alone, then the size of the ellipsoids which approximate interface roughness would be unphysical. Other mechanisms are evidently involved, such as defects [4, 5]. A simple model is obtained by including a coulomb potential within the potential profile at the material-diamond interface [6]. Elsewhere, measurements on a single silicon field emitter tip developed by MCNC showed that changes in the local electric potential due to charges becoming trapped in the oxide accounted for changes in the emission distribution [7]. A simulation of the effects of a coulomb potential in a tunneling barrier therefore would be of use in the analysis of both emission from diamond and from semiconduc
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