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• W2090352463 abstract "We solve numerically the problem of finding the potential and electric field around a negatively charged metallic contact on the surface of an n-type semiconductor. The semiconductor, which has permittivity ∊ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</inf> , fills the half-space y < 0. The contact is an infinitely long strip of width 2a, defined by y = 0,0 ≦ × ≦ 2a, − ∞ < z < ∞. The region y > 0 is vacuum with permittivity ∊ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> . In suitable dimensionless coordinates the potential ϕ satisfies Laplace's equation in y > 0 and the equation ▽ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> ϕ = e <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>ϕ</sup> − 1 in y < 0. On the boundary y = 0, ϕ = ϕ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> < 0, 0 ≦ × ≦ 2a, and the usual electromagnetic boundary conditions at the remainder of the interface. Finite difference schemes are used to solve the resulting boundary value problem. In most practical cases |ϕ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> | » 1 and η = ∊ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> /∊ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</inf> > « 1. We examine in considerable detail the limiting case η = 0, first for the less practical situation where |ϕ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> | « 1 and then for |ϕ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> | » 1. In case the |ϕ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> | « 1 we show that our numerical solution agrees well with the exact analytical solution of a linearized version of the problem. For |ϕ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> | » 1, we give plots of the equipotential curves, curves of equal charge density, and curves of constant electric field amplitude. These results also yield expressions for the capacitance of both a strip and a circular electrode. The modifications of these results when η > 0 are also given in some detail. Finally, we discuss the numerical calculations at some length." @default.
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• W2090352463 date "1970-05-06" @default.
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• W2090352463 title "The Potential Due to a Charged Metallic Strip on a Semiconductor Surface" @default.
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• W2090352463 doi "https://doi.org/10.1002/j.1538-7305.1970.tb01804.x" @default.
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