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Finite-Difference Schemes for the Density-Gradient Equations

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Abstract

Two new finite-difference schemes are derived for solving the density-gradient equations describing quantum transport in semiconductors that improve on a simple linear discretization. The first scheme is also linear but includes additional terms that serve to maintain conservation to second order. The second scheme is a nonlinear exponential-fitting method that is more complicated but also more efficient than the linear schemes. The methods are evaluated numerically using device examples involving both quantum confinement and tunneling and are shown to perform quite well allowing for a substantial easing in the mesh refinement especially in tunneling problems.

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Authors and Affiliations

  1. Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC, 20375, USA

    M.G. Ancona

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  1. M.G. Ancona
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Ancona, M. Finite-Difference Schemes for the Density-Gradient Equations. Journal of Computational Electronics 1, 435–443 (2002). https://doi.org/10.1023/A:1020732515391

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