Adaptive variable-order spherical harmonics expansion of the Boltzmann Transport Equation

K. Rupp, T. Grasser, A. Jungel
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引用次数: 10

Abstract

The spherical harmonics expansion method provides a deterministic solution method for the Boltzmann Transport Equation for semiconductors. While first-order expansions have been used in early works, higher-order expansions are required for modern scaled-down devices. The drawback of higher-order expansion is that the number of unknowns in the resulting system of equations increases quadratically with the expansion order, leading to high memory consumptions and long simulation times. In this work we show that a considerable number of unknowns can be saved by increasing the expansion order only locally in the simulation domain. Moreover, we propose a scheme that adaptively increases the order starting from a uniform first-order expansion. For the considered n+nn+-diode, savings in the number of unknowns of up to a factor of five are obtained without sacrificing any accuracy of the numerical solution.
玻尔兹曼输运方程的自适应变阶球谐展开
球面谐波展开法为半导体玻尔兹曼输运方程提供了一种确定性的求解方法。虽然在早期的作品中使用了一阶扩展,但现代缩小设备需要高阶扩展。高阶展开的缺点是,所得到的方程组中的未知数数量会随着展开的顺序呈二次增长,从而导致高内存消耗和较长的模拟时间。在这项工作中,我们证明了通过在模拟域局部增加扩展阶数可以节省相当数量的未知数。此外,我们还提出了一种从一致一阶展开开始自适应增加阶数的方案。对于考虑的n+nn+二极管,在不牺牲数值解的任何精度的情况下,可以节省多达五倍的未知量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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