Adaptive variable-order spherical harmonics expansion of the Boltzmann Transport Equation
Adaptive variable-order spherical harmonics expansion of the Boltzmann Transport Equation
复制标题
玻尔兹曼传输方程的自适应变阶球谐函数展开
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Jungel
中科院分区：
文献类型：
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作者：
K. Rupp;T. Grasser;A. Jungel
球谐展开法为半导体玻尔兹曼传输方程提供了确定性求解方法。虽然早期作品中已使用一阶展开，但现代按比例缩小的设备需要更高阶展开。高阶展开的缺点是，所得方程组中的未知数数量随展开阶数呈二次方增加，导致内存消耗高和仿真时间长。在这项工作中，我们表明，通过仅在模拟域中局部增加展开阶数可以节省大量未知数。此外，我们提出了一种从统一的一阶展开开始自适应增加阶数的方案。对于所考虑的 n+nn+-二极管，在不牺牲数值解的任何精度的情况下，可以将未知数的数量最多节省五倍。
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.