移动边界截断网格方法应用于半导体设备模拟,在博尔兹曼-巴特纳格-格罗斯-克鲁克方程的框架内
Ming-Yu Li1, Chun-Yaung Lu2, Chia-Chun Chou1
1National Tsing Hua University, Department of Chemistry, Hsinchu 300044, Taiwan.
Physical review. E
|August 1, 2025
概括
一种新的截断网格方法有效地解决了用于半导体设备模拟的博尔兹曼-巴特纳格-格罗斯-克鲁克方程. 这种方法可以降低计算成本,同时准确模拟准弹道运输现象.
科学领域:
- 计算物理学的计算物理.
- 模拟半导体设备的模拟
- 数字方法 数字方法.
背景情况:
- 在半导体中模拟电子传输需要解决复杂的动力方程,如博尔兹曼-巴特纳格-格罗斯-克鲁克 (BBGKY) 方程.
- 传统方法通常面临高计算成本,限制了它们在详细的设备模拟中的应用.
- 准确模拟准弹道运输对于理解现代高性能半导体设备至关重要.
研究的目的:
- 引入和验证先进的移动边界截断网格方法作为BBGKY方程的高效有限差异解答器.
- 为了证明该方法在模拟半导体设备中的准弹道运输方面的有效性.
- 在不牺牲模拟准确性的情况下降低计算费用.
主要方法:
- 开发了移动边界截断网格方法,为BBGKY方程开发了有限差异解法.
- 动态调整了计算领域,以专注于重要的相位空间区域.
- 整合了Boltzmann-Poisson系统用于GaAs同结构,结合了各种散射模型 (恒定放松时间,极光声波).
主要成果:
- 与传统方法相比,截断电网方法显著降低了计算成本.
- 模拟实现了与完整电网解决方案的优异一致.
- 该方法准确地捕获了准弹道运输现象,即使在低密度条件下.
- 在不同的散射模型中表现出适应性.
结论:
- 移动边界截断网格方法是半导体设备模拟中BBGKY方程的高效和准确的解决方法.
- 该方法可以大幅减少运行时间,并忠实地复制关键的运输现象.
- 它的适应性和通用应用性使它适合未来扩展到更复杂的动力模型.
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