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在无序介质中计算载荷密度的空间分布
Alexey V Nenashev1, Florian Gebhard1, Klaus Meerholz2
1Faculty of Physics, Philipps-Universität Marburg, 35032 Marburg, Germany.
Entropy (Basel, Switzerland)
|May 24, 2024
概括
在无序的半导体中精确的电子分布对于光电子性质至关重要. 新的数值方法可以提供更快,更精确的计算,而无需解决施罗丁格方程.
科学领域:
- 物理 物理学 物理
- 材料科学 材料科学 材料科学
- 计算科学 计算科学
背景情况:
- 在无序的半导体中,电子分布 (n,r,T) 决定了光电子特性.
- 在随机潜力中计算n(r,T) 通常需要解决施罗丁格方程,这在计算上是密集的.
- 需要有效的方法来确定n (r,T) 的实际应用.
研究的目的:
- 开发和介绍新的数值技术来计算无序半导体中的空间和温度依赖的电子分布 (n,r,T).
- 为n (r,T) 提供准确的近似,绕过解决施罗丁格方程的需要.
- 通过精确的量子力学解决方案来验证这些新方法的准确性.
主要方法:
- 对于退化系统 (费米统计):矩阵反转和线性方程系统.
- 对于非退化系统 (博尔茨曼统计):通用低通波器和随机波函数.
- 将近似计算与精确的量子力学解决方案进行比较,以评估准确性.
主要成果:
- 开发了四种不同的数值技术,用于近似电子分布 (n,r,T).
- 证明了在不解决施罗丁格方程的情况下获得准确的n ((r,T) 的可行性.
- 通过与精确解决方案的严格比较,证实了开发的近似方法的高准确性.
结论:
- 提出的数值技术为确定无序半导体中的电子分布提供了有效和准确的替代方案.
- 这些方法可以显著降低光电子属性分析中的计算成本.
- 这些发现促进了对无序半导体设备的理解和设计的进步.
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