论文标题
P-N二极管中泊松方程的强大仿真至1μk
Robust Simulation of Poisson's Equation in a P-N Diode Down to 1 μK
论文作者
论文摘要
众所周知，在深层温度下很难模拟半导体设备。今天可以在商业TCAD中模拟的最低温度约为4.2 K，可能是100 mk，而大多数实验量子科学的进行为10 mk或更低。除了运输求解器的挑战外，主要瓶颈之一是静电的不相关，因为对电势的较小变化具有极大的敏感性。本文提议重新调整泊松方程，以消除这种极端的敏感性并改善收敛性。我们使用迭代牛顿 - 拉夫森方案为P-N二极管解决了重新的泊松方程，首次使用标准的IEEE-754算术和双重精度证明了收敛至创纪录的一个微胶菌的创纪录的低温。我们绘制潜在图并解决耗竭层边缘附近载体密度的快速变化。主要python函数在附录中介绍。
Semiconductor devices are notoriously difficult to simulate at deep-cryogenic temperatures. The lowest temperature that can be simulated today in commercial TCAD is around 4.2 K, possibly 100 mK, while most experimental quantum science is performed at 10 mK or lower. Besides the challenges in transport solvers, one of the main bottlenecks is the non-convergence in the electrostatics due to the extreme sensitivity to small variations in the potential. This article proposes to reformulate Poisson's equation to take out this extreme sensitivity and improve convergence. We solve the reformulated Poisson equation for a p-n diode using an iterative Newton-Raphson scheme, demonstrating convergence for the first time down to a record low temperature of one microkelvin using the standard IEEE-754 arithmetic with double precision. We plot the potential diagrams and resolve the rapid variation of the carrier densities near the edges of the depletion layer. The main Python functions are presented in the Appendix.
