Physics Informed Neural Networks for Solving the Drift-Diffusion Equations
Title: Physics Informed Neural Networks for Solving the Drift-Diffusion Equations
标题：用于求解漂移-扩散方程的物理信息神经网络
Computer Science > Machine Learning arXiv:2610.33133 (cs) [Submitted on 23 Oct 2026] Title: Physics Informed Neural Networks for Solving the Drift-Diffusion Equations Authors: Luke Ragan, Matteo G. C. Alasio, Enrico Bellotti, Luca Dal Negro
计算机科学 > 机器学习 arXiv:2610.33133 (cs) [提交于 2026 年 10 月 23 日] 标题：用于求解漂移-扩散方程的物理信息神经网络 作者：Luke Ragan, Matteo G. C. Alasio, Enrico Bellotti, Luca Dal Negro
Abstract: The drift-diffusion equations are the fundamental building block for the modeling, design, and optimization of modern semiconductor devices. Solutions of the drift-diffusion equations rarely give way to analytical forms, and exhibit strong nonlinearity, with the solutions ranging over several orders of magnitude.
摘要：漂移-扩散方程是现代半导体器件建模、设计和优化的基础。漂移-扩散方程的解很少能以解析形式给出，且表现出强非线性，其解的范围跨越了几个数量级。
These attributes have led to research into numerical solvers, and while many commercial Technology Computer Aided Design (TCAD) packages now exist, they may require long simulation times, exhibit sensitivity to initial guesses, and rely on mesh generation. Further, these solvers are not well suited for inverse problems where the design parameters of a device are retrieved from its desired functional characteristics.
这些特性促使了对数值求解器的研究。尽管目前存在许多商业技术计算机辅助设计（TCAD）软件包，但它们可能需要较长的模拟时间，对初始猜测敏感，并依赖于网格生成。此外，这些求解器并不适用于从器件的期望功能特性中反推设计参数的逆问题。
To address all these challenges, this work demonstrates the usage of Physics Informed Neural Networks (PINNs) for the solution of the drift-diffusion equations with errors comparable to traditional simulation software using advanced training techniques to solve problems beyond the well-behaved equilibrium regime.
为了应对所有这些挑战，本工作展示了使用物理信息神经网络（PINNs）来求解漂移-扩散方程，通过先进的训练技术，其误差与传统模拟软件相当，并能解决超出良好平衡状态范畴的问题。
For this study, we specifically choose an abrupt PN-junction in both one and two dimensions that features extreme gradients of the carrier concentrations at the Ohmic contacts and an abrupt discontinuity in the doping profile. Using the proposed PINN architecture, we are able to retrieve accurate results for all observables under all bias conditions.
在本研究中，我们特别选择了一维和二维的突变 PN 结，其特征是在欧姆接触处具有极端的载流子浓度梯度，且掺杂分布存在突变。使用所提出的 PINN 架构，我们能够在所有偏置条件下获得所有可观测量的准确结果。
Additionally, we apply the PINN solver towards the inverse problem of retrieving doping profiles directly from desired electric field distributions or electrostatic potentials under non-zero applied biases. Our work establishes a powerful PINNs-based approach for semiconductor device modeling with the ability to solve inverse problems under non-equilibrium conditions for microelectronics research and discovery.
此外，我们将 PINN 求解器应用于逆问题，即在非零外加偏置下，直接从期望的电场分布或静电势中反推掺杂分布。我们的工作建立了一种强大的基于 PINN 的半导体器件建模方法，能够解决非平衡条件下的逆问题，为微电子研究和发现提供了支持。