A discrete duality finite volume method with harmonic average for semiconductor drift-diffusion equations
摘要
The stationary drift-diffusion model is widely used to model charge transport in semiconductor devices. Classical methods, such as the finite volume Scharfetter--Gummel (FVSG) method, perform well on high-quality Delaunay meshes but struggle on irregular or distorted meshes due to their reliance on Voronoi diagrams. To overcome this mesh limitation, this article introduces a new approach that integrates harmonic average stabilization into the discrete duality finite volume method (DDFV-HA). To validate our scheme, we compare DDFV-HA and FVSG for semiconductor simulations on both high- and low-quality meshes. Experiments show that DDFV-HA matches FVSG on high-quality meshes and is more reliable and accurate on low-quality meshes. Applying DDFV-HA to a real-world thyristor further confirms that it is well-suited for semiconductor simulations in complex, irregular domains where high-quality meshes are not easy to generate.
引用
@article{arxiv.2608.12808,
title = {A discrete duality finite volume method with harmonic average for semiconductor drift-diffusion equations},
author = {Shuya Liu and Zhicheng Liu and Bo Lin and Chijie Zhuang and Qingyuan Shi and Weizhu Bao and Rong Zeng},
journal= {arXiv preprint arXiv:2608.12808},
year = {2026}
}