Thermodynamically consistent stabilization of the drift-diffusion model for arbitrary band structures and carrier statistics

IF 2.5 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Journal of Computational Electronics Pub Date : 2025-09-09 DOI:10.1007/s10825-025-02412-4

Tobias Linn, Max Renner, Christoph Jungemann

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引用次数: 0

Abstract

To this day, the drift-diffusion model remains the most widely applied semiconductor simulation tool. This is due to its unrivaled numerical robustness when it is discretized with the finite volume method and the Scharfetter–Gummel stabilization. Unfortunately, this stabilization is only valid for nondegenerate carrier statistics. Several extensions of the Scharfetter–Gummel scheme to degenerate semiconductors have been proposed; however, they either rely on additional approximations or lack the stability for a full-scale device simulation. In this paper, we address this issue and present a generalization of the Scharfetter–Gummel scheme using no further approximations. Our scheme works for arbitrary band structures and coarse grids and is guaranteed to be thermodynamically consistent. Similar to Scharfetter–Gummel, it leads to a diagonally dominant Jacobian (M-matrix) for the discrete continuity equation preserving its excellent stability properties. An implementation of the algorithm is available online via Zenodo under the MIT license. It has already been used in a 2D device simulation at 4K where it exhibited excellent stability at a negligible runtime penalty.

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任意带结构和载流子统计的漂移-扩散模型的热力学一致稳定化

直到今天，漂移扩散模型仍然是应用最广泛的半导体模拟工具。这是由于用有限体积法和Scharfetter-Gummel稳定化进行离散时，它具有无可比拟的数值鲁棒性。不幸的是，这种稳定化只对非简并载波统计有效。提出了Scharfetter-Gummel格式在简并半导体中的几种扩展；然而，它们要么依赖于额外的近似值，要么缺乏全尺寸设备模拟的稳定性。在本文中，我们解决了这个问题，并提出了不使用进一步逼近的Scharfetter-Gummel格式的推广。我们的方案适用于任意带结构和粗网格，并保证了热力学一致性。类似于Scharfetter-Gummel，它导致离散连续方程的对角占优雅可比矩阵（m矩阵）保持其优异的稳定性。该算法的实现可以在MIT许可下通过Zenodo在线获得。它已经在4K的2D设备模拟中使用，在可以忽略不计的运行时间损失下表现出出色的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED

CiteScore

4.50

自引率

4.80%

发文量

142

审稿时长

>12 weeks

期刊介绍： he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered. In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.