Efficient Calculation of Charging Effects in Electron Beam Lithography Using the SA-AMG

IF 4.1 2区工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Electron Device Letters Pub Date : 2024-08-23 DOI:10.1109/LED.2024.3448504

Wentao Ma;Kangpei Yao;Xiaoyang Zhong;Jie Liu

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引用次数: 0

Abstract

When simulating charging effects in electron beam lithography (EBL) using the drift-diffusion recombination (DDR) model, traditional numerical iterative solvers face issues of slow computational speed and limited scalability. To solve this problem, we employ the Smoothed aggregation algebraic multigrid (SA-AMG) solver based on bi-conjugate gradient stabilized (BICGSTAB) and preconditioned conjugate gradient (PCG) to accelerate the computation of the DDR and Poisson equations separately. Compared to the Gauss-Seidel solver with a time complexity of

${O}\text {(}{n}^{{2}}\text {)}$

and the PCG, BICGSTAB solvers with a time complexity of O (

${n}^{\text {3/ {2}}}\text {)}$

, the SA-AMG solver reduces the time complexity to

${O}\text {(}{n}\text {)}$

. This implies that at a charging time of

$1~\mu $

s, the computation time for simulating charging effects with SA-AMG is 93, 296, and 646 times faster than the Gauss-Seidel solver when the grid point count of

${n} = 10^{{6}}$

$10^{{7}}$

$10^{{8}}$

, respectively. Furthermore, compared to the combined PCG and BICGSTAB solvers, the SA-AMG solver is 4, 7, and 13 times faster for the same grid point counts.

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使用 SA-AMG 高效计算电子束光刻技术中的充电效应

在使用漂移扩散重组（DDR）模型模拟电子束光刻（EBL）中的充电效应时，传统的数值迭代求解器面临计算速度慢和可扩展性有限的问题。为了解决这个问题，我们采用了基于双共轭梯度稳定（BICGSTAB）和预处理共轭梯度（PCG）的平滑聚集代数多网格（SA-AMG）求解器，分别加速 DDR 和泊松方程的计算。与时间复杂度为 ${O}\text {(}{n}^{2}}\text {)}$的高斯-赛德尔求解器和时间复杂度为 O( ${n}^{text {3/ {2}}}\text {)}$的 PCG、BICGSTAB 求解器相比，SA-AMG 求解器将时间复杂度降低到了 ${O}\text {(}{n}\text {)}$。这意味着在充电时间为 1~\mu $ s 时，当网格点数为 ${n} = 10^{{6}}$ 、 $10^{{7}}$ 、 $10^{{8}}$ 时，使用 SA-AMG 仿真充电效应的计算时间分别是高斯-赛德尔求解器的 93 倍、296 倍和 646 倍。此外，与 PCG 和 BICGSTAB 求解器相比，在相同网格点数下，SA-AMG 求解器的速度分别是 PCG 和 BICGSTAB 求解器的 4 倍、7 倍和 13 倍。

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

IEEE Electron Device Letters 工程技术-工程：电子与电气

CiteScore

8.20

自引率

10.20%

发文量

551

审稿时长

1.4 months

期刊介绍： IEEE Electron Device Letters publishes original and significant contributions relating to the theory, modeling, design, performance and reliability of electron and ion integrated circuit devices and interconnects, involving insulators, metals, organic materials, micro-plasmas, semiconductors, quantum-effect structures, vacuum devices, and emerging materials with applications in bioelectronics, biomedical electronics, computation, communications, displays, microelectromechanics, imaging, micro-actuators, nanoelectronics, optoelectronics, photovoltaics, power ICs and micro-sensors.