发表机构
imec（微电子中心（比利时））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究极紫外光刻中电磁散射问题，提出基于PSFD方程训练的PINO，将傅里叶神经算子分解分支训练，保留全矢量耦合减小计算域，降低成本，训练后替代模型误差小，热启动初始化加速求解器。
AI 中文摘要
我们提出了一种基于伪谱频域（PSFD）方程训练的物理信息神经算子（PINO），用于极紫外光刻中的电磁（EM）散射问题。傅里叶神经算子被分解为二维横向（xy）分支和一维轴向（z）分支，并与背景进行自洽训练。通过这种方式，保留了掩模与多层响应之间的全矢量耦合，而无需调用有限阶玻恩近似，显著减小了计算域大小，降低了计算成本。PINO在LithoBench库中随机采样的约16000个掩模设计上进行训练，不使用预计算的电磁场解。对于未参与训练的掩模图案的散射强度，PINO替代模型相对于参考PSFD解的平均绝对误差约为7×10⁻³。结合谱阻尼，PINO热启动初始化加速了背景分解PSFD求解器在更精细离散化上的求解。
英文摘要
We present a physics-informed neural operator (PINO) trained with pseudo-spectral frequency-domain (PSFD) equations for electromagnetic (EM) scattering problems in EUV lithography. The Fourier neural operator is factorized into a two-dimensional lateral ($xy$) branch and a one-dimensional axial ($z$) branch and is trained self-consistently with background decomposition.Thus, the full-vector coupling between the mask and the multilayer response is retained without invoking a finite-order Born approximation. In this way, the computational domain size is significantly reduced, thereby lowering the computational cost. The PINO is trained on approximately 16,000 mask designs from the LithoBench library sampled randomly at each training iteration without using precomputed EM field solutions. The PINO surrogate model yields predictions with a mean absolute error of about $7 \times 10^{-3}$ for the scattered intensity of held-out mask patterns relative to the reference PSFD solution. Combined with spectral damping, the PINO warm-start initialization accelerates the background-decomposed PSFD solver on finer discretizations.
Comments17 pages, 7 figures
