In this paper, we present a multiscale model with application to the plasma etch process on a three dimensions substrate lattice with uniform thickness using the inductive coupled plasma (ICP). Specifically, we focus on a etch process on silicon with patterned resistive mask. And a multiscale model is developed to simulate both the gas-phase reactions and transportation phenomena in Cl₂/Ar plasma chamber as well as the complex interactions that occurs on the silicon substrate. A macroscopic continuous fluid model, which based on partial differential equations (PDEs), is applied to simulate the plasma reactions as well as the transportation phenomena. The fluid model is constructed in COMSOL Multiphysics^TM. Subsequently, the microscopic interactions that taken place on the substrate are simulated by a kinetic Monte Carlo (kMC) model. A spatial-temporal discrete method is applied to address the issue in computing the fluid model and the kMC model concurrently, in which kMC models are parrallelly computed in discrete locations and data exchange between the fluid model as well as the kMC models are implemented in discrete time. Additionally, neural network (NN) is implemented to approximate the kMC model in order to reduce the computational complexity for model-based feedback control. The NN model is then used in a predictive real-time optimizer that optimize the setpoints of a set of critical proportion integral (PI) loops to achieve desired control objectives. Simulation results shows that the model is accurate and the controllers are effective.

在本文中，我们提出了一种多尺度模型，该模型适用于使用感应耦合等离子体（ICP）在具有均匀厚度的三维基板晶格上进行等离子体蚀刻的过程。具体而言，我们专注于具有图案化电阻掩模的硅蚀刻工艺。建立了多尺度模型，以模拟Cl ₂ / Ar等离子体室中的气相反应和传输现象，以及硅衬底上发生的复杂相互作用。应用基于偏微分方程（PDE）的宏观连续流体模型来模拟等离子体反应以及传输现象。流体模型是在COMSOL Multiphysics ^TM中构建的。随后，通过动力学蒙特卡洛（kMC）模型模拟​​在基板上发生的微观相互作用。应用时空离散方法来解决同时计算流体模型和kMC​​模型的问题，其中在离散位置并行计算kMC模型，并在离散模型中实现流体模型与kMC模型之间的数据交换时间。另外，为了减少基于模型的反馈控制的计算复杂性，实现了神经网络（NN）来近似kMC模型。然后，在预测实时优化器中使用NN模型，该模型可优化一组关键比例积分（PI）回路的设定值，以实现所需的控制目标。仿真结果表明，该模型是正确的，并且控制器是有效的。