Balanced truncation model reduction for laser heating wafer model in frequency restricted domain

Abstract

Modeling and simulating laser heating phenomena are crucial for optimizing manufacturing processes and ensuring high-quality final products. A major challenge in semiconductor manufacturing is achieving accurate, real-time temperature control during wafer heating. To reduce the computational burden of complex mathematical models, low-dimensional reduced models can be employed. In this paper, we develop a mathematical model for laser heating in silicon wafers. For model reduction, we use the balanced truncation method, considering both frequency-unrestricted and restricted cases. Additionally, the rational Krylov subspace method is applied to solve high-dimensional sparse matrix equations. To gain key physical insights, we use the COMSOL Multiphysics package. Finally, some numerical experiments are conducted using MATLAB to validate the proposed approach.

Keywords

• Laser heating wafer
• Balanced truncation
• Lyapunov equations
• Gramians
• Rational Krylov subspace