Reduced Order Modelling for Wafer Heating with the Method of Freezing

Accurate and real-time temperature control for wafer heating is one of the main challenges in semiconductor manufacturing processes. With reduced-order modelling (ROM), the computational complexity of the mathematical model can be decreased in order to solve the model quickly at a low computational cost, while still maintaining the computational accuracy. However, the translating temperature profile, due to moving sources, render the standard reduction approaches to be ineffective. We propose to invoke the concept of the “Method of Freezing” and use it in conjunction with the standard ROM approaches to obtain an effective low-complexity model. We finally assess the effectiveness of the proposed approach on the 2-dimensional heat equation with moving heat loads. Numerical results clearly show the potential of the proposed approach over the standard one in terms of computational accuracy and the dimension of the resulting reduced-order model.