Model-Based Control of Rapid Thermal Processing for Semiconductor Wafers

This work describes the application of model-based control system design techniques to rapid thermal processing (RTP). The work considers all aspects of the distributed temperature control problem from physics-based modeling to implementation of the real-time embedded controller. With its exceptionally stringent performance requirements (low non-uniformity of wafer temperature, high temperature ramp rates), RTP temperature control is a challenging distributed temperature control problem. Additionally, it is an important problem in the semiconductor industry because of the progressively smaller ‘thermal budget’ resulting from ever decreasing integrated circuit dimensions. Despite the emphasis on faster cold wall, single-wafer processing RTP chambers, the approach described here for solving distributed temperature control problems is equally applicable to slower distributed thermal systems such as, hot-wall batch-processing furnaces. For the physical model, finite volume techniques are used to develop high-fidelity heat transfer models that may be used for both control design and optimal chamber design. Model-order reduction techniques are employed to reduce these models to lower orders for control system design. In particular, principal orthogonal decomposition (POD) techniques have been used to derive low order models. Multivariable techniques such as LQG, H₂/ H_∞ methods are employed for feedback control design. These methods have been successfully implemented on commercial RTP chambers.