Performance analysis of a rapid thermal processor via physics-based modeling and convex optimization

Rapid thermal processing (RTP) is a key fabrication technology in the advanced cluster tool. Ever-decreasing feature sizes require extremely tight process control, which rely on a good chamber design. The empirical approach to the RTP design has its own limitations in two areas, although widely adopted and successful in delivering necessary performance specifications: (1) reduction in time-to-market and development cost and (2) quantification of performance limits. With the advent of powerful computing resources at relatively low cost, a model-based approach provides an alternative and has better chance to achieve optimal design by virtue of its capability to quantify performance limits at minimal time and cost. In an effort to realize the model-based approach, a physics-based model is derived and validated against experimental data. With a predictive model available, the performances of an RTP design are analyzed via convex optimization to qualify an RTP design, which also serves as a basis for control implementation once the RTP design parameters are set.