Optimal design of a rapid thermal processor via physics-based modeling and convex optimization

摘要

Rapid thermal processing (RTP) is a key fabrication technology in the advanced cluster tool. Ever-decreasing feature sizes require extremely tight process control, especially the temperature trajectory to be precisely followed and the temperature uniformity across the wafer to be closely maintained, both of which rely on a good chamber design. Although widely adopted and successful in delivering necessary performance specifications, the empirical approach to the RTP design has its own limitations in two areas: (1) reduction in time-to-market and development cost (2) quantification of performance limits (e.g. best achievable temperature uniformity at the processing temperature). With the advent of powerful computing resources at relatively low cost, a model-based approach provides an alternative to the empirical approach and has better chance to achieve optimal design by virtue of its capability to quantify performance limits at minimal time and cost. In this paper, a physics-based model is derived and validated against experimental data in an effort to realize the model-based approach. With an accurate and predictive model available, the performances of various RTP designs are analyzed via convex optimization. The resulting performance limit also serves as a guideline for control implementation once the RTP design parameters are set for the optimal design.