Design for optimal trajectory tracking in rapid thermal processing

It is an irreversible trend that semiconductor wafer fabrication requires shorter processing time, greater flexibility and lower capital cost. Rapid Thermal Processing (RTP) has shown the potential to meet such requirements while playing a key role in advanced cluster tools. Ever decreasing feature sizes require extremely tightly controlled processing conditions, especially precisely following of temperature trajectory and maintenance of temperature uniformity across the wafer. In this paper, a 3-dimensional physics-based model is derived, which is then used in quantifying the trajectory following capability of an RTP design via convex optimization. The optimization studies are performed in two ways; the first one minimizes the spatial temperature deviation from the set temperature in the steady state, while the second one tries to make the temporal trajectory follow the specified trajectory during transient conditions. The outcome of the optimization studies indicates the goodness of a given RTP design and may serve as a guideline for control implementation when the RTP chamber is actually built.