Optimal control processing to increase single wafer reactor throughput in LPCVD

In this paper, Optimal Control theory is applied to develop an alternative process protocol in single wafer reactor LPCVD on patterned wafer in an effort to minimize the processing time, for given final step coverage. To achieve this, the operating conditions are changed during the deposition in a prescribed manner. A simplified control model is developed from the simultaneous one-dimensional Knudsen diffusion and chemical reaction description. The optimal control problem is formulated to find a temperature trajectory yielding the minimum processing time and its solution is computed numerically via a modified variation of extremals method. To demonstrate the concept of optimal control CVD (OCCVD), we consider the thermally activated deposition of silicon dioxide (SiO₂) from tetraethylorthosilicate (TEOS). Using the simplified control model, the estimated process time to achieve a 96% step coverage at 98% closure with the constant rate CVD (CRCVD) strategy is 729 seconds. Under the same conditions, the optimal control CVD (OCCVD) process time is 278 seconds. Compared to CRCVD, the process time saved with OCCVD is 62%