Real Time Dynamic Programming Control of Rapid Thermal Processing Furnaces
Résumé
In the rapid thermal processing of a semi-conductor wafer, the temperature of the latter has to follow a preset time evolution profile while keeping spatial uniformity. A model-based open loop control strategy is presented in all its steps. A global and sufficiently accurate thermal model, based on the component interaction network, is used for the prediction of the required instantaneous heat flux distribution gained by the wafer. The same model is used to calculate the distribution of the net heat flux gainedby the wafer for each radiant emitter. The optimal combination of input powers to the radiant emitters is then determined using real time dynamic programming. It consists in minimizing the maximum difference between the required heat flux distribution and the one corresponding to the tested combination of input powers at each time step. The objective function is corrected according to the preceding time step errors, in a way to avoid cumulative temperature deviation. The solution algorithm is described, step by step, and a test case is treated. The results show good temperature tracking and uniformity.