Run-to-run adaptive optimization of a tungsten silicide LPCVD process

We introduce a novel modeling technique, in an effort to develop a physically-motivated empirical model of the deposition rate and spatial deposition nonuniformity for a single-wafer tungsten silicide low pressure chemical vapor deposition (LPCVD) processing step. In general, such a description is difficult to obtain due to the complexity of the mapping between the spatial nonuniformity and manipulated variables. Combining the so-called multiple response surface method with a “feedback-like” model structure, relating reactant partial pressures with manipulated variables, we develop a reasonably accurate description of the deposition rate and spatial deposition nonuniformity across wafer surface. This model offers good fitting accuracy with fewer adjustable parameters compared with the more traditional polynomial-structure models. Further, based on this modeling methodology, we derive a run-to-run adaptive control/optimisation strategy aiming to achieve prescribed values of the average deposition rate and silicon to tungsten ratio at the wafer surface, while minimizing the variation of the deposition rate across the wafer surface