A robust nonlinear model predictive controller for a multiscale thin film deposition process

• The thin film deposition process is simulated using the multiscale approach.
• An uncertainty analysis of the process is performed based on PSEs.
• Closed-form models are identified offline based on data from the multiscale model.
• The developed model is employed in an NMPC algorithm.
• Robust closed-loop control of the process is performed under uncertainty.

The economics of the microelectronics industries depend on the operating policies adopted in the plant. Non-optimal strategies may result in undesired plant performance leading to economic loss or environmental and safety hazards. Model-plant mismatch, actuator constraints and sporadic sensor data can potentially drive the process far from the true optimum. The focus of the current work is to address these issues for the thin film deposition process. The evolution of the thin film can be modeled employing nonlinear partial differential equations (PDEs) embedded with lattice-based kinetic Monte Carlo (KMC) simulations to describe the multiscale nature of the process. Since the KMC simulations are computationally prohibitive for online applications, in this paper, a closed-form model is developed based on the data collected from the multiscale model. The identified closed-form model can be used for online control and optimization applications in the presence of model-plant mismatch. The robust performance is quantified by estimates of the distribution of the controlled variables employing power series expansion (PSE) under model parameter uncertainty. Uncertainties are accounted for in one parameter of the KMC model and in the control actions. To show the applicability of the identified model, the model is embedded within a nonlinear model predictive control (NMPC) framework to predict estimates of the control actions that comply with the process control objectives. The shrinking horizon NMPC algorithm is adopted to minimize the roughness of the thin film while satisfying the constraints on the applied substrate temperature at each time interval and film thickness at the end of the deposition process.