Plasma-enhanced chemical vapor deposition: modeling and control.

Abstract This paper focuses on modeling and control of a single-wafer parallel electrode plasma-enhanced chemical vapor deposition process with showerhead arrangement used to deposit a 500 A s amorphous silicon thin "lm on an 8 cm wafer. Initially, a twodimensional unsteady-state model is developed for the process that accounts for di!usive and convective mass transfer, bulk and deposition reactions, and nonuniform #uid #ow and plasma electron density pro"les. The model is solved using "nite-di!erence techniques and the radial nonuniformity of the "nal "lm thickness is computed to be almost 19%. Then, a feedback control system is designed and implemented on the process to reduce the "lm thickness nonuniformity. The control system consists of three spatially distributed proportional integral controllers that use measurements of the deposition rate at several locations across the wafer, to manipulate the inlet concentration of silane in the showerhead and achieve a uniform deposition rate across the wafer. The implementation of the proposed control system is shown to reduce the "lm thickness radial nonuniformity to 3.8%

Integrating robustness, optimality and constraints in control of nonlinear processes

Abstract This work focuses on the development of a uni"ed practical framework for control of single-input}single-output nonlinear processes with uncertainty and actuator constraints. Using a general state-space Lyapunov-based approach, the developed framework yields a direct nonlinear controller design method that integrates robustness, optimality, and explicit constraint-handling capabilities, and provides, at the same time, an explicit and intuitive characterization of the state-space regions of guaranteed closed-loop stability. This characterization captures, quantitatively, the limitations imposed by uncertainty and input constraints on our ability to steer the process dynamics in a desired direction. The proposed control method leads to the derivation of explicit analytical formulas for bounded robust optimal state feedback control laws that enforce stability and robust asymptotic referenceinput tracking in the presence of active input constraints. The performance of the control laws is illustrated through the use of a chemical reactor example and compared with existing process control strategies