State Observer and Trajectory Tracking Controller Synthesis forWafer RTA Process: Periodic/Nonperiodic Linearization Scheme

Abstract

This thesis interprets the stability of a system in rapid thermal processing, a nonlinear modeling approach based on the process of rapid thermal processing in semiconductor manufacturing. It confirms the performance of periodic and aperiodic linearizations of the system using state observers and controllers through simulation. The central part of the wafer and the thermal equation of the lamp providing heat to the wafer in rapid thermal processing are represented as differential equations and statespace equations based on them. The Lur’e problem, one of the theories that confirm the stability of nonlinear systems, is applied to determine whether the nonlinear system is stable. By applying this to the rapid thermal processing system, it is shown that the nonlinear part satisfies the sector condition, ensuring the stability of the system. Additionally, this is validated through simulation by applying it to the system and observing its convergence. Although the state-space equation of the rapid thermal processing system is nonlinear, it can be converted into a linear model to apply various control theories and make control easy. As a result, Taylor expansion was used for linearization, and Euler’s method was used for discretization because digital processors are used. In rapid thermal processing, the temperature needs to reach the maximum temperature as quickly as possible and maintain it. Therefore, the simulation was carried out by setting the operating point as the part where the temperature changes and performing linearization at each operating point. It was confirmed that when the system was controlled using the linearized system at each operating point, the desired temperature was eached to some extent. However, if the system is linearized only at the operating point, the accuracy of the linearized system decreases in parts other than the operating point. Thus, to ensure better accuracy, aperiodic linearization was performed continuously based on the current state. The simulation shows that the shorter the linearization period, the smaller the error for the reference temperature. Furthermore, to achieve efficient control, aperiodic linearization was performed only where the temperature changes, and linearization was not performed where the temperature is maintained in rapid thermal processing. As a result, it was confirmed that the temperature is maintained at the desired temperature with a small error.