Many modern thermal processing systems involve temperature control of heated plates. In many systems such as Metal-Organic Chemical Vapor Deposition (MOCVD) and epitaxial deposition (Epi) systems, the plates are often thick carriers or susceptors on which one or more wafers are placed. Typically these plates are heated by radiation from hot filaments and the temperature is measured using pyrometers. In many cases the temperature of the system is controlled using a proportional-integral-derivative (PID) controller. However, in cases where the temperature must be changed rapidly while maintaining good temperature uniformity and with tight performance limits, it can be difficult or even impossible to achieve the desired performance using PID controllers. In addition, the dynamic response of these systems typically changes considerably with operating conditions such as temperature, process gas composition, wafer emissivity, or wall emissivity (e.g., in systems where walls coat during process). This can make it difficult to tune a PID controller to give good performance over a broad range of operating conditions.

To overcome some of these limitations, PID controllers are often gain-scheduled by using different PID gains for the different operating conditions, which typically improves performance. Alternatively, even more complex controllers can be designed, such as Linear Quadratic Gaussian (LQG) controllers, but this requires the knowledge and hand of an expert in the field of systems and control. An alternative model-based control approach has been discussed in SC’s earlier publications that can achieve good performance for a wide range of operating conditions. In this approach, a mathematical model of the physics of the system is directly incorporated into the feedback controller, thus allowing the controller to have knowledge of how the system dynamics change with the operating temperature.

In SC’s earlier published studies, the robustness and performance of this model-based controller was compared to that of a gain-scheduled PID controller, as well as an LQG controller for a range of plate properties and operating conditions in terms of handling system modeling uncertainty, tracking performance (overshoot, settling time, etc.), and noise and disturbance accommodation properties. In this presentation, Monte Carlo simulations are used to evaluate the performance robustness with respect to physical parameter variations. Since the ranges of parameter variations are usually known, it is possible to map out the performance space with random selection of parameters within the allowable range using a pre-selected number of simulations. This has the advantage of mapping out the performance space without simulating each parameter variation individually, which could take up considerably more simulations.

In this presentation, we performed a Monte Carlo simulation of the heated plate closed-loop system by varying physical parameters such as the emissivity and effective heat transfer coefficients. We will show how the robustness of the different control methods, evaluated using Monte Carlo simulations, compares to the analytical robustness evaluation performed in our earlier published studies.