Run-to-run Research Articles

EWMA Controller Tuning and Performance Evaluation in a High Mixed System

The exponentially weighted moving average (EWMA) controller is a very popular run-to-run (RtR) control scheme in semiconductor industry. However, in any typical step of semiconductor process, many different products are produced on parallel tools. RtR control is usually implemented with a “threaded” control framework, i.e.: different controllers are used for different combinations of tools and products. In this paper, the problem of EWMA controller tuning and performance evaluation in a mixed product system is investigated by simulation and time series analysis. It was found that as the product frequency changed, the tuning guidelines of a threaded EWMA controller were different for different types of tool disturbances. For a stationary ARMA(1,1) noise, the tuning parameter should be increased as product frequency decreases. If the tool exhibits non-stationary tool dynamics, e.g. ARIMA(1,1,1) noise, the tuning parameter should increase as the product frequency decreases.

A Feed-Forward/Feedback Run-to-Run Control of a Mixed Product Process: Simulation and Experimental Studies

Run-to-run (RtR) control is an important quality assurance method for batch-based manufacturing process. Usually, products of different grades are produced on a tool that will experience gradual drift between maintenance cycles. A feed-forward/feedback RtR control strategy that compensates this drift for all products manufactured on this tool was proposed. This and other RtR control schemes were analyzed and validated by simulation and experimentally using a bench scale reactor that produces silica particles with different diameters by a sol-gel process. A simple EWMA (exponentially weighted moving average) RtR control scheme based on products of the same grade was found to be stable but inefficient for infrequent products. A simple EWMA RtR control scheme that attributed disturbance entirely as the effect of tool drift was found to be unstable. The feed-forward/feedback RtR control proposed was able to maintain stable quality by effectively utilizing information about tool changes to adjust recipes of infrequent products.

Recursive Least Squares Estimation for Run-to-Run Control With Metrology Delay and Its Application to STI Etch Process

Run-to-run (RtR) control technology has received tremendous interest in semiconductor manufacturing. Exponentially weighted moving average (EWMA), double-EWMA, and internal model control (IMC) filters are recognized methods for online RtR estimation. In this paper, we consider recursive least squares (RLS) as an alternative for online estimation and RtR control. The relationship between EWMA-type and RLS-type estimates is analyzed and verified with simulations. Because measurement delay is almost inevitable in semiconductor manufacturing, we discuss and compare the performance of EWMA, RtR-IMC, and RLS controllers in handling measurement delay and measurement noise for processes with a deterministic drift. An ad hoc solution is proposed to handle measurement delay for processes with time-varying drifts. The results are illustrated through several simulations and a shallow trench isolation (STI) etch process as an industrial example.

Run-to-run control methods based on the DHOBE algorithm

Since process models are typically not known exactly in real problems, it is important to estimate the process parameters before one applies the optimal control to a process. In this paper, the Dasgupta–Huang optimal bounding ellipsoid (DHOBE) algorithm is employed to estimate process parameters in semiconductor process run-to-run (RtR) control. At each iteration, the DHOBE algorithm returns an outer bounding ellipsoid of the likely process parameter set. If the vector center of the ellipsoid is taken as the estimate of the process parameter vector, then a model-reference controller results; if the vector within the ellipsoid that produces the worst expected cost is taken as the process parameter estimate, then a worst-case controller results. These two methods are compared with other RtR control schemes: the exponentially weighted moving average (EWMA) method and the optimizing adaptive quality controller (OAQC). Simulation results show that the performance of the model-reference RtR controller based on the DHOBE algorithm is comparable to or better than that of the other two RtR controllers in some specific examples of semiconductor processes.

Robust Model-Based Iterative Feedback Optimization of Steady State Plant Operations

We present a complementary approach to real-time optimization (RTO) for maximizing the operating profit of an existing chemical plant without requiring a model-updating procedure, which is cumbersome and which may not necessarily improve the model. The proposed optimization methodology is based on an analogy between steady-state operation periods in process operation and iterations in numerical optimization. This analogy is also used by optimization-based run-to-run (RtR) control for batch processes. The process measurements are utilized to correct the gradient information used in optimization computations, resulting in better operating conditions. The plant operation is an integral part of the optimization, and this necessitates certain modifications to the optimization algorithm that we use (feasible sequential quadratic programming). The methodology is tested with a CSTR process and is shown to be robust in the presence of substantial model-plant mismatch.

Robust Model-Based Iterative Feedback Optimization for Chemical Plants

We present a complementary approach to real-time optimization (RTO) for maximizing the operating profit of an existing chemical plant without requiring a model updating procedure, which is cumbersome and may not necessarily improve the model. The proposed approach is based on an analogy between steady-state periods in process operation and iterations in numerical optimization. This analogy is also used by optimization based run-to-run (RtR) control for batch processes. The plant measurements are utilized to correct the gradient information used in optimization computations, resulting in better operating conditions. The methodology is tested with a CSTR process and is shown to be robust with respect to substantial modeling error.

Extensions and performance/robustness tradeoffs of the EWMA run-to-run controller by using the internal model control structure

We consider the run-to-run (RtR) correction of input recipes for semiconductor manufacturing processes using measurement information from previous runs. A RtR control algorithm that has been experimentally tested by industry and academia is the EWMA (exponentially weighted moving average) RtR controller. In this paper we provide extensions to this algorithm to address some of its drawbacks and also provide a rigorous theoretical analysis of its properties based on discrete control theory. By formulating the RtR control problem in the internal model control (IMC) structure used in feedback process control, we are able to extend the algorithm to completely eliminate offsets due to unmodeled process drifts, which is a common problem in semiconductor manufacturing. We also develop conditions for robustness with respect to modeling error and measurement delays. Tradeoffs between robustness guarantees and fast RtR response as well as handling of measurement noise are developed and presented in the form of plots that can be used for tuning the parameters of the RtR-IMC controller to accomplish the objectives set by the process engineer. The results are illustrated through several simulations including control of film deposition uniformity in an epitaxial reactor and tungsten deposition rate in a tungsten CVD reactor.

Monitoring and control of semiconductor manufacturing processes

Concerns optical measurement techniques for semiconductor manufacturing process monitoring and control. They can provide previously impossible real-time monitoring of several process variables, in-situ or ex-situ. This further enables the applications of more sophisticated real-time control algorithms, other than SPC. The SPC-based run-to-run (RtR) control, on the other hand, is still an instrumental part of the control algorithm, whenever there is a lack of real-time sensors for measuring critical process metrics. An emerging practice is to integrate RtR with the real-time control design to provide a comprehensive control design algorithm for semiconductor manufacture. The continued trend of semiconductor industry is toward an bigger wafers and smaller devices. This requires more integrated supervisory control, able to provide even tighter control, especially for photolithography, CVD, and etch processes. A unified framework needs to be established, at least for these critical processes, to facilitate and expedite systematic control design and development. In addition, as more sophisticated algorithms are being implemented, the control-related software and hardware should be user-friendly so that it can be operated by nonexpert personnel. Finally, since chip manufacturing consists of various processes, a comprehensive control algorithm on a factory-wide basis should utilize information (process-state, wafer-state, and tool-state data) from the current process as well as upstream and downstream processes.