بررسی کنترل کننده شبکه تیره عصبی اجرا به اجرا با استفاده از تجزیه و تحلیل های شبیه سازی عددی برای فرآیند سایسو

During the past decade, a variety of run-to-run (R2R) control techniques have been proposed and extensively used to control various semiconductor manufacturing processes. The R2R control methodology combines response surface modeling, engineering process control, and statistical process control, with the main objective of fine-tuning the recipe so that the process output of each run can be maintained as close to the nominal target as possible. In this paper, the single-input single-output (SISO) model is addressed. To overcome the shortcomings in the traditional R2R EWMA controller, a fuzzy neural network (FNN) control strategy is proposed. When a process has large autoregressive parameters, traditional EWMA control methods cannot establish stable SISO process control. To solve this problem, an SISO process control model based on an FNN was used to build an SISO process control procedure. The analysis results from a numerical simulation indicated that when the coefficient of autocorrelation ϕ > 0.6, the MSE ratio when using the FNN controller was 97.11% lower than when using the EWMA controller and 61.12% lower than when using an adaptive EWMA controller. This showed that the FNN control method established better SISO process control than the EWMA and adaptive EWMA control methods.

Semiconductor manufacturing is arguably the fastest evolving industry in the world. However, success in this industry requires constant attention to state of the art process tools, processing techniques, and process improvement. In a typical semiconductor manufacturing system, within-run (or batch) variation is usually controlled by automatic controllers built into the equipment. A run-to-run (R2R) controller is necessary because the equipment will experience aging and/or wear over time. Maintenance operations can also change the operating conditions for a process. Therefore, an R2R controller is needed to act as a supervisor to indicate whether a recipe change is needed and suggest new recipes for use in the next product batch (Adivikolanu and Zafiriou, 2000, Butler and Stefani, 1994, Del Castillo and Hurwitz, 1997, Patel and Jenkins, 2000, Sachs et al., 1991 and Sachs et al., 1995). Many researchers have discussed R2R control in the semiconductor industry. Ingolfsson and Sachs, 1993 and Sachs et al., 1995 developed a preliminary R2R control scheme that used a simple exponentially weighted moving average (EWMA) R2R controller statistic to obtain an appropriate recipe adjustment for a silicon epitaxial growth process in a barrel reactor. Del Castillo (2002) discussed the chemical mechanical planarization (CMP) process, using SISO process model response values for the removal rate and to control the variable platen speed. With their method the coefficient of autocorrelation may approach 0.9006. For this reason, the dynamic situation between the current and next batch may exhibit high practical process autocorrelation levels. Processes with large autoregressive parameters, as discussed in Jen, Jiang, and Fan (2004) cannot be well controlled using traditional EWMA control methods to control a single-input single-output (SISO) process. To overcome this problem, this paper proposes a fuzzy neural network (FNN) approach, in which fuzzy logic is integrated with a network’s learning ability. In the past, FNNs have been directly incorporated with the known behavioral aspects of a process, leaving the neural network to empirically capture the unknown aspects. Fuzzy inference systems have been applied in process modeling, adaptive control, and model predictive control (Hasegawa et al., 1995, Lee and Park, 1992, Lin and Lee, 1994 and Shen et al., 2002). According to these studies, an FNN controller is one of the more promising approaches in the R2R control field. Due the SISO R2R controller can compensate for most of the process dynamics and noise disturbances, avoiding complicated calculations. The focus of this paper is an SISO process system with a large autoregressive parameter and the FNN controller is proposed and analyzed. This paper is outlined as follows. In the next section, the structure and procedure of the FNN R2R controller will be introduced. In Section 3, a practical SISO model is simulated, and the control performance of the FNN controller is compared with other controllers. Section 4 concludes the paper and summarizes our findings.

In the previous section, we described the FNN controller and how it can be used as the “R2R process” in adaptive schemes. The major purpose of this research was to improve on the weakness of the traditional EWMA control when the process model has a higher level of autocorrelation. The SISO process model of Del Castillo and Hurwitz (1997) was used to carry out the control task. The control performance of the traditional EWMA, adaptive EWMA, and FNN R2R controllers were compared. From the results of this comparison, the following two conclusions were reached: 1. When the autocorrelation term is ϕ < 0.1 and the FNN controller was utilized to control the process model, the MSE (=0.67905) of the output was about 5.19% higher than the MSE (=0.64552) when using the traditional EWMA controller. The controlled result (MSE) from the FNN system represented a 70.18% reduction in the result of the adaptive EWMA controller. When the parameter range was 0.1 ⩽ ϕ ⩽ 0.6 and the FNN controller was used, the MSE of the output was reduced by about 75.54% compared to the traditional EWMA and 59.9% compared to the adaptive EWMA. When the process had a higher autocorrelation (ϕ > 0.6), the FNN system could obtain less variation than either the traditional EWMA (the MSE of the FNN system was lower by about 97.11%) or the adaptive EWMA controller (the MSE of FNN system was lower by about 61.12%). If the process had higher levels of autocorrelation, the FNN controller could obtain better performance in the control of the dynamic SISO model. 2. Based on the simulation results, when a process model has lower levels (ϕ < 0.1) of autocorrelation, we suggest adopting the EWMA or FNN controller, to obtain superior control effects. If the range of the autocorrelation is 0.1 ⩽ ϕ ⩽ 0.6, the FNN control should be used for the modeling control to obtain better performance. When ϕ > 0.6 it would be better to use the FNN or adaptive EWMA controller to satisfy the control requirement. The contribution of this research is a new applied approach using an FNN for R2R SISO model control. Because the controller was designed using FNN techniques, the correlation between the previous and subsequent runs can be considered. When the process is confronted with higher levels of auto-correlated terms, it is still able to maintain better control. The R2R FNN controller was designed with the transforming skill to update the error function so that the needed information can be acquired. Because the system was based on the steepest descent method with the back-propagation learning rule to correct the parameter weights in the FNN, it enables a more appropriate dynamic process. In this research, we carried out simulations using different controllers under different autocorrelation levels. These simulation results provide an engineer with selection criteria for an appropriate controller to obtain dynamic process control with the best performance. From the investigation results, when the proposed FNN controller is applied to control a dynamic process, the shortcomings of the traditional EWMA controller are eliminated and better control quality than the adaptive EWMA is obtained under models with higher levels of autocorrelation. The R2R FNN controller has great application potential to various semiconductor manufacturing processes.