A multivariate double EWMA process adjustment scheme for drifting processes

The “predictor-corrector” feedback controller, a process adjustment scheme proposed for semiconductor manufacturing run-to-run processes that drift, is extended to the multiple-input-multiple-output case. The controller is based on two coupled multivariate Exponentially-Weighted-Moving-Average (EWMA) equations, thus its performance depends on the choices of EWMA weight matrices. Stability conditions are given for a pure gain process adjusted with a MIMO double EWMA (EWMA) controller. It is shown that the stability conditions are invariant with respect to various realistic drift disturbance models. Recommendations on how to choose the EWMA weight matrices are given. An analysis is conducted to assess the impact of errors in the estimates of the process gains. The proposed MIMO EWMA feedback controller is compared to the common practice of using multiple single-input-single-ouput dEWMA controllers running in parallel.     

On-line tuning system of multivariate dEWMA control based on a neural network approach

The double exponentially weighted moving average (EWMA) controller is a popular algorithm for on-line quality control of semiconductor manufacturing processes. The performance of the closed-loop system hinges on the adequacy of the two weight parameters of the double EWMA equations. In 2004, Su and Hsu presented an approach based on the neural technique for ‘on-line’ tuning the weight of the single EWMA equation in the single-input single-output (SISO) system. The present paper extends the neural network on-line tuning scheme to the double EWMA controller for the non-squared multiple-input multiple-output (MIMO) system, and validates the control performance by means of a simulated chemical–mechanical planarization (CMP) process in semiconductor manufacturing. Both linear and non-linear equipment models are considered to evaluate the proposed controller, coupling with the deterministic drift, the Gaussian noise and the first-order integrated moving average (IMA) disturbance. It has been shown from a variety of simulation studies that the proposed method exhibits quite competitive control performance as compared with the previous control system. The other merit of the proposed approach is that the tuning system, if sufficient training in a neural network is available, can be practicably applied to complex semiconductor processes without undue difficulty.     

General run-to-run (R2R) control framework using self-tuning control for multiple-input multiple-output (MIMO) processes

During recent years, run-to-run (R2R) control techniques have been developed and used to control various semiconductor manufacturing processes. The R2R control methodology combines response surface modelling, engineering process control, and statistical process control. The main objective of such control is to manipulate the recipe to maintain the process output of each run as close to the nominal target as possible. The primary focus of this research is on the multiple-input multiple-output self-tuning control of R2R processes. A general control scheme is presented that can compensate for a variety of noise disturbances frequently encountered in semiconductor manufacturing. The controller can also compensate for various system dynamics, including autocorrelated responses, deterministic drifts, and varying process gains and offsets. Self-tuning controllers are developed to provide on-line parameter estimation and control. A recursive least squares algorithm is normally used to provide on-line parameter estimation to the controller. This type of control strategy used in the proposed self-tuning controller applies the principle of minimizing total cost (in the form of an expected off-target and controllable factors adjustment) to obtain a recipe for the next run. It is shown through the simulation study that even if the control model is non-linear, the self-tuning controller offers satisfactory control performance for R2R applications as compared with those of the control actions provided by the optimizing adaptive quality controller module. At last, a relevant application to chemical mechanical planarization in semiconductor manufacturing, a critical fabrication step involving two quality characteristics (removal rate and within-wafer non-uniformity), is used to illustrate the proposed controller. In this case study, a multivariate statistical process control technique via the Hotelling T?² statistic is also used as a dead-band for further investigation.     

Stability and performance of a double MEWMA controller for drifted MIMO systems

Many semiconductor manufacturing processes have, by nature, Multiple-Input and Multiple-Output (MIMO) variables. For a drifted MIMO process, the double Multivariate Exponentially Weighted Moving Average (dMEWMA) controller is a popular run-to-run controller for adjusting the process mean to a desired target. The stability conditions of a dMEWMA controller have received considerable attention in the literature. There are two limitations in the existed literature. First, these approaches only demonstrate that the asymptotic mean will meet a desired target; however, they do not show that mean square error matrix for a process is bounded. Second, they do not have an explicit expression of the process output of the dMEWMA controller for any production run t. Hence, by using a conventional state space formulation, it is impossible to address the process performance (such as process fallout rate of the dMEWMA controller) analytically. Using a different approach, this paper derives an analytical expression for the process output of a dMEWMA controller. The problems of the stability conditions and the performance of the dMEWMA controller can then be addressed successfully.     

Variable EWMA run-to-run controller for drifted processes

In semiconductor production, the double Exponentially Weighted Moving Average (dEWMA) feedback controller is a popular model-based run-to-run controller for drift processes. Whilst a dEWMA controller with suitable discount factors can guarantee long-term stability under fairly regular conditions, it usually requires a moderately large number of runs to bring the output of a process to its target value. This is impractical for a process with small batches. To reduce a possibly high rework rate, we propose a variable discount factor to tackle the problem. The stability conditions and the optimal variable discount factor of the proposed EWMA controller are derived. The main advantage of the proposed controller is that it is very easy for implementing a run-to-run control scheme. In addition, our proposed controller achieves a better performance than that of a dEWMA controller unless the drift rate is poorly estimated. Hence, it provides us with an efficient tool to adjust a drifted run-to-run process.     

Performance assessment of run-to-run control in semiconductor manufacturing based on IMC framework

The objective of this paper is to propose a universal methodology for performance assessment of run-to-run control in semiconductor manufacturing. The slope of the linear semiconductor process model is assumed to be known or subjected to mild plant/model mismatch. Based on an internal model control framework, analytical expressions of minimum variance performance (MVP) and best achievable performance (BAP) for a series of run-to-run control schemes are derived. In the methodology, closed-loop identification is utilised as the first step to estimate the noise dynamics via routine operating data, and numerical optimisation is employed as a second step to calculate the best achievable performance bounds of the run-to-run control loops. The validity of the methodology is justified by examples of performance assessment for EWMA control, double EWMA control and RLS-LT control, even under circumstances where the processes encounter model mismatch, metrology delay and more sophisticated noises. Several essential characteristics of run-to-run control are discovered by performance assessment, and valuable advice is offered to process engineers for improving the run-to-run control performance. Furthermore, a useful application example for online performance monitoring and optimal tuning of run-to-run controller demonstrates the advantage of the methodology.     

Rejoinder

A closed-loop identification procedure for pure gain-plus noise processes is presented for a family of disturbances that model drift in a discrete-part manufacturing system. Tuning techniques for the identified disturbance are provided for proportional integral (PI)controllers. These include the particular case of exponentially weighted moving average controllers, popular in semiconductor manufacturing. Expressions are derived for the mean squared deviation of the quality characteristic and for the variance of the adjustments. An optimization model is presented that balances adjustment variance with output variance. The optimal trade-off solution for a constrained PI controller is shown to depend on the assumption of no drift.     

A variance-constrained proportional—integral feedback controller that tunes itself

Proportional-Integral (PI) feedback controllers have been shown to provide a very robust process adjustment strategy. Recent work by Box and Luceno [1-3] provides PI controller settings that trade-off the variance of the quality characteristic versus the variance of the adjustments, an important concern in manufacturing. A Quality Engineer may desire a particular maximum adjustment variability, perhaps because of safety considerations or because the resolution of the manufacturing equipment. The graphs and tables provided by these authors were developed by minimizing a weighted sum of adjustment and output variance and will not always provide enough information to guarantee a specific maximum adjustment variance. Specifying a constraint on the adjustment variance is much more natural for a Quality Engineer than specifying the value of the relative weight that satisfies the adjustment constraint, and easier than choosing from a list of possible controller designs. In order to obtain a specific adjustment variance, parameter estimates of the process are needed. Moreover, to allow for rapid control after startup and to minimize scrap, it is desirable that on-line estimation occurs during closed-loop operation. This paper presents a PI controller that tunes its parameters on-line during closed-loop operation for a first order process under the assumption that no prior process information is known before starting the control session. Under these conditions, the proposed PI controller provides the minimum output variance for a specified upper bound in the adjustment variance; the value of the Lagrange multiplier associated with the constraint, similar to the relative weight in Box and Luceno's procedure, is computed internally by the controller and there is no need to specify it a-priori. An analysis of the performance of the controller is presented. It is shown that the proposed controller converges rapidly to the desired configuration without sacrificing the performance during the transient phase. g in Operations     

A Multivariate EWMA Controller for Linear Dynamic Processes

Most research of run-to-run process control has been based on single-input and single-output processes with static input–output relationships. In practice, many complicated semiconductor manufacturing processes have multiple-input and multiple-output (MIMO) variables. In addition, the effects of previous process input recipes and output responses on the current outputs might be carried over for several process periods. Under these circumstances, using conventional controllers usually results in unsatisfactory performance. To overcome this, a complicated process could be viewed as dynamic MIMO systems with added general process disturbance and this article proposes a dynamic-process multivariate exponentially weighted moving average (MEWMA) controller to adjust those processes. The long-term stability conditions of the proposed controller are derived analytically. Furthermore, by minimizing the total mean square error (TMSE) of the process outputs, the optimal discount matrix of the proposed controller under vector IMA(1,?1) disturbance is derived. Finally, to highlight the contribution of the proposed controller, we also conduct a comprehensive simulation study to compare the control performance of the proposed controller with that of the single MEWMA and self-tuning controllers. On average, the results demonstrate that the proposed controller outperforms the other two controllers with a TMSE reduction about 32% and 43%, respectively.     

Partial closed-loop versus open-loop motion estimation for HDTV compression

Motion estimation is a vital function of video coders that use motion compensated prediction to exploit the temporal redundancy of video signals. The reference images used in the motion estimation process can be either original images (open-loop architecture) or reconstructed images (closed-loop architecture). While the closed-loop architecture is intuitively superior to the open-loop architecture, closed-loop motion estimation is more difficult to implement in a real-time video encoder. A compromise is to perform open-loop integer-pel accurate motion estimation followed by closed-loop half-pel accurate estimation. In this article we present a comparative study of the performance of half-pel closed-loop versus open-loop motion estimation for coding of high definition television with the MPEG algorithm. Simulation results indicate that on average, closed-loop half-pel accurate motion estimation provides slightly better performance than open-loop half-pel accurate estimation. This improvement depends on the bit rate of the coded video biststream. For relatively high bit rates, the closed-loop implementation often provides no improvement, and sometimes an actual degradation of performance. An analysis of why a closed-loop implementation does not guarantee a better performance is presented.©1994 John Wiley & Sons Inc     

A kalman filtering process control scheme with an application in semiconductor short run manufacturing

A quality control chart for monitoring a short run process during the start-up phase is presented in this article. The chart is based on the Kalman filter recursive equations being applied to a stable process where the process variance is unknown prior to the start of the production run. The run length properties of this control scheme are discussed. It is shown that for the proposed scheme the run length properties are independent of the unknown process variance and that these properties are appropriate for monitoring a stable process during start-up. An economic model for the optimal design of the control scheme is presented and illustrated with a wet etching process used in semiconductor manufacturing.     

基于输出反馈的不确定非线性系统模糊鲁棒H∞控制

本文针对一类不确定非线性系统,研究了基于输出反馈的模糊鲁棒H∞控制问题。根据模糊T-S模型表征不确定非线性系统,基于状态观测器设计模糊控制器。由线性矩阵不等式和自适应律给出了模糊控制器存在的充分性条件。基于Lyapunov稳定性理论,提出的模糊控制方案在所有闭环信号最终一致有界意义下实现了期望的H∞性能。仿真结果表明了该方案的可行性。本文所提出的模糊跟踪控制器松弛了保守性,避免了匹配条件和上界。与已有的工作相比,本文约简了线性矩阵不等式的维数。     

Development of Run-To-Run (R2R) controller for the multiple-input multiple-output (MIMO) system using fuzzy control theories

Run-to-Run (R2R) control has been extensively applied in semiconductor manufacturing. In particular, del Castillo, E. and Rajagopal, R., A multivariate double EWMA process adjustment scheme for drifting processes. IIE Trans., 2002, 34, 1055–1068, investigated double multivariate exponentially weighted moving average (MEWMA) controller for the multiple-input multiple-output (MIMO) system in an attempt to adjust and maintain the linear dynamic process outputs on target. Multivariate fuzzy control, inherently different from conventional MEWMA-based control, is another promising alternative that consists of fuzzy logic and set concept. Providing the fuzzy control can structure an appropriate membership function for the R2R MIMO system, thus it can be shown a practically useful control tool in comparison to MEWMA control. In this paper, fuzzy logic is utilized to design the multivariate fuzzy controller for the type of R2R applications based primarily on the min-max-gravity method advocated by Gupta, M.M., Kiszka, J.B. and Trojan, G.M., Multivariable structure of fuzzy control systems. IEEE Trans. Sys., Man Cybern., 1986, 16, 638–656. Under a variety of disturbance models, the proposed multivariate fuzzy controller can produce quite competitive control performance when compared to MEWMA control.     

半导体平面工艺在金属微细加工中的应用

借鉴半导体集成电路的制造工艺，运用制版，光刻、腐蚀等平面工艺技术，制造微型金属光栅，是在金属制造工艺方成的一种尝试，也是半导体微细加工技术在其他领域的推广应用。本文简要介绍了这种思路的引出，方案的可行性，试验结果及推广应用实例。     

An adaptive EWMA scheme‐based CUSUM accumulation error for efficient monitoring of process location

The examination of product characteristics using a statistical tool is an important step in a manufacturing environment to ensure product quality. Several methods are employed for maintaining product quality assurance. Quality control charts, which utilize statistical methods, are normally used to detect special causes. Shewhart control charts are popular; their only limitation is that they are effective in handling only large shifts. For handling small shifts, the cumulative sum (CUSUM) and the exponential weighted moving average (EWMA) are more practical. For handling both small and large shifts, adaptive control charts are used. In this study, we proposed a new adaptive EWMA scheme. This scheme is based on CUSUM accumulation error for detection of wide range of shifts in the process location. The CUSUM features in the proposed scheme help with identification of prior shifts. The proposed scheme uses Huber and Tukey bisquare functions for an efficient shift detection. We have used average run length (ARL) as performance indicator for comparison, and our proposed scheme outperformed some of the existing schemes. An example that uses real‐life data is also provided to demonstrate the implementation of the proposed scheme.     

特征扰动频率辨识的自适应倾斜扰动抑制技术

为了抑制倾斜校正系统中的时变扰动,提出了一种基于特征扰动频率辨识的自适应扰动抑制方法。采用最小均方误差准则对闭环系统误差进行特征扰动频率辨识,以实现自适应控制器参数的在线调整,且将辨识的滤波参数与控制器调整并行化设计。同时提出频率分割的方法,将低频扰动以及高频扰动的抑制相结合,进一步提高了特征频率辨识速度以及简化设计流程,实现对闭环带宽内的扰动自适应抑制。所提出的方法在倾斜校正装置中进行了闭环验证,实验结果表明该方法能快速辨识特征扰动并自适应调节控制器,可以在单频或多频时变扰动下提升系统的闭环性能。

     

Some effective control chart procedures for reliability monitoring

Control charts are widely used for process monitoring in the manufacturing industry. Little research is available on their use to monitor the failure process of components or systems, which is important for equipment performance monitoring. Some Shewhart control charts, especially those for the number of defects, can be used for monitoring the number of failures per fixed interval; however, they are not effective especially when the failure frequency becomes small. A recent control scheme based on the cumulative quantity between observations of defects has been proposed which can be easily adopted to monitor the failure process for exponentially distributed inter-failure time. An investigation of its use for reliability monitoring is presented in this paper and the scheme can be easily extended to monitor inter-failure times that follow other distributions such as the Weibull distribution. Furthermore, the scheme is extended to the monitoring of time required to observe a fixed number of failures. The advantages of this scheme include the fact that the scheme does not require any subjective sample size, can be used for both high and low reliability items and can detect process improvement even in a high-reliability environment.     

Using CUSUM Control Schemes for Monitoring Quality Levels in Compound Poisson Production Environment: The Geometric Poisson Process

In contemporary modern and high volume production environments such as wafer manufacturing, a small sustained shift is not very easily detected in a short period of time, but may have a great impact on a manufacturing process. Thus, it is important to be able to detect and identify a small sustained shift of the production process in a timely manner and correct the undesired situation. The cumulative sum (CUSUM) control scheme is considered to be one of the efficient reference tools in detecting a small structure change in a process. However, for control of defects in a production process, too often the assumption is made that the defects follow a Poisson distribution. In practice, the process is more complex and the distributions of defects are more appropriately modeled by the compound Poisson distribution. In this paper, the underlying distribution is the geometric Poisson distribution, a Poisson distribution compounded by a geometric distribution, and the CUSUM control scheme based on the geometric Poisson process is addressed. An effective CUSUM control scheme can provide an adequate average run length (ARL), that can be obtained from the probability transition matrix for the Markov chain proposed by Brook and Evans (1972). With proper ARL selected, the geometric Poisson CUSUM control scheme is developed for process control.     

Relay-based gain and phase margins PI controller design

In this paper, an iterative procedure for achieving gain and phase margin specifications for a PI controller is presented. The iteration scheme is based on the use of two relay tests applied to the closed-loop system. The first relay test is standard, and it is used here to obtain the gain margin of the closed-loop system at each iteration step. The second one is applied to the closed-loop system such that a limit cycle is developed at the loop gain crossover frequency. Under this condition, it is possible to obtain an estimate of the phase margin of the loop transfer function. The procedure is used for PI controller tuning in a vanadium-dioxide (VO/sub 2/) thin-film characterization experiment, with desired gain and phase margin specifications.     

Robust motion control design for dual-axis motion platform using evolutionary algorithm

This paper presents a new approach to deal with the dual-axis control design problem for a mechatronic platform. The cross-coupling effect leading to contour errors is effectively resolved by incorporating a neural net-based decoupling compensator. Conditions for robust stability are derived to ensure the closed-loop system stability with the decoupling compensator. An evolutionary algorithm possessing the universal solution seeking capability is proposed for finding the optimal connecting weights of the neural compensator and PID control gains for the X and Y axis control loops. Numerical studies and a real-world experiment for a watch cambered surface polishing platform have verified performance and applicability of our proposed design.