Extensions and performance/robustness tradeoffs of the EWMArun-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     

Threaded 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 the 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 are 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 $lambda$ should be decreased as product frequency decreases. If the tool exhibits nonstationary tool dynamics, e.g., ARIMA(1,1,1) noise, the tuning parameter should increase as the product frequency decreases.      

A General Harmonic Rule Controller for Run-to-Run Process Control

The existence of initial bias in parameter estimation is an important issue in controlling short-run processes in semiconductor manufacturing. Harmonic rule has been widely used in machine setup adjustment problems. This paper generalizes the harmonic rule to a new controller called general harmonic rule (GHR) controller in run-to-run process control. The stability and optimality of the GHR controller is discussed for a wide range of stochastic disturbances. A numerical study is performed to compare the sensitivity of the GHR controller, the exponentially weighted moving average (EWMA) controller and the variable EWMA controller. It is shown that the GHR controller is more robust than the EWMA controller when the process parameters are estimated with uncertainty.      

A Bayesian Approach for Disturbance Detection and Classification and Its Application to State Estimation in Run-to-Run Control

With growing demand for effective management of abnormal situations in process industry, disturbance detection and classification has drawn considerable interest from researchers in both industry and academia. In this paper, a disturbance detection and classification method is developed using Bayesian statistics. The theoretical derivation of the proposed method as well as its practical implementation are provided. With the introduction of preand post-change windows, detection and classification are achieved simultaneously in the proposed method through matching the posterior probability pattern to predefined patterns. An overlapping window mechanism is incorporated into the proposed method to minimize detection and classification delay. A simulation example is given to illustrate the robustness and effectiveness of the proposed disturbance detection method. One application of the proposed Bayesian disturbance detection and classification algorithm is a Bayesian enhanced exponentially weighted moving average (B-EWMA) state estimator which improves state estimation in the run-to-run control of semiconductor manufacturing processes. The superior performance of B-EWMA compared to the conventional EWMA is demonstrated using an industrial example     

Observability and state estimation for multiple product control in semiconductor manufacturing

Run-to-run control in semiconductor manufacturing is complicated by the use of multiple processing tools and many different products being made during a given time period. This paper investigates a Kalman filter-based state estimation scheme that views a manufacturing area with all the tools, products, and processes it contains as a single interrelated system. This formulation maximizes the amount of information that is shared across different batches by capturing their common characteristics in shared parameters. The estimation scheme performs state updates correctly even when measurement data is missing or delayed. A set of simulations are used to demonstrate the performance of the algorithm under different operating conditions.     

光刻过程RtR控制方法研究进展分析

首先对光刻过程和RtR(Run-to-Run)控制技术的产生背景进行了介绍,对统计过程控制的不足进行了分析并给出了RtR控制器的一般结构。然后从过程建模和控制算法两个角度对三种主要的光刻过程RtR控制器EWMA,MPC和ANN进行了综述和评价,对这三种控制器在非线性控制、单变量控制、多变量控制的适用性和优化控制效果进行了比较分析。最后指出基于MPC的非线性多变量控制器将成为光刻过程RtR控制器的主要研究方向。     

Performance Analysis of EWMA Controllers Subject to Metrology Delay

Metrology delay is a natural problem in the implementation of advanced process control scheme in semiconductor manufacturing systems. It is very important to understand the effect of metrology delay on performance of advanced process control systems. In this paper, the influences of metrology delay on both the transient and asymptotic properties of the product quality are analyzed for the case when a linear system with an initial bias and a stochastic autoregressive moving average (ARMA) disturbance is under an exponentially weighted moving average (EWMA) run-to-run control. Tuning guidelines are developed based on the study of numerical optimization results of the analytical closed-loop output response. In addition, effective metrology delay of a variable time delay system is analyzed based on the resampling technique implemented to a randomized time delay system. A virtual metrology technique is a possible solution to tackle the problem of metrology delay. The tradeoff between additional error of virtual metrology and reduction in time delay is studied. The results are illustrated using an example of control of the tungsten deposition rate in a tungsten chemical–vapor deposition reactor. The basic conclusion is that metrology delay is only important for processes that experience nonstationary stochastic disturbance. In such a case, use of virtual metrology is justified if the error of the virtual metrology method is less than the error caused by stochastic process noise. The accuracy of the virtual metrology noise with respect to the traditional metrology is not critical, provided that the error due to metrology is much less than that due to process disturbances.      

Adaptive symbol and parameter estimation in asynchronous multiuserCDMA detectors

Existing multiuser code-division multiple-access (CDMA) detectors either have to rely on strict power control or near-perfect parameter estimation for reliable operation. A novel adaptive multiuser CDMA detector structure is introduced. Using either an extended Kalman filter (EKF) or a recursive least squares (RLS) formulation, adaptive algorithms which jointly estimate the transmitted bits of each user and individual amplitudes and time delays may be derived. The proposed detectors work in a tracking mode after initial delay acquisition is accomplished using other techniques not discussed here. Through computer simulations, we show that the algorithms perform better than a bank of single-user (SU) receivers in terms of near-far resistance. Practical issues such as the selection of adaptation parameters are also discussed     

ADAPTIVE EQUALIZATION WITH RLS-MLSE ASSISTED BY FEC BLOCK CODING FOR FADING MOBILE RADIO CHANNELS

In this paper, we propose an adaptive maximum-likelihood (ML) sequence estimator with RLS channel estimation, which is assisted by forward error control (FEC) coding. The reliable symbols reconstructed in the FEC decoder are used as the feedback signal to the RLS channel estimator. The scheme is compared with decision feedback equalization (DFE) with RLS algorithm, which is assisted by FEC coding. Computer simulations show that in frequency-selective fast fading mobile radio channels, the proposed scheme performs better at moderate Doppler frequencies. It is suitable for four-phase modulation data transmission at the rate of several 10 kb/s in 900 MHz band or in the 1800 MHz band.     

Performance Assessment of Run-to-Run EWMA Controllers

An iterative method is developed to optimize a performance criterion for best achievable performance for discrete integral controllers used in run-to-run control. An analytical expression is derived so that a realistic assessment of the given integral controller is obtained. Using the theoretical equivalence of discrete integral and exponentially weighted moving average (EWMA) controllers, the method is then extended to performance assessment of EWMA controllers. A semiconductor manufacturing example is used to illustrate the utility of the method.     

Age-based double EWMA controller and its application to CMPprocesses

In the originally proposed run-by-run control scheme, the EWMA statistic is used as an estimate of the process deviation from its target. However, the controller based on the EWMA statistic is not sufficient for controlling a wearing out process. The PCC controller has been thus proposed to enhance the run-by-run controller capability. In this paper, we first reexamine the fundamentals of the PCC formulations and propose an adjustment that is advantageous in controlling processes subject to both random shifts and drifts. The adjusted PCC controller is then further refined to take into account the process age. This age-based double EWMA scheme is then applied to the CMP process, which is known in the semiconductor industry to be rather unstable     

A new time delay estimator based on ETDE

In this paper, we address the problem of online subsample time delay estimation of narrowband signals of known center frequency. We propose a new so-called mixed modulated Lagrange explicit time delay estimation (MMLETDE) algorithm and study its performance through computer simulations. The MMLETDE is a modulated Lagrange ETDE, but the delay estimate adaptation process is based on the truncated sinc fractional delay filter algorithm. We provide theoretical derivations for our proposed estimator, a proof of its convergence performance, learning characteristics of its error performance surface, and an expression for its delay variance. Using simulations, we show that MMLETDE requires only a small filter order and has no noticeable estimation bias over a wide frequency range.     

An Intelligent Run-to-Run Control Strategy for Chemical–Mechanical Polishing Processes

This paper presents a novel intelligent run-to-run control strategy for chemical–mechanical polishing (CMP) processes. With the help of the recursive least squares identification method for model building, a real-coded genetic algorithm is applied to adaptively adjust the discount coefficients for double exponentially weighted moving average (EWMA) controller. The online intelligent scheme can effectively prevent the CMP processes from reaching unstable condition and can thus achieve high control performance. To demonstrate the effectiveness and applicability of the proposed intelligent run-to-run control strategy, two typical case studies are worked out in this paper. Extensive simulation comparisons with traditional double EWMA run-to-run control were performed. The simulation results show that the proposed intelligent run-to-run control is able to achieve better control performance than conventional schemes, especially for a process that has nonlinearities, process noise, and extra large metrology delays.      

A research of UWB rake receiver based on novel RLS adaptive algorithm

A modified RAKE receiver based on novel Recursive Least Squares （RLS） adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band （UWB） channel models （CMI to CM4） show that the novel RLS algorithm can alter the attenuation estimation with the finger＇s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.     

EM-based recursive estimation of channel parameters

Recursive (online) expectation-maximization (EM) algorithm along with stochastic approximation is employed in this paper to estimate unknown time-invariant/variant parameters. The impulse response of a linear system (channel) is modeled as an unknown deterministic vector/process and as a Gaussian vector/process with unknown stochastic characteristics. Using these models which are embedded in white or colored Gaussian noise, different types of recursive least squares (RLS), Kalman filtering and smoothing and combined RLS and Kalman-type algorithms are derived directly from the recursive EM algorithm. The estimation of unknown parameters also generates new recursive algorithms for situations, such as additive colored noise modeled by an autoregressive process. The recursive EM algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods     

A Comprehensive Performance Analysis of Random Early Detection Mechanism

One of the most promising active queue management schemes being proposed for deployment in the Internet is the Random Early Detection (RED) scheme. However, research results on RED performance are highly mixed, especially in the field of tuning its parameters. In this paper, a comprehensive performance analysis of RED is presented. We revisit some features in RED and study them in greater detail. We point out that RED, in general, does not possess proportional loss between flows as claimed and widely adopted in previous research. We suggest the generalization of the PASTA property and give a proof for TCP flows. We also evaluate the performance of the Exponential Weighted Moving Average (EWMA) algorithm in RED. We find that EWMA in RED is an unbiased estimator of the average queue-length, regardless of the weighting value w _q . We also point out the theoretical and practical limits of EWMA in RED. Finally, we propose the use of fuzzy EWMA to RED (fuzzy RED) to alleviate the inflexibility of RED tuning. We use simulations to evaluate the performance of fuzzy RED and compare it with other versions of RED. Our simulations show that, in the case of a high workload and a high level of variation, fuzzy RED, by tracking system variation in an on-line manner, improves RED performance in a number of important router-based metrics like packet loss rate, average queueing delay, link utilization, and global power.     

Just-in-time adaptive disturbance estimation for run-to-run control of semiconductor processes

Run-to-run control is the term used for the application of discrete parts manufacturing control as practiced in the semiconductor industry. This paper presents a new algorithm for use in run-to-run control that has been designed to address some of the challenging issues unique to batch-type manufacturing. Just-in-time adaptive disturbance estimation (JADE) uses recursive weighted least squares parameter estimation to identify the contributions to variation that are dependent upon manufacturing context. The strengths and weaknesses of the JADE algorithm are demonstrated in a series of test cases developed to separate the various disturbances and processing issues a control system would be expected to encounter.     

Exact and approximate maximum-likelihood parameter estimation forquasi-synchronous CDMA signals

In order to construct the optimal decorrelator for a quasi-synchronous (QS) code-division multiple-access receiver, it is necessary to estimate the user delays. However, in a QS system, it is shown that delay estimation is equivalent to estimating a parameter vector which is related linearly to the received signal. An exact maximum-likelihood (ML) solution using alternating maximization is first developed for joint estimation of the user delay vectors and amplitudes. Suboptimal recursive least squares (RLS) and least mean square algorithms are then presented which approximate the true ML solution. It is shown that the optimal decorrelator and demodulated symbols are also generated by the RLS algorithm. Simulation and analytical results are presented for the bit-error rate performance of the adaptive receiver, and the average squared error of the estimated delay vectors is compared with the Cramer-Rao bound     

自适应序贯M估计算法及其性能分析

针对复杂噪声环境下的参数估计问题,提出了一种稳健的自适应序贯M估计算法(Adaptive Recursive M-Estimation,ARME),并从理论分析和Monte Carlo实验仿真两方面分析了该算法的收敛性、渐进无偏特性和稳健性.理论分析和仿真试验表明:在高斯白噪声背景下,ARME具有与序贯最小二乘算法(Recursive Least Square,RLS)相近的性能;在有突出干扰等非高斯噪声背景下,与RLS相比,ARME的参数估计收敛速度更快,估计误差更小,而且在稳健性上大大优于RLS.     

基于RLS的二次加权相关时延估计算法

针对测向定位中时延估计的问题,提出了一种基于递推最小二乘（Recursive Least Squares,RLS）算法的二次加权相关时延估计方法。该方法在二次相关算法基础上,一方面引入RLS算法,在二次相关前进行自适应滤波,提高系统抗噪能力,且具有较快的收敛速度;另一方面借鉴广义互相关的思路,引入加权函数,并且采用二次加权方式,提高时延估计的性能。仿真结果表明,在低信噪比环境下,基于RLS的二次加权相关时延估计法使谱峰更加尖锐,抑制了噪声的影响,提高了估计的精度。