含随机测量时延的批间控制器设计

批间控制(Rt R)是半导体晶圆生产过程控制的有效算法.然而,受测量手段与测量成本的限制,难以实时检测晶圆的品质数据,即:存在一定的测量时延,通常该测量时延是随机,时变的,且直接影响批间控制器的性能.为此,本文基于指数加权移动平均(EWMA)算法,提出一种含随机测量时延的扰动估计方法.在分析测量概率的基础上,建立包含测量时延概率的扰动估计表达式;并采用期望最大化(EM)算法估计该测量时延的概率;然后分析系统可能存在的静差项,给出相应的补偿算法;最后讨论系统的稳定性.仿真实例验证所提算法的有效性.     

测量时延在线估计与批间控制器协同设计

批间控制是半导体批次生产过程中常用算法,其关键问题在于能够及时获取上一批次的制程输出,受测量手段及其成本限制,实际的生产制程很难满足这一要求.为此,本文提出一种基于贝叶斯统计分析的测量时延估计算法.在分析晶圆质量与实测时延、估计时延、以及制程漂移之间的逻辑关系的基础上,并将晶圆的质量信息按加工时间顺序划分两个相邻的滚动时间窗口.基于贝叶斯后验概率函数,及时捕获后一个滚动时间窗口内过程输出发生漂移的概率,从而判断是否有测量时延发生,并估算该时延大小.在此基础上,给出批间控制器的测量时延补偿策略,及时调整制程的控制量,提高晶圆的加工品质.仿真结果验证所提出算法的有效性.     

基于动态MANCOVA的混合制程虚拟测量算法

在晶圆/液晶面板等批次加工过程中,产品质量的及时估计与品质管制是提高产能和降低成本的有效途径.针对"少量多样"的混合制程,利用逐步回归算法挑选该制程的关毽变量,引入产品的效益因子,建立混合制程的虚拟测量模型;为克服系统扰动对模型精度的影响,以产品效益因子为状态量建立该制程的状态方程,利用Kalman滤波器递归估计模型参数得到动态的MANCOVA模型;最后通过某湿式蚀刻制程的工程应用验证了该算法的有效性.     

一种用于估计测量设备之间时间偏差的算法

该文分析了单向时延测量的必要性,并指出测量设备之间存在的时间偏差给时延测量带来了误差;该文提出一种算法用来估计测量设备间存在的时间偏差,利用算法估计的时间偏差来校正测量结果,达到准确测量单向时延的目的。仿真验证了估计算法的准确性。     

主动扰动抑制技术及其在磁悬浮系统的应用

以LMS算法为基础，为存在对象扰动的控制系统设计了自适应对象扰动估计算法和自适应对象扰动抑制算法，从而使系统在不进行扰动测量的情况下，实时地对对象扰动进行估计并进行主动扰动抑制。磁悬浮小球系统的应用结果表明，该方法对磁悬浮系统的对象扰动具有明显的抑制作用。     

一种新的高分辨时延估计算法

多径分量重叠衰落下的精确时延估计对很多系统而言都非常重要,对于定位技术更是如此。近来,MUSIC算法被用来估计信道测量中的多径时间弥散参量,还被用于频域室内几何定位,且性能优于基于IFFT的时域分析。本文首先讨论了MUSIC算法应用于带限脉冲时延估计时存在的问题,针对该问题提出了一种带滑动窗解卷积的、基于MUSIC算法的新的时延估计器,最后将这一算法通过计算机仿真与其它算法作了对比分析。     

基于仿射投影算法的时延估计

在时间延迟估计中,通常利用互相关算法对时延进行估计.然而,互相关算法受噪声影响较大,在低信噪比时无法准确对时延进行估计.LMS、NLMS等自适应算法能够避免噪声的影响,然而其收敛性较差.RLS自适应算法虽具有较好的收敛性,但算法复杂度较高.本文利用的仿射投影(AP)算法则具有较好的收敛性.模拟仿真表明该算法能准确估计时...     

基于积分选择PBFT共识算法的果品质量溯源

针对基于区块链的果品质量溯源系统中存在的共识算法吞吐量低、时延高、主节点随机选择等问题,本文提出了一种基于积分选择的改进PBFT(practical Byzantine fault tolerance)共识算法.该算法引入积分选择协议,通过对一致性协议、视图转换协议以及垃圾回收机制的优化,提高诚实主节点被选择的概率、减...     

超声波测风系统中自适应时延估计算法的研究

在时差法超声波测风系统中,风速的测量精度受到时间延迟估计精度、两超声波传感器的距离精度等的影响。在后者一定的情况下,测风精度对时延估计精度提出了更高的要求。对此,采用了一种基于权值检测的最小均方误差(LMS)自适应时延估计算法,从而实现了高精度时延估计。计算机仿真与实际测试表明:该算法的估计精度满足了所研制的超声波测风系统的设计要求,能够用于机场区域低空风场情况的监测。     

扰动抑制无模型自适应控制的鲁棒性分析

针对一类存在测量扰动的SISO非线性离散时间系统,研究无模型自适应控制算法的扰动作用问题.首先给出了系统输出误差与测量扰动的关系,分析了测量扰动对控制性能的影响.然后提出了一种带有滤波器的改进无模型自适应控制算法,该算法较常规无模型自适应控制算法可有效抑制测量扰动的作用.仿真结果验证了理论分析的正确性.     

Minimum entropy based run-to-run control for semiconductor processes with uncertain metrology delay

A novel run-to-run control methodology for semiconductor processes with uncertain metrology delay which is developed by combining the minimum error entropy and the optimal control strategy is presented. In most semiconductor processes, the product quality data from the previous run are not often available before the start of the next run. Thus, the corrective step is often delayed by one batch or more, and the duration of the delay is uncertain with stochastic characteristics. Coupled with inaccurate process models, the delay may lead to significant variations of the process outputs even with the use of exponentially weighted moving average (EWMA) controllers. This paper proposes a new method of handling the uncertain metrology delay from a probability viewpoint. The fundamentals of the run-to-run control systems are first reexamined, and then an innovative performance index is given by incorporating the entropy (or information potential) and the mean value of tracking error with constraints on control input energy. The probability density function (PDF) based optimal control algorithm is proposed for processes where the disturbance and delay are non-Gaussian and the stability of the algorithm is analyzed. In addition, the methodology of the proposed control strategy is extended to include recursive PDF estimation and on-line real time implementation. The paper also includes a simulation example of minimum entropy control of a tungsten chemical-vapor deposition process to illustrate the methodology. Furthermore, comparisons between the conventional EWMA method and the proposed method are done to show the advantages of our newly proposed method.     

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.     

Prediction of time-varying metrology delay for dEWMA and RLS-LT controllers

This paper investigates how to adaptively predict the time-varying metrology delay that can realistically occur in the semiconductor manufacturing practice. In the presence of metrology delays, the expected asymptotic double exponentially weighted moving average (dEWMA) control output, by using the EWMA and recursive least squares prediction methods, is derived. It has been found that the relationships between the expected control output and target in both estimation methods are equivalent, and six cases are addressed. Within the context of time-varying metrology delay, a new time update scheme to the recursive least squares-linear trend (RLS-LT) controller, combined with zone tests and the moving average (MA) control chart, is proposed. Simulated single input–single output (SISO) run-to-run processes subject to two time-varying metrology delay scenarios are used to assess the effectiveness of the proposed controller.     

Identification of tool and product effects in a mixed product and parallel tool environment

In the semiconductor manufacturing industry, production resembles an automated assembly line in which many similar products with slightly different specifications are manufactured step-by-step, with each step being a complicated physiochemical batch process performed by a number of tools. This constitutes a high-mix production system for which effective run-to-run control (RtR) and fault detection control (FDC) can be carried out only if the states of different tools and different products can be estimated. However, since in each production run, a specific product is performed on a specific tool, absolute individual states of products and tools are not observable. In this work, a novel state estimation method based on analysis of variance (ANOVA) is developed to estimate the relative states of each product and tool to the grand average performance of this station in the fab. The method is formulated in the form of a recursive state estimation using the Kalman filter. The advantages of this method are demonstrated using simulations to show that the correct relative states can be estimated in production scenarios such as tool-shift, tool-drift, product ramp-up, tool/product-offline and preventive maintenance (PM). Furthermore, application of this state estimation method in RtR control scheme shows that substantial improvements in process capabilities can be gained, especially for products with small lot counts. The proposed algorithm is also evaluated by an industrial application.     

基于变折扣因子EWMA的混合产品批间控制方法

批间(run-to-run,简称R2R)控制现今已被广泛用于半导体生产行业.指数加权移动平均(exponet weighted moving average.EWMA)是R2R控制的一种重要算法.折扣因子是EWMA控制期的主要参数.本文在模型中考虑了实际生产过程中混合产品少量多样的特点,引入了基于产品的变折扣因子EWMA控制算法,解决了产品切换时制程输出收敛速度过慢的问题.变折扣因子的引入提高了制程输出的响应速率而并不影响制程输出的稳定性.对实际过程的模拟仿真检验了该控制算法的可行性和优越性.     

Stability analysis and optimal tuning of EWMA controllers – Gain adaptation vs. intercept adaptation

Exponentially weighted moving average (EWMA) controllers are the most commonly used run-to-run controllers in semiconductor manufacturing industry. An EWMA controller can be implemented in two different ways. One way is to keep the process gain as its off-line estimate and update the intercept term at each run, which is termed EWMA with intercept adaptation; the other is to keep the intercept term as its off-line estimate and update the process gain at each run, which is termed EWMA with gain adaptation. Despite the fact that gain variation and adaptation is typical in semiconductor industry, most EWMA formulations are for intercept adaptation and few results exist on the stability and sensitivity of EWMA with gain adaptation. In this paper, we propose a general formulation to analyze the stability of both EWMA controllers. The proposed state-space representation not only reveals the similarities and differences between two types of EWMA controllers, but also explains why the stability conditions for both types of EWMA controllers are independent of process disturbances. In addition, we propose a general framework that unifies the analysis of the optimal control performance for both types of EWMA controllers. The proposed framework is different from existing approaches in that it decouples the state estimation from the control law, and derives the optimal weighting based on the state estimation performance. The proposed framework significantly simplifies the analysis procedure, especially for EWMA with gain adaptation. Using this framework, we derive the optimal EWMA weighting through solving the discrete-time algebraic Riccati equation (DARE) for various process disturbances that are encountered in semiconductor manufacturing industry. Simulation examples are given to illustrate the optimality of the EWMA weighting derived using the framework. Some practical aspects of controller tuning are also discussed based on the simulation results.     

Recursive Bayesian state estimation method for run‐to‐run control in high‐mixed semiconductor manufacturing process

One of the challenges in semiconductor manufacturing processes is the state estimation of a high‐mix production system. The traditional algorithm consists of constructing a context matrix based on the product fabricating thread. The state of the context matrix is estimated using the Moore‐Penrose pseudo‐inverse method. Although the method works well, the context matrix is often singular. Taking an integrated moving average disturbance into consideration, a novel state estimation method is proposed in a high‐mix manufacturing scenario. Furthermore, the recursive Bayesian estimation is presented to obtain the estimations of states combined with a moving window and an analysis of variance model. As a result, the calculation of the inverse of the context matrix is avoided and the unobservability problem is addressed. Both simulated and industrial cases are presented to demonstrate the effectiveness of the proposed algorithm.     

A Kalman filter-based R2R control system with parallel stochastic disturbance models for semiconductor manufacturing processes

A Kalman filter-based run-to-run control system has been proposed for minimum variance control of semiconductor manufacturing process. In the proposed control system, both gain- and bias-varying process models combined with different stochastic disturbance models were considered and identified in parallel. The best-fit model is selected and used for the R2R controller design. Sub-models of the ARIMA(1,1,1) process were considered for stochastic modeling of the bias and gain variation, and the Kalman filters are used to find the optimum model parameter estimation. The control performance was analyzed for each case of the disturbance model to investigate the expected benefit from the control system in comparison with the EWMA filter-based controller.