【Title】1. Optimal Design for Degradation Tests Based on Gamma Process with Random Effects; 

              2. Advanced Process Control in Semiconductor Manufacturing 

【Speaker】1.  Prof. Sheng-Tsaing Tseng, Institute of Statistics, Tsing-Hua University, Hsinchu, Taiwan

                    2.  Prof. David Shan-Hill Wong, Department of Chemical Engineering, Tsing Hua University, Hsinchu,Taiwan

【Host】Dr. Kaibo Wang 

【Time】November 6, 10:00am-12:00pm（Tuesday） 

【Location】Room 510, Shun-de Building

【Abstract】

Talk 1: Degradation models are usually used to provide information on the reliability of highly reliable products that are not likely to fail within a reasonable period of time under the traditional life tests or accelerated life tests. Gamma process is a natural model for describing degradation paths which exhibit a monotone increasing pattern, while the commonly used Wiener process is not appropriate in such a case.

In this talk, we discuss the problem of optimal design for degradation tests based on a gamma degradation process with random effect. In order to conduct a degradation experiment efficiently, several decision variables (such as the sample size, inspection frequency, and measurement numbers) need to be determined carefully. These decision variables affect not only the experimental cost, but also the precision of the estimates of lifetime parameters of interest. Under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal decision variables are found by minimizing the asymptotic variance of the estimate of the 100p-th percentile of the lifetime distribution of the product.

 A laser data is used to illustrate the proposed method. Moreover, the effect of model mis-specification that occurs when the random effects are not taken into consideration in the gamma degradation model are assessed analytically. The numerical results of these effect reveal that the impact of model mis-specification on the accuracy and precision of the prediction of percentiles of the lifetimes of products are somewhat serious for the tail probabilities. A simulation study also shows that the simulated values are quite close to the asymptotic values.

Talk 2: In the last decade, advanced process control technologies including multivariate process statistical monitoring (MVSPC) and fault detection classification (FDC), run-to-run (RtR) control and virtual metrology (VM) has been extensively deployed in the semiconductor industry.  In this talk, we shall review various challenges of implementing APC solutions encountered working with industry.   

Most RtR control algorithms are based on the assumption that there is only a single product fabricated in the manufacturing line. In the semiconductor manufacturing industry, production resembles an automated assembly line in which many products with different specifications are manufactured step-by-step, carried out by a number of “parallel” tools.  In actual practice only a fraction of runs were sampled and the metrology results are often reported in with variable delays.  In this talk, we shall present theoretical and simulation analysis of these stochastic factors on the stability and performance of RtR controllers and their implications; including grouping and information sharing between products, tool and product state estimations and influences of variable delay and sampling rate. 

A modern semiconductor manufacturing line is made of hundreds of sequential batch-processing stages. Each of these stages consists of many steps carried out by expensive tools, which are monitored by numerous sensors capable of sampling at intervals of seconds. The sensor readings of each run constitute profiles, which can include extremely drastic changes. The heterogeneous variations at different profile points are mainly due to on-off recipe actions at specific points. In addition, the analysis of these profiles is further complicated by long-term trends due to tool aging and short-term effects specific to the first wafer in a lot cycle.  MVSPC and FDC failing to take these effects into consideration will lead to frequent false alarms. We shall present a systematic method to address these challenges.

In data driven process monitoring, soft-sensor, or virtual metrology (VM) model is often employed to predict product's quality variables using sensor variables of the manufacturing process. Partial least squares (PLS) are commonly used to achieve this purpose. However, PLS seeks the direction of maximum co-variation between process variables and quality variables. Hence, a PLS model may include the directions representing variations in the process sensor variables that are irrelevant to predicting quality variables. In this work, an adaptive VM based on recursive CVA (RCVA) is proposed. Case study on a numerical example demonstrates the capability of CVA-based VM model compared to PLS-based VM model. Superiority of the proposed model is also presented when it applied to an industrial sputtering process.

We can summarize from these experiences that whereas basic APC tools are available, significant amount of work, both theoretical and practical are still needed for their robust implementation in industry.

【Brief bio】

Dr. Tseng received the B. S. degree in Business Mathematics from Soochow University, the M. S. degree in Applied Mathematics from Tsing-Hua University, and the Ph.D. degree in Management Science from Tamkang University, Taiwan. Currently, he is a chair professor in the Institute of Statistics at Tsing-Hua University, Taiwan. His research interests include reliability lifetime analysis, quality & productivity improvement, and statistical decision methodology. His articles have appeared in numerous technical journals such as Technometrics, Journal of Quality Technology, IIE Transactions, IEEE Transactions on Reliability, EJOR, NRL, JSPI, SS, IEEE Transactions on Semiconductor Manufacturing, and others. He has received the outstanding research award from the Science Council of Taiwan in 1993, 1999, and 2004. He is an elected member of ISI, and a member of the IEEE and a senior member of ASQ.

Dr. Wong received his B.S. degree from California Institute of Technology, USA, and his M.S. and Ph.D. degrees from University of Delaware, USA. His research focuses on the use of statistics and mathematics tools together with knowledge of physics, chemistry and biology to develop models and the application of such models to obtain resource efficient processes and high quality products. He has published more than 60 SCI-indexed papers.

Looking forward to your attendance.