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The increasing use of standard machines in manufacturing process provides opportunities for sharing information from similar operations to improve the accuracy of process model characterization for supporting root cause analysis and process monitoring activities. This article investigates how to integrate data from parallel sites that are alike in some ways but dissimilar in others. The parallel sites could be several machines that accomplish the same process step, several industrial locations that produce the same product or even several different time windows for the same machine. The proposed Bayesian parallel site model flexibly allows for a compromise between pooling the data completely and treating sites as completely unrelated. One of the key features in the hierarchical model is the quasi-common parameters that are different from site to site, but have some commonality between sites. The similarities between the individual quasi-common parameters are modeled through common global hyperparameters which determine the prior distribution for the quasi-common parameters. A case study on the uniformity modeling (across the different dies on a silicon wafer, across slots in a furnace, etc.) illustrates how the hierarchy of a Bayesian model can be used to incorporate correlation structure. The Bayesian approach provides the flexibility for handling many other possible parallel data source scenarios that might be encountered in many applications. Keywords: Bayesian framework, multiple response surface, multistage manufacturing, parallel site model, single response surface, uniformity model, 1. Introduction Most manufacturing systems involve many process steps. For example, in manufacturing semiconductor devices, semiconductor wafers go through chemical deposition, photolithography, etching and several other machines numerous times (May [...]

Due to the development of sensing and computer technology, measurements of many process variables are available in current manufacturing processes. It is very challenging, however, to process a large amount of information in a limited time in order to make decisions about the health of the processes and products. This paper develops a "preprocessing" procedure for multiple sets of complicated functional data in order to reduce the data size for supporting timely decision analyses. The data type studied has been used for fault detection, root-cause analysis, and quality improvement in such engineering applications as automobile and semiconductor manufacturing and nanomachining processes. The proposed vertical-energy-thresholding (VET) procedure balances the reconstruction error against data-reduction efficiency so that it is effective in capturing key patterns in the multiple data signals. The selected wavelet coefficients are treated as the "reduced-size" data in subsequent analyses for decision making. This enhances the ability of the existing statistical and machine-learning procedures to handle high-dimensional functional data. A few real-life examples demonstrate the effectiveness of our proposed procedure compared to several ad hoc techniques extended from single-curve-based data modeling and denoising procedures. Index Terms--Cluster analysis, data mining, data reduction, denoising, wavelet thresholding.

Process modelling is the foundation of developing process controllers for monitoring and improving process/system health. Modelling process behaviours using a pure empirical approach might not be feasible due to limitation in collecting large amount of data. Engineering models provide valuable information about processes’ general behaviours but they might not capture distinct characteristics in the particular process studied. Many recent publications presented various ideas of using limited experimental data to adjust engineering models for making them suitable for certain applications. However, the focuses there are global adjustments, where modification of engineering models impacts the entire model-application region. In practice, some engineering models are only valid in a part of experimental data domain. Moreover, many discrepancies between engineering models and experimental data are in local regions. For example, in a chemical vapour deposition process, at high temperatures a process may be described by a diffusion limited model, while at low temperatures the process may be described by a reaction limited model. To address these problems, this article proposes two approaches for integrating engineering and data models: local model calibration and local model averaging. Through the local model calibration, the discrepancies between engineering’s first-principle models and experimental data are resolved locally based on experts’ feedbacks. To combine models adjusted locally in some regions and also models required little adjustments in other regions, a model averaging procedure based on local kernel weights is proposed. The effectiveness of the proposed method is demonstrated on simulated examples, and compared against a well-known existing global-adjustment method. [ABSTRACT FROM PUBLISHER]

Today's high-tech industries produce complicated products involving many processing steps. The usual approach of modeling and controlling each of these steps in isolation is re-evaluated. This paper develops a data model of synchronized observations collected from several stages of a multistage manufacturing process, and proposes an across-stage automatic control scheme for adjusting nonstationary process drifts. The proposed controller applies dynamic programming tools to optimize multiple goals specified for individual process stages and possible mismatch between stages. Several examples and simulation studies demonstrate that the proposed method is a valuable tool for improving semiconductor manufacturing quality. Index Terms--Advanced process control, data modeling, dynamic programming, minimum mean-square-error control.

This paper reports on a novel in situ sensing technique for monitoring the thickness of selectively grown Si epitaxial layers. The technique can be extended to detect selectivity loss when Si nuclei begin to appear on the insulator surface. In this technique, a quadruple mass spectrometer (QMS) monitors the ionized molecular hydrogen ([H.sub.2+]) signal, which is a by-product of the chemical-vapor deposition process. The thickness of the epitaxial layer is determined by evaluating the area under the hydrogen signal. We have deliberately used silane (Si[H.sub.4]) without HCl or [Cl.sub.2] to achieve both nonselective and selective depositions. We also show that the amount of hydrogen produced by the deposition process is a strong function of the exposed Si area on the wafer and the effect can be accurately monitored by QMS. This finding was exploited to develop an in situ sensing method to detect the selectivity loss. When selectivity is lost, Si nuclei begin to form on the insulator surface increasing the effective Si area on the wafer. Consequently, the rate of hydrogen production increases rapidly as nuclei coalesce, resulting in a distinct change in the functional form of the hydrogen signal. The hydrogen signal was analyzed using an automatic edge detection procedure based on the wavelet transform modulus maxima representation. The technique facilitated the determination of selective film thickness from the time-integrated hydrogen ([H.sub.2+]) signal. To the authors' knowledge, this paper represents one of the first applications of wavelets to in situ process monitoring and fault detection in semi-conductor manufacturing. The authors expect the methodology presented in this paper to be readily transferable to other selective deposition processes, including those that utilize dichlorosilane and disilane since hydrogen is a by-product of those processes as well. Index Terms--Edge detection, in situ selectivity loss detection, rapid thermal chemical-vapor deposition, selective silicon epitaxy, wavelet transform modulus maxima.

Simulation techniques are employed to examine the necessary sample size for using the large sample Gaussian approximation s-confidence interval and the characteristics of the maximum likelihood (ML) estimators in the finite sample situation with various fitting models.

In this paper, a novel objective function is presented that incorporates both local and global error as well as model parsimony in the construction of wavelet neural networks. Two methods are presented to assist in the minimization of this objective function, especially the local error term. First, during network initialization, a locally adaptive grid is utilized to include candidate wavelet basis functions whose local support addresses the local error of the local feature set. This set can be either user-defined or determined using information derived from the wavelet transform modulus maxima (WTMM) representation. Second, during network construction, a new selection procedure based on a subspace projection operator is presented to help focus the selection of wavelet basis functions to reduce the local error. Simulation results demonstrate the effectiveness of these methodologies in minimizing local and global error while maintaining model parsimony and incurring a minimal increase on computational complexity. Index Terms--Local error, objective function, wavelets.

To detect faults in a time-dependent process, we apply a discrete wavelet transform (DWT) to several independently replicated data sets generated by that process. The DWT can capture irregular data patterns such as sharp 'jumps' better than the Fourier transform and standard statistical procedures without adding much computational complexity. Our wavelet coefficient selection method effectively balances model parsimony against data reconstruction error. The few selected wavelet coefficients serve as the 'reduced-size' data set to facilitate an efficient decision-making method in situations with potentially large-volume data sets. We develop a general procedure to detect process faults based on differences between the reduced-size data sets obtained from the nominal (in-control) process and from a new instance of the target process that must be tested for an out-of-control condition. The distribution of the test statistic is constructed first using normal distribution theory and then with a new resampling procedure called 'reversed jackknifing' that does not require any restrictive distributional assumptions. A Monte Carlo study demonstrates the effectiveness of these procedures. Our methods successfully detect process faults for quadrupole mass spectrometry samples collected from a rapid thermal chemical vapor deposition process. Index Terms--Monte Carlo, process fault detection, resampling procedures, reversed jackknifing, wavelets.

A more formal designated optimum design for manufacturing (ODFM) that can efficiently produce the desired result with a minimal investment in cost and time is discussed. Future generations for integrated circuits are expected to shrink further. Thus, the need to highlight TCAD procedures as central to manufacturing issues to yield optimization and product quality should be considered. New procedures that result in the best design are described.

A new model selection procedure, called forward censored regression, proves useful in gathering environmental data with censored observation. Censored data, especially in most environmental data analyses, have values that are reported above some predetermined value. The method was able to estimate the significant factors affecting the total concentration of several contaminants from censored data.

In this paper, a bivariate model is established to characterize the seven-day, two-year ([Q.sub.7,2]) and seven-day, 10-year ([Q.sub.7,10]) low flows of streams in West-Central Florida under the restriction of [Q.sub.7,10] [less than or equal to] [Q.sub.7,2]. Analysis of prediction errors showed that our model describes these stream low flows well. The measurements under the detection limit were treated as censored data and a bivariate imputation method was developed to impute them into pseudo-complete samples. All-subsets regression was applied to these imputed data for selecting appropriate models, which link the low flows to their basin characteristics. The parameters are first estimated by the least-squares method in a bivariate normal regression and then adjusted to yield their maximum likelihood estimates. This process of imputation, model selection and parameter estimation is repeated iteratively until convergence of the selected model terms, parameter estimates, and imputed data. With the established model, predictions of low flows can be made at gauged and ungauged sites according to their basin variables for water-resources management.