E. Del Castillo

An adaptive run-to-run optimizing controller for linear and nonlinear semiconductor processes

This paper presents a new run-to-run (R2R) multiple-input-multiple-output controller for semiconductor manufacturing processes. The controller, termed optimizing adaptive quality controller (OAQC), can act both as an optimizer-in case equipment models are not available-or as a controller for given models. The main components of the OAQC are shown and a study of its performance is presented. The controller allows one to specify input and output constraints and weights, and input resolutions. A multivariate control chart can be applied either as a deadband on the controller or simply to provide out of control alarms. Experimental designs can be utilized for on-line (recursive) model identification in the optimization phase. For testing purposes, two chemical mechanical planarization processes were simulated based on real equipment models. It is shown that the OAQC allows one to keep adequate control even if the input-output transfer function is severely nonlinear. Software implementation including the integration of the OAQC with the University of Michigans Generic Cell Controller (GCC) is briefly discussed.

Model Context Selection for Run-to-Run Control

In the design of run-to-run controllers one is usually faced with the problem of selecting a model structure that best explains the variability in the data. The variable selection problem often becomes more complex when there are large numbers of candidate variables and the usual regression modeling assumptions are not satisfied. This paper proposes a model selection approach that uses ideas from the statistical linear models and stepwise regression literature to identify the context variables that contribute most to the autocorrelation and to the offsets in the data. A simulation example and an application to lithography alignment control are presented to illustrate the approach.

A Bayesian approach for multiple criteria decision making with applications in Design for Six Sigma

Linking end-customer preferences with variables controlled at a manufacturing plant is a main idea behind popular Design for Six Sigma management techniques. Multiple criteria decision making (MCDM) approaches can be used for such purposes, but in these techniques the decision-makers (DM) utility function, if modelled explicitly, is considered known with certainty once assessed. Here, a new algorithm is proposed to solve a MCDM problem with applications to Design for Six Sigma based on a Bayesian methodology. At a first stage, it is assumed that there are process responses that are functions of certain controllable factors or regressors. This relation is modelled based on experimental data. At a second stage, the utility function of one or more DMs or customers is described in a statistical model as a function of the process responses, based on surveys. This step considers the uncertainty in the utility function(s) explicitly. The methodology presented then maximizes the probability that the DMs or customers utility is greater than some given lower bound with respect to the controllable factors of the first stage. Both stages are modelled with Bayesian regression techniques. The advantages of using the Bayesian approach as opposed to traditional methods are highlighted.

Robust parameter design optimization of simulation experiments using stochastic perturbation methods

Stochastic perturbation methods can be applied to problems for which either the objective function is represented analytically, or the objective function is the result of a simulation experiment. The Simultaneous Perturbation Stochastic Approximation (SPSA) method has the advantage over similar methods of requiring only two measurements at each iteration of the search. This feature makes SPSA attractive for robust parameter design (RPD) problems where some factors affect the variance of the response(s) of interest. In this paper, the feasibility of SPSA as a RPD optimizer is presented, first when the objective function is known, and then when the objective function is estimated by means of a discrete-event simulation.

Setup adjustment for discrete-part manufacturing processes with asymmetric cost functions

This paper presents a feedback adjustment rule for discrete-part manufacturing processes that experience errors at the setup operation which are not directly observable due to part-to-part variability and measurement error. In contrast to previous work on setup adjustment, the off-target cost function of the process is not symmetric around its target. Two asymmetric cost functions—constant and quadratic functions—are considered in this paper. By introducing a bias term in the feedback adjustment rule, the process quality characteristic converges to the optimal steady-state target from the lower cost side of the cost function. This minimizes the off-target loss incurred during the transient phase of adjustment. A machining application is used to illustrate the proposed adjustment procedure and to demonstrate the savings generated by the proposed feedback adjustment rule compared to an adjustment rule due to Grubbs and to an integral controller. It is shown that the advantage of the proposed rule is significant when the cost of the items is high, items are produced in small lot sizes and the asymmetry of the cost function is large.

ON THE MONITORING OF TRENDED AND REGULARLY ADJUSTED PROCESSES

Trended and regularly adjusted processes are common in manufacturing industries. Such processes are, for example, related to tool wear, material replenishment or some regular maintenance. When the process has a slow trend or is frequently adjusted, the Shewhart chart can be interpreted in the same way as for a stable process. To facilitate comparison between such a trended and adjusted process to a stable case, and to estimate further the loss of effectiveness when the traditional Shewhart chart is applied to trended and adjusted process, this paper provides a statistical interpretation of traditional Shewhart charts for this type of processes. Formulas are derived for the calculation of alarm rate and average run length (ARL). This study is useful when deciding if a traditional Shewhart chart is sufficient or if a more advanced Statistical Process Control method is necessary. Furthermore, given the in-control and out-of-control ARL, a combined decision with regard to the control limits setting and the adjustment interval can be made. The general formulation is described and a simple linear trend model with an actual data set is used as an illustration.

An adaptive sphere-fitting method for sequential tolerance control

The machining of complex parts typically involves a logical and chronological sequence of n operations on m machine tools. Because manufacturing datums cannot always match design constraints, some of the design specifications imposed on the part are usually satisfied by distinct subsets of the n operations prescribed in the process plan. Conventional tolerance control specifies a fixed set point for each operation and a permissible variation about this set point to insure compliance with the specifications, whereas sequential tolerance control (STC) uses real-time measurement information at the completion of one stage to reposition the set point for subsequent operations. However, it has been shown that earlier sphere-fitting methods for STC can lead to inferior solutions when the process distributions are skewed. This paper introduces an extension of STC that uses an adaptive sphere-fitting method that significantly improves the yield in the presence of skewed distributions as well as significantly reducing the computational effort required by earlier probabilistic search methods.