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Currently, overlay measurements are characterized by “recipe”, which defines both physical parameters such as focus, illumination et cetera, and also the software parameters such as algorithm to be used and regions of interest. Setting up these recipes requires both engineering time and wafer availability on an overlay tool, so reducing these requirements will result in higher tool productivity.
One of the significant challenges to automating this process is that the parameters are highly and complexly correlated. At the same time, a high level of traceability and transparency is required in the recipe creation process, so a technique that maintains its decisions in terms of well defined physical parameters is desirable. Running time should be short, given the system (automatic recipe creation) is being implemented to reduce overheads. Finally, a failure of the system to determine acceptable parameters should be obvious, so a certainty metric is also desirable. The complex, nonlinear interactions make solution by an expert system difficult at best, especially in the verification of the resulting decision network. The transparency requirements tend to preclude classical neural networks and similar techniques. Genetic algorithms and other “global minimization” techniques require too much computational power (given system footprint and cost requirements). A Bayesian network, however, provides a solution to these requirements. Such a network, with appropriate priors, can be used during recipe creation / optimization not just to select a good set of parameters, but also to guide the direction of search, by evaluating the network state while only incomplete information is available. As a Bayesian network maintains an estimate of the probability distribution of nodal values, a maximum-entropy approach can be utilized to obtain a working recipe in a minimum or near-minimum number of steps. In this paper we discuss the potential use of a Bayesian network in such a capacity, reducing the amount of engineering intervention. We discuss the benefits of this approach, especially improved repeatability and traceability of the learning process, and quantification of uncertainty in decisions made. We also consider the problems associated with this approach, especially in detailed construction of network topology, validation of the Bayesian network and the recipes it generates, and issues arising from the integration of a Bayesian network with a complex multithreaded application; these primarily relate to maintaining Bayesian network and system architecture integrity.
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