Throughput and Quality Optimized Down-Selection of Overlay Measurement Markers for Robust Control of the Maximum Overlay Error in a Pattern Layer in Photolithography Processes

This paper presents a metaheuristic optimization-based approach for selecting a pre-determined number of measurement markers from the set of available markers that optimizes the performance of the recently introduced robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm { L}}^{\infty }$ </tex-math></inline-formula> norm overlay control algorithm, which robustly minimizes the worst overlay error across a given pattern layer. This optimization is then used in a Design of Experiments (DOE) setting to build a tractable regression model of a customizable objective function encompassing cost effects of quality losses and throughput benefits resulting from the down-selection of markers selected for robust overlay control. Using this model, one can rapidly determine the optimal proportion of markers for any set of cost parameters, and the optimal subset forming this proportion of available markers can be down-selected to maximize performance of the resulting robust overlay controller. Overlay data and models from a semiconductor manufacturing fab were used to evaluate the newly proposed inspection and control strategy. Results clearly indicate that the novel strategic down-selection of measurement markers coupled with robust overlay control could lead to vastly improved throughputs without decreasing quality relative to what can be achieved using traditional Run-to-Run (R2R) control. Feasibility of the novel DOE-based optimization was demonstrated for two scenarios of cost-effect parameters.