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The multilayer overlay lithography process is one of the most important steps in semiconductor manufacturing. It is a multistage manufacturing process in which errors are introduced in each step, and existing errors accumulated in upstream operations cause occurrence of additional errors in downstream operations. Thus, variations in the previously deposited reference layers will also affect the overlay errors in the subsequently deposited layers. Therefore, a systematic method is needed to model the flow of overlay errors from layer to layer and to mitigate this effect using controllable process parameters. In this paper, a stochastic model for the introduction, accumulation and propagation of multilayer overlay errors of the lithography process is proposed. Based on that model, a sequential optimization method is utilized to find the optimal adjustments of controllable process parameters for minimizing the total multilayer overlay errors. A number of simulation case studies are presented to demonstrate the newly introduced model-based approach to controlling the multilayer overlay errors in lithography processes.