Identification of optimal recipes for multi-step and cyclic etch processes where the outcome of each step depends on the progression of the previous steps is a major challenge. Selecting the order and duration of each step is typically performed by a tedious trial and error process where the number of experimental trials scales exponentially with process complexity. Here we present a simulation-based methodology that significantly accelerates the process. We use limited experimental data taken at various process conditions, which may include pressure, gas type, gas flow rate, power, bias, and time to calibrate a step-aware reduced-order physics-based etch and deposition model. This model is used to generate predictions with steps permuted in any desired order and duration. The calibrated model predicts ordering, timing, and possible cycling of each step to achieve desired etch targets. The methodology is demonstrated on a multilayer stack with three possible steps, including etch and deposition. It is shown that the total number of experiments required for the proposed methodology is significantly less than that required by standard methods like full-factorial design of experiment. We also demonstrate how the etch data and the resulting calibrated model can be used to determine the optimal etch recipe for different aperture and/or mask geometries without having to perform further experiments.
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