Stochastic Variation Estimation in Lithography

The patent segments the stochastic variation prediction into multiple independent components: dose sensitivity prediction, quencher effect prediction, and line edge roughness prediction. Each component is modeled separately using specific equations (Eq. 1 for dose sensitivity, Eq. 2 for quencher effects, Eq. 3 for LER), allowing the complex prediction task to be divided into manageable parts that can be computed efficiently and calibrated independently with experimental data.

The patent implements feedback mechanisms through calibration procedures where model predictions are compared with experimental measurements. Eq. 1 includes a calibration factor CF_dose, Eq. 2 includes CF_quencher, and Eq. 3 includes CF_LER that are determined by fitting model predictions to measured data. This feedback loop allows the model to be continuously refined and adjusted to match actual process behavior, improving prediction accuracy while providing a systematic approach to calibration.

The patent performs preliminary calibration actions by establishing baseline calibration factors (CF_dose, CF_quencher, CF_LER) through initial experimental measurements. Once calibrated, the model can predict stochastic variations for new patterning conditions without requiring re-calibration, as the calibration factors capture the fundamental process characteristics. This preliminary calibration establishes a reliable foundation that can be reused across multiple predictions, reducing the time investment required for each subsequent prediction.