OPC model calibration considerations for data variance

OPC models have been improving their accuracy over the years by modeling more error sources in the lithographic systems, but model calibration techniques are improving at a slower pace. One area of modeling calibration that has garnered little interest is the statistical variance of the calibration data set. OPC models are very susceptible to parameter divergence with statistical variance, but modest caution is given to the data variance once the calibration sequence has started. Not only should the calibration data be a good representation of the design intent, but measure redundancy is required to take into consideration the process and metrology variance. Considering it takes five to nine redundant measurements to generate a good statistical distribution for averaging and it takes tens of thousands of measurements to mimic the design intent, the data volume requirements become overwhelming. Typically, the data redundancy is reduced due to this data explosion, so some level of variance will creep into the model-tuning process. This is a feasibility study for treatment of data variance during model calibration. This approach was developed to improve the model fitness for primary out-of-specification features present in the calibration test pattern by performing small manipulations of the measured data combined with data weighting during the model calibration process. This data manipulation is executed in image-parameter groups (Imin, Imax, slope and curvature) to control model convergence. These critical-CD perturbations are typically fractions of nanometers, which is consistent with the residual variance of the statically valid data set. With this datamanipulation approach the critical features are pulled into specification without diverging other feature types. This paper will detail this model calibration technique and the use of imaging parameters and weights to converge the model for key feature types. It will also demonstrate its effectiveness on realistic applications.