MPC model validation using reverse analysis method

It became more challenging to guarantee the overall mask Critical Dimension (CD) quality according to the increase of hot spots and assist features at leading edge devices. Therefore, mask CD correction methodology has been changing from the rule-based (and/or selective) correction to model-based MPC (Mask Process Correction) to compensate for the through-pitch linearity and hot spot CD errors. In order to improve mask quality, it is required to have accurate MPC model which properly describes current mask fabrication process. There are limits on making and defining accurate MPC model because it is hard to know the actual CD trend such as CD linearity and through-pitch owing to the process dispersion and measurement error. To mitigate such noises, we normally measure several sites of each pattern types and then utilize the mean value of each measurement for MPC modeling. Through those procedures, the noise level of mask data will be reduced but it does not always guarantee improvement of model accuracy, even though measurement overhead is increasing. Root mean square (RMS) values which is usually used for accuracy indicator after modeling actually does not give any information on accuracy of MPC model since it is only related with data noise dispersion. In this paper, we reversely approached to identify the model accuracy. We create the data regarded as actual CD trend and then create scattered data by adding controlled dispersion of denoting the process and measurement error to the data. Then we make MPC model based on the scattered data to examine how much the model is deviated from the actual CD trend, from which model accuracy can be investigated. It is believed that we can come up with appropriate method to define the reliability of MPC model developed for optimized process corrections.