Improvement of simulation accuracy using a non Gaussian kernel

Abstract

We compared a simulator's predictions with the critical dimension (CD) value measured on the wafer. We used sub resolution assist features (SRAF) in the experiment to keep the focus margin, the minimum size of the mask was small and comparable with the absorber's thickness. Therefore, it seems that we need a rigorous model and a variety of parameters for high prediction accuracy.We investigated the prediction error and found its behavior was not complicated. The dependence of the prediction errors was related to the space until the next feature, but the relationship was not linear; rather, it went up and down periodically like a Bessel function. This fact gave us the idea that it might be possible to improve the simulation accuracy by using a special convolution kernel but not a Gaussian function.We used a complementary kernel and tried to find a suitable shape to match the prediction error.The convolution kernel consisted of a complex number in order to represent phase change and amplitude loss. The kernel was applied to the simulator's mask plain. The results showed a significant improvement in simulation accuracy and a reduction in the route mean square (RMS) of the CD fitting error for all features with or without SRAFs. We used this model for optical proximity correction (OPC) and verified its accuracy with a printed wafer image. The range of the final CD variation of 40 nm line on the wafer was 1.9 nm, and the model also showed good agreement with the experimental two-dimensional feature shape.