Fast Lithography Simulation under Focus Variations for OPC and Layout Optimizations

In 90nm technology and beyond, process variations should be considered such that the design will be robust with respect to process variations. Focus error and exposure dose variations are the two most important lithography process variations. In a simple approximation, the critical dimension (CD) is about linearly related to the exposure dose variation, while it is quadratically related to the focus variation. Other kinds of variations can be reduced to these variations effectively as long as they are small. As a metric to measure the effects of exposure dose variations, normalized image log-slope (NILS) is pretty fast to compute once we have the aerial images. OPC software has used it as an optimization objective. But focus variation has not been commonly considered in current OPC software. One way is to compute several aerial images at different defocus conditions, but this approach is very time consuming. In this paper, we derive an analytical formula to compute the aerial image under any defocus condition. This method works for any illumination scheme and is applicable to both binary and phase shift masks (PSM). A model calibration method is also provided. It is demonstrated that there is only about 2-3x runtime increase using our fast focus-variational lithography simulation compared to the current single-focus lithography simulation. To confirm the accuracy, our model is compared with PROLITHTM. This ultra-fast simulator can enable better and faster process-variation aware OPC to make layouts more robust under process variations, and directly guide litho-aware layout optimizations