Determination of spatial CD signatures on photomasks

The production process of photo-masks for memory devices is highly demanding since homogeneity of mask parameters plays a pivotal role for the overall mask quality. Spatially homogeneous mask designs - which are dominant on memory devices - should in the best case be transferred into a mask exhibiting the same homogeneous behavior. This means that CD deviations from the mean should ideally bear no systematic signature but at most some random noise. However, many steps in the mask production process can introduce spatial correlations so that CD deviations are not only stochastically distributed over the mask but exhibit a pronounced signature. Thus, the determination and quantification of these deviations is crucial for a) assessing the mask quality and b) driving process improvements to remove CD signatures. The most common data analysis method for separating signatures from noise is to average over a number of samples. Unfortunately, due to the nature of mask manufacturing often there is only one sample available. In this paper we propose the technique of Thin Plate Spline Smoothing for the determination and quantification of the CD signature of a given single mask. This analysis is complemented by two statistical tests which assess the fit quality by analyzing the residual for normality and correlations.