Mask error tensor and causality of mask error enhancement for low-k 1 imaging: theory and experiments

Three important concepts about the mask error enhancement factor (MEEF) are proposed in this paper. From the fundamental assumption, the MEEF is derived to be a function of the image log slope and the aerial image variation caused by mask making error. Secondly, a mask error common window indicator (MECWIN) is proposed to evaluate the MEEF and mask CD specification by knowing the wafer CD tolerance. This concept is used to define the mask CD specification without any ambiguity. Finally, we describe the complex two-dimensional response to the mask making error around the line-end by a mask error enhancement tensor. Both theoretical derivations and experiments to justify the theory are presented in this paper.