Curvilinear mask metrology: what is the equivalent critical dimension?

One of the most significant changes happening now in the photomask industry is the move from Manhattan masks to curvilinear masks. This change is enabled by multi-beam mask writers and is motivated by benefits to both mask and wafer by using curvilinear mask patterns. Following the breakthrough in full-chip curvilinear inverse lithography technology using GPU acceleration, the adaptation of curvilinear optical process correction (OPC) from edge-segment OPC, and the MULTGON format, wafer fabs are expanding the layers using curvilinear masks at a rapid pace. In the mask-making flow, mask writing, mask critical dimension (CD) scanning electron microscopy (SEM), mask inspection, mask aerial image review, and mask repair are all done in the image or pixel domain, so these processes can handle curvilinear masks naturally. However, for mask metrology there are some unresolved issues, especially the traditional mask CD spec, which is a shared standard between mask shop and wafer fabs and becomes unknown for curvilinear mask patterns. In this work, we propose an equivalent CD spec for curvilinear masks, and we will also use this proposed spec to demonstrate curvilinear masks have smaller mask variation than Manhattan masks.