Traditional model based OPC software operates under a set of simple guiding principles. First, a design is fragmented into finitely sized segments, the sizes and numbers of which are limited by run-time and mask constraints. Within each fragment the intensity profile (aerial image) and edge-placement error (EPE) are calculated at a single location. Finally, the length of the entire fragment is moved to correct for the EPE at that location. This scheme has potential limitations in certain cases. For instance, cases where the aerial image contour (and therefore EPE) vary at a higher frequency than the minimum allowed fragmentation frequency. This so-called aerial image ripple problem can challenge the abilities of simple model based OPC. In addition, certain advanced RET schemes require that EPE be controlled in areas that have no adjacent mask polygon. Similarly, certain double-exposure RETs require the mutual optimization of features on multiple mask layers. Our paper will describe a flexible model based OPC scheme called Matrix OPC, which has proven capabilities of resolving these and many other advanced RET problems.

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