Fast and accurate matrix-OPC with MEEF prediction using Kolmogorov-Arnold network

Accurate correction of a mask segment can be done by taking its neighbor segments into account. In matrix-OPC, this is achieved by mathematically deriving mask bias using the mask error enhancement factor (MEEF) matrix. MEEF from segment i to segment j (µi,j ) denotes the EPE sensitivity of j while unit mask bias is applied to i. Extraction of MEEF matrix is labor intensive, and so matrix-OPC can only be limitedly used, usually in small critical regions of a layout. We employ a Kolmogorov-Arnold network (KAN) for fast prediction of MEEF values. Only geometric features, which are convenient to extract, are used as KAN inputs. The distance and relative angle between segments i and j are chosen; the direction and length of the two segments are also included; local densities around j are extracted as a map. KAN model is adopted due to its use of fewer weight parameters compared to traditional models like ANN, which results in a reduced need for training data. Predicted MEEF values are arranged as MEEF matrices and a linear system is solved for unknown mask biases. Experimental results show that the proposed matrix-OPC with quick prediction of MEEF through KAN is 11 times faster than standard matrix-OPC, with insignificant loss in OPC quality (0.13nm increase of average EPE).