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Comparison of three TCC calculation algorithms for partially coherent imaging simulation

Three kinds of TCC (transmission cross coefficient) calculation algorithms used for partially coherent imaging simulation, including the integration algorithm, the analytical algorithm, and the matrix-based fast algorithm, are reviewed for their rigorous formulations and numerical implementations. The accuracy and speed achievable using these algorithms are compared by simulations conducted on several mainstream illumination sources commonly used in current lithographic tools. Simulation results demonstrate that the integration algorithm is quite accurate but time consuming, while the matrix-based fast algorithm is efficient but its accuracy is heavily dependent on simulation resolution. The analytical algorithm is both efficient and accurate but not suitable for arbitrary optical systems. It is therefore concluded that each TCC calculation algorithm has its pros and cons with a compromise necessary to achieve a balance between accuracy and speed. The observations are useful in fast lithographic simulation for aerial image modeling, optical proximity correction (OPC), source mask optimization (SMO), and critical dimension (CD) prediction.