Fast 3d Lithography Simulation By Convolutional Neural Network

Thin mask model has been conventionally used in optical lithography simulation. In this model the diffracted waves from the mask are assumed to be Fourier transform of the mask pattern. In EUV (Extreme UltraViolet) lithography thin mask model is not valid because the absorber thickness is comparable to the mask pattern size. Fourier transformation is not suitable for calculating the diffracted waves from thick masks. Rigorous electromagnetic simulations such as finite-difference time-domain method, rigorous coupled wave analysis and 3D waveguide model are used to calculate the diffracted waves from EUV masks. However, these simulations are highly time consuming. We reduce the calculation time by adapting a CNN (Convolutional Neural Network).We calculate the far-field diffraction amplitudes from an EUV mask by using the 3D waveguide model. We divide the diffraction amplitudes into the thin mask amplitudes (Fourier transform of the mask pattern) and the residual mask 3D amplitudes. The incident angle dependence of the mask 3D amplitude for each diffraction order is fitted by using three parameters which represent the on-axis and the off-axis mask 3D effects. We train a CNN where the inputs are 2D mask patterns and the targets are the mask 3D parameters of all diffraction orders. After the training, the CNN successfully predict the mask 3D parameters. The CNN prediction is 5,000 times faster than the electromagnetic simulation.We extend the transmission cross coefficient formula to include the off-axis mask 3D effects. Our formula is applicable to arbitrary source shapes and defocus. We can use the eigen value decomposition method to accelerate the calculation.