Ultra-fast aerial image simulation algorithm using wavelength scaling and fast Fourier transformation to speed up calculation by more than three orders of magnitude

An ultra-fast image simulation algorithm is proposed. The new algorithm uses full fast-Fourier-transform (FFT) to calculate the aerial image intensity. The wavelength, 193 nm, was scaled to a number of powers of 2, through scaling the mask with a scaling factor derived from the discrete Fourier transform (FT) format. The mask can then be transformed to the diffraction spectrum in terms of spatial frequency using the FFT algorithm. Similarly, this mask diffraction spectrum can be inverse transformed to the aerial-image by using the inverse-FFT algorithm. The image is finally scaled back to the original image amplitude of the original wavelength and squared to the image intensity. Comparing to the original FT, there is a 4000 × to 5000 × computation speed improvement with only about 3% intensity deviation. This algorithm provides an efficient engine for lithography optimization.