Aerial Image Calculation Method Research Based On Transmission Cross Coefficient

A fast and accurate aerial image model plays an important role in the computational lithography field. Recent aberration metrology techniques and mask optimizations only extracts the linear aberration part in order to meet the requirement of computational time and memory. However, the linear approximation cannot satisfy the development of demands in metrology and optimization techniques. So the influence of quadratic aberration even higher order aberration attracts more attention in the industry. This thesis developed an aberration induced aerial image model based on TCC, which is the forward model in computational lithography for simulating the aberration coupling parts.A fast TCC algorithm was introduced, transforming the integral in frequency domain into products in space domain based on FFT. Decimation is used to release the constraints between the TCC sampling rate and source sampling rate. MATLAB simulation verified the fast algorithm.The aerial image forward model is developed based on the fast TCC algorithm. The study on the binary mask gave the one dimension and two dimension analytical expression respectively. The aerial image included complete TCC information by matrix operation. Simulation difference is on the order of 10-4 between MATLAB and lithography software PROLITH.A cross triple correlation (CTC) concept is introduced in the thesis. Based on the property of the CTC, the aerial image decomposed into the algebra sum of aberration induced aerial image including the quadratic model. This model can be used for analyzing the coupling term in aberration directly.The aberration induced aerial image is the extension of aerial image model. As the foundation of the computational lithography, it is applied to aberration metrology techniques of mask optimization techniques.