Analysis of diffraction orders including mask topography effects for OPC optimization

In recent years, model-based OPC has been an essential technique to achieve better yield or even if resolution itself. Currently available OPC software employs optical simulation with thin-mask model or approximated model. However for 45nm-node and beyond, it is well-known that there is difference between 2D simulation by calculating thin-mask model and 3D rigorous simulation by calculating thick-mask model such as FDTD or RCWA. Especially, it is expected that larger incident angle of off-axis illumination and higher aspect ratio of mask topography lead larger differences between them. On the other hand, thick-mask model OPC consumes much computation time, so it will not be practical. The difference of these two simulation models is caused from the effect of mask topography and behavior of electromagnetic field on 3D rigorous simulation. The effect of mask topography also creates the difference of diffraction amplitude and phase at Fourier optics stage or imaging from diffraction. Then such diffraction orders with thin and thick-mask model was focused and evaluated at first approach. In this paper, the difference of diffraction orders' amplitude between two simulation models caused by illumination angle, mask materials is analyzed and then the difference of OPC bias for various pattern pitches is presented. Then from this result, the compensation methodology of the diffraction differences is discussed and simple compensation approach for OPC to improve the accuracy with thin-mask model's OPC is demonstrated. As a result, one new solution for OPC without additional computer time is proposed.