Lithography mask design through mask functional optimization and spatial frequency analysis
In an electronic design automation technique for optical proximity correction, a mask is represented by a function with an exact analytical form over a mask region. Using the physics of optical projection, a solution based on a spatial frequency analysis is determined. Spatial frequencies above a cutoff are determined by the optical system do not contribute to the projected image. Spatial frequencies below this cutoff affect the print (and the mask), while those above the cutoff only affect the mask. Frequency components in the function below this cutoff frequency may be removed, which will help to reduce computational complexity.
1. A method comprising:
partitioning a layout mask into a plurality of regions, each region comprising geometric shapes;
generating a two-dimensional pixel representation of a region;
generating an analytical function to represent the pixel representation of the region;
performing a transformation on the analytical function to obtain a frequency space representation of the analytical function of the region; and
based on the frequency space representation, removing, by a computer, low frequency components of the analytical function of the region.
2. The method of claim 1 wherein the removing is performed, at least in part, by a central processing unit (CPU) of the computer.
3. The method of claim 1 wherein the removing is performed, at least in part, by a graphics processing unit (GPU) of the computer.
4. The method of claim 1 comprising:
after the removing the low frequency components, performing an inverse transformation to obtain a first finalized mask.
5. The method of claim 4 comprising:
after performing the inverse transformation, generating subresolution assist features to obtain a second finalized mask.
6. The method of claim 1 wherein the layout mask is in a spatial space.
7. The method of claim 1 wherein the transformation uses a Fourier basis.
8. The method of claim 1 wherein the transformation uses a wavelet basis.
9. The method of claim 1 wherein the frequency space representation comprises frequencies up to a multiple of a cutoff frequency.