Mask roughness induced LER: a rule of thumb -- paper Page: 4 of 9
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Fig. 2. A comparison schematic of the traditional method and the simplified method to get the mask roughness induced LER.
We carried out the simulations through focus for 4 different disk illuminations: coherence factors a = 0.15, 0.25, 0.50,
and 0.75. We then extracted the LER in SuMMIT [14], using only nested features for LER analysis, avoiding the outer
200 nm border. We took care to set the binary threshold properly for each sigma value to provide proper sizing of the 50
nm lines at best focus. This was done for each random realization of each mask to build up the statistics. Assuming the
process is ergodic, we could have just as easily used a larger mask with larger lengths of lines instead of numerous
independent realizations. However, due to memory constraints, our chosen method is the preferred one. The LER data
from this traditional approach is now ready for comparison to the new simplified method.
For the simplified method, we modeled each random realization of the clear-field mask under the same illumination
conditions to get the clear-field speckle statistics. We then calculated the ILS using fast 1D aerial-image simulations in
PROLITH [12] for our pattern of lines and spaces for each illumination condition. Finally, using the proposed solution
to mask roughness induced LER described above, we analytically calculated the LER.
It is important to note that the power of the simplified approach lies in the one-time intensive aerial-image simulations of
the clear-field speckle statistics. Once calculated, they are done. By using feature-specific ILS to couple clear-field
speckle to LER in the aerial image, we can analytically extend the LER analysis to an arbitrary set of features with great
ease.
5. VERIFICATION OF THE SIMPLIFIED MODEL
Fig. 3 shows simulated LER results for one illumination setting, a = 0.15. The trends for each correlation length show
fairly constant slopes through focus with no crossover between them. This pattern is consistent for all other
illuminations as well. It is therefore possible, for clarity, to look at just one defocus setting for comparison of the
simulated LER to the simplified approach.
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McClinton, Brittany & Naulleau, Patrick. Mask roughness induced LER: a rule of thumb -- paper, article, March 12, 2010; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc1013103/m1/4/: accessed May 5, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.