54
LITHOGRAPHY
Results for the uniformity test patterns. The model fit is in
Using a single Gaussian density convolution term good agreement with the measured data, and the
and a second order non uniformity polynomial, the range of model residual is significantly smaller
long range model was fitted to all of the long range than the overall range of the input measurement
measurements. The resulting model fit is shown in data. The data suggests that using this mask
Figure 4. The left side of the plot shows the fit for process model the ΔCD variation could be reduced
the density loading test patterns, and the right side by 62% in terms of root mean square (r. m. s.)
error, and by 54% in terms of error range.
Different VEB models were compared over the
entire data set and the simplest model capable of
fitting the data with minimal residual systematic
errors was used. Compared to a constant bias
model, the best model reduces the r. m. s. CD
variation of the adjusted proximity calibration data
by 58%. Figure 5 gives the residual fit error for
line/space features to demonstrate the significant
reduction in the error range possible for various
one-dimensional proximity test structures, as well
as for end to end features and more complex two-
dimensional test patterns. As expected, the largest
residual model fit errors appear on the end to end
features and complex two dimensional patterns.
Figure 4. Calibrated long-range model fit shown in terms of measured
ΔCD, model ΔCD, and their difference Conclusions
The results show that long range mask process non
uniformity and pattern density loading account for
the majority of long range mask process errors. In
our example, compensation for pattern density
loading and mask process non uniformity reduced
mask CD error by 62% as measured on a test
mask. The results also confirm that models that
use a variable etch bias are appropriate for
correction of short range errors. Proximity
correction can reduce mask CD error range by
58% based on proximity data. Independent mask
process correction can reduce overall CD errors by
about 2 times compared to conventional mask
processing. The methodology can also be extended
to include separate exposure and resist models in
addition to etch. CD error can be further reduced
Figure 5. Relative residual proximity error for space and line CDs in by improving the accuracy of measurement data
different one and two dimensional test patterns and applying more sophisticated model forms.
REFERENCES:
1. http://www.itrs.net/Links/2007Winter/2007_Winter_Presentations/09_Litho_2007_JP.pdf
2. J. S. Cho, S. H. Baek, K.-H. Nam, H. J. Cho, D. Courboin, S.-H. Jeong, I.-S. Lee, C. Shin, H.-S. Kim, “Fogging and pattern
loading effect by writing strategy, “Proceedings of the SPIE, “ vol. 4754, pp. 205-16, 2002.
3. H. Lee, S.-H. Yang, J.-H. Park, S.-Y. Moon, S.-W. Choi, and J.-M. Sohn, “Dose-modulation-induced mask CD error on
simultaneous correction of fogging and loading effect, “ Proceedings of the SPIE, vol. 5256, pp. 666-72, 2003.
4. J. Kotani, T. Yanagihara, E. Umeda, T. Senou, Y. Kikuchi, T. Tanaka, and Y. Okuda, “Mask CD uniformity improvement by dry
etching loading effect correction, “ Proceedings of the SPIE, vol. 5256, pp. 758-65, 2003.
5. Y. Granik, “Dry etch proximity modelling in mask fabrication, “ Proceedings of the SPIE, vol. 5130, pp. 86-91, 2003.
6. [RTF bookmark start: }_Ref144558514[RTF bookmark end: }_Ref144558514P. Buck, F. Kalk, K. Nakagawa, “Methods for
analysing and compensating for systematic mask CD errors “, Solid State Technology, December 2006.
7. T. Brunner, et al., “A new long-range proximity effect in chemically amplified photoresist processes: Chemical flare, “ Proceedings
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8. Y. Granik, “Correction for etch proximity: new models and applications, “ Proceedings of the SPIE, vol. 4346, pp. 98-112, 2001.
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www.euroasiasemiconductor.com November 2008
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