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Robust estimation of line width roughness parameters
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10.1116/1.3517718
/content/avs/journal/jvstb/28/6/10.1116/1.3517718
http://aip.metastore.ingenta.com/content/avs/journal/jvstb/28/6/10.1116/1.3517718
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Biased estimate shown as a function of length of the line for (a) different correlation length values with and (b) different roughness exponent values with . The roughness profiles were simulated with .

Image of FIG. 2.
FIG. 2.

SEM image of lines generated by litho-freeze-litho-etch DPL process (Ref. 10).

Image of FIG. 3.
FIG. 3.

(Color online) Illustration of the impact of (a) roughness amplitude, rms roughness, or standard deviation of line width from its mean , (b) autocorrelation length , and (c) roughness exponent on line edge roughness. Note the differences in the oscillatory behavior of the peaks in (b). In (c), the higher value of results in a smoother profile.

Image of FIG. 4.
FIG. 4.

Generalized framework of simulated and digitized SEM data. A typical SEM image can be generalized to consist of lines, where each line has numbers of measurements collected at a spacing . denotes the line width at location on line and denotes the average line width (or CD) of the line.

Image of FIG. 5.
FIG. 5.

(Color online) Graphical representation of the new sequence formed based on lagged version of the sequence . Note that the subscript ’s are dropped from and for clarity.

Image of FIG. 6.
FIG. 6.

(Color online) Graphical representation of the blocks under the block of blocks method. Note that the subscript ’s are dropped from and for clarity.

Image of FIG. 7.
FIG. 7.

(Color online) MSE in and as a function of the block length for (a) and (b) . Total MSE is the normalized sum of MSE of and . The roughness profiles were simulated with , , , and . The results shown here are from 200 sample Monte Carlo simulations.

Image of FIG. 8.
FIG. 8.

Optimal block length computed using the Politis–White method (Ref. 32) for (a) and (b) . The roughness profiles were simulated with , , , and . The block length computed here used the same exact data set as in Fig. 7.

Image of FIG. 9.
FIG. 9.

(Color online) Comparison of two methods of estimating WLS weights for shape parameters (a) and (b) based on 200 sample Monte Carlo experiments. The roughness profiles were simulated with , , , , and .

Image of FIG. 10.
FIG. 10.

(Color online) Comparison of four different estimates of based on 200 sample Monte Carlo simulations in three scenarios: (a) Ideal denotes the absence of any local CD variation and (b) Gaussian denotes the presence of a local Gaussian variation . The roughness profiles were simulated with , , , , and .

Image of FIG. 11.
FIG. 11.

(Color online) Sample fit of variogram using WLS and BBB. Solid line represents the fitted variogram (2.10). The dotted horizontal and vertical lines indicate estimated values of and , respectively.

Image of FIG. 12.
FIG. 12.

(Color online) Comparison of and for various NGL processes.

Image of FIG. 13.
FIG. 13.

(Color online) LWR in nm for various NGL processes. The dotted lines indicate ITRS roadmap values (Ref. 3).

Image of FIG. 14.
FIG. 14.

(Color online) Normalized LWR ( as % of CD) for various NGL processes.

Image of FIG. 15.
FIG. 15.

(Color online) Correlation length for various NGL processes. The dotted lines indicate ITRS roadmap values (Ref. 3).

Image of FIG. 16.
FIG. 16.

(Color online) Roughness exponent for various NGL processes. The ideal value for is 1.

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/content/avs/journal/jvstb/28/6/10.1116/1.3517718
2010-11-29
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Robust estimation of line width roughness parameters
http://aip.metastore.ingenta.com/content/avs/journal/jvstb/28/6/10.1116/1.3517718
10.1116/1.3517718
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