Full spectral analysis of line width roughness

Leunissen, L. H. A.; Lorusso, Gian; Ercken, Monique; Croon, J.A.; Yang, Hu; Azordegan, A.; DiBiase, Tony

doi:10.1117/12.600185

Cited by 22 publications

(29 citation statements)

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“…The fact shows that the LWR of photoresist fine lines of this study has a component with a correlation length approximately of 2870 nm in addition to the short-rangecorrelated component ͑ Х 35 nm͒ that was commonly observed in previous reports. 22,23,31,33 Besides, we notice a trace of oscillatory structure around k =5ϫ 10 −3 nm −1 in Fig. 7.…”

Section: Resultsmentioning

confidence: 78%

“…From a statistical standpoint, the experimental variance var͑w͒ meas of w needs to be calculated by 22,23,33 …”

Section: B Variance Of Nonstochastic Lwrmentioning

confidence: 99%

“…The variance of the intradevice averages depends not only on a population variance of the sizes but also both on the correlation length of the size variation and on the orthogonal-size. [21][22][23][24] For example, the variation in gate lengths of MOSFETs depends on their channel width, which is measured orthogonally to the gate length. Because of this orthogonal-size dependence, the intradevice averages get more widely distributed with the scaling down, and the threshold voltages are further scattered as a result.…”

Section: Introductionmentioning

confidence: 99%

“…Conventionally, the variance of widths has been evaluated based on the sample means and sample variances of the data measured by using the CD-SEMs. [22][23][24] As to the correlation length, most of previous works analyzed autocorrelation functions ͑ACFs͒ or power spectral densities ͑PSDs͒. 17,22,23,26,31 This study adopts a PSD approach because the ACF is not good at decomposing LWR components that have different correlation lengths.…”

Section: Introductionmentioning

confidence: 99%

“…[22][23][24] As to the correlation length, most of previous works analyzed autocorrelation functions ͑ACFs͒ or power spectral densities ͑PSDs͒. 17,22,23,26,31 This study adopts a PSD approach because the ACF is not good at decomposing LWR components that have different correlation lengths. 32 That said, the conventional PSD method had a fatal fault that experimental PSDs were not completely fitted by theoretical ones even in the case when the LWR parameters used in the calculations were appropriate.…”

Section: Introductionmentioning

confidence: 99%

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Spectral analysis of line edge and line-width roughness with long-range correlation

Hiraiwa

Nishida

2010

Journal of Applied Physics

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Large-scale integrations (LSIs) are facing an ever-growing problem of device variability. One of the origins that cause the variability is line-width roughness (LWR) caused by line edge roughness (LER). Accurate characterization of the LWR plays an essential role in controlling the LWR. To do this, we report a methodology, named the “assembly method,” that enables to analyze LWR statistics beyond the conventional correlation length limit, basing on the previous “patchwork” method and recent discrete power spectral density (PSD) method. The methodology virtually assembles a long line by gathering line segments that are randomly scattered on a single line or equally processed different lines. The virtual lines are repeatedly assembled by randomly changing the combination of the segments and the order of the gathered segments while permitting overlaps of the segments between the assembled lines. Squared Fourier transforms of their widths are averaged over the assembled lines to obtain the PSD. By these steps, the statistical noise, which is inherent to experimental PSDs, is markedly reduced. Furthermore, to extract LWR statistics by comparing experimental and theoretical PSDs, we derived an analytic formula of the assembled-line PSD. In the derivation, the randomness of the segment collections played a key role. The PSDs calculated using the formula almost completely fitted experimental PSDs that were obtained by the assembly method. The parameters used in the best-fitted calculation revealed that the photoresist LWR of this study contained a component that had a correlation length of 2780 nm in addition to the previously reported LWR of 35 nm. The LWR variance of the component accounted for approximately 10% of the total variance. The formula also enabled us to evaluate the accuracy of experimentally obtained averages of widths. We find two distinct features in the PSDs by the assembly method. One is the oscillatory structure that shows up in the case when the correlation length is larger than half the length of the segments. A trace of this structure was actually observed in the experimental PSDs of this study. The other is the spikes that are periodically observed as a function of wave number. The spikes originate from a nonstochastic width variation that exists in all the segments in common. Their intensity is proportional to the number of gathered segments in the assembled lines. Because the spikes are excluded from the analysis, the LWR parameters determined by the assembly method are not affected by the nonstochastic variation, unlike the conventional methods. By all these results, we confirm that the assembly method of this study extends the upper limit of analyzable correlation lengths by a factor of approximately 20 and enhances the accuracy as well. This feature also has a practical significance that the widely observed LWR with a correlation length of approximately 35 nm can be analyzed by the assembly method using a conventional critical-dimension scanning-electron-microscope, without resorting to a specially designed one. Accordingly, the method will be a key tool for investigating LER and LWR in developing and manufacturing LSIs. It will also help analyze other stochastic processes in many research and development settings.

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Section: Resultsmentioning

confidence: 78%

“…From a statistical standpoint, the experimental variance var͑w͒ meas of w needs to be calculated by 22,23,33 …”

Section: B Variance Of Nonstochastic Lwrmentioning

confidence: 99%