Fast and accurate laser bandwidth modeling of optical proximity effects

Lalovic, Ivan; Kritsun, Oleg; Bendik, Joeseph; Smith, Mark D.; Sallee, Chris; Farrar, Nigel R.

doi:10.1117/12.746594

Cited by 11 publications

(7 citation statements)

References 9 publications

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“…The Gaussian analytic form, or a more complex combinations of Gaussian and modified Lorentzian, have also been suggested [12] as refinements of the above that may improve the fitting of modern laser spectra. However, as discussed previously, [13] even the best fits to the measured spectrum data using the modified Lorentzian or Gaussian fail to describe the behavior of real laser spectra particularly in the region of the tails. Although the smoothly-varying analytic forms can reduce the simulation run-time and are simple to use with a parametric representation of the bandwidth and spectral shape, the lithographic imaging differences compared to using physically-measured spectra (through focus and pitch) can be significant.…”

Section: Modified Lorentzian Gaussian Fitting and Physical Approximamentioning

confidence: 91%

“…These findings are in agreement with results we reported previously, where we also determined that the 23-point LSA optimized to minimize aerial-image CD errors also maintains sub 0.25nm TIR (or 0.05nm RMS) for full diffusion-reaction resist models. [13] In Figure 5, we summarize the CD accuracy, compared again to the full factory-measured spectra for the XLA 300 laser, as a function of down-sampling different bandwidth model assumptions. As discussed previously, the best Gaussian analytic fit to the factory-measured XLA 300 spectra fails to approach the 1000-point measured input due to the difficulty in matching the intensity in the spectrum tails and the accuracy of the Gaussian does not improve significantly as the number of sampling points are increased.…”

Section: Down-sampling Of the Physical Spectrum Approximationsmentioning

confidence: 99%

“…We have previously described a numerical approximation method, [13] which is based on the physical spectrophotometry measurement of the excimer sources, which results in sub-0.25nm (TIR) residual errors compared to fully-sampled spectra. The resulting physically-based approximations are comprised of 21 to 23 points and have been shown to maintain predictability over a range of pitch and focus settings as well as a range of numerical apertures and illumination conditions.…”

Section: Down-sampling Of the Physical Spectrum Approximationsmentioning

confidence: 99%

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Defining a physically accurate laser bandwidth input for optical proximity correction (OPC) and modeling

Lalovic¹,

Kritsun

McGowan

et al. 2008

Photomask Technology 2008

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In this study, we discuss modeling finite laser bandwidth for application to optical proximity modeling and correction. We discuss the accuracy of commonly-used approximations to the laser spectrum shape, namely the modified Lorentzian and Gaussian forms compared to using measurement-derived laser fingerprints. In this work, we show that the use of the common analytic functions can induce edge placement errors of several nanometers compared to the measured data and therefore do not offer significant improvement compared to the monochromatic assumption. On the other hand, the highlyaccurate laser spectrum data can be reduced to a manageable number of samples and still result in sub 0.5nm error through pitch and focus compared to measured spectra. We have previously demonstrated that a 23-point approximation to the laser data can be generated from the spectrometry data, which results in less than 0.1nm RMS error even over varied illumination settings. We investigate the further reduction in number of spectral samples down to five points and consider the resulting accuracy and model-robustness tradeoffs. We also extend our analysis as a function of numerical aperture and illumination setting to quantify the model robustness of the physical approximations. Given that adding information about the laser spectrum would primarily impact the model-generation run-times and not the run-times for the OPC implementation, these techniques should be straightforward to integrate with current full-chip OPC flows. Finally, we compare the relative performance of a monochromatic model, a 5-point laser-spectral fingerprint, and two Modified Lorentzian fits in a commercial OPC simulator for a 32nm logic lithography process. The model performance is compared at nominal process settings as well as through dose, focus and mask bias. Our conclusions point to the direction for integration of this approach within the framework of existing EDA tools and flows for OPC model generation and process-variability verification.

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Section: Modified Lorentzian Gaussian Fitting and Physical Approximamentioning

confidence: 91%

Section: Down-sampling Of the Physical Spectrum Approximationsmentioning

confidence: 99%

Section: Down-sampling Of the Physical Spectrum Approximationsmentioning

confidence: 99%

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Defining a physically accurate laser bandwidth input for optical proximity correction (OPC) and modeling

Lalovic¹,

Kritsun

McGowan

et al. 2008

Photomask Technology 2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…It can sometimes fit the spectrum better than the modified Lorentzian in the center region of the spectrum [8]. It also does not fit the tails of the spectrum well, however.…”

Section: Laser Bandwidth Modelingmentioning

confidence: 96%

Modeling laser bandwidth for OPC applications

et al. 2009

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With the push toward 32 nm half-pitch, OPC models will need to account for a wider range of sources of imaging variability in order to meet the CD budget requirements. The effects of chromatic aberration on imaging have been a recent area of interest but little work has been done to include this effect in OPC models. Chromatic aberrations in the optical system give rise to a blurring of the intensity distribution in the imaging plane even for highly line-narrowed immersion laser sources. The resulting focus blur can introduce a feature-dependent CD bias of several nanometers. Usually, the empirical components of the resist model can reduce or completely compensate for this imaging effect. However, it is not well known if including a more physical image model over a large range of laser bandwidth conditions will improve the OPC accuracy or process-variability robustness.This study demonstrates the correlation of physical laser bandwidth perturbations with perturbations of the optical model in Calibre. The laser bandwidth is experimentally perturbed to obtain several sets of CD measurements for different bandwidths. These are then used in model calibration with the corresponding perturbation in the optical model. Finally, we quantify the improvement in model accuracy obtained when including an input of laser bandwidth.

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“…We also demonstrate that usage of actual laser spectrum provides better correlation with experimental bandwidth tuning sensitivities than the commonly used modified Lorentzian line shape assumption, which is in agreement with previous findings. [5] All simulation and modeling is performed on Brion Technologies' Tachyon platform.…”

Section: Introductionmentioning

confidence: 99%

Improved model predictability by machine data in computational lithography and application to laser bandwidth tuning

Hunsche¹,

Zhao²,

Xie³

et al. 2009

SPIE Proceedings

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Computational lithography (CL) is becoming more and more of a fundamental enabler of advanced semiconductor processing technology, and new requirements for CL models are arising from new applications such as model-based process tuning. In this paper we study the impact of realistic machine parameters that can be incorporated in a modern CL model, and provide an experimental assessment of model improvements with respect to prediction of scanner tuning effects. The data demonstrates improved model accuracy and prediction by inclusion of scanner-type specific modeling capabilities and machine data in the CL model building process. In addition to scanner effects, we study laser bandwidth tuning effects and the accuracy of corresponding model predictions by comparison against experimental data. The data demonstrate that the models predict well wafer CD variations resulting from laser BW tuning. We also find that using realistic spectral density distribution of the laser can provide more accurate results than the commonly assumed modified Lorentzian line shape.

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Fast and accurate laser bandwidth modeling of optical proximity effects

Cited by 11 publications

References 9 publications

Defining a physically accurate laser bandwidth input for optical proximity correction (OPC) and modeling

Defining a physically accurate laser bandwidth input for optical proximity correction (OPC) and modeling

Modeling laser bandwidth for OPC applications

Improved model predictability by machine data in computational lithography and application to laser bandwidth tuning

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