% % This file was created by the TYPO3 extension % bib % --- Timezone: CEST % Creation date: 2022-06-27 % Creation time: 09-59-45 % --- Number of references % 33 % @Article { FarchminHSWBBH2020, title = {Efficient Bayesian inversion for shape reconstruction of lithography masks}, journal = {Journal of Micro/Nanolithography, MEMS, and MOEMS}, year = {2020}, month = {5}, day = {5}, volume = {2}, number = {19}, pages = {1--11}, tags = {8.4,8.41,UQ,Scatter-Inv}, DOI = {10.1117/1.JMM.19.2.024001}, author = {Farchmin, N and Hammerschmidt, M and Schneider, P I and Wurm, M and Bodermann, B and B{\"a}r, M and Heidenreich, S} } @Article { GrossHB2016, title = {Impact of different stochastic line edge roughness patterns on measurements in scatterometry - a simulation study}, journal = {Measurement}, year = {2017}, month = {2}, day = {1}, volume = {98}, pages = {339--346}, tags = {8.4,8.41,Scatter-Inv}, DOI = {10.1016/j.measurement.2016.08.027}, author = {Gross, H and Heidenreich, S and B{\"a}r, M} } @Article { heidenreich2015bayesian, title = {Bayesian approach to the statistical inverse problem of scatterometry: Comparison of three surrogate models}, journal = {International Journal for Uncertainty Quantification}, year = {2015}, month = {1}, day = {8}, pages = {511}, tags = {8.41, Scatter-Inv, UQ}, DOI = {10.1615/Int.J.UncertaintyQuantification.2015013050}, author = {Heidenreich, S and Gross, H and B{\"a}r, M} } @Article { Bosse_TM2015, title = {Challenges in nanometrology: high precision measurement of position and size}, journal = {Technisches Messen}, year = {2015}, month = {1}, day = {6}, volume = {82}, pages = {346-358}, tags = {8.41, Scatter-Inv}, url = {10.1515/teme-2015-0002}, author = {Bosse, H and Bodermann, B and Dai, G and Fl{\"u}gge, J and Frase, C. G and Gross, H and H{\"a}{\ss}ler-Grohne, W and K{\"o}chert, P and K{\"o}nning, R and Scholze, F and Weichert, C} } @Article { Gross2015, title = {Modeling aspects to improve the solution of the inverse problem in scatterometry}, journal = {Cont. Dyn. S. - S}, year = {2015}, month = {1}, day = {3}, volume = {8}, pages = {497-519}, tags = {8.41,Scatter-Inv}, DOI = {10.3934/dcdss.2015.8.497}, author = {Gro{\ss}, H and Heidenreich, S and Henn, M-A and B{\"a}r, M and Rathsfeld, A} } @Article { Heidenreich2014a, title = {A surrogate model enables a Bayesian approach to the inverse problem of scatterometry}, journal = {J. Phys. Conf. Ser.}, year = {2014}, volume = {490}, number = {1}, pages = {012007}, tags = {8.41,Bayes,Scatter-Inv,Regression,8.42, UQ}, web_url = {http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012007}, publisher = {IOP Publishing}, language = {en}, ISSN = {1742-6596}, DOI = {10.1088/1742-6596/490/1/012007}, author = {Heidenreich, S and Gross, H and Henn, M-A and Elster, C and B{\"a}r, M} } @Article { Henn2014, title = {Improved reconstruction of critical dimensions in extreme ultraviolet scatterometry by modeling systematic errors}, journal = {Measurement Science and Technology}, year = {2014}, volume = {25}, number = {4}, pages = {044003}, tags = {8.41,Scatter-Inv,Scatterometrie, 8.42}, web_url = {http://iopscience.iop.org/article/10.1088/0957-0233/25/4/044003}, publisher = {IOP Publishing}, language = {en}, ISSN = {0957-0233}, DOI = {10.1088/0957-0233/25/4/044003}, author = {Henn, M-A and Gross, H and Heidenreich, S and Scholze, F and Elster, C and B{\"a}r, M} } @Article { Gross2014, title = {Modelling line edge roughness in periodic line-space structures by Fourier optics to improve scatterometry}, journal = {J. Europ.Opt. Soci.Rap. Pub.}, year = {2014}, volume = {9}, pages = {14003}, abstract = {In the present paper, we propose a 2D-Fourier transform method as a simple and efficient algorithm for stochastical and numerical studies to investigate the systematic impacts of line edge roughness on light diffraction pattern of periodic line-space structures. The key concept is the generation of ensembles of rough apertures composed of many slits, to calculate the irradiance of the illuminated rough apertures far away from the aperture plane, and a comparison of their light intensities to those of the undisturbed, {\^a}{\euro}™non-rough{\^a}{\euro}™ aperture. We apply the Fraunhofer approximation and interpret the rough apertures as binary 2D-gratings to compute their diffraction patterns very efficiently as the 2D-Fourier transform of the light distribution of the source plane. The rough edges of the aperture slits are generated by means of power spectrum density (PSD) functions, which are often used in metrology of rough geometries. The mean efficiencies of the rough apertures reveal a systematic exponential decrease for higher diffraction orders if compared to the diffraction pattern of the unperturbed aperture. This confirms former results, obtained by rigorous calculations with computational expensive finite element methods (FEM) for a simplified roughness model. The implicated model extension for scatterometry by an exponential damping factor for the calculated efficiencies allows to determine the standard deviation \(\sigma\){\textbackslash_} r of line edge roughness along with the critical dimensions (CDs), i.e., line widths, heights and other profile properties in the sub-micrometer range. First comparisons with the corresponding roughness value determined by 3D atomic force microscopy (3D AFM) reveal encouraging results.}, keywords = {Scatterometrie,Scatterometry,atomic force microscopy,line edge roughness,power spectrum density}, tags = {8.41,Scatter-Inv}, web_url = {http://www.jeos.org/index.php/jeos{\textbackslash_}rp/article/view/14003}, language = {en}, ISSN = {1990-2573}, DOI = {10.2971/jeos.2014.14003}, author = {Gro{\ss}, H and Heidenreich, S and Henn, M-A and Dai, G and Scholze, F and B{\"a}r, M} } @Phdthesis { Henn_Thesis, title = {Statistical Approaches to the Inverse Problem of Scatterometry}, year = {2013}, keywords = {8.41,8.42,Scatter-Inv,Scatterometrie}, tags = {8.41,Scatter-Inv}, school = {TU Berlin}, author = {Henn, M-A} } @Article { Bodermann2012, title = {Nanometrology at PTB in support of process control of nanoscale features in semiconductor manufacturing}, journal = {International Journal of Nanomanufacturing}, year = {2012}, volume = {8}, number = {1}, abstract = {We report on recent developments at the PTB in the field of dimensional nanometrology with a special focus on instrumentation, measurement and simulation methods, and standards which are used in semiconductor lithography manufacturing processes. Important dimensional measurands to be controlled precisely during the high volume manufacturing processes of nanoscale features (< 32 nm node) are the positions and widths of features on lithographic masks and wafers as well as the relative positioning or overlay of features.}, keywords = {Nanometrology}, tags = {8.41,Scatter-Inv}, author = {Bodermann, B and Scholze, F and Fl{\"u}gge, J and Gro{\ss}, H and Bosse, H} } @Article { Henn2012a, title = {Improved grating reconstruction by determination of line roughness in extreme ultraviolet scatterometry}, journal = {Opt. Lett.}, year = {2012}, volume = {37}, number = {24}, pages = {5229--5231}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, DOI = {10.1364/OL.37.005229}, author = {Henn, M-A and Heidenreich, S and Gro{\ss}, H and Rathsfeld, A and Scholze, F and B{\"a}r, M} } @Article { Henn2012, title = {A maximum likelihood approach to the inverse problem of scatterometry}, journal = {Optics Express}, year = {2012}, volume = {20}, number = {12}, pages = {12771-86}, abstract = {Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 - 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.}, tags = {8.41,Diffraction gratings,Metrology,Scatter-Inv,Scatterometrie,8.42}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=oe-20-12-12771{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {1094-4087}, DOI = {10.1364/OE.20.012771}, author = {Henn, M-A and Gross, H and Scholze, F and Wurm, M and Elster, C and B{\"a}r, M} } @Article { GrosHHRB2012, title = {Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry}, journal = {Appl. Opt.}, year = {2012}, volume = {51}, number = {30}, pages = {7384--94}, abstract = {We investigate the impact of line-edge and line-width roughness (LER, LWR) on the measured diffraction intensities in angular resolved extreme ultraviolet (EUV) scatterometry for a periodic line-space structure designed for EUV lithography. LER and LWR with typical amplitudes of a few nanometers were previously neglected in the course of the profile reconstruction. The two-dimensional (2D) rigorous numerical simulations of the diffraction process for periodic structures are carried out with the finite element method providing a numerical solution of the 2D Helmholtz equation. To model roughness, multiple calculations are performed for domains with large periods, containing many pairs of line and space with stochastically chosen line and space widths. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances is observed and established for different degrees of roughness. In particular, we obtain simple analytical expressions for the bias in the mean efficiencies and the additional uncertainty contribution stemming from the presence of LER and/or LWR. As a consequence this bias can easily be included into the reconstruction model to provide accurate values for the evaluated profile parameters. We resolve the sensitivity of the reconstruction from this bias by using simulated data with LER/LWR perturbed efficiencies for multiple reconstructions. If the scattering efficiencies are bias-corrected, significant improvements are found in the reconstructed bottom and top widths toward the nominal values.}, keywords = {8.41,Diffraction gratings,Metrology,Scatter-Inv,Scatterometrie}, tags = {8.41,Scatter-Inv}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=ao-51-30-7384{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {1539-4522}, DOI = {10.1364/AO.51.007384}, author = {Gro{\ss}, H and Henn, M-A and Heidenreich, S and Rathsfeld, A and B{\"a}r, M} } @Inbook { Gross2012, title = {Stochastic modeling aspects for an improved solution of the inverse problem in scatterometry}, year = {2012}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, editor = {F. Pavese, M. B{\"a}r, J.-R. Filtz, A. B. Forbes, L. Pendrill, K. Shirono}, publisher = {World Scientific New Jersey}, booktitle = {Advanced Mathematical \& Computational Tools in Metrology and Testing IX}, author = {Gro{\ss}, H and Henn, M-A and Rathsfeld, A and B{\"a}r, M} } @Inproceedings { Bodermann2012a, title = {First steps towards a scatterometry reference standard}, year = {2012}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {SPIE Proc.}, author = {Bodermann, B and Hansen, P-E and Burger, S and Henn, M-A and Gross, H and Scholze, F and Endres, J and Wurm, M} } @Incollection { Bodermann2011a, title = {Charakterisierung von Nanostrukturen aund Substraten der Halbleiterindustrie}, year = {2011}, keywords = {8.41,Nanometrology}, tags = {8.41, Scatter-Inv}, booktitle = {PTB-Mitteilungen 2/2011 ''Themenschwerpunkt Nanometrologie''}, author = {Bodermann, B and Fl{\"u}gge, J and Gro{\ss}, H} } @Inproceedings { Bodermann2011, title = {Joint Research on Scatterometry and AFM Wafer Metrology}, year = {2011}, volume = {1395}, number = {1}, pages = {319--323}, abstract = {Supported by the European Commission and EURAMET, a consortium of 10 participants from national metrology institutes, universities and companies has started a joint research project with the aim of overcoming current challenges in optical scatterometry for traceable linewidth metrology. Both experimental and modelling methods will be enhanced and different methods will be compared with each other and with specially adapted atomic force microscopy (AFM) and scanning electron microscopy (SEM) measurement systems in measurement comparisons. Additionally novel methods for sophisticated data analysis will be developed and investigated to reach significant reductions of the measurement uncertainties in critical dimension (CD) metrology. One final goal will be the realisation of a wafer based reference standard material for calibration of scatterometers.}, keywords = {8.41,Scatterometrie}, tags = {8.41, Scatter-Inv}, web_url = {http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3657910}, booktitle = {AIP Conf. Proc.}, ISSN = {1551-7616}, DOI = {10.1063/1.3657910}, author = {Bodermann, B and Buhr, E and Danzebrink, H-U and B{\"a}r, M and Scholze, F and Krumrey, M and Wurm, M and Klapetek, P and Hansen, P-E and Korpelainen, V and van Veghel, M and Yacoot, A and Siitonen, S and El Gawhary, O and Burger, S and Saastamoinen, T and Seiler, D G and Diebold, A C and McDonald, R and Chabli, A and Secula, E M} } @Inproceedings { Henn2011, title = {Improved geometry reconstruction and uncertainty evaluation for extreme ultraviolet (EUV) scatterometry based on maximum likelihood estimation}, year = {2011}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {SPIE Proc. 80830N}, author = {Henn, M-A and Gro{\ss}, H and Scholze, F and Elster, C and B{\"a}r, M} } @Article { Gross2010, title = {Investigations on a robust profile model for the reconstruction of 2D periodic absorber lines in scatterometry}, journal = {J. Europ. Opt. Soc. Rap. Public.}, year = {2010}, volume = {5}, pages = {10053}, abstract = {Scatterometry as a non-imaging indirect optical method in wafer metrology is applicable to lithography masks designed for extreme ultraviolet (EUV) lithography , where light with wavelengths of about 13.5 nm is applied. The main goal is to reconstruct the critical dimensions (CD) of the mask, i.e., profile parameters such as line width, line height, and side-wall angle, from the measured diffracted light pattern and to estimate the associated uncertainties. The numerical simulation of the diffraction process for periodic 2D structures can be realized by the finite element solution of the two-dimensional Helmholtz equation. The inverse problem is expressed as a non-linear operator equation where the operator maps the sought mask parameters to the efficiencies of the diffracted plane wave modes. To solve this operator equation, the deviation of the measured efficiencies from the ones obtained computationally is minimized by a Gauss-Newton type iterative method. In the present paper, the admissibility of rectangular profile models for the evaluations of CD uniformity is studied. More precisely, several sets of typical measurement data are simulated for trapezoidal shaped EUV masks with different mask signatures characterized by various line widths, heights and side-wall angles slightly smaller than 90 degree. Using these sets, but assuming rectangular structures as the basic profiles of the numerical reconstruction algorithm, approximate line height and width parameters are determined as the critical dimensions of the mask. Finally, the model error due to the simplified shapes is analyzed by checking the deviations of the reconstructed parameters from their nominal values.}, keywords = {Scatterometrie,critical dimensions (CD),inverse problem,profile model,scatterometry}, tags = {8.41,Scatter-Inv}, web_url = {http://www.jeos.org/index.php/jeos{\textbackslash_}rp/article/view/10053}, language = {en}, ISSN = {1990-2573}, DOI = {10.2971/jeos.2010.10053}, author = {Gross, H and Richter, J and Rathsfeld, A and B{\"a}r, M} } @Article { Gross2009, title = {Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates}, journal = {Measurement Science and Technology}, year = {2009}, volume = {20}, number = {10}, pages = {105102}, keywords = {8.41,Scatter-EUV,Scatter-Inv,Scatterometrie}, tags = {8.41,Scatter-Inv}, web_url = {http://iopscience.iop.org/article/10.1088/0957-0233/20/10/105102}, publisher = {IOP Publishing}, language = {en}, ISSN = {0957-0233}, DOI = {10.1088/0957-0233/20/10/105102}, author = {Gross, H and Rathsfeld, A and Scholze, F and B{\"a}r, M} } @Inproceedings { Henn2009, title = {On numerical reconstruction of lithographic masks in DUV scatterometry}, year = {2009}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {SPIE Proc. 7390}, author = {Henn, M-A and Model, R and B{\"a}r, M and Wurm, M and Bodermann, B and Rathsfeld, A and Gro{\ss}, H} } @Url { DIPOG, title = {DIPOG Homepage}, year = {2009}, tags = {8.41,Scatter-Inv}, web_url = {http://www.wias-berlin.de/software/DIPOG}, web_url_date = {2015-11-25}, author = {Elschner, J and Hinder, H and Rathsfeld, A and Schmidt, G} } @Article { Model2008, title = {A scatterometry inverse problem in optical mask metrology}, journal = {Journal of Physics: Conference Series}, year = {2008}, volume = {135}, number = {1}, pages = {012071}, keywords = {8.41,Scatter-Inv,Scatterometrie}, tags = {8.41,Scatter-Inv}, web_url = {http://iopscience.iop.org/article/10.1088/1742-6596/135/1/012071}, publisher = {IOP Publishing}, language = {en}, ISSN = {1742-6596}, DOI = {10.1088/1742-6596/135/1/012071}, author = {Model, R and Rathsfeld, A and Gross, H and Wurm, M and Bodermann, B} } @Article { Gross2008, title = {Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures}, journal = {Waves in Random and Complex Media}, year = {2008}, volume = {18}, number = {1}, pages = {129--149}, abstract = {We discuss numerical algorithms for the determination of periodic surface structures from light diffraction patterns. With decreasing details of lithography masks, increasing demands on metrology techniques arise. Scatterometry as a non-imaging indirect optical method is applied to simple periodic line structures in order to determine parameters like side-wall angles, heights, top and bottom widths and to evaluate the quality of the manufacturing process. The numerical simulation of diffraction is based on the finite element solution of the Helmholtz equation. The inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. Restricting the class of gratings and the set of measurements, this inverse problem can be reformulated as a non-linear operator equation in Euclidean spaces. The operator maps the grating parameters to special efficiencies of diffracted plane-wave modes. We employ a Gau{\ss} {\^a}{\euro}“Newton type iterative method to solve this operator equation. The reconstruction ...}, keywords = {8.41,Scatter-Inv,Scatterometrie}, tags = {8.41,Scatter-Inv}, web_url = {http://www.tandfonline.com/doi/abs/10.1080/17455030701481823}, publisher = {Taylor {\&} Francis Group}, language = {en}, ISSN = {1745-5030}, DOI = {10.1080/17455030701481823}, author = {Gro{\ss}, H and Rathsfeld, A} } @Inproceedings { Gross_Model08, title = {Computational methods estimating uncertainties for profile reconstruction in scatterometry}, year = {2008}, pages = {6995OT-1 – 6995OT-9}, tags = {8.41, Scatter-Inv}, publisher = {Proc. SPIE6995}, author = {Gross, H and Rathsfeld, A and Scholze, F and Model, R and B{\"a}r, M} } @Inproceedings { Gross2008, title = {Modellbildung, Bestimmung der Messunsicherheit und Validierung f{\"u}r diskrete inverse Probleme am Beispiel der Scatterometrie}, year = {2008}, pages = {337--346}, tags = {8.41, Scatter-Inv}, booktitle = {Sensoren und Messsystem 2008}, author = {Gro{\ss}, H and Model, R and Scholze, F and Wurm, M and Bodermann, B and B{\"a}r, M and Rathsfeld, A} } @Incollection { Gross_Rathsf97, title = {Intelligent solutions for complex problems}, year = {2007}, tags = {8.41, Scatter-Inv}, booktitle = {Annual Research Report 2007}, author = {Gross, H and Rathsfeld, A} } @Inproceedings { Wurm2007, title = {Numerical analysis of DUV scatterometry on EUV masks}, year = {2007}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {SPIE Proc. 6617}, author = {Wurm, M and Bodermann, B and Model, R and Gro{\ss}, H} } @Inproceedings { Gross2007, title = {Optimal sets of measurement data for profile reconstruction in scatterometry}, year = {2007}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {SPIE Proc. 6617}, author = {Gro{\ss}, H and Rathsfeld, A and Scholze, F and B{\"a}r, M and Dersch, U} } @Article { Gross2006, title = {Mathematical modelling of indirect measurements in scatterometry}, journal = {Measurement}, year = {2006}, volume = {39}, number = {9}, pages = {782--794}, keywords = {8.41}, tags = {8.41, Scatter-Inv}, web_url = {http://www.researchgate.net/publication/223944217{\textbackslash_}Mathematical{\textbackslash_}modelling{\textbackslash_}of{\textbackslash_}indirect{\textbackslash_}measurements{\textbackslash_}in{\textbackslash_}scatterometry}, ISSN = {02632241}, DOI = {10.1016/j.measurement.2006.04.009}, author = {Gro{\ss}, H and Model, R and B{\"a}r, M and Wurm, M and Bodermann, B and Rathsfeld, A} } @Incollection { Model2006b, title = {Inverse Methoden f{\"u}r indirekte Messungen und Partielle-Differentialgleichungs-Modelle}, year = {2006}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {PTB-Mitteilungen 3/2006}, author = {Model, R and Gro{\ss}, H and Haberkorn, W and B{\"a}r, M} } @Incollection { Gross2006a, title = {Sensitivity Analysis for Indirect Measurement in Scatterometry and the Reconstruction of Periodic Grating Structures}, year = {2006}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {WIAS Preprint No. 1164}, author = {Gro{\ss}, H and Rathsfeld, A} } @Inproceedings { Wurm2006, title = {Untersuchungen zur Eignung der EUV-Scatterometrie zur quantitativen Charakterisierung periodischer Strukturen auf Photolithographiemasken}, year = {2006}, keywords = {8.41,Scatter-Inv}, tags = {8.41,Scatter-Inv}, booktitle = {DGaO-Proc.}, author = {Wurm, M and Bodermann, B and Scholze, F and Laubis, C and Gro{\ss}, H and Rathsfeld, A} }