This file was created by the TYPO3 extension bib --- Timezone: CET Creation date: 2023-02-01 Creation time: 04-39-35 --- Number of references 33 article FarchminHSWBBH2020 Journal of Micro/Nanolithography, MEMS, and MOEMS 2020 5 5 2 19 1--11 8.4,8.41,8.43,UQ,Scatter-Inv 10.1117/1.JMM.19.2.024001 NFarchmin MHammerschmidt P ISchneider MWurm BBodermann MBär SHeidenreich article GrossHB2016 Measurement 2017 2 1 98 339--346 8.4,8.41,Scatter-Inv 10.1016/j.measurement.2016.08.027 HGross SHeidenreich MBär article heidenreich2015bayesian International Journal for Uncertainty Quantification 2015 1 8 511 8.41, Scatter-Inv, UQ 10.1615/Int.J.UncertaintyQuantification.2015013050 SHeidenreich HGross MBär article Bosse_TM2015 Technisches Messen 2015 1 6 82 346-358 8.41, Scatter-Inv 10.1515/teme-2015-0002 HBosse BBodermann GDai JFlügge C. GFrase HGross WHäßler-Grohne PKöchert RKönning FScholze CWeichert article Gross2015 Cont. Dyn. S. - S 2015 1 3 8 497-519 8.41,Scatter-Inv 10.3934/dcdss.2015.8.497 HGroß SHeidenreich M-AHenn MBär ARathsfeld article Heidenreich2014a J. Phys. Conf. Ser. 2014 490 1 012007 8.41,Bayes,Scatter-Inv,Regression,8.42, UQ http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012007 IOP Publishing en 1742-6596 10.1088/1742-6596/490/1/012007 SHeidenreich HGross M-AHenn CElster MBär article Henn2014 Measurement Science and Technology 2014 25 4 044003 8.41,Scatter-Inv,Scatterometrie, 8.42 http://iopscience.iop.org/article/10.1088/0957-0233/25/4/044003 IOP Publishing en 0957-0233 10.1088/0957-0233/25/4/044003 M-AHenn HGross SHeidenreich FScholze CElster MBär article Gross2014 J. Europ.Opt. Soci.Rap. Pub. 2014 9 14003 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, ’non-rough’ 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;<prt>\_</prt> 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. Scatterometrie,Scatterometry,atomic force microscopy,line edge roughness,power spectrum density 8.41,Scatter-Inv http://www.jeos.org/index.php/jeos<prt>\_</prt>rp/article/view/14003 en 1990-2573 10.2971/jeos.2014.14003 HGroß SHeidenreich M-AHenn GDai FScholze MBär phdthesis Henn_Thesis 2013 8.41,8.42,Scatter-Inv,Scatterometrie 8.41,Scatter-Inv TU Berlin M-AHenn article Bodermann2012 International Journal of Nanomanufacturing 2012 8 1 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 (&lt; 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. Nanometrology 8.41,Scatter-Inv BBodermann FScholze JFlügge HGroß HBosse article Henn2012a Opt. Lett. 2012 37 24 5229--5231 8.41,Scatter-Inv 8.41,Scatter-Inv 10.1364/OL.37.005229 M-AHenn SHeidenreich HGroß ARathsfeld FScholze MBär article Henn2012 Optics Express 2012 20 12 12771-86 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. 8.41,Diffraction gratings,Metrology,Scatter-Inv,Scatterometrie,8.42 http://www.osapublishing.org/viewmedia.cfm?uri=oe-20-12-12771<prt>&amp;</prt>seq=0<prt>&amp;</prt>html=true Optical Society of America EN 1094-4087 10.1364/OE.20.012771 M-AHenn HGross FScholze MWurm CElster MBär article GrosHHRB2012 Appl. Opt. 2012 51 30 7384--94 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. 8.41,Diffraction gratings,Metrology,Scatter-Inv,Scatterometrie 8.41,Scatter-Inv http://www.osapublishing.org/viewmedia.cfm?uri=ao-51-30-7384<prt>&amp;</prt>seq=0<prt>&amp;</prt>html=true Optical Society of America EN 1539-4522 10.1364/AO.51.007384 HGroß M-AHenn SHeidenreich ARathsfeld MBär inbook Gross2012 2012 8.41,Scatter-Inv 8.41,Scatter-Inv F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill, K. Shirono World Scientific New Jersey Advanced Mathematical & Computational Tools in Metrology and Testing IX HGroß M-AHenn ARathsfeld MBär inproceedings Bodermann2012a 2012 8.41,Scatter-Inv 8.41,Scatter-Inv SPIE Proc. BBodermann P-EHansen SBurger M-AHenn HGross FScholze JEndres MWurm incollection Bodermann2011a 2011 8.41,Nanometrology 8.41, Scatter-Inv PTB-Mitteilungen 2/2011 "Themenschwerpunkt Nanometrologie" BBodermann JFlügge HGroß inproceedings Bodermann2011 2011 1395 1 319--323 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. 8.41,Scatterometrie 8.41, Scatter-Inv http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3657910 AIP Conf. Proc. 1551-7616 10.1063/1.3657910 BBodermann EBuhr H-UDanzebrink MBär FScholze MKrumrey MWurm PKlapetek P-EHansen VKorpelainen Mvan Veghel AYacoot SSiitonen OEl Gawhary SBurger TSaastamoinen D GSeiler A CDiebold RMcDonald AChabli E MSecula inproceedings Henn2011 2011 8.41,Scatter-Inv 8.41,Scatter-Inv SPIE Proc. 80830N M-AHenn HGroß FScholze CElster MBär article Gross2010 J. Europ. Opt. Soc. Rap. Public. 2010 5 10053 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. Scatterometrie,critical dimensions (CD),inverse problem,profile model,scatterometry 8.41,Scatter-Inv http://www.jeos.org/index.php/jeos<prt>\_</prt>rp/article/view/10053 en 1990-2573 10.2971/jeos.2010.10053 HGross JRichter ARathsfeld MBär article Gross2009 Measurement Science and Technology 2009 20 10 105102 8.41,Scatter-EUV,Scatter-Inv,Scatterometrie 8.41,Scatter-Inv http://iopscience.iop.org/article/10.1088/0957-0233/20/10/105102 IOP Publishing en 0957-0233 10.1088/0957-0233/20/10/105102 HGross ARathsfeld FScholze MBär inproceedings Henn2009 2009 8.41,Scatter-Inv 8.41,Scatter-Inv SPIE Proc. 7390 M-AHenn RModel MBär MWurm BBodermann ARathsfeld HGroß url DIPOG 2009 8.41,Scatter-Inv http://www.wias-berlin.de/software/DIPOG 2015-11-25 JElschner HHinder ARathsfeld GSchmidt article Model2008 Journal of Physics: Conference Series 2008 135 1 012071 8.41,Scatter-Inv,Scatterometrie 8.41,Scatter-Inv http://iopscience.iop.org/article/10.1088/1742-6596/135/1/012071 IOP Publishing en 1742-6596 10.1088/1742-6596/135/1/012071 RModel ARathsfeld HGross MWurm BBodermann article Gross2008 Waves in Random and Complex Media 2008 18 1 129--149 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 Gauß â€“Newton type iterative method to solve this operator equation. The reconstruction ... 8.41,Scatter-Inv,Scatterometrie 8.41,Scatter-Inv http://www.tandfonline.com/doi/abs/10.1080/17455030701481823 Taylor <prt>&amp;</prt> Francis Group en 1745-5030 10.1080/17455030701481823 HGroß ARathsfeld inproceedings Gross_Model08 2008 6995OT-1 – 6995OT-9 8.41, Scatter-Inv Proc. SPIE6995 HGross ARathsfeld FScholze RModel MBär inproceedings Gross2008 2008 337--346 8.41, Scatter-Inv Sensoren und Messsystem 2008 HGroß RModel FScholze MWurm BBodermann MBär ARathsfeld incollection Gross_Rathsf97 2007 8.41, Scatter-Inv Annual Research Report 2007 HGross ARathsfeld inproceedings Wurm2007 2007 8.41,Scatter-Inv 8.41,Scatter-Inv SPIE Proc. 6617 MWurm BBodermann RModel HGroß inproceedings Gross2007 2007 8.41,Scatter-Inv 8.41,Scatter-Inv SPIE Proc. 6617 HGroß ARathsfeld FScholze MBär UDersch article Gross2006 Measurement 2006 39 9 782--794 8.41 8.41, Scatter-Inv http://www.researchgate.net/publication/223944217<prt>\_</prt>Mathematical<prt>\_</prt>modelling<prt>\_</prt>of<prt>\_</prt>indirect<prt>\_</prt>measurements<prt>\_</prt>in<prt>\_</prt>scatterometry 02632241 10.1016/j.measurement.2006.04.009 HGroß RModel MBär MWurm BBodermann ARathsfeld incollection Model2006b 2006 8.41,Scatter-Inv 8.41,Scatter-Inv PTB-Mitteilungen 3/2006 RModel HGroß WHaberkorn MBär incollection Gross2006a 2006 8.41,Scatter-Inv 8.41,Scatter-Inv WIAS Preprint No. 1164 HGroß ARathsfeld inproceedings Wurm2006 2006 8.41,Scatter-Inv 8.41,Scatter-Inv DGaO-Proc. MWurm BBodermann FScholze CLaubis HGroß ARathsfeld