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bib
--- Timezone: CEST
Creation date: 2021-09-28
Creation time: 21-07-08
--- Number of references
33
article
FarchminHSWBBH2020
Efficient Bayesian inversion for shape reconstruction of lithography masks
Journal of Micro/Nanolithography, MEMS, and MOEMS
2020
5
5
2
19
1--11
8.4,8.41,UQ,Scatter-Inv
10.1117/1.JMM.19.2.024001
NFarchmin
MHammerschmidt
P ISchneider
MWurm
BBodermann
MBär
SHeidenreich
article
GrossHB2016
Impact of different stochastic line edge roughness patterns on measurements in scatterometry - a simulation study
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
Bayesian approach to the statistical inverse problem of scatterometry: Comparison of three surrogate models
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
Challenges in nanometrology: high precision measurement of position and size
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
Modeling aspects to improve the solution of the inverse problem in scatterometry
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
A surrogate model enables a Bayesian approach to the inverse problem of scatterometry
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
Improved reconstruction of critical dimensions in extreme ultraviolet scatterometry by modeling systematic errors
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
Modelling line edge roughness in periodic line-space structures by Fourier optics to improve scatterometry
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, â€™non-roughâ€™ 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 σ<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
Statistical Approaches to the Inverse Problem of Scatterometry
2013
8.41,8.42,Scatter-Inv,Scatterometrie
8.41,Scatter-Inv
TU Berlin
M-AHenn
article
Bodermann2012
Nanometrology at PTB in support of process control of nanoscale features in semiconductor manufacturing
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 (< 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
Improved grating reconstruction by determination of line roughness in extreme ultraviolet scatterometry
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
A maximum likelihood approach to the inverse problem of scatterometry
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>&</prt>seq=0<prt>&</prt>html=true
Optical Society of America
EN
1094-4087
10.1364/OE.20.012771
M-AHenn
HGross
FScholze
MWurm
CElster
MBär
article
GrosHHRB2012
Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry
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>&</prt>seq=0<prt>&</prt>html=true
Optical Society of America
EN
1539-4522
10.1364/AO.51.007384
HGroß
M-AHenn
SHeidenreich
ARathsfeld
MBär
inbook
Gross2012
Stochastic modeling aspects for an improved solution of the inverse problem in scatterometry
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
First steps towards a scatterometry reference standard
2012
8.41,Scatter-Inv
8.41,Scatter-Inv
SPIE Proc.
BBodermann
P-EHansen
SBurger
M-AHenn
HGross
FScholze
JEndres
MWurm
incollection
Bodermann2011a
Charakterisierung von Nanostrukturen aund Substraten der Halbleiterindustrie
2011
8.41,Nanometrology
8.41, Scatter-Inv
PTB-Mitteilungen 2/2011 "Themenschwerpunkt Nanometrologie"
BBodermann
JFlügge
HGroß
inproceedings
Bodermann2011
Joint Research on Scatterometry and AFM Wafer Metrology
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
Improved geometry reconstruction and uncertainty evaluation for extreme ultraviolet (EUV) scatterometry based on maximum likelihood estimation
2011
8.41,Scatter-Inv
8.41,Scatter-Inv
SPIE Proc. 80830N
M-AHenn
HGroß
FScholze
CElster
MBär
article
Gross2010
Investigations on a robust profile model for the reconstruction of 2D periodic absorber lines in scatterometry
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
Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates
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
On numerical reconstruction of lithographic masks in DUV scatterometry
2009
8.41,Scatter-Inv
8.41,Scatter-Inv
SPIE Proc. 7390
M-AHenn
RModel
MBär
MWurm
BBodermann
ARathsfeld
HGroß
url
DIPOG
DIPOG Homepage
2009
8.41,Scatter-Inv
http://www.wias-berlin.de/software/DIPOG
2015-11-25
JElschner
HHinder
ARathsfeld
GSchmidt
article
Model2008
A scatterometry inverse problem in optical mask metrology
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
Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures
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>&</prt> Francis Group
en
1745-5030
10.1080/17455030701481823
HGroß
ARathsfeld
inproceedings
Gross_Model08
Computational methods estimating uncertainties for profile reconstruction in scatterometry
2008
6995OT-1 – 6995OT-9
8.41, Scatter-Inv
Proc. SPIE6995
HGross
ARathsfeld
FScholze
RModel
MBär
inproceedings
Gross2008
Modellbildung, Bestimmung der Messunsicherheit und Validierung für diskrete inverse Probleme am Beispiel der Scatterometrie
2008
337--346
8.41, Scatter-Inv
Sensoren und Messsystem 2008
HGroß
RModel
FScholze
MWurm
BBodermann
MBär
ARathsfeld
incollection
Gross_Rathsf97
Intelligent solutions for complex problems
2007
8.41, Scatter-Inv
Annual Research Report 2007
HGross
ARathsfeld
inproceedings
Wurm2007
Numerical analysis of DUV scatterometry on EUV masks
2007
8.41,Scatter-Inv
8.41,Scatter-Inv
SPIE Proc. 6617
MWurm
BBodermann
RModel
HGroß
inproceedings
Gross2007
Optimal sets of measurement data for profile reconstruction in scatterometry
2007
8.41,Scatter-Inv
8.41,Scatter-Inv
SPIE Proc. 6617
HGroß
ARathsfeld
FScholze
MBär
UDersch
article
Gross2006
Mathematical modelling of indirect measurements in scatterometry
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
Inverse Methoden für indirekte Messungen und Partielle-Differentialgleichungs-Modelle
2006
8.41,Scatter-Inv
8.41,Scatter-Inv
PTB-Mitteilungen 3/2006
RModel
HGroß
WHaberkorn
MBär
incollection
Gross2006a
Sensitivity Analysis for Indirect Measurement in Scatterometry and the Reconstruction of Periodic Grating Structures
2006
8.41,Scatter-Inv
8.41,Scatter-Inv
WIAS Preprint No. 1164
HGroß
ARathsfeld
inproceedings
Wurm2006
Untersuchungen zur Eignung der EUV-Scatterometrie zur quantitativen Charakterisierung periodischer Strukturen auf Photolithographiemasken
2006
8.41,Scatter-Inv
8.41,Scatter-Inv
DGaO-Proc.
MWurm
BBodermann
FScholze
CLaubis
HGroß
ARathsfeld