K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

G. Bao, “Finite element approximation of time harmonic waves in periodic structures,” SIAM J. Numer. Anal. 32, 1155–1169 (1995).

[Crossref]

M.-A. Henn, H. Gross, F. Scholze, M. Wurm, C. Elster, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20, 12771–12786 (2012).

[Crossref]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).

[Crossref]

B. Bodermann, M. Wurm, A. Diener, F. Scholze, and H. Gross, “EUV and DUV scatterometry for CD and edge profile metrology on EUV masks,” in 25th European Mask and Lithography Conference (2009), pp. 1–12.

F. Campolongo, J. Cariboni, and A. Saltelli, “An effective screening design for sensitivity analysis of large models,” Environ. Model. Software 22, 1509–1518 (2007).

[Crossref]

F. Campolongo, J. Cariboni, and A. Saltelli, “An effective screening design for sensitivity analysis of large models,” Environ. Model. Software 22, 1509–1518 (2007).

[Crossref]

J. Chandezon, G. Raoult, and D. Maystre, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).

[Crossref]

Z. Dong, S. Liu, X. Chen, and C. Zhang, “Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis,” Thin Solid Films 562, 16–23 (2014).

[Crossref]

J. Zhu, S. Liu, X. Chen, C. Zhang, and H. Jiang, “Robust solution to the inverse problem in optical scatterometry,” Opt. Express 22, 22031–22042 (2014).

[Crossref]

X. Chen, S. Liu, C. Zhang, and H. Jiang, “Improved measurement accuracy in optical scatterometry using correction-based library search,” Appl. Opt. 52, 6726–6734 (2013).

[Crossref]

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

G. Dahlen, M. Osborn, H.-C. Liu, R. Jain, W. Foreman, and J. R. Osborne, “Critical dimension AFM tip characterization and image reconstruction applied to the 45-nm node,” Proc. SPIE 6152, 61522R (2006).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

B. Bodermann, M. Wurm, A. Diener, F. Scholze, and H. Gross, “EUV and DUV scatterometry for CD and edge profile metrology on EUV masks,” in 25th European Mask and Lithography Conference (2009), pp. 1–12.

A. Doicu, T. Trautmann, and F. Schreier, Numerical Regularization for Atmospheric Inverse Problems (Springer, 2010).

Z. Dong, S. Liu, X. Chen, and C. Zhang, “Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis,” Thin Solid Films 562, 16–23 (2014).

[Crossref]

J. Eriksson, “Optimization and regularization of nonlinear least squares problems,” Ph.D. thesis, (Dept. of Computing Science, Umea University, Umea, Sweden, 1996).

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

G. Dahlen, M. Osborn, H.-C. Liu, R. Jain, W. Foreman, and J. R. Osborne, “Critical dimension AFM tip characterization and image reconstruction applied to the 45-nm node,” Proc. SPIE 6152, 61522R (2006).

[Crossref]

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Softw. 33, 1–22 (2009).

[Crossref]

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics (Springer, 2009).

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

M.-A. Henn, H. Gross, F. Scholze, M. Wurm, C. Elster, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20, 12771–12786 (2012).

[Crossref]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).

[Crossref]

H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” Waves Random Complex Media 18, 129–149 (2008).

[Crossref]

B. Bodermann, M. Wurm, A. Diener, F. Scholze, and H. Gross, “EUV and DUV scatterometry for CD and edge profile metrology on EUV masks,” in 25th European Mask and Lithography Conference (2009), pp. 1–12.

H. J. Wonsuk Lee and S. H. Han, “Measurement of critical dimension in scanning electron microscope mask images,” J. Micro/Nanolithogr., MEMS, MOEMS 10, 1–8 (2011).

[Crossref]

P. C. Hansen, “Regularization tools—a Matlab package for analysis and solution of discrete ill-posed problems,” Numer. Algorithms 6, 1–35 (1994).

[Crossref]

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Softw. 33, 1–22 (2009).

[Crossref]

H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” J. R. Statist. Soc. B 67, 301–320 (2005).

[Crossref]

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics (Springer, 2009).

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

M.-A. Henn, H. Gross, F. Scholze, M. Wurm, C. Elster, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20, 12771–12786 (2012).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

H.-T. Huang and F. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).

[Crossref]

B. Iooss and P. Lemaître, “A review on global sensitivity analysis methods,” in Uncertainty Management in Simulation–Optimization of Complex Systems: Algorithms and Applications, G. Dellino and C. Meloni, eds. (Springer, 2015), Chap. 5, pp. 101–122.

G. Dahlen, M. Osborn, H.-C. Liu, R. Jain, W. Foreman, and J. R. Osborne, “Critical dimension AFM tip characterization and image reconstruction applied to the 45-nm node,” Proc. SPIE 6152, 61522R (2006).

[Crossref]

J. Zhu, S. Liu, X. Chen, C. Zhang, and H. Jiang, “Robust solution to the inverse problem in optical scatterometry,” Opt. Express 22, 22031–22042 (2014).

[Crossref]

X. Chen, S. Liu, C. Zhang, and H. Jiang, “Improved measurement accuracy in optical scatterometry using correction-based library search,” Appl. Opt. 52, 6726–6734 (2013).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

B. Iooss and P. Lemaître, “A review on global sensitivity analysis methods,” in Uncertainty Management in Simulation–Optimization of Complex Systems: Algorithms and Applications, G. Dellino and C. Meloni, eds. (Springer, 2015), Chap. 5, pp. 101–122.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Quart. Appl. Math. 2, 164–168 (1944).

G. Dahlen, M. Osborn, H.-C. Liu, R. Jain, W. Foreman, and J. R. Osborne, “Critical dimension AFM tip characterization and image reconstruction applied to the 45-nm node,” Proc. SPIE 6152, 61522R (2006).

[Crossref]

Z. Dong, S. Liu, X. Chen, and C. Zhang, “Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis,” Thin Solid Films 562, 16–23 (2014).

[Crossref]

J. Zhu, S. Liu, X. Chen, C. Zhang, and H. Jiang, “Robust solution to the inverse problem in optical scatterometry,” Opt. Express 22, 22031–22042 (2014).

[Crossref]

X. Chen, S. Liu, C. Zhang, and H. Jiang, “Improved measurement accuracy in optical scatterometry using correction-based library search,” Appl. Opt. 52, 6726–6734 (2013).

[Crossref]

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (2004).

J. Chandezon, G. Raoult, and D. Maystre, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).

[Crossref]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

M. D. Morris, “Factorial sampling plans for preliminary computational experiments,” Technometrics 33, 161–174 (1991).

[Crossref]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (2004).

G. Dahlen, M. Osborn, H.-C. Liu, R. Jain, W. Foreman, and J. R. Osborne, “Critical dimension AFM tip characterization and image reconstruction applied to the 45-nm node,” Proc. SPIE 6152, 61522R (2006).

[Crossref]

G. Dahlen, M. Osborn, H.-C. Liu, R. Jain, W. Foreman, and J. R. Osborne, “Critical dimension AFM tip characterization and image reconstruction applied to the 45-nm node,” Proc. SPIE 6152, 61522R (2006).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

J. Chandezon, G. Raoult, and D. Maystre, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).

[Crossref]

H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” Waves Random Complex Media 18, 129–149 (2008).

[Crossref]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

F. Campolongo, J. Cariboni, and A. Saltelli, “An effective screening design for sensitivity analysis of large models,” Environ. Model. Software 22, 1509–1518 (2007).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

M.-A. Henn, H. Gross, F. Scholze, M. Wurm, C. Elster, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20, 12771–12786 (2012).

[Crossref]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).

[Crossref]

B. Bodermann, M. Wurm, A. Diener, F. Scholze, and H. Gross, “EUV and DUV scatterometry for CD and edge profile metrology on EUV masks,” in 25th European Mask and Lithography Conference (2009), pp. 1–12.

A. Doicu, T. Trautmann, and F. Schreier, Numerical Regularization for Atmospheric Inverse Problems (Springer, 2010).

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

H.-T. Huang and F. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).

[Crossref]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Softw. 33, 1–22 (2009).

[Crossref]

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B 58, 267–288 (1996).

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics (Springer, 2009).

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (2004).

A. Doicu, T. Trautmann, and F. Schreier, Numerical Regularization for Atmospheric Inverse Problems (Springer, 2010).

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

C. Vogel, Computational Methods for Inverse Problems (Society for Industrial and Applied Mathematics, 2002).

H. J. Wonsuk Lee and S. H. Han, “Measurement of critical dimension in scanning electron microscope mask images,” J. Micro/Nanolithogr., MEMS, MOEMS 10, 1–8 (2011).

[Crossref]

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

M.-A. Henn, H. Gross, F. Scholze, M. Wurm, C. Elster, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20, 12771–12786 (2012).

[Crossref]

B. Bodermann, M. Wurm, A. Diener, F. Scholze, and H. Gross, “EUV and DUV scatterometry for CD and edge profile metrology on EUV masks,” in 25th European Mask and Lithography Conference (2009), pp. 1–12.

J. Zhu, S. Liu, X. Chen, C. Zhang, and H. Jiang, “Robust solution to the inverse problem in optical scatterometry,” Opt. Express 22, 22031–22042 (2014).

[Crossref]

Z. Dong, S. Liu, X. Chen, and C. Zhang, “Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis,” Thin Solid Films 562, 16–23 (2014).

[Crossref]

X. Chen, S. Liu, C. Zhang, and H. Jiang, “Improved measurement accuracy in optical scatterometry using correction-based library search,” Appl. Opt. 52, 6726–6734 (2013).

[Crossref]

H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” J. R. Statist. Soc. B 67, 301–320 (2005).

[Crossref]

F. Campolongo, J. Cariboni, and A. Saltelli, “An effective screening design for sensitivity analysis of large models,” Environ. Model. Software 22, 1509–1518 (2007).

[Crossref]

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).

[Crossref]

H. J. Wonsuk Lee and S. H. Han, “Measurement of critical dimension in scanning electron microscope mask images,” J. Micro/Nanolithogr., MEMS, MOEMS 10, 1–8 (2011).

[Crossref]

J. Chandezon, G. Raoult, and D. Maystre, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).

[Crossref]

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B 58, 267–288 (1996).

H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” J. R. Statist. Soc. B 67, 301–320 (2005).

[Crossref]

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Softw. 33, 1–22 (2009).

[Crossref]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).

[Crossref]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).

[Crossref]

P. C. Hansen, “Regularization tools—a Matlab package for analysis and solution of discrete ill-posed problems,” Numer. Algorithms 6, 1–35 (1994).

[Crossref]

M.-A. Henn, H. Gross, F. Scholze, M. Wurm, C. Elster, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20, 12771–12786 (2012).

[Crossref]

J. Zhu, S. Liu, X. Chen, C. Zhang, and H. Jiang, “Robust solution to the inverse problem in optical scatterometry,” Opt. Express 22, 22031–22042 (2014).

[Crossref]

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22, 24678–24688 (2014).

[Crossref]

Y.-S. Ku, C.-L. Yeh, Y.-C. Chen, C.-W. Lo, W.-T. Wang, and M.-C. Chen, “EUV scatterometer with a high-harmonic-generation EUV source,” Opt. Express 24, 28014–28025 (2016).

[Crossref]

G. Dahlen, M. Osborn, H.-C. Liu, R. Jain, W. Foreman, and J. R. Osborne, “Critical dimension AFM tip characterization and image reconstruction applied to the 45-nm node,” Proc. SPIE 6152, 61522R (2006).

[Crossref]

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Quart. Appl. Math. 2, 164–168 (1944).

G. Bao, “Finite element approximation of time harmonic waves in periodic structures,” SIAM J. Numer. Anal. 32, 1155–1169 (1995).

[Crossref]

M. D. Morris, “Factorial sampling plans for preliminary computational experiments,” Technometrics 33, 161–174 (1991).

[Crossref]

H.-T. Huang and F. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455-456, 828–836 (2004).

[Crossref]

Z. Dong, S. Liu, X. Chen, and C. Zhang, “Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis,” Thin Solid Films 562, 16–23 (2014).

[Crossref]

H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” Waves Random Complex Media 18, 129–149 (2008).

[Crossref]

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics (Springer, 2009).

C. Vogel, Computational Methods for Inverse Problems (Society for Industrial and Applied Mathematics, 2002).

Y. Khare and R. Muñoz-Carpena, “Global sensitivity analysis: elementary effects method of Morris using sampling for uniformity (SU) Matlab code manual,” 2014 https://abe.ufl.edu/faculty/carpena/software/SUMorris.shtml .

https://jcmwave.com .

B. Bodermann, M. Wurm, A. Diener, F. Scholze, and H. Gross, “EUV and DUV scatterometry for CD and edge profile metrology on EUV masks,” in 25th European Mask and Lithography Conference (2009), pp. 1–12.

B. Iooss and P. Lemaître, “A review on global sensitivity analysis methods,” in Uncertainty Management in Simulation–Optimization of Complex Systems: Algorithms and Applications, G. Dellino and C. Meloni, eds. (Springer, 2015), Chap. 5, pp. 101–122.

A. Doicu, T. Trautmann, and F. Schreier, Numerical Regularization for Atmospheric Inverse Problems (Springer, 2010).

K. Rasmussen, J. B. Kondrup, A. Allard, S. Demeyer, N. Fischer, E. Barton, D. Partridge, L. Wright, M. Bär, H. G. A. Fiebach, S. Heidenreich, M.-A. Henn, R. Model, S. Schmelter, G. Kok, and N. Pelevic, “Novel mathematical and statistical approaches to uncertainty evaluation: best practice guide to uncertainty evaluation for computationally expensive models,” (Euramet, 2015).

J. Eriksson, “Optimization and regularization of nonlinear least squares problems,” Ph.D. thesis, (Dept. of Computing Science, Umea University, Umea, Sweden, 1996).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (2004).