Using Gaussian process regression for efficient parameter reconstruction

Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to different local minimization algorithms for this numerical optimization problem. Bayesian optimization uses Gaussian-process regression to find promising parameter values. We examine how pre-computed simulation results can be used to train the Gaussian process and to accelerate the optimization.

[1]  J. Nocedal,et al.  A Limited Memory Algorithm for Bound Constrained Optimization , 1995, SIAM J. Sci. Comput..

[2]  Frank Schmidt,et al.  The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks , 2007, SPIE Optical Metrology.

[3]  Christopher K. I. Williams.  Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond , 1999, Learning in Graphical Models.

[4]  Jorge Nocedal,et al.  Large Scale Unconstrained Optimization , 1997 .

[5]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[6]  Carl E. Rasmussen,et al.  Derivative Observations in Gaussian Process Models of Dynamic Systems , 2002, NIPS.

[7]  Michael Mrejen,et al.  Plasmonic nanostructure design and characterization via Deep Learning , 2018, Light: Science & Applications.

[8]  Michael I. Jordan.  Learning in Graphical Models , 1999, NATO ASI Series.

[9]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[10]  Frank Scholze,et al.  Reconstructing Detailed Line Profiles of Lamellar Gratings from GISAXS Patterns with a Maxwell Solver , 2017, 1704.08032.

[11]  Frank Schmidt,et al.  Adaptive finite element method for simulation of optical nano structures , 2007, 0711.2149.

[12]  D. Sculley,et al.  Google Vizier: A Service for Black-Box Optimization , 2017, KDD.

[13]  W. Häßler-Grohne,et al.  International photomask linewidth comparison by NIST and PTB , 2008, Photomask Technology.

[14]  Frank Scholze,et al.  Correlated Diffuse X-ray Scattering from Periodically Nano-Structured Surfaces , 2016 .

[15]  Philipp Gutsche,et al.  Chiral scatterers designed by Bayesian optimization , 2017, 1712.07091.

[16]  Carsten Rockstuhl,et al.  Benchmarking Five Global Optimization Approaches for Nano-optical Shape Optimization and Parameter Reconstruction , 2018, ACS Photonics.

[17]  Bernd Bodermann,et al.  Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion , 2017, Optical Metrology.

[18]  Nando de Freitas,et al.  Taking the Human Out of the Loop: A Review of Bayesian Optimization , 2016, Proceedings of the IEEE.

[19]  Bernd Bodermann,et al.  Metrology of nanoscale grating structures by UV scatterometry. , 2017, Optics express.

[20]  Carsten Rockstuhl,et al.  Global optimization of complex optical structures using Bayesian optimization based on Gaussian processes , 2017, Other Conferences.

[21]  Carsten Rockstuhl,et al.  Shape design of a reflecting surface using Bayesian Optimization , 2018 .

[22]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[23]  Matthijs Langelaar,et al.  System Robust Optimization of Ring Resonator-Based Optical Filters , 2016, Journal of Lightwave Technology.

[24]  Sven Burger,et al.  Solving inverse problems appearing in design and metrology of diffractive optical elements by using Bayesian optimization , 2018, Optical Systems Design.