Abstract
A large number of parameters is often required to describe optical dispersion laws, and it is only through the use of an appropriate global optimization procedure that an accurate thin-film index determination can be achieved. In this paper, we propose to investigate the respective performances of three different optimization algorithms, namely Simulated Annealing, Genetic Algorithm and Clustering Global Optimization and compare results with a commercial software dedicated to thin-film index determination. This study is restricted to the single-layer thin-film index determination of transparent and absorbing materials. It includes the theoretical study of simulated reflection and transmission spectra, and the experimental characterization of Ta2O5 and Si layers.
Similar content being viewed by others
References
D. Poelman, P.F. Smet, J. Phys. D, Appl. Phys. 36, 1850–1857 (2003)
C. Caliendo, E. Verona, G. Saggio, Thin Solid Films 292, 255–259 (1997)
C. Jung, B.K. Rhee, Appl. Opt. 41, 3861–3865 (2002)
J. Cardin, D. Leduc, Appl. Opt. 47, 894–900 (2008)
TFCalc, Software Spectra Inc., Portland, OR, USA (2012), www.sspectra.com
Filmwizard, Scientific Computing Int., Encinitas, CA, USA (2012), www.sci-soft.com
OptiLayer, Optilayer Ltd., Moscow, Russia (2012), www.optilayer.com
Essential MacLeod, Thin Film Center Inc., Tucson, AZ, USA (2012), www.thinfilmcenter.com
A.V. Tikhonravov, M.K. Trubetskov, B.T. Sullivan, J.A. Dobrowolski, Appl. Opt. 36, 7188–7199 (1997)
P.G. Verly, A.V. Tikhonravov, M.K. Trubetskov, Appl. Opt. 36, 1487–1495 (1997)
L.C.W. Dixon, G.P. Szegö, Towards Global Optimization, vol. 2 (North-Holland, Amsterdam, 1978)
B. Goffe (2012), www.netlib.no/netlib/opt/simann.f
P. Charbonneau, B. Knapp (2012), download.hao.ucar.edu/archive/pikaia
A. Miler (2012), www.mat.univie.ac.at/~neum/glopt/contrib/global.f90
S. Kirkpatrick, C.D. Gelatt Jr., M.P. Vecchi, Science 220(4598), 671–680 (1983)
N. Metropolis, A.W. Rosenbluth, A.H. Teller, J. Chem. Phys. 21, 1087–1092 (1953)
P.J.M.V. Laarhoven, E.H.L. Aarts, Simulated Annealing: Theory and Applications (Kluwer, Dordrecht, 1989)
W.L. Goffe, G.D. Ferrier, J. Rogers, J. Econom. 60(1–2), 65–99 (1994)
C.P. Chang, Y.H. Lee, S.Y. Wu, Opt. Lett. 15, 595–597 (1990)
T. Boudet, P. Chaton, L. Herault, G. Gonon, L. Jouanet, P. Keller, Appl. Opt. 35, 6219–6226 (1996)
J. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975)
T. Eisenhammer, M. Lazarov, M. Leutbecher, U. Schiffel, R. Sizmann, Appl. Opt. 32, 6310–6315 (1993)
G.Y. Zhou, Y.X. Chen, Z.G. Wang, H.W. Song, Appl. Opt. 38, 4281–4290 (1999)
P.D. Binda, F.E. Zocchi, Proc. SPIE 5536, 97–108 (2004)
A.B. Djurisic, J.M. Elazar, A.D. Rakic, Appl. Opt. 36, 7097–7103 (1997)
R.W. Becker, G.V. Lago, in Proceedings of the 8th Allerton Conference on Circuits and Systems Theory (1970), pp. 3–12
A.A. Törn, in Proceedings of Computer Simulation Versus Analytical Solutions for Business and Economic Models, Gothenburg (1972), pp. 191–206
T. Csendes, Acta Cybern. 8, 361–370 (1988)
T. Csendes, B. Daróczy, Z. Hantos, in System Modelling and Optimization, ed. by A. Prékopa, B. Straziczky. Lecture Notes in Control and Information Sciences, vol. 84 (Springer, Berlin, 1986), pp. 188–192
D.M. Himmelblau, Applied Nonlinear Programming (McGraw-Hill, New York, 1972)
A. Maroosi, B. Amiri, Expert Syst. Appl. 37, 5645–5652 (2010)
M. Tilsch, K. Hendrix, Appl. Opt. 47, C55–C69 (2008)
H.A. Macleod, Thin-film Optical Filters (Institute of Physics Publishing, Bristol and Philadelphia, 2001)
G.E. Jellison Jr., F.A. Modine, Appl. Phys. Lett. 69, 371–373 (1996) 2137
G.E. Jellison Jr., V.I. Merkulov, A.A. Puretzky, D.B. Geohegan, G. Eres, D.H. Lowndes, J.B. Caughman, Thin Solid Films 377–378, 68–73 (2000)
B. v. Blanckenhagen, D. Tonova, J. Ullmann, Appl. Opt. 41, 3137–3141 (2002)
M. Kildemo, R. Ossikovski, M. Stchakovsky, Thin Solid Films 313–314, 108 (1998)
Z.G. Hu, Z.M. Huang, Y.N. Wu, S.H. Hu, G.S. Wang, J.H. Ma, J.H. Chu, Eur. Phys. J. B 38, 431–436 (2004)
R.D.L. Kronig, J. Opt. Soc. Am. 12, 547–556 (1926)
Z.B. Xu, Y. Gao, Sci. China Ser. E 26, 364–375 (1996)
N.N. Schraudolph, R.K. Belew, Mach. Learn. 9, 9–21 (1992)
E. Moll, H.K. Pulker, W. Haag, Method and apparatus for the reactive vapor deposition of layers of oxides, nitrides, oxynitrides, and carbides on a substrate. U.S. Patent 4,619,748, Filed 28 Feb. 1986
E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985)
Acknowledgements
This program has been supported by the French “Agence National de la Recherche” (ANR PNANO SEEC).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gao, L., Lemarchand, F. & Lequime, M. Reverse engineering from spectrophotometric measurements: performances and efficiency of different optimization algorithms. Appl. Phys. A 108, 877–889 (2012). https://doi.org/10.1007/s00339-012-6987-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00339-012-6987-2