Abstract

Post nondestructive analyses of an all-dielectric multilayer Fabry–Perot interference filter developed through a reactive electron beam deposition process have been carried out through numerical reverse engineering of transmission spectra, Rutherford backscattering spectroscopy and quartz crystal monitoring data to derive multilayer geometry, deposited layer thicknesses, densities, refractive indices, compositions, and stoichiometry. These techniques are collectively used to fulfill the missing links with complementary and some supplementary information to inverse synthesize the multilayer geometry. During this investigation it is distinctly understood that the factors associated with real-time deposition have significantly influenced the microscopic parameters, namely, the densities and refractive indices of TiO2 and SiO2 layers. This in turn influenced the layers’ geometric (physical) thicknesses during automated quarter-wave optical layer monitoring and consequently affected the experimental spectral characteristics. The role of oxygen has been observed to be significant in controlling the mass densities of these refractory oxide layers. It is further noticed that the layer density values have been significantly perturbed whether the associated TiO2 or SiO2 oxide dielectric films are substoichiometric (oxygen-deficient), stoichiometric, or superstoichiometric (oxygen-enriched).

© 2013 Optical Society of America

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2009 (2)

2008 (5)

2007 (7)

2006 (6)

2005 (4)

D. Y. Hsu, J. W. Lin, and S. Y. Shaw, “Wide-range tunable Fabry–Perot array filter for wavelength-division multiplexing applications,” Appl. Opt. 44, 1529–1532 (2005).
[CrossRef]

M. Jerman, Z. Qiao, and D. Mergel, “Refractive index of thin films of SiO2, ZrO2, and HfO2 as a function of the films’ mass density,” Appl. Opt. 44, 3006–3012 (2005).
[CrossRef]

X. Yao, C. Xiong, C. Yang, and N. Tong, “Applications of reverse engineering in the fabrication of optical coatings with high performance,” Proc. SPIE 6034, 60341I (2005).
[CrossRef]

J. Wang, J. Shao, and Z. Fan, “Extended effective medium model for refractive indices of thin films with oblique columnar structure,” Opt. Commun. 247, 107–110 (2005).
[CrossRef]

2004 (2)

V. Torres-Costa, F. Pászti, A. Climent-Font, R. J. Martín-Palma, and J. M. Martínez-Duart, “RBS characterization of porous silicon multilayer interference filters,” Electrochem. Solid-State Lett. 7, G244–G246 (2004).
[CrossRef]

R. Rabady, K. Zinoviev, and I. Avrutsky, “High-resolution photometric optical monitoring for thin-film deposition,” Appl. Opt. 43, 143–148 (2004).
[CrossRef]

2002 (5)

A. V. Tikhonravov and M. K. Trubetskov, “Automated design and sensitivity analysis of wavelength-division multiplexing filters,” Appl. Opt. 41, 3176–3182 (2002).
[CrossRef]

R. R. Willey, “Simulation of errors in the monitoring of narrow bandpass filters,” Appl. Opt. 41, 3193–3195 (2002).
[CrossRef]

P. Torchio, A. Gatto, M. Alvisi, G. Albrand, N. Kaiser, and C. Amra, “High-reflectivity HfO2-SiO2 ultraviolet mirrors,” Appl. Opt. 41, 3256–3261 (2002).
[CrossRef]

H. Sakurai and S. Kato, “Theoretical study of the metal oxidation reaction Ti+O2→TiO+O: ab initio calculation of the potential energy surface and classical trajectory analysis,” J. Phys. Chem. A 106, 4350–4357 (2002).
[CrossRef]

J. F. Power, “Inverse problem theory in the optical depth profilometry of thin films,” Rev. Sci. Instrum. 73, 4057–4141 (2002).
[CrossRef]

2001 (2)

N. K. Sahoo, “Multilayer inverse synthesis techniques for the analysis of mixed-mode inhomogeneities in composite and co-deposited dielectric coatings,” Vacuum 60, 411–417 (2001).
[CrossRef]

D. Mergel, “Modeling thin TiO2 films of various densities as an effective optical medium,” Thin Solid Films 397, 216–222 (2001).
[CrossRef]

2000 (4)

J. Ciosek, “Narrow-band interference filters with unconventional spacer layers,” Appl. Opt. 39, 135–140 (2000).
[CrossRef]

R. Vlastou, E. Fokitis, S. Maltezos, G. Kalliabakos, M. Kokkoris, and E. Kossionides, “Characterization of optical UV filters using Rutherford backscattering spectroscopy,” Nucl. Instrum. Methods Phys. Res. B 161–163, 590–594 (2000).
[CrossRef]

A. R. Kumar, V. A. Boychev, Z. M. Zhang, and D. B. Tanner, “Fabry–Perot resonators built With YBa2Cu3O7−δ films on Si substrates,” J. Heat Transfer 122, 785–791 (2000).
[CrossRef]

B. T. Sullivan, G. A. Clarke, T. Akiyama, N. Osborne, M. Ranger, J. A. Dobrowolski, L. Howe, A. Matsumoto, Y. Song, and K. Kikuchi, “High-rate automated deposition system for the manufacture of complex multilayer coatings,” Appl. Opt. 39, 157–167 (2000).
[CrossRef]

1999 (2)

J. Ciosek, J. A. Dobrowolski, G. A. Clarke, and G. Laframboise, “Design and manufacture of all-dielectric nonpolarizing beam splitters,” Appl. Opt. 38, 1244–1250 (1999).
[CrossRef]

E. E. Khawaja, S. M. A. Durrani, and M. A. Daous, “Depth profiling of inhomogeneous zirconia films by optical and Rutherford backscattering spectrometric techniques,” J. Phys. D 32, 388–394 (1999).
[CrossRef]

1998 (2)

T. Boudet, M. Berger, O. Lartigue, and B. Hirrien, “Optical and x-ray characterization applied to multilayer reverse engineering,” Opt. Eng. 37, 2175–2181 (1998).
[CrossRef]

M. Kildemo, R. Brenot, and B. Drévillon, “Spectroellipsometric method for process monitoring semiconductor thin films and interfaces,” Appl. Opt. 37, 5145–5149 (1998).
[CrossRef]

1997 (2)

Y. J. Lee, J. H. Lee, and Y. S. Kim, “Interdiffusion effects in all-dielectric Fabry–Perot filters,” J. Korean Phys. Soc. 30, 550–556 (1997).

A. Wajid, “On the accuracy of the quartz-crystal microbalance (QCM) in thin-film depositions,” Sens. Actuators A 63, 41–46 (1997).
[CrossRef]

1996 (2)

J. N. Musher and R. G. Gordon, “Atmospheric pressure chemical vapor deposition of TiN from tetrakis (dimethylamido) titanium and ammonia,” J. Mater. Res. 11, 989–1001 (1996).
[CrossRef]

M. Laube, F. Rauch, C. Ottermann, O. Anderson, and K. Bange, “Density of thin TiO2 films,” Nucl. Instrum. Methods Phys. Res. B 113, 288–292 (1996).
[CrossRef]

1995 (2)

P. W. Murray, N. G. Condon, and G. Thornton, “Effect of stoichiometry on the structure of TiO2 (110),” Phys. Rev. B 51, 10989–10997 (1995).
[CrossRef]

K. Bange, “Characterization of oxide coatings on glass,” Anal. Bioanal. Chem. 353, 240–245 (1995).
[CrossRef]

1994 (2)

N. K. Sahoo and K. V. S. R. Apparao, “Modified complex method for constrained design and optimization of optical multilayer thin-film devices,” Appl. Phys. A 59, 317–326 (1994).
[CrossRef]

W. Wang, “Reflection and transmission properties of holographic mirrors and holographic Fabry–Perot filters. III. Holographic Fabry–Perot filters,” Appl. Opt. 33, 7883–7894 (1994).
[CrossRef]

1990 (1)

1989 (2)

1988 (1)

1987 (1)

1986 (1)

1985 (3)

1984 (2)

R. Messier, A. P. Giri, and R. A. Roy, “Revised structure zone model for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500–503 (1984).
[CrossRef]

F. Demichelis, E. Mezzetti-Minetti, L. Tallone, and E. Tresso, “Optimization of optical parameters and electric field distribution in multilayers,” Appl. Opt. 23, 165–171 (1984).
[CrossRef]

1983 (1)

1981 (2)

H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20, 82–89 (1981).
[CrossRef]

D. K. Kaushik, S. K. Chattopadhyaya, and N. Kath, “Thin film thickness monitoring using a doubly oscillating quartz crystal and measurement of growth rate,” J. Phys. E 14, 345–348 (1981).
[CrossRef]

1978 (2)

1977 (1)

1975 (2)

C.-S. Lu, “Mass determination with piezoelectric quartz crystal resonators,” J. Vac. Sci. Technol. 12, 578–583 (1975).
[CrossRef]

S. Ogura, N. Sugawara, and R. Hiraga, “Refractive index and packing density for MgF2 films: correlation of temperature dependence with water sorption,” Thin Solid Films 30, 3–10 (1975).
[CrossRef]

1970 (1)

P. H. Lissberger, “Optical applications of dielectric thin films,” Rep. Prog. Phys. 33, 197–268 (1970).
[CrossRef]

1969 (2)

P. H. Lissberger, “Sources of error in the modulated wavelength optical thickness monitor for dielectric layers,” J. Phys. E 2, 875–879 (1969).
[CrossRef]

P. B. Clapham, M. J. Downs, and K. W. Raine, “Quartz crystal monitoring for optical thin films,” Thin Solid Films 4, R39–R42 (1969).
[CrossRef]

Abeysuriya, K.

Adjiman, C. S.

Akiyama, T.

Albrand, G.

Alvisi, M.

Amotchkina, T. V.

Amra, C.

Anderson, O.

M. Laube, F. Rauch, C. Ottermann, O. Anderson, and K. Bange, “Density of thin TiO2 films,” Nucl. Instrum. Methods Phys. Res. B 113, 288–292 (1996).
[CrossRef]

Apparao, K. V. S. R.

N. K. Sahoo and K. V. S. R. Apparao, “Modified complex method for constrained design and optimization of optical multilayer thin-film devices,” Appl. Phys. A 59, 317–326 (1994).
[CrossRef]

Armandula, H.

Arsenault, R.

Avrutsky, I.

Baby, L.

Badoil, B.

Bange, K.

M. Laube, F. Rauch, C. Ottermann, O. Anderson, and K. Bange, “Density of thin TiO2 films,” Nucl. Instrum. Methods Phys. Res. B 113, 288–292 (1996).
[CrossRef]

K. Bange, “Characterization of oxide coatings on glass,” Anal. Bioanal. Chem. 353, 240–245 (1995).
[CrossRef]

Barrett, B. M.

Belanger, P. A.

Belkind, A.

Berger, M.

T. Boudet, M. Berger, O. Lartigue, and B. Hirrien, “Optical and x-ray characterization applied to multilayer reverse engineering,” Opt. Eng. 37, 2175–2181 (1998).
[CrossRef]

Bisht, S.

Black, E.

Bobbs, B.

Boivin, G.

Boudet, T.

T. Boudet, M. Berger, O. Lartigue, and B. Hirrien, “Optical and x-ray characterization applied to multilayer reverse engineering,” Opt. Eng. 37, 2175–2181 (1998).
[CrossRef]

Boulay, R.

Bovard, B.

Boychev, V. A.

A. R. Kumar, V. A. Boychev, Z. M. Zhang, and D. B. Tanner, “Fabry–Perot resonators built With YBa2Cu3O7−δ films on Si substrates,” J. Heat Transfer 122, 785–791 (2000).
[CrossRef]

Brenot, R.

Cagnoli, G.

Cathelinaud, M.

Chattopadhyaya, S. K.

D. K. Kaushik, S. K. Chattopadhyaya, and N. Kath, “Thin film thickness monitoring using a doubly oscillating quartz crystal and measurement of growth rate,” J. Phys. E 14, 345–348 (1981).
[CrossRef]

Chen, S.-H.

Ciosek, J.

Clapham, P. B.

P. B. Clapham, M. J. Downs, and K. W. Raine, “Quartz crystal monitoring for optical thin films,” Thin Solid Films 4, R39–R42 (1969).
[CrossRef]

Clarke, G. A.

Climent-Font, A.

V. Torres-Costa, F. Pászti, A. Climent-Font, R. J. Martín-Palma, and J. M. Martínez-Duart, “RBS characterization of porous silicon multilayer interference filters,” Electrochem. Solid-State Lett. 7, G244–G246 (2004).
[CrossRef]

Condon, N. G.

P. W. Murray, N. G. Condon, and G. Thornton, “Effect of stoichiometry on the structure of TiO2 (110),” Phys. Rev. B 51, 10989–10997 (1995).
[CrossRef]

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Daous, M. A.

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Figures (20)

Fig. 1.
Fig. 1.

Multilayer design and computed spectral characteristic of the Fabry–Perot 21-layer optical interference filter utilizing TiO2/SiO2 thin films.

Fig. 2.
Fig. 2.

Experimental and theoretical spectral characteristics of the 21-layer interference filter depicting the deviation by following the automatic optical layer monitoring process.

Fig. 3.
Fig. 3.

Intended multilayer design and actual outcome of the multilayer structure for the interference filter by adopting the automatic (optical) layer monitoring technique. The layer structure is derived through numerical reverse engineering, as depicted in Fig. 4.

Fig. 4.
Fig. 4.

Numerical inverse engineering of the experimental transmittance spectra for extracting layer parameters. The matching of the experimental and theoretical characteristics distinctly indicates the accuracies in extracting the layer geometry and parameters.

Fig. 5.
Fig. 5.

RBS measurements of the 21-layer Fabry–Perot interference filter depicting special positions of the TiO2 and SiO2 layers. The data have been fitted, taking into account all the microstructural and compositional factors for the layers.

Fig. 6.
Fig. 6.

Compositional and layer density factor distributions with respect to Ti and Si atomic contributions in TiO2 and SiO2 layers, respectively, as per RBS data analysis.

Fig. 7.
Fig. 7.

Compositional and layer density factor distributions with respect to oxygen molecular contributions in TiO2 and SiO2 layers, respectively, as per RBS data analysis.

Fig. 8.
Fig. 8.

Computed spectral layer sensitivities with respect to the slight changes in the physical thickness of the layers depicting the most and least sensitive layers.

Fig. 9.
Fig. 9.

Computed spectral layer sensitivities with respect to the slight changes in the refractive index of the layers depicting most and least sensitive layers.

Fig. 10.
Fig. 10.

Experimental derivation of the physical thicknesses and mass densities of the TiO2 layers indicating a process dynamics influencing the layer quality and microstructure.

Fig. 11.
Fig. 11.

Experimental derivation of the physical thicknesses and mass densities of the SiO2 layers indicating a process dynamics influencing the layer quality and microstructure.

Fig. 12.
Fig. 12.

Comparative analysis of the all the TiO2 layers microstructures by three independent techniques, namely, (i) RBS measurements, (ii) real-time quartz-crystal monitoring (QCM), and (iii) numerical reverse engineering techniques, depicting an excellent correlation.

Fig. 13.
Fig. 13.

Comparative analysis of all the SiO2 layers microstructures by three independent techniques, namely, (i) RBS measurements, (ii) real-time quartz-crystal monitoring, and (iii) numerical reverse engineering techniques, depicting an excellent correlation.

Fig. 14.
Fig. 14.

Computational analysis for the quartz-crystal monitor indicating the erroneous thickness reading influence by the layer density fluctuations for the same frequency change of 1 kHz and with a Z-factor (acoustic impedance) of 0.8. This implies that thickness values given by the real-time quartz-crystal monitor need to be dynamically recalibrated as per the layer density fluctuations in order to establish the real or accurate thickness value.

Fig. 15.
Fig. 15.

Similar computational formulation depicting influence of acoustic impedance values of the layers for given density of 3.6gm/CC and frequency change of 1 kHz. The analysis indicates less influence of acoustic impedance on the layer thickness value. This indicates that the layer density fluctuations have serious implications over acoustic impedance variable of the layers in quartz-crystal monitoring.

Fig. 16.
Fig. 16.

Correlating influence of oxygen molecular fractions on the layer densities of the TiO2 layers. The investigations indicated that superstoichiometry has yielded a better density than substoichiometry.

Fig. 17.
Fig. 17.

Correlating influence of oxygen molecular fractions on the layer densities of the SiO2 layers. The investigations indicated that superstoichiometry has yielded a better density than substoichiometry.

Fig. 18.
Fig. 18.

Presenting the one-to-one correlation between the real-time experimental deposition pressures (dominantly oxygen gas) with the film stoichiometry. The real-time variation of the oxygen pressure during the deposition has strongly influenced the oxygen deficiencies (substoichiometry) or enrichments (superstoichiometry) in the oxide films as evident from RBS.

Fig. 19.
Fig. 19.

Comparison of areal densities values of TiO2 layers determined by the RBS experiment with the material density values computed from a combinatorial approach. Some of the less thick layers (i.e., relatively thin layers) depicted a deviation from the linearity, implying substantial stoichiometric fluctuations.

Fig. 20.
Fig. 20.

Comparison of areal densities values of SiO2 layers determined by the RBS experiment with the material density values computed from a combinatorial approach. Some of the less thick layers (i.e., relatively thin layers) depicted a deviation from the linearity, implying substantial stoichiometric fluctuations.

Tables (1)

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Table 1. Experimental Results and Output from RBS Measurements, Quartz-Crystal Monitoring, and Numerical Reverse Engineeringa

Equations (6)

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M(p)=[1Li=1LWi(DiδFi)m]1/m,
Di=FiT(exp)FiC(di,ni,ki,ϕi,λ),(1iL),
Tf=DqDf·Nq·Zf(π)·fc·Zq·tan1{ZqZf·tan[π(1fcfq)]},
n2=(1p)nv4+(1+p)nv2n02(1+p)nv2+(1p)n02,
ρ=pρ0+(1p)ρv.
ρ(gm/cm3)=(Areal Density)(atoms/cm2)Thickness×(amu/molecule)NA,

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