Methods for optical modeling and cross-checking in ellipsometry and scatterometry

Abstract

Indirect optical methods like ellipsometry or scatterometry require an optical model to calculate the response of the system, and to fit the parameters in order to minimize the difference between the calculated and measured values. The most common problem of optical modeling is that the measured structures and materials turn out to be more complex in reality than the simplified optical models used as first attempts to fit the measurement. The complexity of the optical models can be increased by introducing additional parameters, if they (1) are physically relevant, (2) improve the fit quality, (3) don't correlate with other parameters. The sensitivity of the parameters can be determined by mathematical analysis, but the accuracy has to be validated by reference methods. In this work some modeling and verification aspects of ellipsometry and optical scatterometry will be discussed and shown for a range of materials (semiconductors, dielectrics, composite materials), structures (damage and porosity profiles, gratings and other photonic structures, surface roughness) and cross-checking methods (atomic force microscopy, electron microscopy, x-ray diffraction, ion beam analysis). The high-sensitivity, high-throughput, in situ or in line capabilities of the optical methods will be demonstrated by different applications.

Full text

Methods for optical modeling and cross-checking in
ellipsometry and scatterometry
P. Petrika,c,d, B. Fodora,b, E. Agocsa,e , P. Kozmaa, J. Nadora,c, N. Kumard, J. Endrese, G.
Juhasza, C. Majora, S. F. Pereirad, T. Lohnera, H. P. Urbachd, B. Bodermanne, M. Frieda,c
aInstitute for Technical Physics and Materials Science, Centre for Energy Research, Hungarian
Academy of Sciences, Konkoly Thege Rd. 29-33, 1121 Budapest, Hungary
bDoctoral School of Physics, Faculty of Science, University of P´ecs, Ifj´us´ag Str. 6, 7624 P´ecs,
Hungary
cDoctoral School of Molecular- and Nanotechnologies, Faculty of Information Technology,
University of Pannonia, Egyetem Str. 10, 8200 Veszpr´em, Hungary
dDepartment of Imaging Physics, Faculty of Applied Sciences, Delft University of Technology,
P. O. Box 5046, 2600GA Delft, The Netherlands
ePhysikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
ABSTRACT
Indirect optical methods like ellipsometry or scatterometry require an optical model to calculate the response of
the system, and to fit the parameters in order to minimize the difference between the calculated and measured
values. The most common problem of optical modeling is that the measured structures and materials turn out to
be more complex in reality than the simplified optical models used as first attempts to fit the measurement. The
complexity of the optical models can be increased by introducing additional parameters, if they (1) are physically
relevant, (2) improve the fit quality, (3) don’t correlate with other parameters. The sensitivity of the parameters
can be determined by mathematical analysis, but the accuracy has to be validated by reference methods. In
this work some modeling and verification aspects of ellipsometry and optical scatterometry will be discussed and
shown for a range of materials (semiconductors, dielectrics, composite materials), structures (damage and poros-
ity profiles, gratings and other photonic structures, surface roughness) and cross-checking methods (atomic force
microscopy, electron microscopy, x-ray diffraction, ion beam analysis). The high-sensitivity, high-throughput, in
situ or in line capabilities of the optical methods will be demonstrated by different applications.
Keywords: Ellipsometry, Scatterometry, Cross-checking, Comparative Study, Optical characterization, Thin
films
1. INTRODUCTION
Thin film characterization methods are of primary importance in numerous key technologies like microelectron-
ics, photovoltaics or sensorics. Vertical compositions can usually be determined by removing the films (e.g. by
sputtering) during surface-sensitive measurements (such as secondary ion mass spectrometry, sputtered neutral
mass spectrometry, X-ray photoelectron spectrometry, Auger electron spectrometry, glow-discharge optical emis-
sion spectrometry, glow-discharge mass spectrometry, Raman depth profiling), by non-destructive depth-profiling
techniques (such as Rutherford backscattering spectrometry, elastic recoil detection analysis, angle-dependent
soft X-ray emission spectroscopy, grazing incidence X-ray diffraction, ellipsometry), or by cross sectioning tech-
niques (such as electron microscopy, scanning Auger electron microscopy, time-of-flight secondary ion mass
spectrometry, Raman mapping).1From the perspective of the above list and the features of thin film metrolo-
gies, the advantages of optical techniques like ellipsometry and scatterometry are three-fold. (1) They allow a
quick measurement. Ellipsometry is typically capable of measuring a broad spectrum (≈200-1700 nm) within
less than one second, whereas the other destructive (layer removal by sputtering) and cross-sectional methods
require minutes or rather hours (e.g. in case of electron microscopy) for measuring in one point. (2) The second
Corresponding author: Peter Petrik, petrik@mfa.kfki.hu

important feature is the sensitivity, especially in terms of vertical resolution, or geometrical parameters in case
of scatterometry. Also, the lateral scale of characterization can vary from the diffraction limit (down to about
one micron) to even meters. (3) Finally, the speed and sensitivity allows measurements on large surfaces2, 3 and
in situ or in line characterizations during thin film growth,4–6 processing7–14 and manufacturing.15, 16
However, there is also a major challenge: the quantification is made through optical models and numerical
methods, and therefore the interpretation of the results is not straightforward.17–19 Methods like the above
mentioned complementary techniques,1extended by scanning probe methods like atomic force microscopy (AFM)
or scanning tunneling microscopy, are often used for cross-checking and verification. As shown below, these
techniques also have drawbacks, such as different information depths. In this paper we show several results and
point out some challenges, mainly focusing on our own results as examples.
2. OPTICAL METHODS
Some of the widely used optical surface and thin film characterization methods are reflectometry,20, 21 ellipsome-
try17–19 (polarimetry in general) and scatterometry.22 All these methods measure the change of electromagnetic
radiation during reflection from or transmission through the investigated sample. The advantage of ellipsometry
over reflectometry is that the input intensity does not have to be known, and the sensitivity is higher due to the
capability of measuring the phase change between reflections polarized parallel and perpendicular to the plane
of incidence. Ellipsometry can be considered as a special kind of interferometry, in which the reference beam is
that of the orthogonal polarization. Scatterometry provides additional information if the sizes of characteristic
surface features or structures are comparable or larger than the wavelength used for the characterization. A new
possibility is the combination of the two methods,23 although ellipsometry has already been used for scattering
or diffracting samples in specular or normal-incidence configurations.24–27 The high speed of optical methods
can also be utilized in large area mapping of thin film properties,2, 3, 28 e.g. photovoltaic29 or display panels.
Currently a 40-point spectroscopic line-scan can be made in 10 s, and the near-future aim is a spectroscopic map
of a 60 cm by 120 cm photovoltaic panel within 1 min.29
An emerging powerful method is Fourier scatterometry, which measures the light scattered from the focus
of a large numerical aperture objective by imaging the Fourier plane.30, 31 Consequently, the major advantage
of the method is that a large range of scattering and azimuth angles (0-64 and 0-360 degrees for reflection and
azimuth angles, respectively, with a numerical aperture of 0.9) can be measured quickly and simultaneously.
A great challenge is currently the quick calculation based on the large number of acquired measurement data.
Improved sensitivity has been demonstrated by utilizing a scanning focused spot,32–38 interferometry39, 40 or
ellipsometry.23
3. MODELING
Being indirect methods, optical techniques like reflectometry, scatterometry or ellipsometry require some a pri-
ori information on the investigated structure, which helps to build proper optical models. When investigating
complex samples (e.g. involving special features like the line edge roughness,41 overlayer thickness and bottom
rounding,42 vertical inhomogeneity43 or the parameterization of the dielectric function for spectroscopic mea-
surements44) the number of fit parameters increases, and a reliable fit approaching the global minimum of the
system can only be achieved by sophisticated procedures45 like the maximum likelihood method,46 random global
search,47 simulated annealing or genetic algorithms.48
The sensitivity of the parameters can be checked by uncertainty analysis.23,32, 49 In case of spectroscopy and
characterization of material properties, the parameterization of the dielectric function is a major issue from which
a lot of technologically important material properties can be obtained, like for the case of polycrystalline semi-
conductors.50, 51 Also in scatterometry, using different wavelengths in a broad range can increase the accuracy,
reliability and the number of fit parameters.52
For the modeling of structures, the most widely used approach is to think in terms of stratified systems
composed of layers with plane and parallel boundaries, and to calculate the optical response using the transfer
matrix method53 or (in case of diffracting samples) by the rigorous coupled wave analysis (RCWA).14, 26, 27, 54, 55
Finite element (FEM)56, 57 and finite difference in time domain (FDTD) methods58–60 are also rapidly emerging.

In terms of materials, there is a wide range of parameterizations depending on the electron structure (mostly
categorized as dielectrics, metals or semiconductors).61, 62 Optical parameter reconstruction requires a lot of
computation, therefore, grid computing (as applied in Ref. 63) or using graphics processing units64, 65 are
becoming more and more important.
4. METHODS FOR CROSS-CHECKING
Because of their indirect character, the validation of optical methods is of primary importance. It means that
the method has to be traceable to a reference standard.66 Although a reference standard is a stable and highly
reproducible structure,67 it is suitable for validation only when measured and cross-checked with other reference
methods.66 As a primary aim, it is also crucial to achieve accurate optical measurements at the industrial level.68
There are numerous thin film characterization techniques including depth profiling like secondary ion mass
spectrometry, X-ray photoelectron spectrometry, Auger electron spectrometry, glow-discharge optical emission or
mass spectrometry, Raman depth profiling, non-destructive techniques such as Rutherford backscattering spec-
trometry, heavy ion elastic recoil detection, angle-dependent soft X-ray emission spectroscopy, grazing incidence
X-ray diffraction or ellipsometry. Finally, there are the most traditional cross-sectioning techniques like scanning
electron microscopy, scanning Auger electron microscopy, or Raman mapping.1Table 2 of Ref. 1 gives a nice
overview of the main characteristics of a large number of thin film profiling techniques. Most importantly, there
were significant deviations observed between the different methods by measuring on the same structure, which
also pointed out the importance of validation, and the significance of suitable reference and calibration structures
and methods.
5. PERIODIC SURFACE STRUCTURES
The most frequently applied structures used for the validation of scatterometry are two-dimensional gratings
evaluated by RCWA54, 55 or FEM57 using goniometric scatterometry,52,69 Fourier scatterometry30–32 or ellip-
sometry.14, 25–27 Most of these studies use scanning electron microscopy (SEM) and AFM for cross checking.
However, the measurement of side-wall angles and corner roundings are challenging with both methods, for which
only transmission electron microscopy (TEM) can be used as the most reliable reference method.
Measurement of height and side-wall angles are major weaknesses for SEM and AFM, respectively. Even with
TEM, a possible lateral inhomogeneity remains a great problem (also for line edge roughness characterizations31),
since the spot size of the optical measurements are usually much larger than the TEM image area. In Ref. 69,
the deviation between the different SEM approaches was comparable with its deviation from the optical results.
From top view SEM, a critical dimension deviation of approximately 3 nm was claimed with sophisticated signal
analysis for line widths of ≈100 nm. A typical agreement within several nanometers is obtained between the
scatterometric and electron microscopic results37–39 (with accurate height values measured only by AFM) and
also between different scatterometric approaches (Table 1), slightly depending on the methods for fitting and
modeling,70 e.g. considering a possible unintentional surface overlayer.38, 71
There is a large potential in the optical characterization of other two- or three-dimensional periodic structures
from biological72 or bio-inspired73, 74 to special fiber75 or sensor structures.76, 77 In all these, the measurement on
small areas (like single scales of butterfly wings78) or non-uniform surfaces is an important challenge, as well as the
capability of the proper alignment of the sample surface. Efficient and powerful calculation methods53–55, 57, 60, 79
with sophisticated algorithms45, 46, 48, 63 are also becoming increasingly needed.
6. SURFACE ROUGHNESS AND ULTRA-THIN LAYERS
The high surface sensitivity of ellipsometry makes it especially suitable for roughness measurements for both
surfaces80 and interfaces81–83 on the nanometer scale. Besides other sophisticated methods like the Rayleigh-
Rice theory,84 the most popular and robust method for surface roughness measurement is the effective medium
approximation (EMA).80, 85–87 Although a good correlation was revealed between the root mean square roughness
measured by AFM and the thickness of the roughness layer measured by ellipsometry using the EMA, some effects
like the window size in AFM have to be taken into account for a proper comparison and quantification (Fig. 1).

Table 1. Best-fit reconstruction of Si gratings using deep ultraviolet (DUV) scatterometry and Fourier scatterometry,
utilizing the maximum likelihood estimation (MLE) and the non-linear least squares fit. The parameters of the grating
are listed in the first column. [Reprinted from the SPIE Proceedings 9132 (2014) 913208-1, Endres et al., ”Measurement
comparison of goniometric scatterometry and coherent Fourier scatterometry”.]
Figure 1. Root mean square (RMS) roughness measured by atomic force microscopy (AFM) correlated with the roughness
determined by spectroscopic ellipsometry (SE), for different AFM window sizes.87 [Reprinted from Thin Solid Films
315 (1998) 186, Petrik et al., ”Surface roughness measurement on polysilicon produced by low pressure chemical vapor
deposition using spectroscopic ellipsometry and atomic force microscopy”. Copyright 1998, with permission from Elsevier.]

Figure 2. Damage depth profiles in Si, induced by implantation of Xe+, Ar+and N+
2ions at different energies (see graphs)
measured by spectroscopic ellipsometry (lines) verified by Rutherford backscattering spectrometry (RBS). The optical
models were based on coupled half-Gaussians97, 98 with equal sublayer thicknesses (Model 1) or sublayer thicknesses
inversely proportional to the slope of the profile (Model 2,92). Reprinted from the Journal of Applied Physics 93 (2003)
1987, Petrik et al., ”Ellipsometric characterization of damage profiles using an advanced optical model”.
In case of ultra-thin (several nanometers) layers the interface roughnesses82, 83 and the surface contamination
are crucial questions. It was shown that native oxide covered samples acquire 0.1 to 0.2 nm of organic con-
tamination within two hours stored in closed but nonvacuum conditions. Subsequently, another 0.2 to 0.5 nm
layer is deposited, which is saturated in approximately in one week.88 The thickness in that study was a kind
of ’SiO2-equivalent’ thickness – the accurate analytical measurement of low surface contamination is also very
challenging.89 The above contamination layer is the reason why ellipsometry usually slightly overestimates the
thicknesses of ultra-thin layers when compared with methods measuring in vacuum (see the comprehensive study
involving ion beam, X-ray, electron and optical investigations in Ref. 90).
7. DEPTH PROFILING IN SEMICONDUCTORS
For optical techniques accessing higher photon energies (e.g. the direct interband transition energies of 3.4
and 4.2 eV in Si), the long range order and minute changes in the crystal lattice can be measured with high
sensitivity. This is the reason why ellipsometry can be applied for the measurement of polycrystalline and ion
implanted semiconductors. Damage profiles can be determined from the optical measurements using multilayer
models with the EMA and the transfer matrix method. Besides TEM, an accurate verification method for
damage profile measurement is the ion beam analysis (when the sample is single-crystalline or the grains of
the polycrystal are not randomly oriented91) irradiated from channeling directions. Fig. 2 demonstrates the
agreement in damage profiles measured by ellipsometry and Rutherford backscattering spectrometry (RBS).92
In case of very thin layers, medium energy ion scattering is even more accurate than RBS.93, 94 The combination
of RBS with ellipsometry is also a powerful method for density measurements, because ellipsometry provides an
accurate thickness value, whereas RBS delivers the number of atoms per unit surface.95
In case of near surface cavities in Si, the high sensitivity is ensured by the large optical contrast between
void and Si. In this case, TEM is the most suitable verification method. We have obtained good agreements in
different studies.63,96
Finally, it should be pointed out that the decreased penetration depth at direct interband transition photon
energies is not only a problem, but it can also be utilized for depth scanning, when properly choosing the
wavelength range used for the optical characterization (Fig. 3). By a systematic scan of the wavelength range,
the penetration depth can be varied in a controlled way, which allows a model-independent direct depth scan.
This might open new directions in the optical characterization of vertically non-uniform absorbing films.99

Figure 3. Extinction coefficient (k) and optical penetration depth (OPD) of a polycrystalline silicon layer (see TEM image
on the right-hand side) as a function of the wavelength. The uncertainty of the fitted thickness is also shown as a function
of the cut-off wavelength.
CONCLUSIONS
We have shown some aspects of optical modeling and cross-checking in ellipsometry and scatterometry. Proper
quantification and the need for reference samples remain major challenges in the future, not only for optical but
also for most other metrologies.1, 89, 90
ACKNOWLEDGMENTS
Support from ENIAC E450EDL, KMR 12 1 2012 0225, EMRP IND17 joint research project on scatterometry
and from OTKA grant K81842 are greatly acknowledged. The EMRP is jointly funded by the EMRP partici-
pating countries within EURAMET and the European Union.
REFERENCES
1. Abou-Ras, D., Caballero, R., Fischer, C.-H., Kaufmann, C. A., Lauermann, I., Mainz, R., M¨onig, H.,
Sch¨opke, A., Stephan, C., Streeck, C., Schorr, S., Eicke, A., D¨obeli, M., Gade, B., Hinrichs, J., Nunney, T.,
Dijkstra, H., Hoffmann, V., Klemm, D., Efimova, V., Bergmaier, A., Dollinger, G., Wirth, T., Unger, W.,
Rockett, A. A., Perez-Rodriguez, A., Alvarez-Garcia, J., Izquierdo-Roca, V., Schmid, T., Choi, P.-P., M¨uller,
M., Bertram, F., Christen, J., Khatri, H., Collins, R. W., Marsillac, S., and K¨otschau, I., “Comprehensive
comparison of various techniques for the analysis of elemental distributions in thin films,” Microscopy and
Microanalysis 17, 728 (2011).
2. Juhasz, G., Horvath, Z., Major, C., Petrik, P., Polgar, O., and Fried, M., “Non-collimated beam ellipsome-
try,” Physica Status Solidi C 5, 1081 (2008).
3. Fried, M., Juhasz, G., Major, C., Petrik, P., Polgar, O., Horvath, Z., and Nutsch, A., “Expanded beam
(macro-imaging) ellipsometry,” Thin Solid Films 519, 2730 (2011).
4. Kurunczi, S., Nemeth, A., Hulber, T., Kozma, P., Petrik, P., Jankovics, H., Sebestyen, A., Vonderviszt,
F., Fried, M., and Barsony, I., “In situ ellipsometric study of surface immobilization of flagellar filaments,”
Appl. Surf. Sci. 257, 319 (2010).
5. Nemeth, A., Kozma, P., Hulber, T., Kurunczi, S., Horvath, R., Petrik, P., Muskotal, A., Vonderviszt,
F., H˝os, C., Fried, M., Gyulai, J., and Barsony, I., “In situ spectroscopic ellipsometry study of protein
immobilization on different substrates using liquid cells,” Sensor Letters 8, 1 (2010).

6. Kozma, P., Kozma, D., Nemeth, A., Jankovics, H., Kurunczi, S., Horvath, R., Vonderviszt, F., Fried, M.,
and Petrik, P., “In-depth characterization and computational 3d reconstruction of flagellar filament protein
layer structure based on in situ spectroscopic ellipsometry measurements,” Appl. Surf. Sci. 257, 7160 (2011).
7. Collins, R. W. and Yang, B. Y., “In situ ellipsometry of thin-film deposition: Implications for amorphous
and microcrystalline si growth,” J. Vac. Sci. Technol. B7, 1155 (1989).
8. Vuye, G., Fisson, S., Van, V. N., Wang, Y., Rivory, J., and Abel`es, F., “Temperature dependence of the
dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233, 166 (1993).
9. Tachibana, K., Shirafuji, T., Hayashi, Y., and Maekawa, S., “In situ ellipsometric monitoring of the growth
of polycrystalline silicon thin films by rf plasma chemical vapor deposition,” Japanese Journal of Applied
Physics 33, 4191 (1994).
10. Lehnert, W., Berger, R., Schneider, C., Pfitzner, L., Ryssel, H., Stehle, J. L., Piel, J.-P., and Neumann, W.,
“In situ spectroscopic ellipsometry for advanced process control in vertical furnaces,” Thin Solid Films 313-
314, 442 (1998).
11. P. R. Lefebvre, Zhao, C., and E. A. Irene, “An in situ and ex situ ellipsometry comparison of the interfaces
of si and gaas resulting from thermal and plasma oxidation,” Thin Solid Films 313-314, 454 (1998).
12. Maynard, H. L., Layadi, N., and Lee, J. T. C., “Plasma etching of submicron devices: in situ monitoring
and control by multi-wavelength ellipsometry,” Thin Solid Films 313-314, 398 (1998).
13. Petrik, P., Lehnert, W., Schneider, C., Fried, M., Lohner, T., Gyulai, J., and Ryssel, H., “In situ spectro-
scopic ellipsometry for the characterization of polysilicon formation inside a vertical furnace,” Thin Solid
Films 364, 150 (2000).
14. Huang, H.-T. and Terry Jr, F. L., “Erratum to Spectroscopic ellipsometry and reflectometry from gratings
(Scatterometry) for critical dimension measurement and in situ, real-time process monitoring [Thin Solid
Films 455456 (2004) 828836],” Thin Solid Films 468, 339–346 (Dec. 2004).
15. Piel, J.-P., Stehle, J.-L., and Thomas, O., “The fastest real time spectroscopic ellipsometry: Applications
and limitations for in situ and quality control,” Thin Solid Films 233, 301 (1993).
16. Schneider, C., Berger, R., Pfitzner, L., and Ryssel, H., “In situ ellipsometry for real-time feedback control
of oxidation furnaces,” Appl. Surf. Sci. 63, 135 (1993).
17. Tompkins, H. G. and Irene, E. A., [Handbook Of Ellipsometry ], William Andrew (2005).
18. Fujiwara, H., [Spectroscopic Ellipsometry: Principles and Applications], Wiley, New York (2007).
19. Losurdo, M. and Hingerl, K., [Ellipsometry at the Nanoscale], Springer-Verlag, Heidelberg (2012).
20. Gumprecht, T., Petrik, P., Roeder, G., Schellenberger, M., Pfitzner, L., and Pollakowski, B., “Characteri-
zation of Thin ZnO Films by Vacuum Ultra-Violet Reflectometry,” 1494 (2012).
21. Neˇcas, D., ˇ
Cudek, V., Vod´ak, J., Ohl´ıdal, M., Klapetek, P., Benedikt, J., R¨ugner, K., and Zaj´ıˇckov´a, L.,
“Mapping of properties of thin plasma jet films using imaging spectroscopic reflectometry,” Measurement
Science and Technology 25, 115201 (Nov. 2014).
22. Bodermann, B., Buhr, E., Danzebrink, H.-U., B¨ar, M., Scholze, F., Krumrey, M., Wurm, M., Klapetek,
P., Hansen, P.-E., Korpelainen, V., van Veghel, M., Yacoot, A., Siitonen, S., O. El Gawhary, Burger,
S., and Saastamoinen, T., “Joint research on scatterometry and AFM wafer metrology,” AIP Conference
Proceedings 1395, 319 (2011).
23. Petrik, P., Kumar, N., Fried, M., Fodor, B., Juhasz, G., Pereira, S. F., Burger, S., and Urbach, H. P., “Fourier
ellipsometry – an ellipsometric approach to Fourier scatterometry,” Journal of the European Optical Society:
Rapid Publications 10, 15002 (Jan. 2015).
24. Niu, X., Jakatdar, N., Bao, J., Spanos, C., and Yedur, S., “Specular spectroscopic scatterometry in DUV
lithography,” Proceedings of SPIE - The International Society for Optical Engineering 3677(I), 159–168
(1999).
25. Huang, H.-T., Kong, W., and Terry, F. L., “Normal-incidence spectroscopic ellipsometry for critical dimen-
sion monitoring,” Applied Physics Letters 78, 3983 (2001).
26. Antos, R., Pistora, J., Ohlidal, I., Postava, K., Mistrik, J., Yamaguchi, T., Visnovsky, S., and Horie, M.,
“Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick
transparent plate,” Journal of Applied Physics 97(5), 053107 (2005).

27. Antos, R., Pistora, J., Mistrik, J., Yamaguchi, T., Yamaguchi, S., Horie, M., Visnovsky, S., and Otani, Y.,
“Convergence properties of critical dimension measurements by spectroscopic ellipsometry on gratings made
of various materials,” Journal of Applied Physics 100(5), 054906 (2006).
28. Fried, M., Juhasz, G., Major, C., Nemeth, A., Petrik, P., Polgar, O., Salupo, C., Dahal, L. R., and
Collins, R. W., “Application of a Dual-spectral-range, Divergent-beam Spectroscopic Ellipsometer for High-
Speed Mapping of Large-area, Laterally-inhomogeneous, Photovoltaic Multilayers,” MRS Proceedings 1323,
mrss11–1323–c03–12 (June 2011).
29. Fried, M., “On-line monitoring of solar cell module production by ellipsometry technique,” Thin Solid
Films 571, 345–355 (Nov. 2014).
30. Boher, P., Luet, M., Leroux, T., Petit, J., Barritault, P., Hazart, J., and Chaton, P., “Innovative rapid
photo-goniometry method for CD metrology,” SPIE Proceedings 5375, 1302 (2004).
31. Boher, P., Petit, J., Foucher, J., Desieres, Y., Hazart, J., and Chaton, P., “Optical Fourier transform
scatterometry for LER and LWR metrology,” SPIE Proceedings 5752, 192 (2005).
32. El Gawhary, O., Kumar, N., Pereira, S. F., Coene, W. M. J., and Urbach, H. P., “Performance analysis of
coherent optical scatterometry,” Applied Physics B 105, 775 (2011).
33. Roy, S., El Gawhary, O., Kumar, N., Pereira, S. F., and Urbach, H. P., “Scanning effects in coherent fourier
scatterometry,” Journal of the European Optical Society - Rapid Publications 7, 12031 (2012).
34. Kumar, N., El Gawhary, O., Roy, S., Kutchoukov, V. G., Pereira, S. F., Coene, W., and Urbach, H. P.,
“Coherent Fourier scatterometry (tool for improved sensitivity in semiconductor metrology),” SPIE Pro-
ceedings 8324, 83240Q (2012).
35. Kumar, N., El Gawhary, O., Roy, S., Pereira, S. F., and Urbach, H. P., “Phase information in coherent
Fourier scatterometry,” SPIE Proceedings 8788, 87881P (2013).
36. Kumar, N., El Gawhary, O., Roy, S., Pereira, S. F., and Urbach, H. P., “Phase retrieval between overlapping
orders in coherent Fourier scatterometry using scanning,” Journal of the European Optical Society - Rapid
Publications 8, 13048 (2013).
37. Kumar, N., Petrik, P., Ramanandan, G. K. P., El Gawhary, O., Roy, S., Pereira, S. F., Coene, W. M. J., and
Urbach, H. P., “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent
Fourier scatterometry.,” Optics express 22, 24678–88 (Oct. 2014).
38. Kumar, N., Coherent Fourier Scatterometry, PhD thesis, Delft University of Technology (2015).
39. Paz, V. F., Peterh¨ansel, S., Frenner, K., and Osten, W., “Solving the inverse grating problem by white light
interference fourier scatterometry,” Nature Light: Science and Applications 1, e36 (2012).
40. Roy, S., Kumar, N., Pereira, S. F., and Urbach, H. P., “Interferometric coherent fourier scatterometry: a
method for obtaining high sensitivity in the optical inverse-grating problem,” Journal of Optics 15, 075707
(2013).
41. Gross, H., Henn, M.-A., Heidenreich, S., Rathsfeld, A., and B¨ar, M., “Modeling of line roughness and its
impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry,” Applied
Optics 51, 7384 (Oct. 2012).
42. Endres, J., Diener, A., Wurm, M., and Bodermann, B., “Investigations of the influence of common approxi-
mations in scatterometry for dimensional nanometrology,” Measurement Science and Technology 25, 044004
(Apr. 2014).
43. Petrik, P., “Ellipsometric models for vertically inhomogeneous composite structures,” Physica Status Solidi
A205, 732 (2008).
44. Basa, P., Petrik, P., Fried, M., Dobos, L., P´ecz, B., and T´oth, L., “Si nanocrystals in silicon nitride: An
ellipsometric study using parametric semiconductor models,” Physica E 38, 76 (2007).
45. Polgar, O., Petrik, P., Lohner, T., and Fried, M., “Evaluation strategies for multi-layer, multi-material
ellipsometric measurements,” Applied Surface Science 253, 57 (2006).
46. Henn, M.-A., Gross, H., Scholze, F., Wurm, M., Elster, C., and B¨ar, M., “A maximum likelihood approach
to the inverse problem of scatterometry.,” Optics Express 20(12), 12771–86 (2012).
47. Petrik, P., Cayrel, F., Fried, M., Lohner, T., Polg´ar, O., Gyulai, J., and Alquier, D., “Optical models
for cavity profiles in high-dose helium-implanted and annealed silicon measured by ellipsometry,” J. Appl.
Phys 97, 123514 (2005).

48. Polg´ar, O., Fried, M., Lohner, T., and B´arsony, I., “Comparison of algorithms used for evaluation of
ellipsometric measurements random search, genetic algorithms, simulated annealing and hill climbing graph-
searches,” Surface Science 457, 157–177 (June 2000).
49. Germer, T. A., Patrick, H. J., Silver, R. M., and Bunday, B., “¡title¿Developing an uncertainty analysis for
optical scatterometry¡/title¿,” in [Proceedings of SPIE - The International Society for Optical Engineering],
Allgair, J. A. and Raymond, C. J., eds., 7272, 72720T–72720T–11 (Mar. 2009).
50. Petrik, P. and Fried, M., “Ellipsometry of semiconductor nanocrystals,” in [Ellipsometry at the Nanoscale],
Losurdo, M. and Hingerl, K., eds., Springer-Verlag, Heidelberg (2012).
51. Petrik, P., “Characterization of nanocrystals using spectroscopic ellipsometry,” in [Nanocrystals - Syn-
thesis, Characterization and Applications], Neralla, S., ed., InTech (2012). DOI: 10.5772/48732,
ISBN: 978-953-51-0714-9, http://www.intechopen.com/books/nanocrystals-synthesis-characterization-and-
applications/characterization-of-nanocrystals-using-spectroscopic-ellipsometry.
52. Scholze, F., Bodermann, B., Burger, S., Endres, J., Haase, A., Krumrey, M., Laubis, C., Soltwisch, V.,
Ullrich, A., and Wernecke, J., “Determination of line profiles on photomasks using DUV, EUV, and x-ray
scattering,” in [Proceedings of SPIE - The International Society for Optical Engineering], Behringer, U.
F. W., ed., 9231, 92310M, SPIE (Oct. 2014).
53. Azzam, R. M. A. and Bashara, N. M., [Ellipsometry and Polarized Light], Elsevier (1987).
54. Moharam, M. G., Pommet, D. A., and Grann, E. B., “Stable implementation of the rigorous coupled-wave
analysis for surface-relief gratings: enhanced transmittance matrix approach,” Journal of the Optical Society
of America 12, 1077 (1995).
55. van Kraaij, M. G. M. M., Forward Diffraction Modelling: Analysis and Application to Grating Reconstruc-
tion, PhD thesis, Technische Universiteit Eindhoven (2011).
56. Burger, S., K¨ohle, R., Zschiedrich, L., Gao, W., Schmidt, F., M¨arz, R., and N¨olscher, C., “Benchmark
of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” in [Proceedings of SPIE - The
International Society for Optical Engineering], Weed, J. T. and Martin, P. M., eds., 5992, 599216–599216–12
(Oct. 2005).
57. Burger, S., Zschiedrich, L., Pomplun, J., Schmidt, F., and Bodermann, B., “Fast simulation method for pa-
rameter reconstruction in optical metrology,” Proc. SPIE 8681, Metrology, Inspection, and Process Control
for Microlithography XXVII 8681, 868119 (2013).
58. Cheung, K. T., Foo, Y., To, C. H., and Zapien, J. A., “Towards FDTD modeling of spectroscopic ellipsometry
data at large angles of incidence,” Applied Surface Science 281, 2–7 (Sept. 2013).
59. Foo, Y., Cheung, K. T., To, C. H., and Zapien, J. A., “On the modeling of ellipsometry data at large angles
of incidence using finite-difference time-domain,” Thin Solid Films 571, 669–674 (Nov. 2014).
60. P. Klapetek and M. Valtr, gsvit FDTD solver. http://www.gsvit.net (2015).
61. Fried, M., Lohner, T., and Petrik, P., “Ellipsometric characterization of thin films,” in [Handbook of Surfaces
and Interfaces of materials: ”Solid Thin Films and Layers”], Nalwa, H. S., ed., Academic Press, San Diego
(2001).
62. Collins, R. W. and Ferlauto, A. S., “Optical physics of materials,” in [Handbook of ellipsometry], Irene,
E. G. and Tomkins, H. G., eds., William Andrew, Norwich, NY (2005).
63. Petrik, P., Fried, M., Vazsonyi, E., Basa, P., Lohner, T., Kozma, P., and Makkai, Z., “Nanocrystal charac-
terization by ellipsometry in porous silicon using model dielectric function,” Journal of Applied Physics 105,
024908 (2009).
64. Klapetek, P. and Valtr, M., “Near-field optical microscopy simulations using graphics processing units,”
Surface and Interface Analysis 42, 1109–1113 (Apr. 2010).
65. Klapetek, P., Valtr, M., Poruba, A., Neˇcas, D., and Ohl´ıdal, M., “Rough surface scattering simulations
using graphics cards,” Applied Surface Science 256, 5640–5643 (July 2010).
66. Bodermann, B., Loechel, B., Scholze, F., Dai, G., Wernecke, J., Endres, J., Probst, J., Schoengen, M.,
Krumrey, M., Hansen, P.-E., and Soltwisch, V., “Development of a scatterometry reference standard,” in
[Proceedings of SPIE - The International Society for Optical Engineering], Gorecki, C., Asundi, A. K., and
Osten, W., eds., 9132, 91320A, SPIE (May 2014).

67. Bodermann, B., Hansen, P.-E., Burger, S., Henn, M.-A., Gross, H., B¨ar, M., Scholze, F., Endres, J., and
Wurm, M., “First steps towards a scatterometry reference standard,” SPIE Proceedings 8466, 84660E–1
(2012).
68. Bodermann, B., K¨oning, R., Bergmann, D., H¨aß ler Grohne, W., Fl¨ugge, J., and Bosse, H., [Road towards
accurate optical width measurements at the industrial level], Springer Berlin Heidelberg, Berlin, Heidelberg
(2014).
69. Raymond, C. J., Murnane, M. R., Prins, S. L., Sohail, S., Naqvi, H., McNeil, J. R., and Hosch, J. W., “Mul-
tiparameter grating metrology using optical scatterometry,” Journal of Vacuum Science and Technology B:
Microelectronics and Nanometer Structures 15(2), 361–368 (1997).
70. Endres, J., Kumar, N., Petrik, P., M.-A. Henn, Heidenreich, S., Pereira, S. F., Urbach, H. P., and Bo-
dermann, B., “Measurement comparison of goniometric scatterometry and coherent fourier scatterometry,”
SPIE Proceedings 9132, 913208–1 (2014).
71. Kumar, N., Petrik, P., Pereira, S. F., and Urbach, P., “Reconstruction of unintentional surface over-layer
thickness on si-etched gratings,” to be published.
72. Arwin, H., Magnusson, R., Garcia-Caurel, E., Fallet, C., J¨arrendahl, K., Foldyna, M., De Martino, A.,
and Ossikovski, R., “Sum decomposition of Mueller-matrix images and spectra of beetle cuticles,” Optics
Express 23(3), 1951–1966 (2015).
73. Bir´o, L. and Vigneron, J., “Photonic nanoarchitectures in butterflies and beetles: valuable sources for
bioinspiration,” Laser & Photonics Reviews 5, 27–51 (Jan. 2011).
74. Tam´aska, I., V´ertesy, Z., De´ak, A., Petrik, P., Kert´esz, K., and Bir´o, L. P., “Optical properties of bioinspired
disordered photonic nanoarchitectures,” Nanopages 8, 17 (2013).
75. Hansen, P.-E. and Burger, S., “Investigation of microstructured fiber geometries by scatterometry,” in
[Proceedings of SPIE - The International Society for Optical Engineering], Bodermann, B., Frenner, K.,
and Silver, R. M., eds., 8789, 87890R (May 2013).
76. Kert´esz, K., Piszter, G., Jakab, E., B´alint, Z., V´ertesy, Z., and Bir´o, L. P., “Temperature and saturation
dependence in the vapor sensing of butterfly wing scales.,” Materials science & engineering. C, Materials
for biological applications 39, 221–6 (June 2014).
77. Piszter, G., Kert´esz, K., V´ertesy, Z., B´alint, Z., and Bir´o, L. P., “Substance specific chemical sensing with
pristine and modified photonic nanoarchitectures occurring in blue butterfly wing scales.,” Optics express 22,
22649–60 (Sept. 2014).
78. Kert´esz, K., Moln´ar, G., V´ertesy, Z., Ko´os, A., Horv´ath, Z., M´ark, G., Tapaszt´o, L., B´alint, Z., Tam´aska, I.,
Deparis, O., Vigneron, J., and Bir´o, L., “Photonic band gap materials in butterfly scales: A possible source
of blueprints,” Materials Science and Engineering: B 149, 259–265 (Apr. 2008).
79. T. Germer, Polarized Light Scattering C++ Class Library. http://pml.nist.gov/Scatmech/html/index.htm
(2015).
80. Aspnes, D. E., Theeten, J. B., and Hottier, F., “Investigation of effective-medium models of microscopic
surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292 (1979).
81. Aspnes, D. E. and Theeten, J. B., “Spectroscopic analysis of the interface between si and its thermally
grown oxide,” J. Electrochem. Soc. 127, 1359 (1980).
82. Petrik, P., Lohner, T., Fried, M., Gyulai, J., Boell, U., Berger, R., and Lehnert, W., “Ellipsometric study
of the polysilicon/thin oxide/single-crystalline silicon structure and its change upon annealing,” Journal of
Applied Physics 92, 2374 (2002).
83. Petrik, P., Szil´agyi, E., Lohner, T., Battistig, G., Fried, M., Dobrik, G., and Bir´o, L. P., “Optical models for
ultrathin oxides on Si- and C-terminated faces of thermally oxidized SiC,” Journal of Applied Physics 106,
123506 (2009).
84. Franta, D., Ohl´ıdal, I., and Necas, D., “Optical quantities of rough films calculated by Rayleigh-Rice theory,”
physica status solidi (c) 5, 1395–1398 (May 2008).
85. Aspnes, D. E., “Optical properties of thin films,” Thin Solid Films 89, 249 (1982).
86. Liu, Q., Wall, J. F., and Irene, E. A., “Interface studies by spectroscopic immersion ellipsometry and atomic
force microscopy,” J. Vac. Sci. Technol. A A12, 2625 (1994).

87. Petrik, P., Bir´o, L. P., Fried, M., Lohner, T., Berger, R., Schneider, C., Gyulai, J., and Ryssel, H., “Surface
roughness measurement on polysilicon produced by low pressure chemical vapor deposition using spectro-
scopic ellipsometry and atomic force microscopy,” Thin Solid Films 315, 186 (1998).
88. Strein, E. and Allred, D., “Eliminating carbon contamination on oxidized Si surfaces using a VUV excimer
lamp,” Thin Solid Films 517, 1011 (2008).
89. Nutsch, A., Beckhoff, B., Altmann, R., Van den Berg, J., Giubertoni, D., Hoenicke, P., Bersani, M., Leibold,
A., Meirer, F., M¨uller, M., Pepponi, G., Otto, M., Petrik, P., Reading, M., Pfitzner, L., and Ryssel, H.,
“Complementary Metrology within a European Joint Laboratory,” Solid State Phenomena 145-146, 97–100
(2009).
90. van den Berg, J. A., Reading, M. A., Parisini, A., Kolbe, M., Beckhoff, B., Ladas, S., Fried, M., Petrik, P.,
Bailey, P., Noakes, T., Conard, T., and Gendt, S. D., “High Resolution Depth Profile Analysis of Ultra Thin
High-k Hf Based Films Using MEIS Compared with XTEM, XRF, SE and XPS,” ECS Transactions 25,
349 (2009).
91. Petrik, P., Lohner, T., Fried, M., Kh´anh, N. Q., Polg´ar, O., and Gyulai, J., “Comparative study of ion im-
plantation caused damage depth profiles in polycrystalline and single crystalline silicon studied by spectro-
scopic ellipsometry and rutherford backscattering spectrometry,” Nuclear Instruments and Methods B B147,
84 (1999).
92. Petrik, P., Polg´ar, O., Fried, M., Lohner, T., Kh´anh, N. Q., and Gyulai, J., “Ellipsometric characterization
of damage profiles using an advanced model,” Journal of Applied Physics 93, 1987 (2003).
93. Giubertoni, D., Pepponi, G., Beckhoff, B., Hoenicke, P., Gennaro, S., Meirer, F., Ingerle, D., Steinhauser,
G., Fried, M., Petrik, P., Parisini, A., Reading, M. A., Streli, C., van den Berg, J. A., Bersani, M., Secula,
E. M., Seiler, D. G., Khosla, R. P., Herr, D., Michael Garner, C., McDonald, R., and Diebold, A. C., “Multi-
technique characterization of arsenic ultra shallow junctions in silicon within the ANNA consortium,” in
[AIP Conference Proceedings], 1173, 45–49, AIP (2009).
94. Mohacsi, I., Petrik, P., Fried, M., Lohner, T., Van Den Berg, J. a., Reading, M. a., Giubertoni, D., Barozzi,
M., and Parisini, a., “Characterisation of ultra-shallow disorder profiles and dielectric functions in ion
implanted Si,” Thin Solid Films 519, 2847–2851 (Feb. 2011).
95. Szil´agyi, E., Petrik, P., Lohner, T., Ko´os, A. A., Fried, M., and Battistig, G., “Oxidation of sic investigated
by ellipsometry and rutherford backscattering spectrometry,” Journal of Applied Physics 104, 014903 (2008).
96. Fodor, B., Cayrel, F., Agocs, E., Alquier, D., Fried, M., and Petrik, P., “Characterization of in-depth cavity
distribution after thermal annealing of helium-implanted silicon and gallium nitride,” Thin Solid Films 571,
567–572 (2014).
97. Fried, M., Lohner, T., J´aroli, E., Hajdu, C., and Gyulai, J., “Non-destructive determination of damage
depth profiles in ion-implanted semiconductors by multiple-angle-of-incidence single-wavelength ellipsome-
try,” Nucl. Instr. Meth. B 55, 257 (1991).
98. Fried, M., Lohner, T., Aarnink, W. A. M., Hanekamp, L. J., and van Silfhout, A., “Nondestructive de-
termination of damage depth profiles in ion-implanted semiconductors by spectroscopic ellipsometry using
different optical models,” Journal of Applied Physics 71, 2835 (1992).
99. Petrik, P., Agocs, E., Volk, J., Lukacs, I., Fodor, B., Kozma, P., Lohner, T., Oh, S., Wakayama, Y., Nagata,
T., and Fried, M., “Resolving lateral and vertical structures by ellipsometry using wavelength range scan,”
Thin Solid Films 571, 579 (2014).