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Ellipsometry at the Nanoscale pp 341–410Cite as

Generalized Ellipsometry Characterization of Sculptured Thin Films Made by Glancing Angle Deposition

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Abstract

Generalized ellipsometry, a non-destructive optical characterization technique, is employed to determine geometrical structure parameters and anisotropic dielectric properties of highly spatially coherent three-dimensionally nanostructured thin films in the spectral range from 400 to 1700 nm. The analysis of metal slanted columnar thin films fabricated by glancing angle deposition reveals their monoclinic optical properties and their optical response can be modeled with a single homogeneous biaxial layer. This homogeneous biaxial layer approach is universally applicable to sculptured thin films and effective optical properties of the nanostructured thin films are attained. We provide a nomenclature and categorization for sculptured thin films based on their geometry and structure. A piecewise homogeneous biaxial layer approach is described, which allows for the determination of principal optical constants of chiral and achiral multi-fold and helical sculptured thin films. It is confirmed that such sculptured thin films have modular optical properties. This characteristic can be exploited to predict the optical response of sculptured thin films grown with arbitrary sequential substrate rotations. As an alternative model approach, an anisotropic effective medium approximation based on the Bruggeman formula is presented, which provides results comparable to the homogeneous biaxial layer approach and in addition provides the volume fraction parameters for slanted columnar thin films and their depolarization factors.

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Notes

  1. 1.

    The term chiral is derived from the Greek word for hand and is used to describe an object that is non-superposable on its mirror image.

  2. 2.

    New nomenclatures are introduced for different sculptured thin film geometries. See Table 10.1.

  3. 3.

    The abbreviation “s” comes from the German word senkrecht for perpendicular.

  4. 4.

    Unless used unambiguously as running index, the symbol “\(i\)” addresses the imaginary unit \(\sqrt{-1}\).

  5. 5.

    Considerations are given for a reflection set up, but hold for the complex-valued ratio of polarized plane wave components in the transmission arrangement as well.

  6. 6.

    In this notation the first index denotes the incident polarization mode, and the second index refers to the outgoing polarization mode.

  7. 7.

    The Stokes parameters have dimensions of intensities.

  8. 8.

    Sample, mirrors, rotators, optical devices within the light path, and any combinations thereof.

  9. 9.

    Note that \(\mathbf{A }^{-1} = \mathbf{A }^T\), where \(\{\cdot \}^T\) denotes the transpose of a matrix.

  10. 10.

    For purely dielectric material without internal or external magnetic fields, due to invariance upon time-reversal, there is no directional dependence along one axis (Onsager principle).

  11. 11.

    Note the uncommon assignment of unit cell angles. This notation is chosen here because it is equivalent to the definition of the ellipsometric analysis software WVASE32\(^\circledR \) [79] and is illustrated in Fig. 10.5.

  12. 12.

    Further details and analytical solutions for \(\mathbf{T }_{\mathrm{p }}\) can be found in the literature [68, 82].

  13. 13.

    At one wavelength, a symmetrical thin-film combination (periodically stratified medium) is equivalent to a single film, characterized by an equivalent index and equivalent thickness [87].

  14. 14.

    Very fast substrate rotation (\(<\)2 nm vertical growth per revolution) results in V-STFs, i.e., a screw degenerates to a straight column because the pitch is too small. Optical properties of V-STFs are not discussed in this chapter, however, the nanostructured film has uniaxial properties with the ordinary dielectric constant in the substrate interface and the extraordinary along the columns and normal to the substrate.

  15. 15.

    For nomenclature see Table 10.1.

  16. 16.

    For materials with monoclinic and triclinic symmetry \(\varepsilon _j(\omega )\) depend on the polarization functions \(\varrho _{a}, \varrho _{b}, \varrho _{c}\) and their non-Cartesian axes \(\mathbf{a }\), \(\mathbf{b }\), and \(\mathbf{c }\) as described in Sect. 10.3.4.

  17. 17.

    Mueller matrix elements of the fourth row cannot be resolved because the polarization state analyzer (2) does not comprise a rotating compensator [66, 67].

  18. 18.

    A DC offset calibration determines the detector noise level without source illumination.

  19. 19.

    Cobalt has a specified purity of 99.95 % and titanium 99.995 %. Supermalloy is composed of 79.8 % Ni, 15.1 % Fe, and 5.1 % Mo.

  20. 20.

    In case the sample under investigation does not exhibit non-reciprocal properties, Mueller matrix elements not shown in Fig. 10.13 can be obtained by symmetry operations: \(M_{21}(\varphi )=M_{12}(\varphi +\pi )\) and \(M_{3j}(\varphi )=-M_{j3}(\varphi +\pi )\) with \(j=1,2\). No inversion operation is necessary to convert \(M_{12}(\varphi )\) into \(M_{21}(\varphi +\pi )\) because these elements depend on the symmetric \(\cos \) function only whereas this is not true for all other elements. See for example (10.10). \(\pi \) denotes a sample rotation by \(180^\circ \).

  21. 21.

    Optical constants for bulk Co have been taken from Palik [106].

  22. 22.

    Bulk optical constants have been generated with an isotropic Bruggeman EMA (\(L^{\scriptscriptstyle \text{ D} \scriptstyle }_\mathrm{iso }=\frac{1}{3}\) for spherical inclusions) and optical constants for Ni, Fe, and Mo were taken from Palik [106]. For further details on Bruggeman EMA see also Sect. 10.3.6.

  23. 23.

    Here, data is compared that has been taken immediately after deposition and consequently no oxide layer was included within the AB-EMA.

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Acknowledgments

The authors acknowledge support from and fruitful discussion with Tino Hofmann, Ralf Skomski, Han Chen, Xingzhong Li, Natale Ianno, Sy-Hwang Liou, Keith Rodenhausen, Stefan Schöche, Philipp Kühne, Ann Kjerstad, Alexander Boosalis, Eric Montgomery, Derek Sekora, (University of Nebraska-Lincoln, U.S.A.), Andrew Sarangan (University of Dayton, U.S.A), Benjamin Booso (SAIC, U.S.A.), Craig Herzinger, John Woollam (J.A. Woollam Company, U.S.A.), Mario Saenger (InvenLux, U.S.A.), Ravi Billa (InVisage, U.S.A.), Venkata Voora (Globalfoundries, U.S.A.), Olle Inganäs, Hans Arwin (Linköping University, Sweden), Christian Müller (Chalmers University of Technology, Sweden), Brian Bell (University of South Florida, U.S.A), Beri Mbenkum (CSIC, Spain), and Thomas Oates (ISAS, Germany). The research was funded in part by the National Science Foundation, the J.A. Woollam Foundation, and the University of Nebraska-Lincoln.

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  1. University of Nebraska-Lincoln, Lincoln, NE, USA

    Daniel Schmidt, Eva Schubert & Mathias Schubert

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  1. CNR Bari, Ist. Metodologie Inorganiche, Università Bari, Via Orabona 4, Bari, 70126, Italy

    Maria Losurdo

  2. Zentrum für Oberflächen- und, Nanoanalytik (ZONA), Universität Linz, Linz, 4040, Austria

    Kurt Hingerl

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Schmidt, D., Schubert, E., Schubert, M. (2013). Generalized Ellipsometry Characterization of Sculptured Thin Films Made by Glancing Angle Deposition. In: Losurdo, M., Hingerl, K. (eds) Ellipsometry at the Nanoscale. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33956-1_10

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