Optical Characterization of a Thin-Film Material Based on Light Intensity Measurements

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Abstract

Light interacts with materials in a variety of ways; this article focuses on determination of refraction and absorption characterized by a material’s refractive index. We discuss some of the useful models for the frequency dependence of the refractive index, and practical approaches to calculating refractive indices of thin films and thick substrates. The efficiency of manufacturing of existing and successful creation of new devices of solid-state micro- and nanoelectronics largely depends on the level of development of the technology for manufacturing layers of various materials with a thickness of several nanometers to tens of micrometers. A high degree of perfection of layered structures and particularly structures based on dielectric and/or metallic films with nanometer thickness is needed for their successful application in micro-, nano-, acousto-, microwave and optoelectronics. It is impossible to achieve high degree of perfection without the use of high-precision methods of measuring electrophysical parameters of dielectric and semiconductor materials and structures, metallic films. We have developed the program “Multilayer”, which serves both to simulate the propagation of light through multilayer thin-film layered media, and to determine the dielectric (permittivity tensor of anisotropic films) and geometric (physical and optical thicknesses of the film) parameters of various thin-film coatings. The base mathematical models applied for the description of the light wave propagation through a homogeneous optical medium and for the determination of the optical characteristics of thin layers of optical materials based on the results of light intensity measurements are described. The main mathematical formalism employed in the program is based on solving the Maxwell’s equations for propagation of light through anisotropic stratified media. The algorithm uses the Berreman matrices of order

About the authors

K P Lovetskiy

Peoples’ Friendship University of Russia (RUDN university)

Author for correspondence.
Email: lovetskiy_kp@rudn.university
Candidate of Physical and Mathematical Sciences, Associate Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University) 6, Miklukho-Maklaya str., Moscow, 117198, Russian Federation

N E Nikolaev

Peoples’ Friendship University of Russia (RUDN university)

Email: nikolaev_ne@pfur.ru
Candidate of Physical and Mathematical Sciences, Associate Professor of Institute of Physical Research and Technologies of Peoples’ Friendship University of Russia (RUDN university) 6, Miklukho-Maklaya str., Moscow, 117198, Russian Federation

A L Sevastianov

Peoples’ Friendship University of Russia (RUDN university)

Email: sevastianov_al@rudn.university
Candidate of Physical and Mathematical Sciences, Associate Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University) 6, Miklukho-Maklaya str., Moscow, 117198, Russian Federation

References

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  3. M. Born, E. Wolf, “Basic Properties of the Electromagnetic Fields” and “Elements of the Theory of Interference and Interferometers”, Chap. 1 and Chap. 7, 5th Edition, Pergamon Press, NY, 1975.
  4. R. M. A. Azzam, N. M. Bashara, “Propagation of Polarized Light Through Polarizing Optical Systems” and “Reflection and Transmission of Polarized Light by Stratified Planar Structures”, Chap. 2 and Chap. 4, Elsevier, Amsterdam, 1977.
  5. P. Yeh, C. Gu, “Electromagnetic Propagation in Anisotropic Media”, “Jones Matrix Method” and ”Extended Jones Matrix Method”, Chap. 3, Chap. 4 and Chap. 8, John Wiley & Sons Inc., 1999.
  6. D. W. Berreman, Optics in Stratified and Anisotropic Media: 4 × 4-Matrix Formulation, J. Opt. Soc. Amer. 62 (4) (1972) 502-510.
  7. S. P. Palto, An Algorithm for Solving the Optical Problem for Stratified Anisotropic Media, JETP 92 (4) (2001) 552-560.
  8. R. Bellman, Introduction to Matrix Analysis, 2nd Edition, Soc. for Industrial and Applied Math., Philadelphia, PA, USA, 1997.

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