Generalized ellipsometry and complex optical systems

M. Schubert

doi:10.1016/S0040-6090(97)00841-9

Generalized ellipsometry and complex optical systems

M. Schubert

Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

127 Scopus citations

Abstract

Extension of spectroscopic rotating-analyzer ellipsometry with automated compensator function to generalized ellipsometry (GE) is reported in order to define and determine three normalized elements of the optical Jones reflection or transmission matrices r or t, respectively. These elements can be measured regardless of the specific structural and/or anisotropic properties of a nondepolarizing sample. An analytically processed 4 × 4-matrix algebra based on the Berreman 4 × 4 formalism is reviewed to calculate the Jones reflection and transmission matrix elements for arbitrarily anisotropic and homogeneously layered systems. Special solutions are available for continuously twisted biaxial media (chiral liquid crystals), and materials with arbitrary antisymmetric dielectric properties (e.g. free-carrier magneto-optics in semiconductors). The combination of both the 4 × 4-matrix algorithm and GE allows for the analysis of complex multilayered samples with inherent and arbitrarily oriented anisotropies. We present our first applications of GE to birefringent layered dielectrics (TiO₂), chiral liquid crystals, spontaneously ordered semiconductor III-V compounds (AL_x-Ga_1-xInP₂), and polycrystalline boron nitride thin films.

Original language	English (US)
Pages (from-to)	323-332
Number of pages	10
Journal	Thin Solid Films
Volume	313-314
DOIs	https://doi.org/10.1016/S0040-6090(97)00841-9
State	Published - Feb 13 1998

Keywords

Anisotropy
Generalized ellipsometry
Liquid crystals
Magneto-optics
Optical Jones matrix
Polycrystalline media
Refractive indices

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Surfaces and Interfaces
Surfaces, Coatings and Films
Metals and Alloys
Materials Chemistry

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10.1016/S0040-6090(97)00841-9

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@article{59d43c600cd545a4b303723b64ce0dd4,

title = "Generalized ellipsometry and complex optical systems",

abstract = "Extension of spectroscopic rotating-analyzer ellipsometry with automated compensator function to generalized ellipsometry (GE) is reported in order to define and determine three normalized elements of the optical Jones reflection or transmission matrices r or t, respectively. These elements can be measured regardless of the specific structural and/or anisotropic properties of a nondepolarizing sample. An analytically processed 4 × 4-matrix algebra based on the Berreman 4 × 4 formalism is reviewed to calculate the Jones reflection and transmission matrix elements for arbitrarily anisotropic and homogeneously layered systems. Special solutions are available for continuously twisted biaxial media (chiral liquid crystals), and materials with arbitrary antisymmetric dielectric properties (e.g. free-carrier magneto-optics in semiconductors). The combination of both the 4 × 4-matrix algorithm and GE allows for the analysis of complex multilayered samples with inherent and arbitrarily oriented anisotropies. We present our first applications of GE to birefringent layered dielectrics (TiO2), chiral liquid crystals, spontaneously ordered semiconductor III-V compounds (ALx-Ga1-xInP2), and polycrystalline boron nitride thin films.",

keywords = "Anisotropy, Generalized ellipsometry, Liquid crystals, Magneto-optics, Optical Jones matrix, Polycrystalline media, Refractive indices",

author = "M. Schubert",

note = "Funding Information: The author acknowledges valuable discussions with Professor H. Schmiedel, and B. Rheinl{\"a}nder, University Leipzig, and Professor J. A. Woollam, University of Nebraska. In particular, I wish to thank Eva Franke, Institute for Surface Modification Leipzig, and Christiane Cramer, University Leipzig, for their leading participation in the boron nitride and liquid crystal aspects of this work, respectively. I am indebted to Ines Pietzonka and Volker Gottschalch, University Leipzig, for growth and preparation of the AlGaInP samples. It is a pleasure to acknowledge the contributions of Craig M. Herzinger and Blaine Johs, J.A. Woollam Co., for the experimental realization of the generalized ellipsometry measurements presented in this work. Part of the work was supported by the Deutsche Forschungsgemeinschaft under contract No.Rh.28/1-1. We thank the Center for Microelectronic and Optical Materials Research at the University of Nebraska for financial support during part of the work.",

year = "1998",

month = feb,

day = "13",

doi = "10.1016/S0040-6090(97)00841-9",

language = "English (US)",

volume = "313-314",

pages = "323--332",

journal = "Thin Solid Films",

issn = "0040-6090",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Generalized ellipsometry and complex optical systems

AU - Schubert, M.

N1 - Funding Information: The author acknowledges valuable discussions with Professor H. Schmiedel, and B. Rheinländer, University Leipzig, and Professor J. A. Woollam, University of Nebraska. In particular, I wish to thank Eva Franke, Institute for Surface Modification Leipzig, and Christiane Cramer, University Leipzig, for their leading participation in the boron nitride and liquid crystal aspects of this work, respectively. I am indebted to Ines Pietzonka and Volker Gottschalch, University Leipzig, for growth and preparation of the AlGaInP samples. It is a pleasure to acknowledge the contributions of Craig M. Herzinger and Blaine Johs, J.A. Woollam Co., for the experimental realization of the generalized ellipsometry measurements presented in this work. Part of the work was supported by the Deutsche Forschungsgemeinschaft under contract No.Rh.28/1-1. We thank the Center for Microelectronic and Optical Materials Research at the University of Nebraska for financial support during part of the work.

PY - 1998/2/13

Y1 - 1998/2/13

N2 - Extension of spectroscopic rotating-analyzer ellipsometry with automated compensator function to generalized ellipsometry (GE) is reported in order to define and determine three normalized elements of the optical Jones reflection or transmission matrices r or t, respectively. These elements can be measured regardless of the specific structural and/or anisotropic properties of a nondepolarizing sample. An analytically processed 4 × 4-matrix algebra based on the Berreman 4 × 4 formalism is reviewed to calculate the Jones reflection and transmission matrix elements for arbitrarily anisotropic and homogeneously layered systems. Special solutions are available for continuously twisted biaxial media (chiral liquid crystals), and materials with arbitrary antisymmetric dielectric properties (e.g. free-carrier magneto-optics in semiconductors). The combination of both the 4 × 4-matrix algorithm and GE allows for the analysis of complex multilayered samples with inherent and arbitrarily oriented anisotropies. We present our first applications of GE to birefringent layered dielectrics (TiO2), chiral liquid crystals, spontaneously ordered semiconductor III-V compounds (ALx-Ga1-xInP2), and polycrystalline boron nitride thin films.

AB - Extension of spectroscopic rotating-analyzer ellipsometry with automated compensator function to generalized ellipsometry (GE) is reported in order to define and determine three normalized elements of the optical Jones reflection or transmission matrices r or t, respectively. These elements can be measured regardless of the specific structural and/or anisotropic properties of a nondepolarizing sample. An analytically processed 4 × 4-matrix algebra based on the Berreman 4 × 4 formalism is reviewed to calculate the Jones reflection and transmission matrix elements for arbitrarily anisotropic and homogeneously layered systems. Special solutions are available for continuously twisted biaxial media (chiral liquid crystals), and materials with arbitrary antisymmetric dielectric properties (e.g. free-carrier magneto-optics in semiconductors). The combination of both the 4 × 4-matrix algorithm and GE allows for the analysis of complex multilayered samples with inherent and arbitrarily oriented anisotropies. We present our first applications of GE to birefringent layered dielectrics (TiO2), chiral liquid crystals, spontaneously ordered semiconductor III-V compounds (ALx-Ga1-xInP2), and polycrystalline boron nitride thin films.

KW - Anisotropy

KW - Generalized ellipsometry

KW - Liquid crystals

KW - Magneto-optics

KW - Optical Jones matrix

KW - Polycrystalline media

KW - Refractive indices

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U2 - 10.1016/S0040-6090(97)00841-9

DO - 10.1016/S0040-6090(97)00841-9

M3 - Article

AN - SCOPUS:0031999915

SN - 0040-6090

VL - 313-314

SP - 323

EP - 332

JO - Thin Solid Films

JF - Thin Solid Films

ER -

Generalized ellipsometry and complex optical systems

Abstract

Keywords

ASJC Scopus subject areas

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