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 -