Anisotropic Substrates

  • Mathias Schubert
Part of the Springer Tracts in Modern Physics book series (STMP, volume 209)


A prerequisite for infrared ellipsometry investigations of semiconductor layer structures is an accurate knowledge of the substrate materials’ dielectric functions. Appropriate consideration of the anisotropic optical properties of noncubic substrate materials is the subject of the present chapter. The goal must be to determine the intrinsic dielectric functions to the most accurate level, because these functions will be incorporated during the best-fit data analysis of the unknown heteroepitaxial layers.1 Errors on the substrate dielectric function data base will propagate into those for the materials of interest.The required information - the major polarizability functions ϱa, ϱb, ϱc, and their center-of-gravity system by vectors a,b,c described in Sect. 2.6 - cannot be simply obtained from a single surface alone. Measurements should be done on samples with surfaces cut under different crystallographic angles from the same bulk crystal. For low-symmetry surfaces, use of the generalized ellipsometry concept is mandatory. For systems with orthogonal vectors a,b,c, however, the standard ellipsometry approach can be maintained if the sample can be oriented such that all of vectors a,b,c are parallel to the laboratory coordinate axes. For many bulk crystals this can be achieved to a sufficient level of accuracy. Identification of good starting values (phonon mode parameters) for the best-fit model lineshape analysis presents another difficulty, even if the ellipsometry data were acquired correctly. A procedure for identification of phonon modes and their symmetry for trigonal, tetragonal, hexagonal, and orthorhombic symmetry materials is therefore described in this chapter. This procedure makes use of the characteristic reflectivity signatures due to the so-called bands of total reflection. In order to enlighten the reflectivity signatures and there connection with the intrinsic phonon mode parameters the analytical behavior of the p- and s- polarized reflection coefficients for high-symmetry orientations of the anisotropic samples will be inspected. Once the understanding of the reflection coefficients have been obtained, it is straightforward to “read” these signatures from the ellipsometric parameters. The goal is to identify the number of TO-LO pairs for each lattice direction and to guess reasonable starting values for the numerical data regression procedures. Sapphire (tetragonal) and stibnite (orthorhombic) are discussed exemplarily.


Dielectric Function Phonon Mode Polarization Parallel Longitudinal Optical Phonon Ellipsometric Parameter 
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Authors and Affiliations

  • Mathias Schubert
    • 1
  1. 1.Institut für Experimentelle Physik IIUniversität LeipzigLeipzigGermany

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