Daniel Franta, Adam Dubroka, Chennan Wang, Angelo Giglia, Jiří Vohánka, Pavel Franta, Ivan Ohlídal
Temperature-dependent dispersion model of float zone crystalline silicon
Applied Surface Science 421 (2017) 405-419
In this paper, we present the temperature dependent dispersion model of float zone crystalline silicon. The theoretical background for valence electronic excitations is introduced in the theoretical part of this paper. This model is based on application of sum rules and parametrization of transition strength functions corresponding to the individual elemental phonon and electronic excitations. The parameters of the model are determined by fitting ellipsometric and spectrophotometric experimental data in the spectral range from far infrared (70 cm-1) to extreme ultraviolet (40 eV). The ellipsometric data were measured in the temperature range 5-700 K. The excitations of the valence electrons to the conduction band are divided into the indirect and direct electronic transitions. The indirect transitions are modeled by truncated Lorentzian terms, whereas the direct transitions are modeled using Gaussian broadened piecewise smooth functions representing 3D and 2D van Hove singularities modified by excitonic effects. Since the experimental data up to high energies (40 eV) are available, we are able to determine the value of the effective number of valence electrons. The Tauc-Lorentz dispersion model is used for modeling high energy electron excitations. Two slightly different values of the effective number of valence electrons are obtained for the Jellison-Modine (4.51) and Campi-Coriasso (4.37) parametrization. Our goal is to obtain the model of dielectric response of crystalline silicon which depends only on photon energy, temperature and small number of material parameters, e.g. the concentration of substituted carbon and interstitial oxygen. The model presented in this paper is accurate enough to replace tabulated values of c-Si optical constants used in the optical characterization of thin films placed onto silicon substrates. The spectral dependencies of the optical constants obtained in our work are compared to results obtained by other authors.
DOI: 10.1016/j.apsusc.2017.02.021
You can also contact one of the authors: franta@physics.muni.cz, vohanka@physics.muni.cz, ohlidal@physics.muni.cz