Determination of the optical properties and size dispersion of Si nanoparticles within a dielectric matrix by spectroscopic ellipsometry

Abstract : We report on a comparative study between dielectric functions of Si nanoparticles (Si-NPs) obtained from Bruggeman effective medium approximation (BEMA), Maxwell-Garnett (MG), and a modified Maxwell-Garnett (MMG) models. Unlike BEMA and MG, a size-distribution dependent dielectric function of Si-NPs is considered in the introduced MMG model. We show that the standard deviation sigma of a size distribution can be evaluated by analyzing the imaginary part of the dielectric functions of Si-NPs extracted from BEMA and MMG. In order to demonstrate this, several samples composed of Si-NPs embedded in silicon-rich silicon nitride are investigated by spectroscopic ellipsometry over the photon energy range varying between 2 and 4 eV. Assuming a lognormal size distribution of the Si nanoparticles, it is evidenced that the parameter sigma ranges between 1.15 and 1.35. The values of size dispersion deduced by this methodology are in good agreement with TEM observations.
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Journal of Applied Physics, American Institute of Physics, 2014, 116 (10), pp.103520. 〈10.1063/1.4894619〉
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A. -S. Keita, A. En Naciri, Y. Battie, F. Delachat, Marzia Carrada, et al.. Determination of the optical properties and size dispersion of Si nanoparticles within a dielectric matrix by spectroscopic ellipsometry. Journal of Applied Physics, American Institute of Physics, 2014, 116 (10), pp.103520. 〈10.1063/1.4894619〉. 〈hal-01517452〉

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