Thickness and Temperature Dependence of the Dielectric Function of Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$

We have determined the dielectric functions of a series of Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ films grown on sapphire substrates. Temperature dependent in-situ ellipsometry spectra were obtained for several samples with varying thicknesses ranging from 5 nm to 60 nm. After the dielectric functions were modeled using the in-situ spectra, they were represented by Kramers-Kronig consistent oscillators. We observe that the dielectric function of Bi$_{\mathrm{2}}$Se$_{\mathrm{3\thinspace }}$has a slight thickness dependence and that it also varies with temperature. Specifically, the oscillators red-shift as temperature increases, which was modeled using a Bose-Einstein distribution.