Temperature Dependence of the Dielectric Function of Monolayer MoSe₂

The dielectric function [Formula: see text] of monolayer molybdenum diselenide (MoSe₂) is obtained and analyzed at temperatures from 31 to 300 K and at energies from 0.74 to 6.42 eV. The sample is a large-area, partially discontinuous monolayer (submonolayer) film of MoSe₂ grown on a sapphire substrate by selenization of pulsed laser deposited MoO₃ film. Morphological and optical characterizations verified the excellent quality of the film. The MoSe₂ data were analyzed using the effective medium approximation, which treats the film and bare substrate regions as a single layer. Second derivatives of ε with respect to energy were numerically calculated and analyzed with standard lineshapes to extract accurate critical-point (CP) energies. We find only 6 CPs for monolayer MoSe₂ at room temperature. At cryogenic temperatures 6 additional structures are resolved. The separations in the B- and C-excitonic peaks are also observed. All structures blue-shift and sharpen with decreasing temperature as a result of the reducing lattice constant and electron-phonon interactions. The temperature dependences of the CP energies were determined by fitting the data to the phenomenological expression that contains the Bose-Einstein statistical factor and the temperature coefficient.