Temperature-induced evolutions in critical point optical transitions in HfS2 investigated by spectroscopic ellipsometry

A thorough understanding of the temperature-dependent optical properties and underlying physical mechanisms of a novel material is critical for the optimization of related optoelectronic devices. In this study, we comprehensively investigate the optical properties of the transition metal dichalcogenide HfS₂ over a broadband energy range of 0.75–5.91 eV with the temperatures changing from 100 K to 600 K by using the spectroscopic ellipsometry, critical point analysis, and first-principles calculations. The temperature-dependent dielectric functions are determined, and seven critical points (A–G) and their associated optical transitions are quantitatively revealed. We found that the central energies of these critical points exhibit temperature-induced blueshifts, consistent with the Varshni equation and Bose-Einstein model. The behavior of the critical points is significantly different as affected by thermal expansion and electron-phonon interactions of varying degrees. Due to the temperature-induced reversible phase transition of HfS₂, critical points C and E exhibit dramatically increasing broadening and ultimately disappear. The locations of these optical transitions in the Brillouin zone and the involved carriers are further identified through energy band structure and projected density of states by combining the critical points analysis and first-principles calculations.