Quantitative analysis of the temperature dependency in Raman active vibrational modes of molybdenum disulfide atomic layers.

Raman spectroscopy is utilized to quantify the temperature dependency of the vibrational modes in molybdenum disulfide (MoS2) atomic layers. These analyses are essential for understanding the structural properties and phononic behaviors of this two-dimensional (2D) material. We quantitatively analyze the temperature dependent shifts of the Raman peak positions in the temperature range from 300 to 550 K, and find that both planar and out-of-plane characteristic modes are highly sensitive to temperature variations. This temperature dependency is linear and can be fully explained by the first-order temperature coefficient. Using a semi-quantitative model, we evaluate the contributions of the material's thermal expansion and intrinsic temperature effects to this dependency. We reveal that the dominating source of shift in the peak position of planar mode E2g(1) for samples of all thicknesses investigated is the four-phonon process. In addition to the four-phonon process, thermal expansion plays a significant role in the temperature dependency of the out-of-plane mode, A1g. The thickness dependency of the temperature coefficient for MoS2 and a drastic change in behaviors of samples from bi- to single-layered are also demonstrated. We further explore the role of defects in the thermal properties of MoS2 by examining the temperature dependency of Raman modes in CVD-grown samples.