Quantitative Analysis of Temperature Dependence of Raman shift of monolayer WS2

We report the temperature-dependent evolution of Raman spectra of monolayer WS2 directly CVD-grown on a gold foil and then transferred onto quartz substrates over a wide temperature range from 84 to 543 K. The nonlinear temperature dependence of Raman shifts for both E-2g(1) and A(1g) modes has been observed. The first-order temperature coefficients of Raman shifts are obtained to be -0.0093 (cm(-1)/K) and -0.0122 (cm(-1)/K) for E-2g(1) and A(1g) peaks, respectively. A physical model, including thermal expansion and three-and four-phonon anharmonic effects, is used quantitatively to analyze the observed nonlinear temperature dependence. Thermal expansion coefficient (TEC) of monolayer WS2 is extracted from the experimental data for the first time. It is found that thermal expansion coefficient of out-plane mode is larger than one of in-plane mode, and TECs of E-2g(1) and A(1g) modes are temperature-dependent weakly and strongly, respectively. It is also found that the nonlinear temperature dependence of Raman shift of E-2g(1) mode mainly originates from the anharmonic effect of three-phonon process, whereas one of A(1g) mode is mainly contributed by thermal expansion effect in high temperature region, revealing that thermal expansion effect cannot be ignored.