Phonon anharmonicity in multi-layered WS2 explored by first-principles and Raman studies

Anharmonicity is an essential property of two-dimensional materials due to its significant impact on lattice dynamics – involving interactions between phonons, thermal expansion of the structure, and interaction with the substrate. The effects manifest in temperature-dependent redshifts of the phonon frequencies and reduced lifetime. In this work, we investigate phonon anharmonicity in supported 1–5 layered WS2 by performing Raman measurements in the temperature range of 80–500 K and explore the results by ab-initio DFT study. An ab-initio model including three-phonon interaction processes and thermal expansion of all geometrical degrees of freedom (in-plane lattice constant, interlayer distance, and monolayer thickness) well describes the experimental temperature trends of the fundamental E2g1 (in-plane) and A1g (out-of-plane) phonon modes, giving a great promise of using simulation to quantitatively analyze phonon propagation and heat transport in multi-layered two-dimensional materials. The models predict a noticeable increase in the temperature-induced slope of A1g vibrations’ frequency with the number of layers – primarily due to the thermal expansion of interlayer distance. Additionally, we study the impact of the substrate on the phonon properties – concerning cumulated effects of induced strain and electron doping. We show that the effect of biaxial strain is the most significant in the E2g1 phonon mode and independent of the number of layers, while the excess charge is more significant in thin films and affects mainly the A1g mode. The presented studies based on a combination of ab-initio and experimental approaches can be extended to quantitatively analyze phonon evolution with structural modification and external stimuli.