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 WS ₂ 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 E _2g ¹ (in-plane) and A _1g (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 A _1g 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 E _2g ¹ phonon mode and independent of the number of layers, while the excess charge is more significant in thin films and affects mainly the A _1g 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.