Phonons in single and few-layer MoS2 and WS2

TL;DR

This paper presents ab-initio calculations of phonon dispersion in single and few-layer MoS2 and WS2, analyzing how Raman active modes vary with layer number and explaining the underlying dielectric screening effects.

Contribution

It provides a detailed theoretical analysis of phonon modes in layered dichalcogenides and explains the layer-dependent frequency shifts observed in Raman spectroscopy.

Findings

A1g mode frequency increases with more layers.

E2g mode frequency decreases with more layers.

Dielectric screening explains the E2g mode shift.

Abstract

We report ab-initio calculations of the phonon dispersion relations of the single-layer and bulk dichalcogenides MoS2 and WS2. We explore in detail the behavior of the Raman active modes, A1g and E2g as a function of the number of layers. In agreement with recent Raman spectroscopy measurements [C. Lee et. al., ACS Nano Vol. 4, 2695 (2010)] we find that the A1g mode increases in frequency with increasing layer number while the E2g mode decreases. We explain this decrease by an enhancement of the dielectric screening of the long-range Coulomb interaction between the effective charges with growing number of layers. This decrease in the long-range part over-compensates the increase of the short-range interaction due to the weak inter-layer interaction.