Substrate-free layer-number identification of two-dimensional materials: A case of Mo$_{0.5}$W$_{0.5}$S$_2$ alloy

TL;DR

This paper presents a substrate-free, robust method for determining the layer number of 2D alloy materials using shear and layer-breathing modes, unaffected by substrate or material variations.

Contribution

It introduces a substrate-independent technique based on shear and LB modes to identify layer number in 2D alloys, demonstrated on Mo$_{0.5}$W$_{0.5}$S$_2$.

Findings

Disorder effect is absent in shear and LB modes of 2D alloys.

Monatomic chain model accurately estimates mode frequencies.

Layer number can be identified regardless of substrate or material properties.

Abstract

Any of two or more two-dimensional (2D) materials with similar properties can be alloyed into a new layered material, namely, 2D alloy. Individual monolayer in 2D alloys are kept together by Van der Waals interactions. The property of multilayer alloys is a function of their layer number. Here, we studied the shear (C) and layer-breathing (LB) modes of Mo$_{0.5}$W$_{0.5}$S$_2$ alloy flakes and their link to the layer number of alloy flakes. The study reveals that the disorder effect is absent in the C and LB modes of 2D alloys, and the monatomic chain model can be used to estimate the frequencies of the C and LB modes. We demonstrated how to use the C and LB mode frequency to identify the layer number of alloy flakes deposited on different substrates. This technique is independent of the substrate, stoichiometry, monolayer thickness and complex refractive index of 2D materials, offering a robust and substrate-free approach for layer-number identification of 2D materials.