Quantitative Characterization of Structural Heterogeneities in 2D Materials by Medium Energy Ion Scattering

As-synthesized two-dimensional transition metal dichalcogenides (TMDs) inherently present both lateral and vertical structural heterogeneities [1]. Conventional characterization techniques for 2D materials, such as Raman spectroscopy and atomic force microscopy (AFM), probe limited local areas, requiring extensive mapping to obtain statistically representative data. To overcome this limitation, we establish a framework combining Medium Energy Ion Scattering (MEIS) with the PowerMEIS simulation code [2] to extract macroscopic global parameters of TMDs, including surface coverage, effective monolayer thickness, and multilayer thickness distributions.

In this study, different regimes of TMD morphological heterogeneity were analyzed. As a representative example of these regimes, Figure 1 illustrates a MoS2 sample, where the optical microscopy of the irradiated area (Fig. 1a) and its magnified view (Fig. 1b) reveal a prevalent heterogeneity characterized by monolayer triangular flakes, nucleation points of multilayer stacking, and regions of exposed SiO2 substrate. To capture this complexity, a novel framework was implemented within the PowerMEIS simulation code. This methodology utilizes the optical microscopy of the specific irradiated region to reconstruct the sample pixel by pixel using 3D voxel matrices, defining an approach we termed the Image-Reconstructed Voxel Model (IRVM). Consequently, this allows for the direct MEIS simulation of the complete structural heterogeneity within the entire beam-probed area. Figures 1c and 1d display the reconstructed matrix, where blue regions represent pixels indexed as monolayer MoS2, red regions denote pixels indexed as stacked multilayers, and the white void spaces correspond to the exposed substrate between the layers.

Applying this geometric reconstruction, Figure 1e presents the experimental MEIS spectrum for the Mo and S surface peaks, alongside the simulated data. The total simulated yield can be decomposed into the individual contributions of the monolayer and multilayer domains. The inset highlights the magnified Mo surface peak, revealing in detail how the model captures the complex spectral features, particularly the tail broadening of the surface peak induced by the thicker regions. The smooth behavior of this tail suggests that the multilayers present a continuous average thickness distribution. This follows from the fact that a single multilayer component, combined with the monolayer curve, is sufficient to fit the experimental data. From this decomposition, quantitative structural parameters were extracted, including the fractional coverage area (33.7% monolayer and 4.1% multilayer), an effective monolayer thickness of (0.71 ± 0.05) nm, and an average thickness of (3.06 ± 0.20) nm for the multilayer domains. Moreover, these results demonstrate that the IRVM successfully decodes the structural information embedded in the surface peak, yielding statistically representative parameters for the macroscopic area probed by the beam. 

References

[1] Shun-Li Shang, Greta Lindwall, Yi Wang, Joan M. Redwing, Tim Anderson, and Zi-Kui Liu. Lateral versus vertical growth of two-dimensional layered transition-metal dichalcogenides: Thermodynamic insight into mos2. Nano Letters, 16(9):5742–5750, 2016. PMID: 27540753.

[2] G G Marmitt, I Alencar, H Trombini, F F Selau, B Konrad, and P L Grande. PowerMEIS 3: A versatile tool for simulating ion and electron scattering. Comput. Phys. Commun., 313(109639):109639, August 2025.