Local Optical Properties in CVD-Grown Monolayer WS2 Flakes

Excitons dominate the light absorption and re-emission spectra of monolayer transition-metal dichalcogenides (TMD). Microscopic investigations of the excitonic response in TMD almost invariably extract information from the radiative recombination step, which only constitutes one part of the picture. Here, by exploiting imaging spectroscopic ellipsometry (ISE), we investigate the spatial dependence of the dielectric function of chemical vapor deposition (CVD)-grown WS2 flakes with a microscopic lateral resolution, thus providing information about the spatially varying, exciton-induced light absorption in the monolayer WS2. Comparing the ISE results with imaging photoluminescence spectroscopy data, the presence of several correlated features was observed, along with the unexpected existence of a few uncorrelated characteristics. The latter demonstrates that the exciton-induced absorption and emission features are not always proportional at the microscopic scale. Microstructural modulations across the flakes, having a different influence on the absorption and re-emission of light, are deemed responsible for the effect.


Modelling the laterally-averaged SE data
In order to model the ellipsometry data, we adopted the following strategy. On the same sample considered in the main text, we performed an SE measurement with a J.A. Woollam VASE equipped with focusing probe; then, we adapted the model presented in Ref.
[1] to reproduce the experimental data from VASE. Briefly, we used a patented PSEMI dispersion formula (US patent 5,796,983, Aug. 18, 1998, Herzinger et al.) to describe the WS2 optical response, and used a linear Effective Medium Approximation to properly take into account the surface coverage of WS2. In this way, we obtained a model that can satisfactorily describe the "average" optical properties of the WS2 flake described in the main text. In the following, we review in detail each step.
The structure of the model (i.e. number of layers and oscillators) is the same of Ref.
[1]. The substrate was measured with SE before the WS2 deposition, and its ellipsometric response was modelled independently with a Cauchy dispersion formula; the amplitude and center position of each oscillator in the WS2 layer was fitted to the VASE data. We fed into the model the actual surface coverage of WS2 in the area probed by VASE, that is, 30% (this value was obtained from the analysis of optical microscopy images), and the WS2 thickness (0.8 nm, obtained from AFM data in Supporting Information IV). Therefore, the model was effectively adapted to describe the specific sample under investigation.
The accuracy of the model was good (MSE=5.4); the experimental and calculated data are compared in Fig. SI1. Indeed, the model reproduces very well the features corresponding to the A and B excitons, while at the higher energies, the accuracy seems to decrease. However, it must be noted that due to depolarization and low intensity on the detector, the experimental datapoints at higher energies have a relatively large uncertainty (at least ±1 in Ψ and ±2.5 in Δ); for this reason, the relative weight of those datapoints within the fitting calculations is smaller, resulting in a higher discrepancy between generated and experimental data. The validated model allows to generate ellipsometry data that can be compared with the ISE data reported in the main text. There, we calculated SE data by considering a 100% surface coverage of WS2 and 40° angle of incidence, in order to match the conditions in which the ISE data were acquired. From the model, we also calculate the complex dielectric function of monolayer WS2 in the case of 100% surface coverage. In both cases, the analysis on the laterally-averaged SE data provides an "average" reference for the ISE data and local dielectric function.

IPL data fitting
The PL spectra of monolayer WS2 on SiO2 typically exhibit a major peak and much less intense, broader, and redshifted one; they are determined by the neutral excitons and charged excitons (trions), respectively. The two peaks are represented in Fig. SI3 as two Lorentzian functions fitted to one IPL spectrum. In the IPL data of this work, the trion peak was often so small that it became undistinguishable from the background; therefore, only the main peak (neutral exciton) is discussed in the main text.

Supporting Information V Raman spectra
Representative Raman spectra confirmed that the flake is composed of a monolayer WS2. The Raman spectrum acquired within the top inner triangular region (red dot in Fig. SI6) describes the typical fingerprint of a monolayer WS2, as indicated by the Raman mode (2LA(M)+E 1 2g)/A1g intensity ratio greater than 5. [2,3] The same spectral pattern is measured on the bisector. In the center of the flake, however, the features depart from those of typical monolayer WS2 ((2LA(M)+E 1 2g)/A1g ∼2), due to the fact that this region corresponds to the center of nucleation, where structural defects are formed during the growth of the flake.