# Raman Spectra of ZrS\({}_{2}\) and ZrSe\({}_{2}\) from Bulk to Atomically Thin Layers
## 4 Discussion  
Thin layers of ZrX\({}_{2}\) have been obtained by mechanical exfoliation and inspected by optical and atomic force microscopy, as can be seen in Figure 2 and Appendix B. The estimation of the number of layers was calculated by dividing the AFM experimental height by the \(c\) parameter of the unit cell (5.827 A for ZrS\({}_{2}\) and 6.1282 A for ZrSe\({}_{2}\); see Appendix A). Nevertheless, as already observed in graphene, the experimental height of a monolayer is usually overestimated compared with the expected crystallographic one due to the presence of adsorbates, as water molecules, between the substrate and the thin layer [32]. As further discussed in Appendix B, this phenomenon could introduce an error of \(\pm\)1 layer in the estimation of the number of layers, especially for thick flakes. For Raman spectra, the in-plane mode (E\({}_{\rm g}\)) and the out-of-plane mode (A\({}_{\rm 1g}\)) can be observed in the bulk and the thicker samples inspected (see Figures 3 and 4 and Appendix C). For ZrS\({}_{2}\), the obtained values are 249.7 \(\pm\) 0.8 cm\({}^{-1}\) for the E\({}_{\rm g}\) peak and 334.0 \(\pm\) 1.4 cm\({}^{-1}\) for the A\({}_{\rm 1g}\) peak. The broadening of the A\({}_{\rm 1g}\) peak at 319.9 \(\pm\) 0.6 cm\({}^{-1}\) (denoted with \"**\" in Figure 3) is attributed to non-harmonic effects (i.e., the phonon can emit acoustic phonons, with practically no energy, that give rise to that huge broadening) while some authors ascribed it to the infrared mode A\({}_{\rm 2u}\) that would be coupled to the Raman spectra thanks to the long-range Coulomb forces due to the charges on atoms [33]. However, as recently reported, the IR mode must be at a higher frequency (it has been observed to be around 500 cm\({}^{-1}\)[34]) since the zirconium atom vibrates against the sulfur atom and the reduced mass is much higher. Further discussion can be found in Appendix D. Regarding ZrSe\({}_{2}\), a small peak appears at 145.80 \(\pm\) 0.19 cm\({}^{-1}\) for the E\({}_{\rm g}\) peak and a clear one at 195.5 \(\pm\) 0.2 cm\({}^{-1}\) for the A\({}_{\rm 1g}\) one. These values are in good accordance with the ones previously reported in the literature [31]. Moreover, in the wider spectra shown in Figure 1 (see Appendix C), a broad band at 682.8 \(\pm\) 0.5 cm\({}^{-1}\) and three  
Figure 4: Thickness dependence of the Raman spectra for ZrSe\({}_{2}\) (\(\lambda\) = 638 nm) on a silicon substrate with 285 nm of SiO\({}_{2}\). Inset: zoom of Raman spectra in the A\({}_{\rm 1g}\) characteristic peak for the thinnest layers. The intensity has been normalized to the height of the silicon phonon peak. peaks at 109 \(\pm\) 1 cm\({}^{-1}\), 140.0 \(\pm\) 0.3 cm\({}^{-1}\), and 193.2 \(\pm\) 0.3 cm\({}^{-1}\) can be observed for ZrS\({}_{2}\), while for ZrSe\({}_{2}\) (Figure C4) there are four peaks at 107.4 \(\pm\) 0.3 cm\({}^{-1}\), 133.61 \(\pm\) 0.09 cm\({}^{-1}\), 243.09 \(\pm\) 0.17 cm\({}^{-1}\), and 267.61 \(\pm\) 0.10 cm\({}^{-1}\). All these peaks can be attributed to the density of two phonon states of ZrX\({}_{2}\)[35]. For thin layers, the Raman peaks coming from the silicon substrate are detected as well. In particular, we observed the silicon phonon peak at 520.71 \(\pm\) 0.03 cm\({}^{-1}\) and second-order Raman peaks as the broad peak centered at 301 \(\pm\) 1 cm\({}^{-1}\) and the Raman band at 950 cm\({}^{-1}\), in accordance with the reported ones in the literature [36]. As qualitatively shown in Figures 3 and 4 and quantitatively analyzed in Tables 1-3, we find that when reducing the thickness the intensity of the Raman peaks decreases; in strict contrast with what is observed in group VI TMDCs as MoS\({}_{2}\)[26], no significant shift is found in their position. Moreover, the relative intensity between the E\({}_{\text{g}}\) peak and the A\({}_{\text{lg}}\) one is reduced in a non-monotonic way and, for the thinner layers, only the out-of-plane mode can be resolved.