## 3 Results and Discussion  
The lattice structure of the \(\sqrt{3}\)-Sn/Si(111) surface is illustrated in Figure 1a, showing an in-plane 30\({}^{\circ}\) rotation and \(\sqrt{3}\times\sqrt{3}\) reconstruction of a Sn layer relative to a Si(111) surface. Each Sn atom is back-bonded to three Si atoms beneath, with a remaining dangling bond at the surface. Figure 1b presents the lattice structure of T-phase SnSe\({}_{2}\) (T-SnSe\({}_{2}\)). As a typical MX\({}_{2}\) of PTMCs, single layer T-SnSe\({}_{2}\) consists of two layers of chalcogenides and a layer of transition metal sandwiched between them, presenting a Se-Sn-Se sandwich-like structure. Within the layer, covalent bonding is achieved through Se-Sn, while interlayer stacking is achieved through Se-Se van der Waals interactions, presenting the lattice constants as \(\mathbf{a}=3.81\) and \(\mathbf{c}=6.14\)[23]. Figure 1c-e present the RHEED patterns of an annealed Si(111)-(7 \(\times\) 7) surface, a \(\sqrt{3}\)-Sn/Si(111) surface and an ML SnSe\({}_{2}\) film along the Si\(\left[\overline{1}\overline{1}0\right]\) direction, respectively. Corresponding RHEED patterns along the Si\(\left[\overline{1}\overline{1}2\right]\) direction are also obtained by 30\({}^{\circ}\) rotating the sample in-plane, as shown in Figure 1f-h. From Figure 1c,f, we can see the clearly (7 \(\times\) 7) reconstructed patterns of the annealed Si surface, which disappear and are displaced by a new pair of (1 \(\times\) 1) diffraction stripes after the \(\sqrt{3}\)-Sn passivation, as shown in Figure 1d,g. Subsequently, from Figure 1e,h, we can see the new (1 \(\times\) 1) diffraction stripes from the epitaxial SnSe\({}_{2}\) film, which are very clear and sharp, implying the high-quality crystallization. By performing Lorentz fittings on the corresponding RHEED patterns, we can accurately obtain the (1 \(\times\) 1) main diffraction stripe spacings of both substrates and the SnSe\({}_{2}\) films (see Figure S1 of the Supplementary Materials for details), on which we can conduct more detailed analysis and calculations. The orientation of the \(\sqrt{3}\)-Sn buffer layer is in-plane rotated by 30\({}^{\circ}\) relative to the Si(111), with the calculated lattice constant as \(\mathbf{a}_{\sqrt{3}\text{-Sn}}=6.66\pm 0.05\) A, approximately equal to \(\sqrt{3}\) times \(\mathbf{a}_{\text{Si(111)}}=3.84\) A. This result is consistent with the previous reports [24; 25]. Subsequently, the epitaxial SnSe\({}_{2}\) film is rotated by 30\({}^{\circ}\) again relative to the \(\sqrt{3}\)-Sn/Si surface, resulting in the same in-plane orientation with the Si(111) substrate. Furthermore, the in-plane lattice constant of ML  
Figure 1: (**a**) Top-view lattice structure of \(\sqrt{3}\)-Sn/Si(111) reconstruction. (**b**) Top-view lattice structure of a ML T-SnSe\({}_{2}\). (**c–e**) RHEED patterns of (**c**) Si(111)-(7 \(\times\) 7) surface, (**d**) \(\sqrt{3}\)-Sn/Si(111) surface and (**e**) ML SnSe\({}_{2}\) film along the Si\(\left[\overline{1}\overline{1}0\right]\) direction, respectively. (**f–h**) RHEED patterns of (**f**) Si(111)-(7 \(\times\) 7) surface, (**g**) \(\sqrt{3}\)-Sn/Si(111) surface and (**h**) ML SnSe\({}_{2}\) film along the Si\(\left[\overline{1}\overline{1}2\right]\) direction, respectively. (**i.j**) (i) STM topography of ML SnSe\({}_{2}\) film and (**j**) the corresponding height profiles along the green line in (**i**). SnSe\({}_{2}\) is also obtained as \(\alpha_{\text{SnSe}_{2}}=3.83\pm 0.05\) A, which is in agreement with the previous report [23], and shows no obvious interfacial strain effect considering the \(\pm 0.05\) A errors in RHEED analysis. After growth, we utilized the in situ STM to investigate the surface morphology of ML SnSe\({}_{2}\) grown on \(\sqrt{3}\)-Sn/Si(111), as shown in Figure 11. Different from three-dimensional (3D) island growth mode on graphene substrates [26], the SnSe\({}_{2}\) grown on \(\sqrt{3}\)-Sn/Si(111) tends to be layer-by-layer growth mode, which provides the better film flatness.