Monolayer-to-bilayer transformation of silicenes and their structural analysis

Silicene, a two-dimensional honeycomb network of silicon atoms like graphene, holds great potential as a key material in the next generation of electronics; however, its use in more demanding applications is prevented because of its instability under ambient conditions. Here we report three types of bilayer silicenes that form after treating calcium-intercalated monolayer silicene (CaSi2) with a BF4− -based ionic liquid. The bilayer silicenes that are obtained are sandwiched between planar crystals of CaF2 and/or CaSi2, with one of the bilayer silicenes being a new allotrope of silicon, containing four-, five- and six-membered sp3 silicon rings. The number of unsaturated silicon bonds in the structure is reduced compared with monolayer silicene. Additionally, the bandgap opens to 1.08 eV and is indirect; this is in contrast to monolayer silicene which is a zero-gap semiconductor.

ionic liquid, whereas the interior of the particle features a metallic luster. The F concentration gradually decreased from the edge to the interior in the cross-section of both CaSi 2 F X compound particle. The CaSi 2 crystal was changed to a CaSi 2 F X compound (0 ≦ x ≦ 2.3), through the diffusion of F -. The Si:Ca concentration ratio was kept constant at 2:1 in the entire area of both compounds. The F concentration of the CaSi 2 F X compound indicated three constant (plateau) composition regions (CaSi 2 F 1.8 , CaSi 2 F 2.0 , CaSi 2 F 2.3 ); however, the plateau is not always observed in CaSi 2 F X compound particles. The ionic liquid [BMIM] [BF 4 ] used for annealing consists of H, B, C, N and F. Because the B, C and N concentrations of the CaSi 2 F X compound are below 0.1 wt%, which is within the detection limit, only F is recognised in the CaSi 2 F X compound; we note that it is not possible to detect H by EPMA.  [11] w-BLSi incident directions ( [1][2][3][4][5][6][7][8][9][10] CaF2 ). b, HAADF-STEM image in the [10] w-BLSi and  Si and CaF2 directions. c, HAADF-STEM image in the [13] w-BLSi and  Si and CaF2 directions.  [13] direction. d, [11] direction. e, [10] direction. direction, the image of w-BLSi differs from that of re-BLSi in the [10] direction.
Because the experimental w-BLSi in the present study has higher symmetry on the b-axis than re-BLSi, the lattice constant of re-BLSi is the twice the period of that of w-BLSi on the b-axis.

HAADF-STEM images
Because w-BLSi 2D crystals exist as one multi-phase in a crystallite, the lattice constants and atomic positions of w-BLSi could not be characterised by X-ray diffraction. In general, a HAADF-STEM image at high magnification with atomic resolution often suffers distortion due to specimen drift during the scan time. Thus, we determined the structure of w-BLSi by high-resolution transmission electron microscopy (HRTEM) and HAADF-STEM images as accurately as possible.
HAADF-STEM and HRTEM images taken of the CaF 2 region were used as standard images for calibrating the magnification and distortion.
The 2D lattice constants of w-BLSi were determined as a = 0.661 (2)  Assuming that the thickness of w-BLSi (a distance from the center plane between the top Si of the five-membered ring and the F atomic plane to the other one, shown by black arrows in Supplementary Fig. 7a) is regarded to be virtually periodic in the third dimension, we could describe the 3D crystal structure as shown in Supplementary Table   1.

Supplementary Note 3: HAADF-STEM simulation
HAADF-STEM image simulations were performed using the structural parameters of the ab initio MD result in Supplementary By using long-period stacking structure models ( Supplementary Fig. 12a) the same as the stacking sequence in Supplementary Fig. 7a, HAADF-STEM image simulations were performed to confirm the relative position between w-BLSi and the CaF 2 crystals as well as the F site occupancy on the CaF 2 (111) surface at the interface. As shown in Supplementary Fig. 12b, the simulated image calculated by the model with vacancies in half of the F sites shows better agreement with the observed contrast than that without vacancies ( Supplementary Fig. 12c). In addition, Supplementary Figs. 13a to c show HAADF-STEM simulation images of the long-period stacking structure model ( Supplementary Fig. 12a) in the [11] w-BLSi , [10]  HAADF-STEM image simulations were performed to confirm the occupancy of F atoms at the vacancy site (red arrow in Supplementary Fig. 12a). Supplementary Fig. 14 shows observed and simulated HAADF-STEM images for occupancies ranging from 0.0 to 1.0. Line profiles obtained from the observed and simulated images are shown in Supplementary Fig. 15. The former was obtained from an average of the line profiles with or without a vacancy ( Supplementary Fig. 14a), whereas the latter is the simulation result obtained by varying the occupancy from 0.0 to 1.0 ( Supplementary Fig. 14b). The occupancy of F atoms at the vacancy site can be estimated as less than 0.4 by comparing the observed and simulated profiles (black arrows in Supplementary Fig. 15).

Supplementary Note 4: Atomic positions of the w-BLSi crystal determined by the ab initio MD result
Average atomic positions of the w-BLSi structure was determined by the ab initio MD result as shown in Supplementary Fig. 18d, which is the structure obtained in the quenching process at 0 K in the ab initio MD simulation. The experimentally determined lattice parameters a and b were employed in the ab initio MD run.
Supplementary Table 2 Table 5 shows the lattice constants, space group and atomic positions of the w-BLSi crystal of the ab initio MD result.

Supplementary Note 5: Optical properties of w-BLSi
The main phases of the CaSi 2 F 1.  Fig. 19) is converted to the Kubelka-Munk function (K/S), which is proportional to the absorption coefficient, as shown in Fig. 3c.
The composition change from CaSi 2 to CaSi 2 F X by F diffusion shows a primarily discontinuous increase and indicates several constant composition regions (CaSi 2 F 1.5-1.8 , CaSi 2 F 2.0 , and CaSi 2 F 2.3 ), as shown in Supplementary Fig. 2c. Therefore, the CaSi 2 F X composition and structure would immediately change upon F diffusion. When CaSi 2 F X consists of only one type of Si structure, the relationship between the theoretical composition values and the layered compound structures is indicated as follows: The key to understanding the surface morphology of w-BLSi is the presence of the dangling bonds on the "atop" atoms and the charge transfer between Si and Ca in the CaF 2 crystal. The total DOS for w-BLSi in a vacuum [see (b)] shows a half-filled band, which is mainly dominated by the p z electrons from the dangling bonds on the "atop" atoms. Peierls instability is often induced in such a case; thus, the up-down arrangement of the "atop" atoms is formed, being seen as a Peierls distortion (w-BLSiII) 6

Supplementary Method
Synthesis of CaSi 2 F X compound. The CaSi 2 crystal structure has a two-dimensional Si network (silicene) equivalent to a buckled honeycomb Si (111) plane of bulk Si ( Supplementary Fig. 1c). There are two types of CaSi 2 phases with different stacking sequences at ambient pressure: tr6-CaSi 2 (a = 0.3855 nm, c = 3.062 nm) 7 and tr3-CaSi 2 (a = 0.3829 nm, c = 1.590 nm) 8 . The tr6-CaSi 2 single-phase crystal was used as a starting material in the present study ( Supplementary Fig. 1b) and to examine the structural stability of BLSi using the Vienna Ab initio Simulation Package (VASP) 10 . The projector augmented wave method 11  The transformation immediately took place when the simulation was started with initial atomic velocities at 300 K. The upper and lower Si layers began to slide in opposite directions to each other, and some of the Si atoms (in the upper layer) were pushed down or up (in the lower layer), which resulted in a w-BLSi-like structure having four-and five-membered rings (note that the F vacancy was not included in this transformation simulation). Once the transformation took place, the dimensions of the space for the BLSi were readjusted to match the experimentally measured dimensions, and the F vacancy of 0.5 was introduced. The system was then equilibrated, and the resultant BLSi structure was found to perfectly agree with the experimentally observed w-BLSi structure. The 300 K first principles (FP) MD run was performed for ~1 ps following the equilibration process, confirming the stability of the w-BLSi structure.
The DOS for the w-BLSi was calculated for the structure obtained in the quenching process (shown in Supplementary Fig. 18d) following the 300 K run.