New Findings on Multilayer Silicene on Si(111)√3×√3R30°–Ag Template

We report new findings on multilayer silicene grown on Si(111)√3 × √3 R30°–Ag template, after the recent first compelling experimental evidence of its synthesis. Low-energy electron diffraction, reflection high-energy electron diffraction, and energy-dispersive grazing incidence X-ray diffraction measurements were performed to show up the fingerprints of √3 × √3 multilayer silicene. Angle-resolved photoemission spectroscopy displayed new features in the second surface Brillouin zone, attributed to the multilayer silicene on Si(111)√3 × √3 R30°–Ag. Band-structure dispersion theoretical calculations performed on a model of three honeycomb stacked layers, silicene grown on Si(111)√3 × √3 R30°-Ag surface confirm the experimental results.


Introduction
The first synthesis of multilayer silicene on Si(111) • -Ag interface used as a template was recently reported [1]. Experimental results, mainly including the structural and electronic properties investigated through Auger electron spectroscopy, low-energy electron diffraction (LEED), scanning tunneling microscopy/spectroscopy (STM/STS), in situ Raman spectroscopy, energy-dispersive (ED) grazing incidence X-ray diffraction (GIXRD), and angle-resolved photoelectron spectroscopy (ARPES) in communion with the density functional theory (DFT) calculations prove the possibility of obtaining silicene beyond the first layer and almost directly grown on silicon substrate [1].
If on one hand the X-ray diffraction results give the size of the new √ 3 × √ 3 elementary cell of the silicene superstructure, on the other, the results of the theoretical calculations provide for the first, second, and third layers of stacked silicene an alternative structure to that of diamond-type for silicon [1].
The first silicene layer is considered as free-standing, whereas the succession of bilayer and three-layer silicene on Si(111) • -Ag surface are stacked with an AA'-and AA'B-type structure, following a relative minimum energy in close agreement with all the experimental findings [1].
The concept of a metastable system holds both from the experimental and the theoretical point of view for the delicate preparation of the samples, whose growth parameters, above all the temperature of the substrate and the flux of the silicon evaporation source, reside in a quite narrow window. This led to a spread of results that fueled the debate on the possible nonexistence of the silicene multilayer, as composed of stacked layers with internal honeycomb structure [2][3][4][5][6][7][8].
Empty-and filled-state STM at 15 × 15 nm 2 (50 pA and -1.0 V) and 5 × 5 nm 2 (50 pA and 0.4 V) atomic resolution images show the √3 × √3 multilayer silicene (unit cell is drawn) and (c), which is the line profile of the black line traced in (b) that clearly quantifies the side of the √3 × √3 reconstruction as 6.40 Å, in nice agreement with references [16,23,24]. The three-dimensional representation side view, along the [112] direction, of the DP4 model [1] is reported in (d).  6.40 Å, in nice agreement with references [16,23,24]. The three-dimensional representation side view, along the [112] direction, of the DP4 model [1] is reported in (d).
To scrutinize the crystallographic structure of materials, X-ray diffraction is the most widely used technique. The basic principle behind all investigations is the solution of Bragg's equation, 2.d hkl .sinϑ = n.λ. Where the energy-dispersive X-ray diffraction is used, the Bragg angle (ϑ) is kept constant during measurements, the value of the lattice plane distance (d hkl ) in Bragg's equation being obtained via the experimental determination of the polychromatic radiation diffracted beam wavelength (λ) [31]. Indeed, when ED experiments are performed, a continuous spectrum radiation-typically the Bremmstrahlung of an X-ray tube, often called white by analogy with the visible light-is used as probe and the scattering angle remains fixed [31]. The detection is accomplished by an SSD, probing the incoming photons and their energy. The main drawback related to the ED mode is the reduced q resolution, due to the contribution of the SSD energy resolution, enlarging the diffraction peaks. However, when, as in the present case, ex situ measurements are performed and the same scattering volume must be sampled, high precision is gained despite the lower resolution, and different diffraction patterns can be easily compared in order to observe small variations.
Among the advantages of this technique, the ED method gains data over a larger q range (q = (4π.sin ϑ)/λ = 2π/d hkl [Å −1 ]), giving better real-space structural resolution, which is crucial in our experiment. Indeed, the inverse relation between X-ray energy and d hkl implies that when X-rays of high energy are available (for instance, up to 55 keV, as in the case), then the diffraction from small d values can be recorded, resulting in a larger spanned q range.
Importantly, for the experiments presented in this paper, the fixed geometry of the ED experimental setup allowed a set of cradles to be allocated in the optical center of the diffractometer, enabling in-plane and out-of-plane rotations to be performed.
In this way, since ED mode permits a multiple acquisition, the data collection, simultaneously as a function of the scattering angle ϑ, energy dispersive grazing wide-angle X-ray scattering (GWAXS), and grazing small-angle X-ray scattering (GSAXS) measurements was performed, tilting the sample along the in-plane direction (± α) and out-of-plane direction (Ψ), as shown in Figure 2. In this way, structural information along the z direction and along the x-y in-plane direction was obtained. A schematic draft, here, for GWAXS and GSAXS geometry, is shown in Figure 2. To scrutinize the crystallographic structure of materials, x-ray diffraction is the most widely used technique. The basic principle behind all investigations is the solution of Bragg's equation, 2.dhkl.sinϑ = n.λ. Where the energy-dispersive X-ray diffraction is used, the Bragg angle (ϑ) is kept constant during measurements, the value of the lattice plane distance (dhkl) in Bragg's equation being obtained via the experimental determination of the polychromatic radiation diffracted beam wavelength (λ) [31]. Indeed, when ED experiments are performed, a continuous spectrum radiation-typically the Bremmstrahlung of an x-ray tube, often called white by analogy with the visible light-is used as probe and the scattering angle remains fixed [31]. The detection is accomplished by an SSD, probing the incoming photons and their energy. The main drawback related to the ED mode is the reduced q resolution, due to the contribution of the SSD energy resolution, enlarging the diffraction peaks. However, when, as in the present case, ex situ measurements are performed and the same scattering volume must be sampled, high precision is gained despite the lower resolution, and different diffraction patterns can be easily compared in order to observe small variations.
Among the advantages of this technique, the ED method gains data over a larger q range (q = (4π.sin ϑ)/λ = 2π/dhkl [Å -1 ]), giving better real-space structural resolution, which is crucial in our experiment. Indeed, the inverse relation between x-ray energy and dhkl implies that when x-rays of high energy are available (for instance, up to 55 keV, as in the case), then the diffraction from small d values can be recorded, resulting in a larger spanned q range.
Importantly, for the experiments presented in this paper, the fixed geometry of the ED experimental setup allowed a set of cradles to be allocated in the optical center of the diffractometer, enabling in-plane and out-of-plane rotations to be performed.
In this way, since ED mode permits a multiple acquisition, the data collection, simultaneously as a function of the scattering angle ϑ, energy dispersive grazing wide-angle x-ray scattering (GWAXS), and grazing small-angle x-ray scattering (GSAXS) measurements was performed, tilting the sample along the in-plane direction (± α) and out-of-plane direction (Ψ), as shown in Figure 2. In this way, structural information along the z direction and along the x-y in-plane direction was obtained. A schematic draft, here, for GWAXS and GSAXS geometry, is shown in Figure 2. At first, a rocking curve (RC) analysis was performed upon the 10 MLs √3 × √3 Si film grown on reconstructed Si(111)√3-Ag, moving symmetrically the sample along the ±α directions, thus keeping the whole scattering-angle unchanged (see Figure 2), to minimize the Si(111) contribution along the At first, a rocking curve (RC) analysis was performed upon the 10 MLs results at different α-values are shown in Figure 3.
The Si(111) diffraction peak (black dots) was observed at qz Si(111) = 2.003 (5) Å -1 , corresponding to dz Si(111) = 3.136 Å, matching literature [ICDD card Nr. 00-04-0783], and as the RC analysis was performed, interestingly, the presence of multilayer silicene diffraction peaks located at qz 10 MLs = 2.032 (5) Å -1 became evident (red and blue dots) dz 10 MLs = 3.092 (5) Å, in good agreement with reference [1,23]. In Figure 3b and c, the highly tilted EDXD patterns are highlighted, collected at α = 0.50° and 1.50°, respectively, in order to better evidence the coexistence of both crystalline signatures (Si(111) and 10 MLs silicene). The reported diffraction peak deconvolution was obtained by means of gaussian fits (black line). The Gaussians' full width at half maximum are: FWHM Si(111) = 0.023 Å -1 ; FWHM 10 MLs = 0.011 Å -1 at α = 0.50°; FWHM Si(111) = 0.033 Å -1 ; FWHM 10 MLs = 0.019 Å -1 at α =1.50°. Subsequently, to deduce in-plane structural information, the cradle was tilted along the Ψdirection, thus partially projecting the x-ray momentum transfer on the film plane. In this way, tilting both α and Ψ, simultaneous acquisition of in-plane and out-of-plane structural features was gained, and the substrate contribution was minimised. Indeed, as visible in Figure 4, not only the previously described Si(111) and multilayer silicene diffraction peaks (qz) were observed, but the inplane Si(111)√3-Ag reconstruction and 10 MLs √3 × √3 Si film in-plane reflections were detected. Subsequently, to deduce in-plane structural information, the cradle was tilted along the Ψ direction, thus partially projecting the X-ray momentum transfer on the film plane. In this way, tilting both α and Ψ, simultaneous acquisition of in-plane and out-of-plane structural features was gained, and the substrate contribution was minimised. Indeed, as visible in Figure 4, not only the previously described Si(111) and multilayer silicene diffraction peaks (q z ) were observed, but the in-plane Si(111) √   Subsequently, to minimize the strong silicon contribution, rocking curve analysis was performed and ED-GIXRD pattern was collected, fixing α ~ 0.020° and ψ ~ 0.060°, respectively. In Table 1, we have summarized all ED-GIXRD-collected scattering vectors qxy (in-plane)/qz (outof-plane) and the corresponding lattice parameters/vertical separations d from the Si(111) substrate, Si(111)√3-Ag template, and 10 MLs multilayer film, grown at ∼ 200 °C on the Si(111)√3-Ag template.  (5) 3.240 (10) 13.030 (15)   Subsequently, to minimize the strong silicon contribution, rocking curve analysis was performed and ED-GIXRD pattern was collected, fixing α~0.020 • and ψ~0.060 • , respectively. In Table 1, we have summarized all ED-GIXRD-collected scattering vectors q xy (in-plane)/q z (out-of-plane) and the corresponding lattice parameters/vertical separations d from the Si (111)  These results are in close agreement with the atomic distances between Ag triangles and Si trimers of the well-known HCT model for the √ 3-Ag reconstruction on Si(111) at room temperature [9,[32][33][34] and those reported in reference [1], confirming the accuracy of the data.

3-Ag reconstruction and 10 MLs
The presence of √ 3 × √ 3 multilayer silicene reconstruction was also confirmed by the RHEED pattern, collected at RT (E P = 18.6 keV) electron beam along the [112]. Figure 6 shows the typical RHEED patterns of clean Si(111) 7 × 7 (a) with, in addition, those recorded on the Si(111) √ 3-Ag interface (b) and after the growth of 4 MLs of silicon, grown at temperature of~200 • C, just above a few degrees Celsius from getting an amorphous silicon film. The These results are in close agreement with the atomic distances between Ag triangles and Si trimers of the well-known HCT model for the √3-Ag reconstruction on Si(111) at room temperature [9,[32][33][34] and those reported in reference [1], confirming the accuracy of the data.
The presence of √3 × √3 multilayer silicene reconstruction was also confirmed by the RHEED pattern, collected at RT (EP = 18.6 keV) electron beam along the [112]. Figure 6 shows the typical RHEED patterns of clean Si(111) 7 × 7 (a) with, in addition, those recorded on the Si(111)√3-Ag interface (b) and after the growth of 4 MLs of silicon, grown at temperature of ~ 200 °C, just above a few degrees Celsius from getting an amorphous silicon film. The √3-Ag in (b) displays short RHEED streaks up to the second order (02,0-2), whereas in the √3 × √3 pattern after the Si deposition are clearly visible streaks until the fourth order (04,0-4).     The bands dispersion at RT, reported in Figure 7a, showed three surface states: S 1 , S 2 , and S 3 , located at~−0.2 and −0.9 eV below the Fermi level at Γ 1 are in good agreement with results of Si(111) √ 3-Ag, extensively explored in the past [35-42]. The S 1 state, with a downward convex dispersion, the less dispersive S 2 , and the upward convex largely dispersing S 3 were attributed, by first-principle calculation and scanning tunneling spectroscopy measurements, to surface states derived mainly from Ag 5p x and 5p y orbitals (S 1 ), and states consisting mainly of Ag 5s orbitals with some Ag 5p contribution (S 2 and S 3 ) [43-45]. All these bands were well reproduced by present DFT calculations, as Figure 8a shows. keeping the Si(111)√3-Ag template at ~200 °C. The red (blue) arrows in (b) and (c) indicate the (0,0) and the higher RHEED streaks order of √3-Ag and √3 × √3-Si. Figure 7 shows the second derivative ARPES results taken at RT for pristine Si(111)√3-Ag interface (a); the growth of 4 MLs Si layers at high temperature of ~ 250 °C and low temperature: ~200 °C, (b) and (c), respectively. The band dispersions were collected in the second BZ at the highsymmetry point 1, coincident with (1 1), along the [112] direction.  Materials 2019, 12, x FOR PEER REVIEW 9 of 13 k = 1.09 Å -1 along the [112] direction. The three surface states S1, S2, and S3 belonging to the Si(111)√3-Ag interface are labeled, as well as S, S*, and FB from Si. The solid red line in (a), as well as the white dotted line in (c) are a guide for the eyes. Indeed, the dotted red curve is the best fit of the free-electronlike parabola of S1 in (b), superimposed to S* in (c).
These characteristic surface states S1, S2, and S3 were observed in the dispersion of Figure 7b from Si film grown at ~ 250 °C on Si(111)√3-Ag, indicating that the Si layers consisted of similar electronic structures as those reported in (a), although the S1 surface state was slightly down-shifted in energy, most likely due to an extra doping from Ag atoms [37,46,47]. These findings are in nice agreement with results recently reported on the surfactant role of the Ag atoms in the growth of tetragonal Si layers on Si(111)√3-Ag upon the growth at temperature of ~ 250 °C [4].
However, a band similar to S1, albeit with slightly different dispersion, could also be obtained for certain multilayer silicene structures without on-top Ag atoms. Figure 8b and e show the calculated band structure for the lowest energy structure of 3 MLs silicone, described by the model B1 (3 MLs silicene) of Ref. [1]. Indeed, the band structure projected on the top Si layer and Ag layer, respectively, showed that the situation is more complicated and the presence of Ag atoms is not required to get the band structure reminiscent of the bare √3-Ag reconstruction. This finding sheds additional light on the long-standing discussion whether grown multilayer silicene is covered by Ag atoms or not [2][3][4][5][6][7][8]. Of course, this does not solve the problem, but certainly weakens arguments against uncovered multilayer silicene based on ARPES data.  3-Ag upon the growth at temperature of~250 • C [4]. However, a band similar to S 1 , albeit with slightly different dispersion, could also be obtained for certain multilayer silicene structures without on-top Ag atoms. Figure 8b and e show the calculated band structure for the lowest energy structure of 3 MLs silicone, described by the model B1 (3 MLs silicene) of Ref. [1]. Indeed, the band structure projected on the top Si layer and Ag layer, respectively, showed that the situation is more complicated and the presence of Ag atoms is not required to get the band structure reminiscent of the bare √ 3-Ag reconstruction. This finding sheds additional light on the long-standing discussion whether grown multilayer silicene is covered by Ag atoms or not [2][3][4][5][6][7][8]. Of course, this does not solve the problem, but certainly weakens arguments against uncovered multilayer silicene based on ARPES data.
Let us now examine the dispersion of the panel shown in Figure 7c from Si layers grown at lower temperature of about 200 • C. Here, we can easily observe that the old S 1 and S 3 structures disappeared, giving place to two new structures S and S*, located at~−1.15 and~−0.6 eV below the Fermi level, set at 0 eV, (separated by 0.55 eV) with a gap of~0.6 eV at Γ 1 . While the nondispersive S 2 band was replaced by a well-evident flat band (FB), even located at~−1.0 eV. To better distinguish these bands, we have reported in Figure 7c the trace of S 1 and S 3 (in red) from panel (c) and traced the new dispersion of features S and S * with a dotted line (in white). It can be immediately noticed that both their shape and energy position are different from S 1 and S 3 bands, suggesting that they belong to different origins. In addition, we fit the S 1 state in Figure 7b as a free-electron-like parabola (red dotted curve). In order to better show the relevant difference between S 1 , Ag-derived state and S*, Si-derived state, we superimpose this parabola to S*. The FB is also labeled.
We hypothesize that these extremely localized bands around K (1 × 1) belong to the 4 MLs multilayer silicene, although they are electronically affected by the presence of a confined two-dimensional electrons gas of the layer of Ag atoms trapped-quantum confined-between the silicon substrate and the silicene layers. This could explain the difference between these electronic structures and those, π and π* related to the Dirac cone, obtained from the epitaxial-grown silicene multilayer on single-crystal Ag(111) [15,48].
This hypothesis can be supported by the band structure calculated for the DP4 model for three-layer of silicene grown on Si(111) √ 3-Ag interface. This model predicts a layers stacking with internal honeycomb structure, showing a silicene √ 3 × √ 3 supercell on top of unperturbed Ag atoms. Clearly, band S* with similar intensity variations can be observed in Figure 8c,f. It looks like the top of the S* band is located at the Fermi level around point K 1 and disperses down until the Γ 1 point. Moreover, the band features strong intensity variation. In fact, this is composed by two different bands: a flat band, around K 1 , pinned to the Fermi level with Si 3p z character and the dispersive band crossing the E F due to Ag antibonding d orbitals (see Figure 8f). Since the Ag interface is covered by Si layers, the intensity of this Ag band measured by ARPES must be suppressed, leaving evident the new S* structure, Si related. This explains the apparent intensity variations. Furthermore, a flat band similar to S 2 and labeled as FB in Figure 8c, also comes from the 3p z orbitals of top Si atoms, according to the DP4 model. This band is located at lower energy, in near agreement with the ARPES data of Figure 7c. These Si-related bands, being almost flat and composed of p z orbitals, are likely formed by the quantum size effect. Similar, the band S also comes from top Si atoms, but it has 3p xy character. Note that we do not expect perfect agreement between DFT results and the ARPES spectra, since the calculations have been performed for the structure, which could have different number of Si layers than in the experiment. Nevertheless, some qualitative or even semiquantitative conclusions can be drawn. In particular, main features of the band structure, like for example surface-and interface-related states, should be present, independently of thickness of multilayer silicene. Therefore, we expect the proper atomic structure of multilayer silicene to have features of the DP4 model [1].

Conclusions
We reported new fingerprints of multilayer silicene grown on Si(111) √ 3 × √ 3 R30 • -Ag at~200 • C, by performing the energy-dispersive out-of-plane rocking curves and grazing incidence XRD patterns that clearly show the stacked distance between the silicene layers of 3.092 (5) Å and the first and multiple XRD orders of the √ 3 × √ 3 silicene unit cell size of 6.484 (5), both values different from tetragonal Si. Experimental angle-resolved photoemission spectroscopy on multilayer silicene evidences new electronic structures S, S*, and a flat band, FB, at Γ 1 , point, i. e. K (1 × 1) at 1.09 Å −1 in the second BZ along the [112] direction. They are separated by 0.55 eV and are similar to multilayer silicene grown on Ag(111) single crystal, whose characteristics are influenced by the 2D electrons gas of Ag atoms, confined between Si(111) substrate and multilayer silicene. Band-structure calculations performed on three honeycomb-stacked silicene layers confirm the ARPES results.
This work corroborates the results already presented in Ref. [1], through both new structural data and electronic properties, excluding the formation of ordinary tetragonal silicon and instead reinforcing the