La induced Si3 trimer monolayer on Si(111) surface: an ab initio study

The π-bond Seiwatz chain (SC) is one of the well-known reconstruction induced by alkaline or rare earth metals on Si(111) surface. Here we identify by ab initio calculations a new reconstruction of La induced quasi-two-dimensional Si3 trimer monolayer on Si(111)- (3×3)R30° surface. Its surface unit cell has one La atom and one Si3 trimer with the same La coverage (1/3 monolayer) as SC structure and the Si3 trimer satisfies the electron counting rule with a transfer of valence electrons from La atom, formally as La3+[Si−]3 , in correspondence to the milkstool model for Bi trimers on Si(111) surface. Band structure calculations show a semiconducting character with an indirect surface band gap of 0.76 eV. Moreover, a two-stage conversion process between the Si3 trimer and SC structure is verified by the climbing-image nudged elastic band method. These findings pave the way for further exploration of the new surface structure and its outstanding properties.

In this paper, we report by ab initio calculations a new reconstruction of La induced quasi-2D Si 3 trimer monolayer on Si(111)-( cell with one La atom and one Si 3 trimer, and the Si 3 trimer satisfies the ECR with a transfer of valence electrons from La atoms, formally as La 3+ [Si − ] 3 , in correspondence to the milkstool structure for Bi and Sb trimers on Si(111) surface [17][18][19][20][21]. Electronic band structure calculations show that this Si 3 trimer structure has a semiconducting character with an indirect surface band gap of 0.76 eV. Ab initio molecular dynamics simulations demonstrate that Si 3 trimer structure can be derived from SC structure at high temperature. Moreover, a two-stage conversion pathway between these two structures is verified by the climbing-image nudged elastic band method.

Computational method
Our density functional theory calculations are performed using the Vienna ab initio simulation package (VASP) [49,50] with the projected augmented wave potential [51,52]. The generalized gradient approximation developed by Perdew-Burke-Ernzerhof is used to treat the exchange and correlation functional [53]. The valence states 3s 2 3p 2 for Si and 5s 2 5p 6 5d 1 6s 2 for La are used with an energy cutoff of 500 eV for the plane-wave basis set. A supercell XYZ = 6.65 Å × 6.65 Å × 42.73 Å with a ( √ 3 × √ 3)R30 • periodic lattice is used to simulate the surface structure. There are six Si layers with a vacuum region of ∼20 Å in the Z direction. The dangling bonds of the lowest Si layer are passivated by hydrogen atoms. The Brillouin zone is sampled using the Monkhorst-Pack scheme [54] with a 9 × 9 × 1Γ-centered k grid. Throughout the calculations, three bottom Si layers are fixed, while other atoms are fully relaxed. The energy minimization is done over the atomic and electronic degrees of freedom using the conjugate gradient iterative technique. The convergence criteria of electronic self-consistent is set to 10 −4 eV for total energy.

Structural stability
We first characterize the La induced Si 3 trimer monolayer structure on Si(111)-( surface unit cell (black solid lines in figure 1(a)) with one La atom and one Si 3 trimer (red spheres) and such Si 3 trimers satisfy the ECR with a transfer of valence electrons from La atoms, formally as La 3+ [Si − ] 3 , in correspondence to the milkstool structure for Bi and Sb trimers on Si(111) surface [17][18][19][20][21]. Like as Bi trimer on Si(111) surface [19], each Si 3 trimer is located on the T 4 site with a Si-Si bond length of 2.44 Å. Meanwhile, each Si atom in trimer is bonded to substrate Si atom with almost same bond length of 2.45 Å. The bond length between La and its nearest neighboring Si in trimer is 2.98 Å. It is worth noting that La atom is located on another T 4 site and has the same height with Si 3 trimer (see the side view in figure 1(b)). For comparison, the SC reconstruction on Si(111)-(2 × 3) surface is shown in figures 1(c) and (d). In the unit cell, two La atoms are located on the T 4 and H 3 site, respectively, and six surface Si atoms (red spheres) form a Si atom chain along [1 10] orientation. The unit cell of SC structure is as twice as large Si 3 trimer structure and both Si 3 trimer and SC structures have the same La and Si atom density on Si(111) surface. Total energy calculations show that SC is slightly lower than Si 3 trimer with an energy difference of 43 meV per LaSi 3 unit, suggesting the stability for both structures are very close. It is worth noted that these SC and Si 3 trimer structures have a low La coverage of 1/3 ML, and at high La coverage of 2/3 ML, a Si 3 trimer bilayer structure might be formed on the Si(111) surface [55].
To examine the thermal stability of this new Si 3 trimer monolayer structure, we have further performed ab initio molecular dynamics (AIMD) simulations with the canonical (NVT) ensemble at a temperature of 300 K, using the Nosé thermostat [56] with a step of 1 fs. We rebuild the 2 √ 3× 3 supercell (XYZ = 13.3 Å × 11.52 Å × 50.46 Å) containing four La atoms and twelve surface Si atoms on Si(111) substrate. The energy fluctuations for Si 3 trimer on Si(111) surface are plotted in figure 2. The initial structure at step 0 and final structure at step 8000 are also given in insets of figure 2, respectively. It is shown that after running 8 ps at 300 K, the Si 3 trimer structure can keep well. The La atoms and Si 3 trimers deviate from the equilibrium positions (T 4 site) slightly, but they can be relaxed back to the initial positions, suggesting robust stability of Si 3 trimer structure at room temperature. Figure 3(a) presents the two-dimensional electron localization function (2D ELF) map across the Si 3 trimer monolayer section on Si(111)-(

Surface electronic properties
surface with a range from 0.2 to 0.8. The ELF = 0 or ELF = 1 represent the complete delocalization or localization of electrons [57][58][59], respectively. 2D ELF shows that the electrons are predominantly localized on Si atoms of trimer and few localized around La atom. This  means that a number of electrons transfer from La atoms to surrounding Si atoms of trimer. Thus, the ELF maps demonstrate an ionic bonding feature between La and its nearest-neighbor Si trimer. The calculated electronic band structures for Si 3 trimer monolayer structure is plotted in figure 3(b), where the valence band maximum (VBM) is located at Γ point and the conduction band minimum (CBM) is located at K point, respectively, showing a semiconducting feature with an indirect band gap of 0.76 eV. The band gap reflects Si 3 trimer structure satisfying the ECR in La 3+ [Si − ] 3 form. Such electronic band structure property is analogous to that of Bi 3 trimer on Si(111) surface with an indirect band gap of 0.45 eV [21]. We can see that this new Si 3 trimer monolayer structure with a low La coverage of 1/3 monolayer satisfies the ECR and has a larger band gap of 0.76 eV. However, at high 2/3 ML La coverage, Si 3 trimer bilayer structure has a small surface band gap of 42 meV, where two La atoms have different valence states, La 2+ and La 3+ [55].
To clarify the atomic origin of the bands near the Fermi energy level (E F ), the band-decomposed charge density distributions (BDCDDs) for the lowest conduction band (CB1) and the highest valence band (VB1) of Si 3 trimer structure are calculated, as shown in figures 3(c) and (d). The CB1 band is mainly contributed by La atoms (see figure 3(c)), while the VB1 band is mainly contributed by Si 3 trimers (see figure 3(d)), suggesting that CB1 and VB1 are two surface bands. Therefore, the BDCDDs pictures indicate that CB1 is empty state contributed by La atom and VB1 is full state contributed by surface Si 3 trimer, which is consistent with ELF results in figure 3(a).
We have further simulated the scanning tunneling microscope (STM) images of Si 3 trimer structure.  [21] due to they have similar valance states.

Structure conversion pathway
We finally examine the kinetic conversion pathway at the atomic scale between SC and Si 3 trimer structures using the climbing-image nudged elastic band (CI-NEB) method [60,61] implemented in VASP. To simulate structural transition state, we use a supercell XYZ = 6.65 Å × 11.52 Å × 50.46 Å with a √ 3× 3 periodic lattice (marked as black dotted lines in figures 1(a) and (c)), which ensures the same number of atoms for both Si 3 trimer and SC structure (see figure 4(b)). The k-point sampling of 5 × 3 × 1 is used. Throughout the CI-NEB calculations, the energy convergent criterion is 10 −4 per supercell, and the forces on all relaxed atoms are less than 0.05 eV Å −1 .
The relative total energy along the path from SC structure toward Si 3 trimer structure is plotted in figure 4(a). The key structural snapshots along the pathway at step 0, 10, 19, 28 and 38 are given in figure 4(b). It is verified a two-stage conversion process between the Si 3 trimer and SC structures. At the first stage, from step 0 to step 10, the relative total energy initially increases due to the bond breaking between Si1-Si6 and Si2-Si4 atoms; from step 10 to step 19, the relative total energy obviously decreases owing to bond rebonding between Si1-Si2 and Si4-Si6 atoms, forming Si-123 trimer and Si-456 trimer. As a result, the quasi-1D SC structure is broken and a quasi-2D intermediate structure is formed. For this intermediate structure, Si-123 trimer and La(I) atoms are located on the H 3 site, and Si-456 trimer and La(II) atoms are located on the T 4 site, respectively. The corresponding conversion barrier is estimated to be 0.58 eV per √ 3 × √ 3 unit cell (with one La atom and three surface Si atoms). This low kinetic barrier  suggests that the Si-Si bond breaking and rebonding can easily take place. However, the intermediate structure is very unstable due to Si-123 trimer and La(I) atoms are located on the unfavorable H 3 site. At the second stage, from step 19 to step 28, the relative total energy again increases due to the atomic shifting of La(I) atom and bond breaking between Si2, Si3 and substrate Si atoms (blue spheres) with Si-123 trimer anticlockwise whirling; from step 28 to step 38, the relative total energy decreases owing to atomic shifting of La(I) atom and bond rebonding between Si2, Si3 and substrate Si atoms with Si-123 trimer anticlockwise whirling. In this stage, Si-123 trimer rotates anticlockwise from H 3 site toward T 4 site and La(I) atom basically moves linearly shifting from H 3 toward T 4 site, while Si-456 trimer and La(II) atoms are basically stock-still at T 4 site. The corresponding conversion barrier is estimated to be 0.33 eV, suggests that structure transition can easily take place. As a result, Si 3 trimer structure can be obtained from SC structure via a two-stage conversion process. On the contrary, the structure conversion from Si 3 trimer structure to SC structure is more difficult with a larger energy barrier of 0.64 eV.
To examine the thermal stability of SC structure and the possible structure transition from SC toward Si 3 trimer, we have further carried out AIMD simulations with the canonical (NVT) ensemble using the Nosé thermostat [56] with a step of 1 fs at temperature of 300 K and 900 K, respectively. The energy fluctuations for SC structure on Si(111) surface are plotted in figure 5(a) at 300 K and figure 5(b) at 900 K, respectively. At room temperature (300 K), the SC structural energy fluctuations are very small and geometry remains intact on the whole. With the temperature increasing up to 900 K, as shown in figure 5(b), the SC structure can convert to Si 3 trimer structure gradually. These results suggest that the SC structure is stable at room temperature and structure transition from SC structure to Si 3 trimer structure will undergo spontaneously at high temperature. Based on our MD simulations, we can see that this new Si 3 trimer structure can be derived from SC structure at high temperature, and once Si 3 trimer structure is formed, it can be kept at room temperature as shown in figure 2.

Summary
In summary, we have identified a new La induced Si 3 trimer monolayer reconstruction on Si(111)-( √ 3 × √ 3)R30 • surface with 1/3 ML La coverage and systematically studied its structural stability and electronic properties. In each √ 3 × √ 3 unit cell, Si 3 trimer satisfies the ECR with a transfer of valence electrons from La atom, formally as La 3+ [Si − ] 3 . Electronic band structure calculations show that this Si 3 structure has a semiconducting character with an indirect surface band gap of 0.76 eV. Ab initio molecular dynamics simulations demonstrate that Si 3 trimer structure can be derived from SC structure at high temperature. Our results suggest that Si 3 trimer structure as well as SC structure can be formed on Si(111) surface due to their small energy difference and low conversion barrier between them. These results provide a new surface structure and expand our understandings for the REM induced reconstruction on Si(111) surface.