Conference-JRSSS-6-Atomic structure of the Al / Si ( 111 ) phases studied using STM and total-energy calculations

V.G. Lifshits Institute for Automation and Control Processes Far Eastern Branch of the Russian Academy of Sciences, 5 Radio Street, 690041, Vladivostok, Russia, and Faculty of Physics and Engineering, Far Eastern State University, 690000 Vladivostok, Russia, and Department of Electronics, Vladivostok State University of Economics and Service, 690600 Vladivostok, Russia (Received 26 October 2004; Accepted 2 February 2005; Published 16 February 2005)


I. INTRODUCTION
Starting from the pioneering work of Lander and Morrison [1], the ordered submonolayer phases in Al/Si(111) system have been an object of numerous investigations.It has been established that depending on growth temperature and Al coverage four surface phases are formed as follows, α-7×7, √ 3× √ 3, √ 7× √ 7 and γ-phase.The γphase was labelled originally as γ-7×7 [1], but subsequent investigations have caused doubts on its 7×7 periodicity [2].Though the Al/Si(111) surface phases have been extensively studied by many groups over almost 40 years, sofar the √ 3× √ 3 phase is still the only one which atomic structure has been established conclusively.The √ 3× √ 3-Al structure is relatively simple consisting of Al adatoms occupying the T 4 sites on the almost bulk-like terminated Si(111) surface.The other Al/Si(111) surface phases exhibit a more sophisticated structure and remain debated subjects [3].In the present paper, we review the results of our recent investigations of the structure of the phases formed in the submonolayer Al/Si(111) system using STM and total-energy calculations.

II. EXPERIMENTAL
Experiments were carried out in the ultra-high vacuum chamber with a base pressure of 8×10 −11 Torr equipped with STM ("Omicron") and four-grid optics for LEED observations and AES analysis.Atomically-clean Si(111)7×7 surfaces were prepared in situ by flashing to 1250 • C after the samples were first outgassed at 600 • C for several hours.Aluminum was deposited from a heated Al-cowered W wire.The samples were heated by passing DC current through them.For STM observations, electro-chemically etched tungsten tips cleaned by in situ heating were employed.

A. Si(111)-α-7×7-Al phase
The α-7×7-Al phase develops at the early stages of Al deposition (up to ∼0.35 ML) onto the Si(111) substrate held at temperatures ranging from 475 to 600 • C.This phase has been recognized as being essentially a highly-ordered superlattice of the Al nanoclusters on the ISSN 1348-0391 c 2005 The Surface Science Society of Japan (http://www.sssj.org/ejssnt)Si(111)7×7 surface [4][5][6], as illustrated by Fig. 1 showing the surface after deposition of ∼0.35 ML of Al at 575 • C. One can see that every half of the 7×7 unit cells (HUC) is occupied by the identical-size triangle-shaped cluster.The cluster shows up as a group of three protrusions in the filled states (Fig. 2a) and as a group of six protrusions in the empty states (Fig. 2b).This STM appearance of Al clusters coincides exactly with the STM appearance recently reported for the magic clusters of Ga and In adatoms [7,8].The atomic structure of the magic clusters as elucidated by means of first-principles total energy calculations [8] is shown in Fig. 2c.The structure was originally proposed for the Ga magic clusters formed on Si(111) √ 3× √ 3-Ga reconstruction [9] and it consists of six metal atoms linked through three Si atoms to form a triangle-shape configuration with satisfied bonding.The six protrusions seen in the empty-state STM images correspond to the location of metal atoms, the three protrusions seen in the filled-state STM images consequently to the location of the top Si atoms.
The magic cluster consumes three edge Si adatoms of the original Si(111)7×7 DAS structure and, hence, in the ideal case, would preserve the original top Si atom density of 102/49 ∼ = 2.08 ML.However, the corner Si adatoms are also involved in the reaction with deposited Al and become partially replaced by Al atoms.In the empty states, the Al adatoms are seen as more bright, as revealed by comparison with the Si adatoms on the bare Si(111)7×7 surface.Discrimination between Si and Al adatoms allows the insight into the atomic-scale processes involved in the formation of the superlattice of magic Al clusters.There are three various adsorption sites for Al apatoms.First, Al adatom can be incorporated in the magic cluster (There are six such sites per 7×7 HUC).Second, Al adatom can substitute for the corner Si adatom (three sites per 7×7 HUC).Third, Al adatom can substitute for the edge Si adatom in the 7×7 HUC, which preserves the original DAS structure (three sites per 7×7 HUC).Variation in the occupation number for each site in the course of deposition is illustrated in Fig. 3. Three distinct stages can be distinguished, labelled I, II, and III.
At the stage I (below ∼1.5 Al atoms per HUC, i.e., ≤0.06 ML of Al), formation of the magic clusters is a minor process and the most of deposited Al adatoms simply substitute for Si adatoms.The substitution of edge adatoms prevails over substitution of corner adatoms and the occupation of the faulted HUCs prevails over occupation of the unfaulted HUCs.At the stage II (from ∼1.5 to ∼5 Al atoms per HUC, i.e., at 0.06-0.20 ML of Al), the growth of the magic clusters is the major process.Recall, that for the formation of each cluster, six Al adatoms and three Si adatoms are needed.The required number of Al atoms is get as a sum of the edge adatoms, substituted by Al at the initial stage, and arriving Al adatoms.Say, if all three edge adatoms in the HUC have been substituted by Al atoms, additional three Al adatoms have to be supplied by deposition.Supply of Si adatoms is another crucial process for the cluster formation.At the stage I, Si adatoms, expelled by Al atoms, agglomerate into islands and, thus, they cannot contribute to the subsequent cluster growth.At the stage II, the area occupied by islands has been found to remain practically unchanged, which means that most of the Si adatoms liberated upon Al substitution are involved in cluster formation.In other words, the growth of the cluster in a certain HUC takes place through the supply Si adatoms displaced from the neighbouring HUCs.The main contribution comes from the substitution of the edge adatoms.The contribution from the Al substituted corner adatoms is not so essential as indicated by slow increase in their occupation number.The second stage is completed when about 75% of HUCs are occupied by the magic clusters.
At the stage III (from ∼5 to ∼8 Al atoms per HUG, i.e., at 0.20-0.33ML of Al), all the left HUCs become filled by the magic clusters.As the edge adatoms as a source of Si http://www.sssj.org/ejssnt(J-Stage: http://ejssnt.jstage.jst.go.jp) adatoms have been already exhausted at the stage II, the Si adatoms are mostly supplied by the Al substitution of the corner adatoms.As a result, the number of the Al substituted corner adatoms increases rapidly, so that eventually about half of the corner adatom sites become occupied by Al atoms.

B. Si(111)-
The √ 3× √ 3-Al phase is developed in the temperature range from 600 to 750 • C. Its atomic structure is well established as consisting of 1/3 ML of adsorbate adatoms, which reside in T 4 sites of the almost bulk-like Si(111) surface.Each adatom is bonded to the three top Si atoms, hence all silicon dangling bonds are completely terminated.Note that the model concerns the ideal √ 3× √ 3-Al structure.In practice, the Si(111)-√ 3× √ 3-Al surface contains a certain density of surface defects, the most principal of which are vacancies and substitutional defects (Al adatoms substituted for Si atoms).In the STM images, vacancies are seen as deep depressions at both polarities.Si adatoms are seen darker than Al adatoms in the empty states, but brighter in the filled states as one can see in Fig. 4.
We have found that the most homogeneous  surface and is illustrated in the inset in Fig. 6b.Thus, from Fig. 6b, one obtains that the center of the Al trimer is located in the on-top (T 1 ) site, while Al adatoms forming a trimer reside close to the T 4 site with a slight shift from the exact T 4 position in the direction outward from the trimer center.
Taking these findings into account, the model of atomic arrangement of the Si(111) √ 7× √ 7-Al phase can be proposed as shown in Fig. 7a.The new model differs qualitatively from the models proposed by Hamers (Fig. 7b) and Hansson (Fig. 7c).In the new model, Al adatoms are located about T 4 sites and the center of the trimer is in the on-top site.In the Hamers' model, Al adatoms occupy the bridge sites in between two neighboring top Si atoms and the center of the trimer is in the T 4 site.In the Hansson's model, Al adatoms reside in the H 3 sites and the center of the trimer is located in the on-top site.
To examine stability of the structures represented in the models, we have performed the total-energy calculations which details are given elsewhere [12].Upon evaluation of our model, we have obtained that in the optimized structure, the Al-Al interatomic distance in the trimer is 4.08 Å, the distance between Al atom and the top Si atom in the center of the trimer is 2.72 Å and the Al-Si bond length is 2.54 Å. Upon optimization of the Hansson's model, the Al atoms shift from the ideal H 3 sites in the direction outward the trimer center and the structural parameters of the optimized structure are close to those of our model: the Al-Al distance is 4.08 Å, the distance between Al atom and the central Si atom is 2.64 Å and the Al-Si bond length is 2.49 Å.However, in comparison with our model, the optimized Hansson's model appears to be less stable by 0. bridge site is unstable and upon structure optimization Al adatom moves towards the neighboring T 4 site, hence, the structure evolves to that proposed in our model.

D. Al/Si(111) γ-phase
Figure 8 illustrates the general features of the Al/Si(111) γ-phase surface structure [13].On the large scale of thousands Å (Fig. 8a), the surface shows up as consisting of two levels which are one Si(111) bilayer (3.14 Å) apart.On the medium scale of hundreds Å (Fig. 8b), the surface is built of triangle-shaped subunits.The subunits have a close, but not identical, size and, hence, their arrangement does not display the definite long-range order.On the atomic scale (Fig. 8c), the interior of the triangular units is seen in empty states as a well-ordered hexagonal array of the round protrusions.These protrusions correspond to the Al atoms which substitute for the Si atoms in the outermost atomic layer of the bulk-like Si(111)1×1 surface [10,14].The relative shift of the Al atomic rows in the neighbouring triangles indicates that every second triangle contains a stacking fault in the surface layer.From the comparison of the periodicities extracted from the fast Fourier transforms of the 7×7 and γ-phase STM images, we have found that the spacing between Al atoms in the triangle interior is 1.09±0.02times greater than the lattice constant a Si 0 = 3.84 Å of the undistorted Si(111)1×1 surface.The increase of the surface lattice constant is a natural consequence of the incorporation of Al into the top Si(111) bilayer, as Al atomic radius (1.43 Å) is large than that of Si (1.18 Å).Assuming the preservation of the tetrahedral coordination of atoms in the surface (111) bilayer, one can estimate the lattice constant of this mixed Al-Si layer.The estimation yields the value of 1.11a Si 0 , which is close to the experimental value.The misfit between the Al-incorporated layer and the Si sample bulk is relieved through the formation of the domain walls which produce the characteristic triangleshaped superstructure.
The close inspection of numerous STM images of the Al/Si(111) γ-phase obtained upon various formation conhttp://www.sssj.org/ejssnt(J-Stage: http://ejssnt.jstage.jst.go.jp) ditions have revealed that two types of the γ-phase can be distinguished.As will be shown below, the basic difference between them is associated with the structure of their domain walls.The γ-phase of the first type (hereinafter referred to as "light" γ-phase) contains the light domain walls (i.e., the domain walls which are depleted of Al)(Figs.9a and 10a).The γ-phase of the second type (hereinafter referred to as "heavy" γ-phase) contains the heavy (i.e., Al-enriched) domain walls (Fig. 11a).Both phases can be grown by Al deposition onto the heated Si(111) surface or by room temperature deposition of Al followed by annealing.The "light" γ-phase is produced by depositing almost "stochiometric" amount of Al (∼0.7 ML), while the formation of the "heavy" γ-phase requires the Al supersaturation.Transition from the "light" γphase to the "heavy" γ-phase is not abrupt.The fraction of the heavy domain walls increases gradually with Al deposition and becomes substantial after depositing more than 1 ML of Al.It should be noted that "heavy" γ-phase always contains a certain fraction of the light domain walls.
The difference in the domain wall structure affects the averaged characteristics of the γ-phase.The results of the experimental characterization for the two phases are summarized in Table I.Al coverage has been determined from the high-resolution STM images by direct counting the Al-associated protrusions at the fixed area, which scale was evaluated from the spacing between Al atoms, 1.09×3.84∼ = 4.19 Å.The obtained values are 0.64±0.05ML for the "light" γ-phase and 0.76±0.04ML for the "heavy" γ-phase.Note that not all deposited Al atoms become incorporated into the γ-phase (especially, into the "heavy" γ-phase).The excess Al atoms agglomerate into scarce random Al islands.
The development of the two-level system of islands and holes (see Fig. tive consideration of Si mass transport according to the relation [15] Θ where 2.08 (102/49) ML is the top Si atom density of the original Si(111)7×7 surface and S the area fraction occupied by the upper-level γ-phase (see Fig. 8a).The "light" γ-phase has been found to incorporate 1.01±0.03ML of Si.In the "heavy" γ-phase, more Si atoms are substituted by Al and its top Si atom density is lower, 0.84±0.05ML.
The periodicity of the γ-phase superstructure is associated with the mean size of the triangular subunits.From comparison of the LEED patterns of the γ-phases and the original Si(111)7×7 surface, the periodicity (expressed in the units of the Si(111)1×1 lattice constant, a Si 0 = 3.84 Å) has been found to increase slightly from 9.2±0.3 for the "light" γ-phase to 9.8±0.3 for the "heavy" γ-phase.
Consider the possible atomic structure of the domain walls.Let us start with the light domain walls.Figure 9a shows a high-resolution empty-state STM image of the "light" γ-phase, in which the domain walls show up as the dark furrows.The sketch in Fig. 9b illustrates the arrangement of the Al atoms around the domain wall.As one can see, the Al atoms which border the domain wall on the opposite sides are arranged in the zigzag manner.To account for the present experimental findings, we propose a structural model of the "light" γ-phase, as shown in Fig. 9c.The model incorporates a stacking fault structure with triangular subunits being through a Si zigzag chain.It reproduces the zigzag arrangement of the Al atoms along the domain wall, takes into account the enlarged spacing between Al atoms and yields a reasonable Al coverage of between 0.6 and 0.7 ML.
Besides the above structure, another type of the domain wall can be found, as shown in Fig. 10a.Aluminum atoms which border this domain wall face each other and the width of the boundary is considerably smaller than that of the zigzag-chained structure (Fig. 10b).However, it should be noted that the occurrence of this domain wall is very seldom (e.g., only a single domain wall can be found in the 500×500 Å2 STM image) and they border only relatively small triangular subunits (typically, of four Al atoms a side).
An example of the domain walls in the "heavy" γ-phase is shown in Fig. 11a.The domain wall contains two atomic rows with spacing between them somewhat smaller than the spacing between the rows in the interior of the triangular subunits.The boundary is plausibly built of Al atoms, i.e., it comprises a heavy domain wall.Unfortunately, the bonding geometry within this domain wall remains unclear, as we have been unable to make any reasonable guess how to tie the observed arrangement of Al atoms to the regular sites on the underlying Si(111)1×1 surface.The possible reason is that the strain due to accumulation of the extra Al atoms in the "heavy" γ-phase induces the noticeable distortions in the underlying Si(111) layer, which is no longer a bulk-like plane.

IV. SUMMARY
Using STM and total-energy calculations, we have studied the phase formation in the submonolayer Al/Si(111) system.The structural properties of the surface phases have been elucidated.
The Si(111)-α-7×7-Al phase has been shown to be essentially a superlattice of the identical-size nanoclusters built of six Al atoms linked through three Si atoms.The most homogeneous Si(111) √ 3× √ 3-Al surface has been found to contain 0.25 ML of Al adatoms and 0.08 ML of Si adatoms.The Si(111) √ 7× √ 7-Al phase has been determined to consist of Al adatoms located about T 4 sites and forming the trimers with the centers in the on-top sites.For the Al/Si(111) γ-phase, two modifications have been distinguished, which differ by the composition and structure of the domain walls.The Al/Si(111) γ-phase of the first type contains the light domain walls depleted of Al, while the phase of the second type contains the heavy Al-enriched domain walls.

FIG. 2 :
FIG. 2: (a) Filled state (+2.0 V) and (b) empty state (−2.0 V) STM appearance of the Al magic clusters.(c) Atomic structure of the magic cluster of the Group III metals, as established in Refs.7-9.The magic cluster is built of six metal atoms (grey circles) linked through three top Si atoms.The protrusions seen in filled states correspond to the location of the top Si atoms, the protrusions seen in empty states to that of the metal atoms.The 7×7 unit cell is outlined.

FIG. 3 :
FIG. 3: Variation of the occupation numbers for the three adsorption sites, namely, in the magic clusters (open squares), in the edge adatom sites (open circles), in the corner adatom sites (open triangle), versus Al coverage.The occupation numbers and deposited Al coverage are expressed in the unitl of the mean number of Al atoms per 7×7 half unit cell (HUC).Three distinct stages are indicated.The growth temperature is 560 • C.

3 -FIG. 7 :√ 7 -
FIG. 6: (a) Empty-state (−2.4 V) STM image of the surface with coexisted regions of the √ 7× √ 7-Al and √ 3× √ 3-Al reconstructions.(b) The area outlined in (a) superposed on a grid with nodes in T4 sites.Inset illustrates schematically the orientation of the Si(111) substrate, thus, showing the mutual locations of the T4, H3 and on-top (T1) sites.One can see that the empty-state √ 7× √ 7 protrusions are located at around T4 sites and form trimers with centers at T1 sites.

FIG. 9 :
FIG. 9: (a) High-resolution empty-state STM image of the "light" γ-phase.The domain wall is indicated by arrow.(b) Schematic sketch illustrating the arrangement of Al atoms around the domain wall.The Al atoms, which border the domain wall (shown by grey circles), are arranged in a zigzag fashion.(c) Structural model, which accounts for the domain wall of this type.
FIG. 10: (a) High-resolution empty-state STM image of the "light" γ-phase showing the rare type of the domain wall (indicated by the arrow).(b) Schematic sketch illustrating the arrangement of Al atoms around the domain wall.The Al atoms, which border the domain wall (shown by grey circles), face each other.(c) Structural model, which accounts for the domain wall of this type.
Following the lines in Fig.5, one can clearly see that the centers of the empty-state trimers coincide with the location of the filled-state protrusions.