Surface Science 429 (1999) 260–273

www.elsevier.nl/locate/susc

Stability and nuclear formation of Si(111)-7×7 structure as
determined from charge redistribution in surface layers
Koji Miyake a, *,1, Haruhiro Oigawa a, Kenji Hata a, Ryuji Morita b,
Mikio Yamashita b, Hidemi Shigekawa a,ca Institute of Applied Physics, and Center for TARA, Tsukuba Advanced Research Alliance, CREST,
Japan Science and Technology Corporation (JST), University of Tsukuba, Tsukuba 305-8573, Japanb Department of Applied Physics, CREST, Japan Science and Technology Corporation (JST), Hokkaido University,
Sapporo 060-8628, Japanc Department of Chemistry and Biotechnology, Graduate School of Engineering, The University of Tokyo, Hongo,
Tokyo 113-8656, Japan
Received 27 April 1998; accepted for publication 22 February 1999

Abstract
By considering the charge transfer from adatoms to rest atoms, the structure of the dimer and stacking-fault (DS)layers in the Si(111) dimer–adatom–stacking-fault (DAS ) structure was analyzed at a subunit level on a quenchedsurface. In comparison with the modified model of Vanderbilt, corner holes with a completed DS structure in thesecond layer, completed corner holes, were confirmed to play a key role not only in the mechanism to stabilize the
DAS structure, but also in its formation process. The formation of the completed corner hole works as a rate-limiting
process for the growth of the DAS structure. This mechanism was shown to be quite consistent with the experimental
results obtained using scanning tunneling microscopy on the quenched Si(111) surface. © 1999 Elsevier Science B.V.
All rights reserved.
Keywords: Low index single crystal surface; Scanning tunneling microscopy; Silicon; Surface relaxation and reconstruction

1. Introduction
The reconstruction of the Si(111) surface has
been extensively studied by various experiments
and theoretical considerations [1–5], and the 7×7
structure has been concluded to be the most stablephase on the Si(111) surface in equilibrium condition. In fact, the 7×7 phase is completed on thewell-annealed surface, and a phase transition* Corresponding author.
E-mail addresses: miyake@ims.tsukuba.ac.jp ( K. Miyake),hidemi@ims.tsukuba.ac.jp (H. Shigekawa)
1 Internet address: http://dora.ims.tsukuba.ac.jp

between high-temperature ‘1×1’ and 7×7 phases
was directly observed around the critical temperature by using scanning tunneling microscopy(STM ) [6,7]. The dimer–adatom–stacking-fault(DAS ) structure proposed by Takayanagi et al.
[1], which is compatible with the experimental andtheoretical results, is widely accepted as the modelfor the Si(111)-7×7 reconstructed surface structure, and atomic arrangement of the DAS structurein the static form is now well established. However,since the DAS structure involves few surface layers
and is very complicated, the dynamics of thesurface, the mechanism for the formation and thestabilization processes of the structure have not0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved.
PII: S0 0 39 - 6 0 28 ( 99 ) 0 03 8 7 -8

K. Miyake et al. / Surface Science 429 (1999) 260–273

yet been completely clarified, and is still attracting
considerable attention.
In the non-equilibrium Si(111) surface prepared, for example, by laser-annealing or quenching, metastable (non-7×7) phases are known tobe formed on the surface: 9×9, 11×11, 2×2,c(2×4) and 앀3×앀3 (all of which have higher
atomic densities than the 7×7), and 5×5 and2×1, which have lower atom densities than 7×7[8–12]. Since the stability and dynamics of themetastable structures on the surface are essential
factors in understanding the mechanism of thesurface reconstruction, it is very important toelucidate the structures in detail.
Recently, the dynamic growth step of(2n+1)×(2n+1) DAS structures was directly
observed on a quenched Si(111) surface at~750 K using STM [13]. All of the metastable(2n+1)×(2n+1) DAS domains (n≠3) thatformed on the quenched surface did not survive,
but transformed into the 7×7 DAS domains at
the end. However, during the fluctuation, growth
and annihilation of (2n+1)×(2n+1) DAS,
domains were observed to occur with a single(2n+1)×(2n+1) stacking-fault (SF ) half-cell as
the building unit. The (2n+1)×(2n+1) DAS
domains grow in a triangular shape with thesuccessive addition of single SF half-cells to a(2n+1)×(2n+1) DAS domain side. In the growth
process, SF half-cells were formed sharing cornerholes.
On the other hand, Vanderbilt analyzed theenergetics of the Si(111) surface, and proposed amodel to explain the phase diagram on the surface[14]. Experimentally, Yang and Williams [12] measured the atomic density of the high-temperature‘1×1’ structure, and explained the stability of thereconstructed structures by analyzing the energybalance based on the idea of atomic conservation;
the formation of each phase is governed by theatomic density around the area. This mechanism
was quantified by Vanderbilt by introducing theidea of the chemical potential for Si atoms in thesurface layer [15]. With this model, the stabilityof the 7×7 structure and the formation of theother metastable (non-7×7) phases on the Si(111)
surface were explained, which was in good261

agreement with the experimental results. However,since the analysis was performed at the level ofthe DAS unit, the prediction was still very limited.
For example, the mechanism to explain the growthof the DAS domains in a triangular shape has notbeen clarified yet. In order to understand the phasetransition from the standpoint of the dynamics inmore detail, it is necessary to obtain information
about the stability and change in the reconstructedstructures at a subunit level.
As a factor in the subunit level to stabilize the
DAS structure, the role of the structure consistingof a dimer and adatom pair was pointed out first[16 ]. However, from the observation of the stable
dimer and stacking-fault (DS) cell, the effect of
the adatoms was considered to be not essential[17]. In fact, in the Vanderbilt model the effect of
the adatoms is treated as an additional factor toshift the energy diagram [14]. On the other hand,
the importance of the corner hole has also been
pointed out recently. For example, from the analysis of the structural growth of the 7×7 structurefrom the step edge, Ohdomari proposed a modelthat the DAS structure is stabilized by the structureof the corner holes fixed with oxygen atoms [18].
Experimentally, the important role of the cornerhole in stabilizing the DAS structure was recognized recently even in the breakdown process ofthe 7×7 structure by analyzing the HBO molecu2
lar adsorption process; the structure of the cornerhole was observed to be maintained along theboundaries between the 7×7 and the disordered
areas [19]. In addition, various (2n+1)×(2n+1)
SF half-cells were observed to grow on a quenched
Si(111) surface sharing corner holes. These results
suggest that corner holes play an important role
not only in the mechanism to stabilize the DAS
phase, but also in the formation process of the
DAS structure. However, as is well known, theDAS structure has a very complicated under-layer
structure consisting of dimers and stacking-faults,
i.e. the DS structure. Therefore, in order to understand the mechanism, clarification is needed of thedetailed structure of corner holes including the DS
structure. However, STM images generally giveinformation only about the topmost layer, and theunder-layer structure has not been analyzed indetail.

262

K. Miyake et al. / Surface Science 429 (1999) 260–273

In this paper, we present our recent results
concerning the mechanism for the stabilizationand formation processes of the DAS structure ata subunit level, i.e. the role of the corner holes
with the completed DS structure in the second
layer. The under-layer of the DAS structure isdiscussed by analyzing the bias dependence of
STM images on a quenched Si(111) surface as aresult of the charge transfer from adatoms to therest atoms in a unit [20,21].

2. Experimental
Phosphorus-doped n-type Si(111) (1 V cm) substrates were chemically cleaned and loaded into
the UHV-STM chamber. After prebaking for
1 day, samples were flashed at ~1100°C, and theformation of a clean 7×7 structure was confirmed
by STM. Then, samples were heated to ~1000°C,
and quenched by turning off the heating power.
STM measurements were performed at room temperature using an electrochemically etched tungsten tip. All STM images shown in this paper weretaken in the constant-current mode.

3. Results and discussion
3.1. Role of the corner hole in the stabilization
mechanism3.1.1. Structural analysis model and its application
to the analysis of the boundary between 7×7 anddisordered areas
Fig. 1a shows an STM image of a quenched
Si(111) surface (sample bias voltage V and tunnels
ing current I are −2.0 V and 0.3 nA respectively).
t
Triangular areas with disordered structure are
surrounded by the 7×7 structure, as shown in the
figure. Fig. 1b shows a magnified image along thestraight part of the boundary between the 7×7
and disordered structural areas. There exist adatoms along the outside edge of the 7×7 triangulardomain, and corner holes are formed along theboundary, as previously pointed out [19,21,22].
This structure can be seen commonly. For example,
see fig. 5(c) in Ref. [23]. As a subunit factor, theFig. 1. (a) STM image of a quenched Si(111) surface(V =−2.0 V, I =0.3 nA), and (b) a magnification of a boundstary between the 7×7 and disordered areas.

structure of the corner hole has been pointed out
as playing an important role in stabilizing the 7×7
structure as described above. Therefore, first, let
us examine the under-layer structure of the boundary between the 7×7 and disordered areas.
It is well known that the DAS structure has acharacteristic electronic property: the chargetransfer from the top-layer adatoms to the rest
atoms in the under-layer [24,25]. Since the amountof charge transfer from adatoms to rest atoms
depends on the number of rest atoms that surroundthe adatoms, the structure of the under-layer canbe discussed by considering the charge redistribution on the adatoms caused by the charge transferfrom adatoms to the rest atoms [20,21]. Fig. 2aand b schematically show two possible models, inwhich an SF is formed (Fig. 2a) and not formed( Fig. 2b). Under-layer dimers and SF regions are
represented by closed ellipses and hatched triangles
respectively. If the dimers in the second layer areformed along the boundary and around the cornerK. Miyake et al. / Surface Science 429 (1999) 260–273

263

represent those adatoms that are observed darker
and those not observed in the filled state image.
The difference in the brightness of the adatoms
depends on the amount of charge transferred fromthe adatoms to the rest atoms. Normal corner andcenter adatoms have one and two rest atoms intheir nearest neighbor sites. Adatoms that havethree rest atoms in their nearest neighbor sites are
not observed in the filled-state image. The numberof rest atoms in the second nearest neighbor sites
has an influence on the brightness of those adatoms
represented by gray circles.
Let us compare the structural model describedin Fig. 2 with the STM results actually obtained
at a domain boundary. Fig. 3a and b shows themagnified STM images of a boundary region taken
at positive and negative sample bias voltages. In
the empty-state image shown in Fig. 3a (V =s
2.0 V, I =0.3 nA), it is clear that corner holes existtalong the boundary between the 7×7 and disordered areas. As shown in Fig. 3b, the adatoms at
the boundary and around the corner holes arebright even in the filled-state image (V =−0.5 V,s
I =0.3 nA). In consideration of the charge transfertin the surface layers, these corner holes are sur-Fig. 2. Schematics of the domain boundary between the 7×7
and disordered areas, in which (a) an SF is formed and (b) notformed. Bright and dark adatoms and under-layer dimers areindicated by open and filled circles, and closed ellipses
respectively.

holes through the formation of an SF as shown in
Fig. 2a, the number of rest atoms around adatoms
becomes the same as that in the regular 7×7 DAS
structure. Therefore, the adatoms forming thecorner holes and those along the boundary mustbe bright even in the filled-state STM image inthis case. On the other hand, if an SF is notformed, as shown in Fig. 2b, charge transfer fromthe adatoms increases because the number of rest
atoms around the adatoms increases comparedwith that in the regular 7×7 DAS structure.
Thereby, the adatoms in the disordered area must
be darker in the filled-state STM image. Normal
corner and center adatoms are represented bywhite circles. Gray and filled circles respectively

Fig. 3. Magnified images of a boundary between 7×7 and disordered areas taken at positive and negative bias voltages are shown in (a) V =2.0 V, I =0.3 nA and (b) V =sts−0.5 V, I =0.3 nA respectively. Adatoms at the boundary aret
indicated by dots.

264

K. Miyake et al. / Surface Science 429 (1999) 260–273

rounded by a completed SF structure, and there
exist dimer chains along the outside edge of the
SF units, as is shown in Fig. 2a. These results
suggest that the ‘completed corner hole’, i.e. acorner hole with a DS structure, plays an important role in the stability of the 7×7 structure.
3.1.2. Analysis of the other DAS structures
In order to generalize the results obtained forthe boundary between 7×7 and disordered areas,
structures concerning the other DAS phases are
examined next. Fig. 4a shows an STM image takenover a more highly quenched area (V = 2.0 V,s
I = 0.3 nA). As is shown in Fig. 4a, metastabletphases such as 5×5, 9×9, and 11×11 structures
exist in addition to the 7×7 structure. Fig. 4bshows the relative amounts of these DAS units
observed on the surface. According to the model
discussed by Yang and Williams [12] andVanderbilt [15], this coexistence of DAS families
is caused by a change and fluctuation in thechemical potential during the quenching. In fact,
extra Si atoms are observed in the disordered area
between the domains of the ordered structures.
When the surface is annealed for long enough at
higher temperatures, those extra Si atoms areincorporated by the steps, and the surface becomescovered by only the 7×7 phase. It was reported
that the 9×9 phase with a higher atomic density
grows in a fluctuation during annealing thequenched surface at a low temperature around
750 K [13], which is considered to be realized by
the higher atomic density occasionally formed
around the boundary due to the lower diffusion
velocity of Si atoms at this temperature.
As expected, a structure similar to that observed
for the 7×7 domain boundary was also observed
for the other (2n+1)×(2n+1) DAS structural
domain boundaries. An example observed for the
9×9 phase is shown in Fig. 5a (V =2.0 V,s
I =0.3 nA) and Fig. 5b (V =−0.5 V, I =0.3tstnA). Here, the adatoms at the boundary between
the 9×9 structural domain and the disordered
area are bright even in the filled-state image,indicating the existence of the DS structure in theunder-layer there. The observed results suggest theexistence of a general mechanism over the role ofthe corner hole in stabilizing the DAS structure.

Fig. 4. (a) STM image taken over a more highly quenched surface (V =2.0 V, I =0.3 nA). (b) Relative amounts of DAS
stunits observed on the surface.

3.2. Role of the corner hole in the formation process
3.2.1. Nucleation of the DAS structures
In order to elucidate the role of corner holes inmore detail, we examined the structure of the DAS
fragments in a disordered area. Fig. 6a and bshows empty-state (V =2.0 V, I =0.3 nA) andstfilled-state (V =−0.5 V, I =0.3 nA) STM images.
st
In the empty-state image ( Fig. 6a), it is clearlyshown that the half-unit cells of 7×7, 9×9, andK. Miyake et al. / Surface Science 429 (1999) 260–273

265

corner hole works as a nucleation center for the
DAS structural formation process in the disordered area, resulting in the growth of the various(2n+1)×(2n+1) SF cells from the same cornerhole. The schematic model of this structure isshown in Fig. 6c. Open, gray and filled circles
indicate the adatoms with different electronic structures similar to those defined in Fig. 2.

Fig. 5. STM image of a 9×9 domain structure on a quenchedsurface. (a) V =2.0 V, I =0.3 nA and (b) V =−0.5 V,sts
I =0.3 nA. Adatoms at the boundary are indicated by dots.
t

11×11 structures share the same corner hole. In
addition, the adatoms existing along the boundaries of the half-unit cells are bright even in thefilled-state image, as shown in Fig. 6b. Therefore,
according to our structural analysis model [20,21],
the DS structure must exist there. One exception
is about the center adatom in the 7×7 SF unit at
the boundary indicated by an arrow in Fig. 6b.
The adatom looks darker in the filled-state image.
However, it is brighter than the other darker
adatoms in the 11×11 SF unit in Fig. 6b, and its
shape is much closer to the normal center andcorner adatoms. Therefore, we consider thisadatom to be influenced, for example, by gas
adsorption. The result obtained strongly suggests
the possibility that formation of a completed

3.2.2. Relation between 7×7 and 9×9 phases
Fig. 7 shows an STM image in which three 9×9
domains exist sharing corner holes with a 7×7
triangular domain (V =−0.5 V, I =0.3 nA).
st
According to the model by Yang and Williams[12] and Vanderbilt [15], the 9×9 phase is formed
at a lower temperature than the 7×7 phase, due
to the increase in the chemical potential induced
by quenching, as described above. Therefore, 9×9
domains are considered to be formed from thecorner hole on the side of the 7×7 domain, whichindicates that corner holes have a key role even in
the formation process, as pointed out above. In
fact, during the dynamic fluctuation of the DAS
structure observed by Ohdomari and coworkers
on the quenched surface [13], it was generally
observed that various (2n+1)×(2n+1) DAS halfcells nucleate at the side of the DAS domains
sharing corner holes. Concerning the under-layerof the corner holes, since the adatoms forming
corner holes are bright in the filled-state image, as
shown in Fig. 7, the corner holes are completedwith the DS structure. These results support themodel that growth of the DAS structure is governed by the formation of the completed cornerhole.
3.2.3. A model to explain the DAS formation
process
On the basis of the results obtained, a possiblemodel for the formation mechanism of the DAS
structure is shown in Fig. 8, in which the formationof a completed corner hole serves as the trigger
and the rate-limiting step for the 7×7 structural
growth. First, a corner hole with a DS structure
nucleates in the high-temperature disordered area
( Fig. 8a to b). Then, SF half cells of(2n+1)×(2n+1) DAS structures grow from thecorner hole (Fig. 8c). When two neighboring SF

266

K. Miyake et al. / Surface Science 429 (1999) 260–273

Fig. 7. STM image of a quenched Si(111) surface(V =−0.5 V, I =0.3 nA). Three 9×9 domains exist sharingstcorner holes with a 7×7 triangular domain.

units have the same size, a DAS structure is formed
completely by the formation of the structure ofcorner holes that exist on the other end of the SF
unit. After formation of the corner holes, anotherSF cell will grow sharing the corner holes( Fig. 8d ). Therefore, the growth of the 9×9
domains from the completed corner holes on the
7×7 domain sides, observed in Figs. 6 and 7, canalso be explained by this model.
There exist domains consisting of single 9×9phase; however, 9×9 domains prefer to sharecorner holes with 7×7 domains, as shown in
Fig. 7. This result suggests the existence of a barrierheight to form the completed corner hole shownin Fig. 8. On the other hand, as shown in Fig. 8,
there exist three different steps in the DAS growth
process: (1) nucleation process (Fig. 8a to b), (2)S-process ( Fig. 8b to c) and (3) P-process (Fig. 8cto d). S- and P-processes will be explained in
Section 3.4.2. Therefore, some mechanism, such as
the oxygen-related process proposed by Ohdomari[18], may exist to induce the first nucleation
process.
Fig. 6. Magnifications of the DAS fragments: (a)V =2.0 V, I =0.3 nA and (b) V =−0.5 V, I =0.3 nA. (c)ststSchematic model of (b). White and gray circles indicate adatoms with normal and dark brightness in the filled-state image(b). Black circles indicate the adatoms that are bright in theempty-state image (a) but disappeared in the filled-state image(b).

K. Miyake et al. / Surface Science 429 (1999) 260–273

267

3.2.4. Theoretical model based on the chemical
potential
In order to examine the model proposed here,
let us discuss the results observed by the theoreticalmodel proposed by Vanderbilt [14]. As describedabove, following the STM work on a quenchedsurface by Yang and Williams [23], Vanderbilt
introduced the idea of the chemical potential m for
Si atoms in the surface layer, and explained theeffects of variable atomic density on the stabilityof the reconstructed structures [15]. Vanderbilt
gave the free energy of the DAS structure per 1×1
cell relative to the 1×1 phase as [15]DE=Df/2+(2nDw+Dc∞)/(2n+1)2−mDN,

Fig. 8. Schematic diagram of the formation process of the DAS
structure: (a) high-temperature disordered area, (b) nucleationof a corner hole, (c) growth of half-unit cells of DAS structures
including an SF from the corner hole and (d) complete formation of the DAS structure.

(1)

where Df, Dw, Dc∞, and DN are respectively thefaulting energy, the dimer wall formation energy,
the normalized corner hole formation energy(including the effect of the adatom decoration),and the excess density of atoms in the surface layer
per 1×1 cell relative to the simple adatom phases{DN =−(8n+9)/[4(2n+1)2]}. Substituting thevalues of Df, Dw and Dc∞ by 0.06 eV, −0.65 eV
and 1.33 eV respectively, obtained by a combination of ab initio and empirical calculations, Eq.
(1) gives the most stable phase on the Si(111)
surface to be the 7×7 structure.
This model was originally derived from theanalysis of the energetics among the DAS phases
relative to the 1×1 structure. The comparison was
based on the completed DAS units in a staticform. However, the model was possibly applied tothe analysis of the phase transition on a quenchedsurface, by introducing the idea of the chemical
potential m. From Eq. (1), the formation of thequasi-equilibrium structures (non-7×7 structures)
could be explained well as a result of the fluctuation or the change in the chemical potential during
the formation processes. Namely, m is usuallypinned to the bulk cohesive energy by step-mediated exchange of Si atoms. However, a supersaturated condition is apparently reached as Vanderbilt
pointed out, for example, on a surface preparedby laser-annealing or quenching. In fact, various
DAS phases were observed by STM on thequenched surface experimentally, indicating that

268

K. Miyake et al. / Surface Science 429 (1999) 260–273m=m(t) (t: time after starting quench) for eachphase was realized on the surface during thequenching.
As shown in Fig. 4b, almost 20% of the DAS
structures formed on the surface in the area shownin Fig. 4a is the 9×9 phase. From Eq. (1), withan increase in m=m(t) due to the change in theatomic density during quenching, the DAS structure formed on the surface changes from 7×7 tothe high atomic density phase. The change inDE(n) of Eq. (1) for various values of the chemical
potential is shown in Fig. 9. As is shown in Fig. 9,
7×7 is the most stable phase for the positive
chemical potential up to m=0.1145 eV, where 9×9
and 7×7 phases have the same free energy. The
structure of the 7×7 phase is stable for the chemical potential in a wide range, which must be thereason for the high amount of the 7×7 phaseobserved in Fig. 4.
There exist 5×5 and 11×11 phases in Fig. 4,
but they are only in the form of the half-SF cells.
Concerning the 5×5 phase, since the atomic density is considered to be higher on the surface
prepared by quenching, the 5×5 phase must be
less stable in this condition, which is in good
agreement with the observed results. In fact, asshown in Fig. 9, 7×7 is the most stable phase evenin the negative region of the chemical potential

down to m=−0.0179 eV, where 5×5 and 7×7
phases now have the same free energy. Therefore,
existence of the 5×5 SF half-cells may be due tothe fluctuation in the local atomic density during
quenching. On the other hand, the 11×11 phaseis essentially not stable, as shown in Fig. 9, whichis consistent with the observed result. In fact, thelarge DAS domains grown on a quenched surface
observed by Yang and Williams [23] andOhdomari and coworkers [11] was up to the
9×9 phase.
As is shown here, the observed result is consistent with the mechanism introduced by Yang andWilliams, and Vanderbilt [15,23]. Excess atoms
are produced during the phase transition from thehigher atomic density ‘1×1’ phase to the 7×7
phase, and remain on the surface by quenching
instead of being incorporated at the step edges,
which induces the formation of the higher atomic
density phase. In fact, excess Si atoms are scatteredin the disordered area on the surface, as shown in
Fig. 4a. However, since the energy balance analyzed in this model is related to the units of the(2n+1)×(2n+1) DAS structures, its prediction
is still limited to the comparison in a static form.
Therefore, in order to understand the role of thecompleted corner hole in more detail, it is necessary
to understand the stability of the DAS structure
at a subunit level. Let us discuss the model shownin Fig. 8 further.

3.3. Energetic analysis of the DAS formation
process at a subunit level

Fig. 9. Change in the relative structural energy of DE(n)[Eq. (1)] with the value of the chemical potential.

Fig. 10 shows the schematic model for the formation of one 7×7 SF half-cell. Several formation
paths are possible at the atomic level. Then, inorder to estimate the structural energies, discussion
here is limited to the (2n+1)×(2n+1) SF structures: (a) 3×3 (completed corner hole), (b) 5×5,(c) 7×7, (d ) 7×7+dimer, (e) 7×7+corner hole
without SF, and (f ) completed 7×7 SF unit. Fromthe experimental results, the (2n+1)×(2n+1)
DAS structure grows from a completed cornerhole to form a 7×7 SF structure (Fig. 10a–c), anddimers are formed on the other side in Fig. 10d.

K. Miyake et al. / Surface Science 429 (1999) 260–273

269

Fig. 10. Schematic of the formation of 7×7 SF half-cell. The change in the relative structural energy is also shown.

The 7×7 structure is formed completely by theformation of the corner holes that exist on theother end of the SF unit ( Fig. 10f ). Relative
structural energies corresponding to the schematics
in Fig. 10 were estimated using the values of Df, p(dangling bond energy), d (contribution per dimer
to the surface energy), and c (contribution per
corner hole to the surface energy) that Vanderbilt
adopted to obtain the Eq. (1) [14]. As is shownin Fig. 10, growth of the fractional SF structures
increases the energy, and the 7×7 SF cell isstabilized by the formation of the dimers on theother end of the SF cell. The observed structuresin Fig. 6 are quite consistent with this model. A
similar analysis including the effect of oxygen wasrecently carried out by Hoshino et al. using theextended Hückel method on the cluster model[26 ]. Their analysis can be compared with thechange in Fig. 10a–d. The general characteristic of

the energy diagram, which mainly depends on thenumber of dangling bonds, is quite consistent
between the two cases. The existence of oxygen
lowers the structural energy, but since the generalcharacteristic is similar, we treat the oxygen-freestructure here.
For further growth of the 7×7 phase on thesurface, corner holes must be formed on the otherend of the newly formed SF cell ( Fig. 10e). Whenan apparent corner hole without an SF structure
is formed on the surface the structural energy
increases as c+p=4.16 eV for each one (Fig. 10e),
which is considered to be a possible barrier heightin the process of the formation of the completed
corner hole; see Fig. 10d–f. As is shown in Fig. 10,
there exist two barrier heights for the growth of
7×7 structure: the formation of the SF cell (fromFig. 10a–d), and the formation of the completed
corner holes (from Fig. 10d–f ). Since the barrier

270

K. Miyake et al. / Surface Science 429 (1999) 260–273

height in the latter is higher, the formation of thecompleted corner hole may work effectively as therate-limiting process in this model. In fact, as
described above, during the annealing of thequenched surface, the growth and annihilation of
single (2n+1)×(2n+1) SF cells (Fig. 10a to c ord) were observed to occur. After the structure of
the corner hole is completed on the other end of
the SF cell (Fig. 10f ), growth of the SF cells isfollowed sharing the corner holes, which is also ingood agreement with the observed results. Since
the activation energy for the formation of thecompleted corner hole (Fig. 10d–f ) seems to behigh, the oxygen-related process proposed by
Ohdomari and coworkers may play some role in
reducing the barrier height [18,26 ].
As has been shown, the results obtained lookquite consistent. However, if the formation of thecompleted corner hole is the only limiting process,SF cells can be formed from a corner hole of an
SF cell into two symmetric directions. This still
does not explain the triangular shape of the(2n+1)×(2n+1) DAS domain growth with successive additions of single SF half-cells. Therefore,
there must exist some other factor in the domain
growth process. Let us examine the remaining
problem next.
3.4. Phase matching in the formation process
When formation of the completed corner holeis the rate-limiting process, phase matching of the
SF units strongly affects the formation process of
the DAS structure. Namely, when different sizes
of DAS structures are formed from the same
corner hole, the domain growth of a single phase
DAS structure must be hampered by the phasemismatching, which is considered to govern thegrowth velocity of the DAS domains. From thisstandpoint, let us examine the formation processof the DAS domain in detail.
3.4.1. Characteristic structure of the boundaries
between the DAS and disordered areas
An STM image obtained over a quenched surface is shown in Fig. 11a. Here, we chose the area
which has a zigzag boundary consisting of SF halfunits for the analysis of the growth process.

Fig. 11. (a) STM image of a quenched Si(111) surface(V =−2.0 V, I =0.3 nA). Characteristic structure of thestboundary with (b) positive (V =2.0 V, I =0.3 nA) and (c)stnegative (V =−0.5V, I =0.3nA) bias voltages. Corner holes atst
the boundary with complete and incomplete structures are indicated by white and black circles respectively.

Fig. 11b and c show the empty-state (V =2.0 V,s
I =0.3 nA) and filled-state (V =−0.5 V, I =tst
0.3 nA) STM images of a characteristic zigzag
structure at the boundary between the 7×7 anddisordered structural areas. From comparison
between Fig. 11b and c, it is clear that the structureof corner holes and dimer chains are formed along
the straight domain boundaries, as expected. On
the other hand, the structure of corner holes is notcompleted at the kink sites; triangular edges of the
7×7 structural area formed in the disordered area.

K. Miyake et al. / Surface Science 429 (1999) 260–273

Namely, growth of 7×7 domain is considered tobe suppressed at the edges. In Fig. 11, corner holes
at the boundary with complete and incomplete
structures are indicated by white and black circles
respectively. When the structure of a corner holeis completed at an edge of the boundary, anotherSF cell of the DAS structure must be formed toreproduce the observed structure. The observed
result also supports the model that the formationof the completed corner hole is the rate-limiting
process in the growth of the DAS structure.
3.4.2. P- and S-processes in the formation
mechanism
A schematic of the boundary structure is shownin Fig. 12a. From the edge of the SF unit indicatedby E in Fig. 12a, there are two possible processes
for an SF cell to be formed; an SF unit can growin the directions parallel or perpendicular to thedomain boundary, as shown in Fig. 12b by thearrows P and S respectively. We term these twoprocesses P- and S-processes respectively.
According to high temperature STM studies, the
7×7 domain grows by forming SF cells along
domain boundaries between the 7×7 and disordered structural areas, instead of perpendicular tothe boundary [13], corresponding to the P-process.
Let us compare the two formation processes ofan SF unit more in detail. Fig. 13 schematicallyshows the recombination progress of each Si-bondFig. 12. (a) Schematic of the boundary structure in Fig. 11. E
indicates an edge of the SF unit in the domain. (b) Two possible
growth processes for an SF unit from the edge E in (a).

271

in the formation of an SF cell by the P- andS-processes. In any case, a DAS structure is formed
from a completed corner hole and is stabilized by
the formation of the dimers that exist on the otherend of the SF cell, as shown in Fig. 10d. For
further growth, corner holes must be completed asshown in Fig. 10f. In the case of the P-process,since two of three corner hole positions are fixedfrom the beginning, the formation of the SF cellis performed easily. On the other hand, in the caseof the S-process, since the SF unit begins to growfrom one corner hole, there exists an uncertainty
for the positions of the another end of the SF cell.
The uncertainty has already been observed in thecase of the DAS fragment formation in a disordered area shown in Fig. 6. When DAS structureswith different sizes are formed sharing the same
corner hole, they must change so that their sizes
become the same for the growth of the structural
domain consisting of a single size DAS structure.
In addition, the dangling bond energy of 1.45 eV
dominantly affects the change in the energy during
the formation process, and the number of dangling
bonds appearing in the process is larger for the
S-process, as shown in Fig. 13c. In the moredetailed energetic analysis by Hoshino et al., theP-process-like formation was concluded to be themost probable path [26 ]. For the reasons shown
here, an SF unit must be formed in the P-process
more easily than in the S-process. This fact causes
the preferential growth of the DAS structural
domains along the domain boundary, resulting in
the growth of the domains with a rather straightdomain boundary. Once a straight boundary isformed the structural energy is lowered, as shownin Fig. 10a. This process is quite consistent withthe experimental result obtained by Ohdomari andcoworkers [13]. As described above, a similar
structure was observed in a breakdown process
induced by HBO irradiation; completed corner2holes remain on the straight boundary between
7×7 and disordered phases [19]. Therefore, thestability of the completed corner hole is also
working in the breakdown process of the DAS
structure.
Let us examine again the structure where the
9×9 phase was formed in additional to the 7×7
domain during quenching (Fig. 7). When the272

K. Miyake et al. / Surface Science 429 (1999) 260–273

Fig. 13. A schematic of the recombination process of each Si-bond in the formation of an SF unit by the P- and S-processes shownin Fig. 12b.

corner holes on the boundary between the 7×7
triangular domain and the disordered areas areshared, the 9×9 domain growth must adopt the
S-process in order for phase matching. In fact, the
9×9 domains are formed in the direction perpendicular to the boundary between the 7×7 anddisordered areas, as shown in Fig. 7.
Since the 7×7 structure has already grownaround the step edges even on the quenched surface, it is difficult to analyze the detailed formation
process at the step edges here. However, the 7×7
structure may easily be formed at step edges by

the P-process in a similar fashion to that shownin Fig. 12.

4. Conclusion
By considering the charge transfer from adatoms to rest atoms, the structure of the dimer andstacking fault layers in the Si(111) DAS structure
was analyzed at the subunit level on a quenchedsurface. A corner hole with a completed stacking
fault and dimer structures in the second layer, i.e.

K. Miyake et al. / Surface Science 429 (1999) 260–273

a completed corner hole, was confirmed to play
an important role not only in the mechanism tostabilize the DAS phase, but also in the formation
process of the DAS structure; the formation of thecompleted corner hole is the rate-limiting process
for the growth of the DAS structure. The results
obtained were shown to be quite consistent withthe mechanism previously proposed by Yang andWilliams [12] and Vanderbilt [15] on the basis of
the effect of the excess atoms, i.e. the chemical
potential for Si atoms in the surface layer. With
this mechanism, the growth process of the DAS
structure was explained comprehensively.

Acknowledgements
This work was supported by the Shigekawa
Project of TARA, University of Tsukuba. Support
of a Grant-in-Aid for Scientific Research from the
Ministry of Education, Science, Sports and Cultureof Japan is also acknowledged.

References[1] K. Takayanagi, Y. Tanishiro, M. Takahashi, S. Takahashi,
J. Vac. Sci. Technol. A: 3 (1985) 1502.
[2] G. Binnig, H. Rohrer, Ch. Gerber, E. Weibel, Phys. Rev.
Lett. 50 (1983) 100.
[3] R.M. Tromp, R.J. Hamers, J.E. Demuth, Phys. Rev. B 34
(1986) 1188.

273[4] C.B. Duke, Chem. Rev. 96 (1996) 1237.
[5] R.J. Hamers, Y. Wang, Chem. Rev. 96 (1996) 1261.
[6 ] S. Kitamura, T. Sato, M. Iwatsuki, Nature 351 (1991) 215.
[7] K. Miki, Y. Morita, H. Tokumoto, T. Sato, M. Iwatsuki,
M. Suzuki, T. Fukuda, Ultramicroscopy 42–44 (1992) 851.
[8] R.S. Becker, J.A. Golovchenko, G.S. Higashi, B.S. Swartzentruber, Phys. Rev. Lett. 57 (1986) 1020.
[9] M. Tomitori, F. Katsuki, O. Nishikawa, J. Microscopy 152(1988) 337.
[10] M. Tomitori, F. Iwawaki, N. Hirano, F. Katsuki, O. Nishikawa, J. Vac. Sci. Technol. A: 8 (1990) 222.
[11] T. Hoshino, K. Kokubun, K. Kumamoto, T. Ishimaru, I.
Ohdomari, Jpn. J. Appl. Phys. 34 (1995) 3346.
[12] Y.-N. Yang, E.D. Williams, Phys. Rev. Lett. 72 (1994)
1862.
[13] K. Kumamoto, T. Hoshino, K. Kokubun, T. Ishimaru, I.
Ohdomari, Phys. Rev. B 53 (1996) 12 907.
[14] D. Vanderbilt, Phys. Rev. B 36 (1987) 6209.
[15] D. Vanderbilt, Scanning Microsc. 8 (1996) 794.
[16 ] M.C. Payne, J. Phys. C: 20 (1987) L983.
[17] K. Kumamoto, T. Hoshino, K. Kokubun, T. Ishimaru, I.
Ohdomari, Phys. Rev. B 52 (1995) 10 784.
[18] I. Ohdomari, Surf. Sci. 271 (1992) 170.
[19] K. Miyake, M. Ishida, K. Hata, H. Shigekawa, Phys. Rev.
B 55 (1997) 5360.
[20] K. Miyake, H. Shigekawa, R. Yoshizaki, Appl. Phys. Lett.
66 (1995) 3468.
[21] K. Miyake, M. Ishida, M. Uchikawa, K. Hata, H. Shigekawa, Y. Nannichi, R. Yoshizaki, Surf. Sci. 357–358(1996) 464.
[22] T. Hoshino, K. Kumamoto, K. Kokubun, T. Ishimaru, I.
Ohdomari, Phys. Rev. B 51 (1995) 14 594.
[23] Y.-N. Yang, E.D. Williams, Scanning Microsc. 8 (1996)
781.
[24] R. Wolkow, Ph. Avouris, Phys. Rev. Lett. 60 (1988) 1049.
[25] Ph. Avouris, R. Wolkow, Phys. Rev. B 39 (1989) 5091.
[26 ] T. Hoshino, N. Kamijou, H. Fujiwara, T. Watanabe, I.
Ohdomari, Surf. Sci. 394 (1997) 119.