Jpn. J. Appl. Phys. Vol. 38 (1999) pp. 2904–2909
Part 1, No. 5A, May 1999c
°1999
Publication Board, Japanese Journal of Applied Physics

Spontaneous Fluctuation between Symmetric and Buckled Dimer Domainsof Si(100) at 80 K
Kenji H ATA ∗1 , Tomohiko K IMURA, Yasuyuki S AINOO, Koji M IYAKE,
Ryuji M ORITA1 , Mikio YAMASHITA1 , and Hidemi S HIGEKAWA ∗2
Institute of Applied Physics and CREST, Japan Science and Technology Corporation (JST),
University of Tsukuba, Tennodai 1-1-1, Tsukuba 305-8573, Japan
1 Department of Applied Physics and CREST, Japan Science and Technology Corporation (JST),
Hokkaido University, Sapporo 060-8628, Japan(Received August 27, 1998; revised manuscript received January 22, 1999; accepted for publication March 4, 1999)

At 80 K, not all the dimers of Si(100) appear buckled in the scanning tunneling microscopy (STM) images but a certain
number of the dimers are observed in a symmetric configuration. We report on observations of a two-dimensional spontaneous
fluctuation of the symmetric⇔buckled dimer domains at some particular locations. We interpret the spontaneous fluctuation
to be induced by the competition of several antiphased c(4 × 2) buckled domains to expand. The fluctuation of domains wasinterpreted by two mechanisms: a fast switching between buckled dimer domains; and symmetric dimers induced by migrationof P defects.
KEYWORDS: Si(100), dimers, fluctuation, STM, P defect, C defect

1. Introduction
At room temperature, most of the dimers of Si(100) appear
in a symmetric configuration in the scanning tunneling microscopy (STM) images.1) The observed apparent symmetricdimers in the STM images were first considered to support theconcept of symmetric dimers. However, many experimental2)
and theoretical3) studies revealed buckled dimers to be morestable than symmetric dimers, and at present, it might be safe
to conclude that the concept of buckled dimers is well accepted. Indeed, below 200 K, most of the dimers are observedin a buckled configuration in the STM images.4) In order tointerpret the apparent symmetric dimers observed by STM atroom temperature within the framework of buckled dimers,
the concept of flip-flop motion was introduced.5) Buckled
dimers flip-flop much faster than the scanning rate of STM
at room temperature, providing an apparent symmetric dimerin the STM images, while the flip-flop motion is frozen at low
temperatures, hence the dimers appear buckled.
As the surface temperature is lowered below the criticaltemperature (∼200 K) of the symmetric⇔buckled phase transition, buckled dimer domains nucleate and grow.6–12) Defects and steps on the surface critically influence the nucleation and growth of buckled dimer domains in a sophisticatedmanner, for instance, step edges suppress the formation ofbuckled dimer domains,6) A defects7) serve as growth nuclei,
and kink sites induce buckling.8) What is more important isthat there exist two types of c(4 × 2) domains which are antiphased with respect to each other. Consequently, the surface
does not reconstruct to a single domain, but is divided into
many small antiphased domains. Many of the boundaries of
the antiphased c(4×2) buckled dimer domains appear as symmetric dimer domains in the STM images. Therefore, even at
temperatures far below 200 K, not all the dimers are buckled,
but a certain ratio of dimers appear symmetric which are induced by the defects and boundaries.9) The surface is divided
into buckled and symmetric dimer domains.
In this article we report on the observation of spontaneous∗1 E-mail: hata@ims.tsukuba.ac.jp∗2 E-mail hidemi@ims.tsukuba.ac.jp

WWW: http://dora.ims.tsukuba.ac.jp

fluctuations between the symmetric⇔buckled dimer domainsof Si(100) at 80 K. The spontaneous fluctuation is observed
only at some particular regions of the surface. In most cases,
the spontaneous symmetric⇔buckled transition can be interpreted as a result of competition among several antiphasedc(4 × 2) buckled domains to expand. During each spontaneous transition, several dimer rows change their configuration in an orchestrated manner: the observed transition is twodimensional. We present two different approaches to explain
the observed fluctuation between dimer domains.
2. Experiment and Results
Si samples were phosphorus-doped with a conductivity of
0.005 Äcm. After the samples were prebaked at ∼700◦ C for
12 h, they were flashed once to 1250◦ C for 30 s, followed bya slow cooling. The base pressure was kept under 5 × 10−8 Paduring flashing. Electrochemically etched tungsten tips wereused for the STM observations.
We begin with an STM image of Si(100) (Fig. 1) to demonstrate the coexistence of symmetric and buckled dimer domains at a low temperature (80 K). In the top-left region, thedimers appear in a symmetric configuration, while in the bottom right region the dimer rows appear as zigzagged chains.
The zigzagged chains reflect the antiferromagnitic alignmentof buckled dimers, since only the upper or lower atoms of the
dimers are observed in STM images depending on whether
the filled or empty state is probed (STM images presented inthis article are of the empty states). This ordering provides asurface reconstruction of c(4 × 2).
In Fig. 1, there exists a C defect at the boundary of thebuckled-symmetric dimer domains13) indicated by an arrow.
When the filled states are probed (not shown), the C defectappears to be two adjacent Si atoms missing along the dimerrow direction while it is observed as a bright protrusion in theempty states.13) The C defects act as phase shifters in a complete set of buckled dimers,9) and frequently the C defects areobserved at the boundaries of buckled and symmetric dimer
domains. It can be considered that the boundaries and theshape of domains are regulated by these defects.
Spontaneous fluctuations between the symmetric-buckled
dimer domains were observed at some particular locations.

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Fig. 1. An STM image of Si(100) at 80 K showing a boundary of a symmetric-buckled dimer domain. The white protrusion in the middle is a C
defect. The scan direction is displayed by the arrow. Tunneling conditions: surface bias = +0.8 V; tunneling current = 1 nA. The scanning time
is about 35 sec for one image (512 × 512 pixel). The displayed image
shows the whole scanned image.

An example is displayed in Fig. 2. In the initial stage shownin Fig. 2(a), a wide (large) symmetric dimer domain exists inthe middle (colored dark). The symmetric dimer domain issurrounded by several buckled dimers domains, and many ofthe boundaries seem to be regulated by defects, particularly
the C defects. There is a step edge and a bounding lower
terrace in the bottom-right region which is not shown. We
did not observe any kind of fluctuation in domains which extended beyond the step edges. After 4 min, the first transition was observed. As shown in Fig. 2(b), the symmetricdimer domain observed in the initial state was converted into abuckled dimer domain, and a small symmetric dimer domain(colored dark) emerged in the center. Again it appears that
this small symmetric dimer domain was regulated by some C
defects. As displayed in the set of STM images of Fig. 2,
we observed an endless switching of the surface morphology between these two particular configurations of Figs. 2(a)and 2(b) during the period of observation.
Some ambiguity exists concerning the attribution of buckled and symmetric dimers (colored dark) at some locations.
When the symmetric⇔buckled boundaries are not regulatedby the defects, the configuration of the symmetric⇔buckled
dimers seems to change gradually to a buckled/symmetricconfiguration, making a definite determination of the dimers
configuration difficult. This is why the shape of the large andsmall symmetric dimer domains in Fig. 2 are displayed asif they change their shape after each transition, however webelieve that their configurations basically remain unchanged.
It must be noted that the spontaneous symmetric⇔buckledphase transition is not observed everywhere but only occurs
at some particular regions. The observed endless switchingof the surface morphology between the two configurations
suggests that the two configurations, however different they
are, have a similar total free energy, and thermal fluctuation

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between the two configurations is observed as a spontaneoustransition.
An example of a more complicated spontaneous transitionof the dimers is displayed in a set of consecutive STM images in Fig. 3. In this case, switching between two particular configurations was not observed, but changes in surface
configuration with each transition were observed. Figure 3(a)shows the initial configuration. The white protrusions are theC defects. There are two medium sized symmetric dimer domains colored dark on the left side. Two types of c(4 × 2)
buckled dimer domains antiphased with respect to each otherare hatched with horizontal and vertical lines. After the first
spontaneous transition shown in Fig. 3(b), the medium sized
symmetric dimer domain at the upper-left region converted
into a buckled dimer domain and was absorbed into the buckled dimer domain on the right (hatched with horizontal lines).
By the second transition, the medium sized symmetric dimer
domain at the bottom-left region extended and the buckled
dimer above it was divided into two [Fig. 3(c)]. After 42 min,the final transition occurred and the most dramatic change
was observed [Fig. 3(d)]. During the course of the transition,
the large buckled dimer domain in the middle converted into
a symmetric dimer domain. This transition is quite different
from that displayed in Fig. 2 in the sense that the configuration of the surface changes after each transition and does
not switch between two particular configurations. During thecourse of observation, the surface did not revert to its originalstate. Transitions of this type were observed very rarely.
3. Discussion
We propose two different explanations for the observed
spontaneous fluctuation. The two explanations are different
in the interpretation of the symmetric dimers observed in the
STM images at 80 K, a temperature far below the critical temperature (200 K) of the symmetric⇔buckled phase transition.
The first explanation attributes the origin of symmetricdimer domains to fast switching of buckled dimer domains,which we refer to as “symmetric dimers induced by switchingof buckled dimer domains” in the following. Two domains ofc(4 × 2) exist which differ in the phase alignment of the buckled dimers. The site (i, j) is defined to belong to the (±) phasewhen (−1)i + j Si, j = ±1, where Si, j = ±1 corresponds to thetwo possible configurations of the buckled dimer. Usually asymmetric dimer domain is sandwiched between two buckled
dimer domains which belong to different phases. Therefore,
it is possible to consider that the symmetric dimer domain
emerges as a result of fast switching between the surrounding (+) and (−) phased buckled dimer domain11, 12) as shown
schematically in Fig. 4(a). This concept was introduced fromtheoretical researches using Monte Carlo simulations to study
the dynamical characteristics of the dimers.10–12)
Another interpretation of the symmetric dimer domains isthat numerous phasons nominated as P defects migrate along
the buckled dimer rows much faster than the scanning rate of
STM where the dimers appear symmetric.14, 15) This mechanism is referred to as “symmetric dimers induced by migration of P defects”. In such a case, basically the dimers arebuckled, though they appear symmetric in the STM images.
The P defects are two adjacent dimers buckled in the same
direction (ferromagnetic ordering), and they act as phase defects when located in the antiferromagnetic ordered buck-

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K. H ATA et al.

Fig. 2. A set of consecutive STM images of Si(100) at 80 K showing a spontaneous fluctuation of symmetric-buckled dimer domains.
The dark colored regions represent apparent symmetric dimer domains. White protrusions are the C defects. Tunneling conditions:surface bias = +0.8 V; tunneling current = 1 nA. Scanning scale = 30 nm. The arrow shows the scanning direction. The scanning rate
is about 35 s for one image. The time displayed indicates the duration in minutes and seconds from the end of scanning of Fig. 2(a)to the end of scanning of each image.

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Fig. 3. Another example of a set of STM images of Si(100) showing a spontaneous fluctuation of symmetric-buckled dimer domains.
Tunneling conditions: surface bias = +0.6 V; tunneling current = 1.5 nA. Scanning scale = 30 nm. The arrow shows the scanning
direction. The scanning rate is about 35 s for one image. The time displayed indicates the duration in minutes and seconds from theend of scanning of Fig. 3(a) to the end of scanning of each image.

led dimers in the c(4 × 2) phase as shown schematically in
Fig. 4(b). The P defects are movable and do not appear as
bright protrusions when probing the empty states. Existenceof the P defects was first directly confirmed by STM observations at 6 K.16) At 80 K, P defects migrate much faster than
the scanning rate of STM. Therefore, areas where the P defects exist and migrate should appear as symmetric dimers in
the STM images as shown in Fig. 4(b). At 80 K, symmetricdimer domains can be regarded as a “sea” of these phasonsimprisoned in a particular area by the C defects and the surrounding antiphased c(4 × 2) buckled dimer domains.
Interpretation of the observed transition of the dimer domains shown in Fig. 2 by the two approaches is a simple andstraightforward procedure. In Fig. 5 we show the schematics of the large [Fig. 5(a)] and small [Fig. 5(b)] symmetricdimer domains of Fig. 2 with the surrounding buckled dimer
domains. Careful analysis of the phase of the buckled dimers
reveals that there exist two antiphased buckled dimer domains[(A) hatched with horizontal lines], and [(B) hatched with ver-tical lines] surrounding the symmetric dimers domain. The
boundary of the two buckled dimer domains is observed assymmetric dimer domains [regions (C) and (D)] which is regulated by the surrounding C defects.
We interpret that the observed spontaneous transition is induced by the competition of the two buckled dimer domains(A) and (B) to expand. The power balance between the twodomains should be delicate enough to fluctuate either by perturbation of the scanning tip or thermal fluctuation. From thestandpoint of symmetric dimers induced by fast switching ofbuckled dimers, the fluctuation of the symmetric dimer domains represents a change in the region switching between
domains (A) and (B). A transition from the configuration ofFig. 5(a) to Fig. 5(b) means that the buckled dimer domain(A) has expanded. The transition observed in Fig. 3 can be
explained in a similar manner. From the standpoint of symmetric dimers induced by migration of P defects, some P defects migrate along the dimer rows in regions (C) and (D).
The observed spontaneous transition is a result of a change of

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Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 5A

from the standpoint of symmetric dimers induced by switching, because individual switching between buckled dimer domains must occur very fast (if not, symmetric dimer domains
would not be observed at low temperatures in the first place)and should be two-dimensional. On the other hand, from thestandpoint of symmetric dimers induced by migration of P defects, this aspect is more complicated to explain. We assume
that a strong interaction exists among the symmetric dimerrows, the origin of which we attribute to a strong attractive interaction between the P defects in adjacent symmetric dimer
rows. Indeed, at 80 K, it is reported that the P defects in adjacent dimer rows have a strong tendency to form pairs.17)
We interpret that the observed two-dimensional transition is
induced by a concord migration of the P defects which originates from the strong attractive interaction.
Further work is required to give a complete atomic scale
description of the transition and to combine the two different
mechanisms presented here.
4. Conclusion

Fig. 4. (a) A schematic showing apparent symmetric dimer domains
caused by a fast switching between two c(4 × 2) antiphased buckled dimer
domains. Domains (A) and (B) represent buckled dimer domains in the(+) and (−) phase, respectively. The boundaries of domain (C) in between(A) and (B) are regulated by the defects represented by the black boxes in
the corners. The buckled dimers in domain (C) switching fast between the(+) and (−) phases, and as a result observed as symmetric dimers by STM.
(b) A stick and ball schematic showing the structure of the P defects (black
circles). The circles represent the down (up) atoms of the buckled dimers.
The P defect is composed of two buckled dimers aligned in the same direction. It is highly mobile as indicated by the arrows. Accompanied with the
migration of the P defect, the adjacent buckled dimer flip-flops to the otherconfiguration. The schematic on left side shows many P defects migrating
along the dimer rows resulting in an apparent symmetric configuration of
dimers in the STM images.

Fig. 5. Schematics showing the configuration of dimers and the location of
the C defects at the boundaries of the surface area of Fig. 2. The C defects
at the boundaries are represented as dark spots. (a) Schematic showing
the configuration of the large symmetric dimer domain, and (b) the small
dimer domain. Regions hatched with horizontal and vertical lines are antiphased c(4 × 2) buckled dimer domains, while regions colored black represent symmetric dimer domains.

To conclude, we have observed a spontaneous fluctuation
between buckled and apparent symmetric dimer domains on
Si(100) at 80 K by using a scanning tunneling microscope.
We interpret that most of the fluctuations are induced by a sophisticated competition among the neighbouring antiphased
the area in which the P defects migrate with ease. A transition
from the configuration of Fig. 5(a) to Fig. 5(b) means that theP defects in region (C) are confined to the small region (D)accompanied with the expansion of region (A).
Defects seriously influence the configurations of the dimer
domains and thus the transitions. Configuration of dimers
on surfaces with low densities of C defects (1%∼ similar
to our experiments) has been studied by Monte Carlo simulations.10–12) Defects on the surface were demonstrated tosignificantly influence the configuration of the dimers in the
STM images. What is more important, Nakamura et al. haveshown that the influence of a combination of several defects
is much stronger than the sum of the influence of isolated defects.11) When several defects are located in a particular configuration (in their calculations four C defects at the cornersof a rectangle), the influence of the defects extends to the adjacent dimer rows and the regions surrounded by defects show
a strong tendency to appear as symmetric dimers in the simulated STM images.11) We interpret that the middle region of(D) where dimers always remain symmetric is such a location.
Some commonly observed aspects of the transition provide important implications on the interaction between dimersand defects. It is important to note that the intervals between transitions are on the time scale of a few minutes,
while the transition is accomplished instantly when comparedto the time scale of scanning of STM (∼msec.). We call it
an avalanche type transition; the rate limiting process is tostart the transition and once the transition is triggered, the accompanied transformation of dimers is quickly accomplished(which makes it difficult to analyze the details of the transition by STM). In the course of each transition, many dimerschange their configuration in an orchestrated manner in a very
short time, while once the transition is accomplished they remain in the same configuration for a long time. Moreover, thetransition extends to the adjacent dimer rows: the transition is
two-dimensional. It is very simple to understand this aspectJpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 5Ac(4 × 2) domains to expand, where the boundaries of the domains are observed as symmetric dimer domains. We present
two different approaches to explain the observed fluctuation
between domains: a fast switching between buckled dimer
domains and symmetric dimer domains induced by migrationof P defects.

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