VOLUME 86, NUMBER 14

PHYSICAL REVIEW LETTERS

2 APRIL 2001

Atomically Resolved Local Variation of the Barrier Height of the Flip-Flop Motionof Single Buckled Dimers of Si(100)K. Hata,* Y. Sainoo, and H. Shigekawa†
Institute of Applied Physics and CREST, Japan Science and Technology Corporation (JST), University of Tsukuba,
Tennodai 1-1-1, Tsukuba 305-8573, Japan(Received 18 April 2000; revised manuscript received 7 November 2000)
The dynamics of the flip-flop motion of single buckled dimers of Si(100) was elucidated by locating
the tip of a scanning tunneling microscope over a single flip-flopping dimer and measuring the tunnelingcurrent (time trace). Based on a statistical analysis of the time trace, we succeeded in estimating theactivation energy and the energy splitting between the two stable configurations of buckling. Strong dependence of the dynamics of the flip-flop motion on the local environment was found: Activation energy
differs significantly (directly measured 32 meV, estimated ⬃110 meV) for dimers in different domains.
DOI: 10.1103/PhysRevLett.86.3084

PACS numbers: 68.35.Dv, 68.35.Bs, 68.37.Ef

Progress in nanotechnology and the general trend to fabricate devices on an ever-smaller dimension spur the demand to understand the local characteristics (electronic,
optical, and dynamical) of the surface at the atomic scale.
This is because the atomic scale local characteristics ofthe surface influence fundamental processes (e.g., crystal
growth, chemical reaction, and etching) that are involvedin fabricating nanostructures. Influence of the fluctuationof the atomic scale local characteristics would be smearedout on a macroscopic scale, though it would become increasingly important at smaller scales.
On the Si(100) surface, which is the standard templateof modern silicon technology, the buckled dimers are
the basic building blocks of the surface reconstruction.
According to the symmetry of the structure, there exist
two identical stable configurations for the buckling [lookat schematic Fig. 1(a)]. Buckling and dimerization generate a strong stress field on the surface that is possible
to partially relax by an antiferromagnetic ordering of thebuckled dimers. This effect leads to a strong- and longranged correlation between the configuration of the dimers.
Defects, steps, and impurities disturb this ordering, and,as a result, the local characteristics (configuration, phasetransition temperature, and electronic structure) of the surface show a strong atomic scale local fluctuation [1–12].
For example, the SA steps are reported to suppress thesymmetric-buckled phase temperature observed around200 K [6].
One particular feature of the dynamics of the buckled
dimers is the flip-flop motion; i.e., at room temperature,
the dimers are vibrating between the two possible configurations. Any local fluctuation of the dynamics of theflip-flop motion would seriously influence the local properties of many important processes such as epitaxial growth,
etching, and chemical reaction. In this sense, it is very
important to measure the dynamics of the flip-flop motion
and spatially map out its local fluctuation.
Recently, Sato et al. have shown that the flip-flop motion of the buckled dimers of Ge(100) can be observed byscanning tunneling microscopy (STM) at reduced temperatures [12]. They noticed flickering features at particularregions in the STM images of the dimers that they interpreted to be caused by a sudden change of the height ofthe dimer as a result of a flip-flop motion. When the tip
was located above the flickering features, the tunneling current switched between two particular values. In this way,several (up to ten) consecutive flip-flop events of a single
dimer were observed.
In this article, we used this method to observe theatomic scale local fluctuation of the dynamics of theflip-flop motion of Si(100). A large accumulation number(up to 200 000) of sequential dynamical flip-flop eventsof a single dimer enables one to carry out quantitative
statistical analyses, from which we succeed in estimating
the activation energy and the energy splitting between
the two configurations of buckling. Spatially mappingof the dynamics of single dimers shows that the dynamics differs significantly from dimer to dimer anddomain to domain. Our results show that the atomic scale
local environment of the surface, e.g., surrounding defects,
steps, and domains, seriously influences the dynamics ofthe surface.
Standard methodology was employed to fabricate aclean Si(100) surface [11]. Figure 1(b) shows an STM
image of the clean Si(100) surface obtained at 70 K. In
both sides of the image, static buckled dimers aligned in
the c共4 3 2兲 phase that belong to different domains areobserved [13]. In the middle, dimers appear somewhat
more symmetric and numerous flickers are observed here
and there. An enlarged image [Fig. 1(c)] shows that the
flickering features are observed only in particular regions,excluding the possibility of flickering features caused bya noisy tip. A careful registry reveals that the flickering
regions are located on top of the atoms of the dimers.
One scanning line was extracted and displayed with theenvelope curves of the flickering features [Fig. 1(d)].
Based on this finding, we placed the tunneling tip over apreselected flickering feature and measured the tunneling3084© 2001 The American Physical Society

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VOLUME 86, NUMBER 14

PHYSICAL REVIEW LETTERS

2 APRIL 2001

FIG. 2. (a) Total interval histogram of a single flip-flopping
dimer at 70 K with the theoretical curve based on a random
event. ( b) Interval histograms of the two configurations andtheir corresponding theoretical curves. Note: a different dimerfrom that shown in Fig. 1.

FIG. 1. (a) Schematic of the two stable configurations of abuckled dimer. Assignment of configuration 1 or 2 is an arbitrarychoice provided the same rules are adopted for all of the dimers.
( b) An STM image showing coexistence of flip-flopping andstatic dimers. (c) Enlarged STM image of the middle region of( b). (d ) One scanning line of (c). Sample preparation procedure:Si(100) samples were prebaked at ⬃600 ±C for 12 h followed
by a flashing at 1200 ±C for 30 s, and an additional flashing
共⬃5 s兲. Phosphorus-doped 共0.1 V cm兲 Si samples were used.
Base pressure: 3 3 1029 Pa. All of the measurements werecarried out at 70 K. (e) Time trace of an atom of flip-flopping
dimer. Sampling rate 16.7 kHz. (f ) Time trace of an atomof a static buckled dimer. Imaging conditions: Vs 苷 10.6 V,
It 苷 1.0 nA, T 苷 70 K.

current, a typical example shown in Fig. 1(e). Immediately, it is apparent that the tunneling current switches toand fro between two particular values that reflect the two
possible configurations of buckling. We conclude that weare observing the flip-flop motion. Switching was not observed in the time traces obtained on static buckled dimers[Fig. 1(f)]. The sampling rate was 16.7 kHz, and, for thisparticular case, frequency of the flip-flop motion y was
0.81 kHz. Typical time traces of the flip-flop motion of asingle dimer consisted of ⬃500 000 1 500 000 sampling
points, and contains ⬃20 000 200 000 flip-flop events.
From the time traces, we calculate the histogram, H共t兲,of the interval between flip-flop events [Fig. 2(a)]. If weassume a stochastic process, an assumption whose validity
would be addressed below, H共t兲 should be described by asimple equation as
H共t兲 苷 Np共1 2 p兲t ,(1)where p is the probability to flip-flop, N is the number offlip-flop events, and t is time. Since N and p can be determined from the time trace, no fitting parameter exists, andH共t兲 can be obtained solely, displayed in Fig. 2(a) as thereal line. The fit of Eq. (1) to H共t兲 is substantial at short intervals, though deviates significantly at long intervals. We
can definitely state the existence of this deviation because
the error bar is small even at long intervals, a situation thatis made possible due to large N. The failure of Eq. (1) isbecause the dimer feels a preference for one configuration.
H共t兲s of the two configurations (configurations 1 and 2)
are deduced individually from a time trace with their corresponding theoretical curves [Fig. 2(b)]. Immediately, it
is apparent that the average intervals of the two stable configurations are different and that matching between the experimental data and theoretical curves is excellent. Hence,
the total interval histogram of a buckled dimer can be described as
H共t兲 苷

NN
p1 共1 2 p1 兲0 1
p2 共1 2 p2 兲0 ,
2
2

(2)

where p1 and p2 are the probability to flip-flop at configurations 1 and 2, respectively. N兾2 comes from theswitching characteristic of the flip-flop motion. The characteristics of the total histogram at long (short) intervals are
determined by the histogram of configuration 1 (2) [configuration with longer (shorter) mean interval]. This is thereason of the deviation in Eq. (1) [p1 苷 p2 gives Eq. (1)].
The influence of the local environment on the dynamics of the flop-flop motion can be mapped out by executing the measurements on neighboring dimers. We foundthat the details of the dynamics of the flip-flop motion
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differ from dimer to dimer. Time traces of 11 dimers inthe same dimer domain were measured, of which four examples are shown in Figs. 3(a)–3(d) with their locations
indicated in Fig. 3(d). In some cases, a preferred configuration exists which has a strong tendency to switch
alternatively both in the dimer and dimer row directions[Figs. 3(a)–3(c)]. In other cases, no preferred configuration was found [Fig. 3(d)]. All of the dimers measured
in this domain had a similar y on the range of 1–2 kHz.
This was not a peculiar case, and, for all of the measured
domains (more than ten), most of the dimers, except thoseat the boundaries, had a similar y that we nominate as theaverage flip-flop frequency of a domain, ydom .
From domain to domain, ydom varies many orders, anaspect demonstrated by three time traces [Fig. 4(a)] takenfrom dimers that belong to different domains. In fact,
the time traces presented in this article represent casesof which ydom occasionally fell into the bandwidth of thepreamplifier, and most of the apparent symmetric dimers
are flip-flopping much faster, thus they must have a smaller
activation energy, E [14]. On the other end, the static
buckled dimers that constitute most of the surface can beconsidered as dimers that have larger E. At this stage, noapparent relationship was found between ydom and the sizeand shape of the domains.
A further statistical analysis based on the autocorrelation function provides deeper insight of the nature of the

FIG. 3. Interval histograms (configurations 1 and 2) of four
dimers that belong to a same domain with lines of theoreticalpredictions. Locations of the dimers are shown in the insetof (d ). Imaging conditions: Vs 苷 10.6 V, It 苷 1.0 nA, T 苷
70 K. The average flip-flopping frequencies are displayed in the
figures. Note: This experiment is extremely sensitive to noise,and the small deviations from the theoretical lines are caused bybubbling of liquid nitrogen.

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flip-flop motion. We assume stochastic dynamics, andadopt a doubled well potential energy curve [Fig. 4(b)] of
a function of the tilting angle, u, to describe the flip-flop
dynamics. The two global minimums at 6u0 represent
the two stable buckling configurations, and the transition
rate constants between them are taken as k1 and k2 . Furthermore, we assume thermal equilibrium at temperature
T 苷 70 K. The autocorrelation function of the configuration of a dimer, separated by delay t, is defined as
g共t兲 苷 具S共t 1 t兲S共t兲典兾具S共t兲典2 ,(3)

where S共t兲 苷 61 corresponds to the two stable configurations at 6u0 . A simple probability calculation based on
the stochastic scheme leads to the following theoretical expression for the correlation function:
∂
µ
k1 k2
k 1 2 k2 2
2共k1 1k2 兲tg共t兲 苷 4e1. (4)共k1 1 k2 兲2
k 1 1 k2

FIG. 4. (a) Three time traces of single dimers that belong todifferent domains. All of the other measured dimers in the domains showed a similar flip-flop frequency. Imaging conditions:Vs 苷 10.6 V, It 苷 1.0 nA, T 苷 70 K. ( b) A schematic of adoubled well potential energy curve. (c) Autocorrelation functions of four flip-flopping dimers of where 共W, X兲 and 共Y, Z兲
belong to the same domain at 70 K. The inset shows the dependence of the rate transitions, k1 , (circles) and k2 , (squares)on the tunneling current (200 pA, 500 pA, 1 nA, 2 nA, 4 nA,
from the left). Vt 苷 10.6 V, T 苷 70 K. All of the measurements were carried out on the same dimer, and for each condition more than 50 000 flip-flop events were counted. (d ) The
black and gray bars show the measured and estimated relative
difference in E, respectively. The absolute values in the bottom
were obtained with an assumption of y0 苷 4.8 3 1012 Hz. 2a:
E of the dimer in Fig. 2(a). FPC: E obtained by first principle
calculation (Ref. [17]).

VOLUME 86, NUMBER 14

PHYSICAL REVIEW LETTERS

No fitting parameter exists in Eq. (4) because k1 and k2
can be determined from the time traces. Figure 4(c) shows
the autocorrelation functions of four dimers W ⬃ Z, withthe corresponding theoretical curves. Dimers 共X, Y 兲 thathave no preferred configurations obey limt!` g共t兲 苷 0,
while those 共W , Z兲 that have a preferred configuration donot. Correlation functions of dimers 共W , X兲 that belong
to the same domain show a decay characteristic on thesame time scale that is different from the other dimers
共Y , Z兲 located in a different domain. Matching between
the theoretical and experimental autocorrelation functions
is substantial; thus, we conclude that the flip-flop motion isindeed a stochastic process described by a two level systemand that thermal equilibrium holds for dimers having y
above 1 kHz at 70 K.
As a result of coupling to the local environment, individual dimers feel a preference for one configuration thatgives an energy splitting, DE. Under thermal equilibrium, DE can be obtained by a detailed balance: k1 兾k2 苷
exp共2DE兾kb T 兲. The energy splitting, DE, was measured
for 47 dimers, and lay in the range from 0 to 10 meV (formost cases only a few meV). If we assume that the attempt frequency, y0 , is independent of site, the relative
difference of E among dimers can be obtained by comparing the average flip-flop transition rates. For the slowest
and fastest flip-flopping dimers shown in Fig. 4, the difference in E is 32 meV. However, as mentioned above, there
are dimers both at the faster and slower ends. If we estimate 20 kHz (sampling rate) as the slowest limit for thesymmetric dimers, and 2.7 3 1024 Hz (one flip-flop perhour, a typical observation time) as the fastest limit for thestatic buckled dimers, the relative difference in E would
be 110 meV. Obviously, faster and slower dimers exist;
hence, the maximum difference should be larger.
Knowledge of y0 is required to obtain the absolute valueof E. However, conventional Arrhenius plot analysis cannot be applied, since the dynamics seriously differs fromdimer to dimer; thus, the measurement must be carriedout on the same dimer at different temperatures, a taskthat is intractable for our STM. Kawai [15] has estimatedy0 苷 4.8 3 1012 Hz from the energy of the dimer rocking
mode associated to buckling (20 meV) measured by electron energy loss spectroscopy [16]. If we use this value, Eof the dimer in Fig. 2(a) is 136 meV. All of the estimatedEs are presented in the energy bars in Fig. 4(d), where
FPC indicates E calculated by first principle methods [17].
On an ideal and complete Si(100) surface without defects
and steps, all of the dimers are identical and they should
flip-flop with the same E (FPC). This means that the wide
range of the activation energy must be induced by defects
and steps on the surface. We believe that the long-ranged
strain field produced by steps and defects induces this sophisticated and intriguing effect.
When a dynamical process is studied by STM, the influence of the tip and the electric field applied to the tunneling gap must be carefully addressed. We measured the

2 APRIL 2001

time traces of the same single dimer with various tunneling conditions (tunneling current: It 苷 ⬃200 pA 4 nA,
for each condition over 50 000 events were counted) andobtained the interval histograms and autocorrelation functions (not shown), and calculated the transition rates [inset
of Fig. 4(c)]. All of them were independent of the tunneling conditions; hence, we conclude that the influence of
tip is negligible at typical tunneling conditions.
In conclusion, we have elucidated that the dynamics ofthe flip-flop motion strongly depends on the local environment and that the activation energy must vary at least
110 meV for dimers belonging to different domains.
Helpful discussions with Y. Nakamura, H. Kawai,
and N. Nishijima are acknowledged. The support of a
Grant-in-Aid for Scientific Research from the Ministryof Education, Science and Culture of Japan is also
acknowledged.

*On leave to Harvard University.
†
Electronic address: hidemi@ims.tsukuba.ac.jp
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