Progress in Surface Science 76 (2004) 147–162
www.elsevier.com/locate/progsurf

Progress Highlight

Ground state of the Si(0 0 1) surface
revisited—is seeing believing?
T. Uda a, H. Shigekawa b, Y. Sugawara c, S. Mizuno d,e,H. Tochihara d, Y. Yamashita f, J. Yoshinobu f, K. Nakatsuji f,
H. Kawai g, F. Komori f,*a

Advanced Research Laboratory, Hitachi, Ltd., 1-280 Higashi-Koigakubo, Kokubunji,
Tokyo 185-8601, Japanb
Institute of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japanc
Department of Applied Physics, Graduate School of Engineering, Osaka University,
2-1 Yamada-oka, Suita 565-0871, Japand
Department of Molecular and Material Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japane
PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japanf
Division of Nanoscale Science, The Institute for Solid State Physics, The University of Tokyo,
5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japang
Department of Physics, Faculty of Sciences, Kyushu University, Ropponmatsu, Fukuoka 810-8560, Japan

Abstract
The stable structure of clean Si(0 0 1) surface around 100 K is the c(4 · 2) arrangement constructed by buckled dimers. This structure was widely accepted as the ground state in 1990Õs.
The view was challenged at the beginning of 2000Õs by the observations of a p(2 · 1) structure
below 20 K with scanning tunneling microscopy (STM). Recent experimental studies conﬁrm
that the dimer is buckled below 30 K. Large tip–surface interaction, and/or tunneling current
induced dynamical eﬀect are now experimentally evident in the STM images at low temperatures. Moreover, a current induced structure transformation is discovered below 40 K even in
the study by low energy electron diﬀraction. Dynamical electronic and vibrational eﬀects aretheoretically studied for accounting the observation of a p(2 · 1) structure below 20 K.
 2004 Elsevier Ltd. All rights reserved.

*

Corresponding author. Tel.: +81 4 7136 3310; fax: +81 4 7136 3474.
E-mail address: komori@issp.u-tokyo.ac.jp (F. Komori).

0079-6816/$ - see front matter  2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.progsurf.2004.05.015

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PACS: 68.35.Bs; 68.35.Ja; 68.37.Ef
Keywords: Surface structure; Low temperature; Silicon; Germanium; STM; AFM; LEED; PES

Contents
1.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

2.

Theoretical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

3.

STM observations below 50 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

4.

Noncontact AFM observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5.

Electron beam irradiation effect in LEED measurements of Si(0 0 1) below 40 K 154

6.

Evidence of asymmetric dimers of the Si(0 0 1) surface at low temperature byhigh resolution Si 2p photoelectron spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 156

7.

Reversible and local transformation between c(4 · 2) and p(2 · 2) on aGe(0 0 1) surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

8.

Vibration of the dimer on the Si(0 0 1) surface excited by STM current . . . . . . . 159

9.

Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

1. Introduction
After the discovery of p(2 · 1) superstructure of the Si(0 0 1) surface [1], the reconstruction of the surface has been extensively investigated both experimentally [2–11]
and theoretically [12–21]. A reversible second-order phase transition between the disordered p(2 · 1) and ordered c(4 · 2) phases occurs at 200 K in low-energy electron
diﬀraction (LEED) measurements on the Si(0 0 1) surface [2,3], and the most stablephase was concluded to have the c(4 · 2) structure. According to scanning tunnelingmicroscopy (STM) studies between 80 and 140 K [4–8], the c(4 · 2) structure was
conﬁrmed to be the most stable arrangement of the buckled dimers at this temperature range. Chadi [12] has found from energy minimization calculations thatthe asymmetric dimer due to buckling lowers the total energy. The buckling isaccompanied with a charge transfer from the lower atom to the upper atom of the
dimer. This was consistent with the core level photoelectron spectra suggestingthat two types of surface atoms exist [10]. All these results seemed to have settled
the controversy about the ground state of Si(0 0 1), and the p(2 · 1) phase observed

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149

by STM at room temperature was attributed to the quick ﬂip-ﬂop motion of
the buckled dimers [17,22,23]. In the precious calculations, the total energy diﬀerence between c(4 · 2) and p(2 · 2) is 1.2 meV/dimer [18]. From these studies, it
was widely accepted that the buckled dimers construct a c(4 · 2) structure as theground state.
In recent studies on the low-temperature phase of Si(0 0 1) by STM and atomic
force microscopy (AFM), however, c(4 · 2), p(2 · 2)/c(4 · 2), and symmetric dimer
images have been observed below 80 K [7,24–28]. These experimental results
have questioned the generally accepted picture of the buckled dimer with ac(4 · 2) ordering as the ground state of the Si(0 0 1) surface. A similar structuralchange was also suggested by LEED measurements below 40 K [29]. It has beenargued from the early stage of the STM observations that strong tip–surface
interaction in STM might change the real structure [30]. Thus, several independent groups have studied the surface using other experimental techniques at low
temperatures in addition to further STM observations. The ground state and thetip–surface interaction have been also theoretically investigated again. Now it is evident that the tip–surface interaction makes the image of the buckled-dimer
symmetric.
In this article, the latest progress of the research on this subject is reviewed. First
we brieﬂy summarize the theoretical studies on this surface, and then discuss the
structures observed by STM below 50 K. In the STM study [27], both the c(4 · 2)
and p(2 · 2) structures are observed depending on doping species, temperatureand the sample bias voltage. In Sections 4–6, structural studies by AFM at 5 K[26], by LEED down to 24 K, and by Si-2p photoelectron spectroscopy down to
30 K [31] are described. All the results indicate the buckled dimer. Moreover, thec(4 · 2) structure is suggested as the ground state below 40 K by LEED. The
transitions between c(4 · 2) and p(2 · 2) induced by tunneling current in STM is
described for the clean Ge(0 0 1) surface below 80 K [32] in Section 7. A similar interaction is expected on the Si(0 0 1) surface. In Section 8, vibrational excitation of the
dimers by STM current is proposed as a possible origin of its symmetric image on theSi(0 0 1) surface.

2. Theoretical overview
Nearly half century ago, Schlier and Farnsworth [1] observed a p(2 · 1) structure
in a LEED experiment. This is caused by surface atoms moving together in pairs toform dimers. The formation of dimers eliminates one of the two dangling bonds(DB) per surface atom, thereby lowering the surface energy. On the basis of various
experimental studies, the c(4 · 2) reconstruction was suggested as the ground state
structure.
Theoretical studies, on the other hand, took oﬀ two decades later. In 1978 Chadidemonstrated that buckled dimers are favored through empirical tight-binding
method [12]. The DB on the upper dimer atom is an sp3 orbital with larger s-component and accordingly has lower energy, while that on the lower dimer atom is of

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p-character with higher energy. The buckling is caused when energy gain due tocharge transfer from the higher to the lower levels is greater than the energy cost
due to on-site Coulomb energy, compensated by the Madelung energy. More sophisticated ﬁrst-principles calculation based on the density functional theory (DFT) by
Yin and Cohen [13] conﬁrmed on a 2 · 1 unit cell that an asymmetric dimer is favored to a symmetric dimer.
Since 1985 when Car and Parrinello developed an eﬃcient ﬁrst principles algorithm, a number of total energy minimization calculations [14–16,18,21] has been
performed on the 4 · 2 unit cell. These agree that the building blocks are buckled dimers, and the direction of buckling alternates along a dimer row. The formation ofp(2 · 2) or c(4 · 2) corresponds to adjacent rows in phase or out of phase orientations. In order to obtain conclusive result for the subtle stability diﬀerence betweenc(4 · 2) and p(2 · 2), careful modeling of the surface was required. In most calculations, a repeated slab geometry is adopted. One calculates the total energy by ﬁxing
the bottom layer at the bulk position, terminating DBs on that layer by hydrogenatoms. In another method, the innermost two layers are frozen and the outermost
layers on each side of the slab are allowed to relax. The layer thickness should be
doubled but the calculation is free from the eﬀect of induced dipoles at the bottom
layer. Inversion symmetry is imposed to accelerate the computation. In either
method, the c(4 · 2) surface is about 1 meV/dimer lower in energy than thep(2 · 2) surface [18], when a thick sample is used with at least ﬁve layers allowed
to relax. Some earlier calculations, which resulted in favor of p(2 · 2) thanc(4 · 2), used thinner slabs [14]. Thus c(4 · 2) was accepted as the lowest energy
structure in the early 1990Õs.
This picture was challenged by recent experimental work. The STM studies below
80 K showed that c(4 · 2) becomes unstable and p(2 · 2) domains appear [8]. It wasreported independently by two groups [24,25] that further cooling below 20 K causes
the dimers to appear again symmetric.
Theoretically, electron correlation should be reconsidered carefully because ﬁrst
principles calculations based on DFT may not properly describe its role at present.
Healy et al. performed quantum Monte Carlo calculation [33] on large cluster models of the surface, and concluded that buckling remains energetically favorable,
undermining the ability of DFT to accurately describe the ground state reconstruction of the Si(0 0 1) surface. Thus the old theoretical conclusion still survives thatc(4 · 2) is the ground state structure and the energy diﬀerence with p(2 · 2) is as
small as 1 meV/dimer. The result is supported by the recent experimental work
reviewed in the following sections. The coexistence of c(4 · 2) and p(2 · 2) israther natural considering the small energy diﬀerence between the two. These twophases can be transformed each other by the tip–surface interaction in STM. In certain conditions the buckled dimer may be observed as symmetric due to thisinteraction.
On the whole, the experiments at very low temperatures do not contradict theDFT calculations at 0 K. However, this fortuitous agreement brings forward a
new serious problem why and how c(4 · 2) is stabilized again at about 100 K in
STM observations. This is left to be explained.

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3. STM observations below 50 K
Fig. 1(a)–(c) show typical STM images obtained for the Si(0 0 1) surface (P-dope,
0.01–0.001 X cm) at 29, 43 and 50 K, respectively [34]. In this case, c(4 · 2) (red),p(2 · 2) (blue), and unstable (gray) dimer areas are seen. Fig. 1(d) and (e) show
the magniﬁed topographic and current images of the squared area in Fig. 1(b),respectively. In the current image, unstable dimers are shown as scratched, whichindicates that the dimers are ﬂip-ﬂopping during the STM measurement. A remarkable point is that the c(4 · 2) and p(2 · 2) structures are dominant at 80 and 10
K, respectively, and they gradually change into the other structure via an unstable
disordered structure with temperature as shown in Fig. 1(f). Since a second-orderphase transition, the disordered p(2 · 1) to the ordered c(4 · 2), exists at 200 K,
some additional mechanism may be necessary to explain the appearance of the second structural change below 50 K.
At the transition temperature, the c(4 · 2) or p(2 · 2) structure emerges into thep(2 · 2) or c(4 · 2) area, respectively, with the introduction of P-defects, which aremovable topological defects [6,7,35,36]. The P-defect consists of two adjacent dimers
which buckle with the same orientation. It can migrate along a dimer row as one ofits two dimers changes the buckling orientation. In addition, there appears to be ahigh percentage of ﬂip-ﬂopping dimer areas as shown in Fig. 1(f). The appearanceof the ﬂip-ﬂopping dimers during the transition directly indicates the instability ofFig. 1. (a)–(c) STM images for the Si(0 0 1) surface at 29, 43 and 50 K. (d), (e) Magniﬁed topographic (d)and current (e) images of the squared area in (b). (f) Change in the structure components between 29 and
50 K [34].

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the buckled dimer structures at these temperatures. The existence of the disorder
structure due to the mixture and ﬂuctuation between the c(4 · 2) and p(2 · 2) phases
indicates that the mutual structural change is easy at the transition temperature, 45
K. If the structure is thermally disordered at 45 K, the barrier height between c(4 · 2)
and p(2 · 2) should be smaller than that at 80 K.
It is well known that the dimer structures are stabilized with a delicate balance
between the electronic and elastic interactions of dimers [37]. Therefore, a possible
explanation is to relate the phenomena to the change in the strain and the carrier
density depending on the temperature. These are supposed to play an important rolein the change in the interaction.
Recently, the inﬂuence of the measurement conditions has been reconsidered indetail [27,30,38,39]. An interesting characteristic is the dopant dependence, namely,a p(2 · 2) single phase at 10 K more easily appears for a sample with the following attributes: (1) n-type, (2) high doping, and (3) very low defect density [27]. Another important point is the tip-induced eﬀect. At low temperatures, the STM tip
comes closer to the sample surface due to the low conductivity of the sample andthus activates the structural change such as the ﬂip-ﬂop motion of buckled dimers[30,38]. In fact the applied bias voltage and tunneling current strongly inﬂuence
the observed structures [27,39]. The transformation of the c(4 · 2) structure top(2 · 2) is observed at 5 K with increasing the bias voltage from 1.3 to 1.4 V [39].
These eﬀects must be taken into consideration to understand the structural change
shown in Fig. 1.

4. Noncontact AFM observations
In all STM experiments of the ground state structures, it is possible that the electric ﬁeld and/or the tunneling current aﬀect the ground state structure. That is, themotion of the atoms occurs due to an excitation by the electric ﬁeld of the biased
tip and/or due to an energy injection by the tunneling current. To investigate theground state structure, it is necessary to remove tip-induced excitation eﬀect. Noncontact AFM is an alternative tool for high-resolution imaging, which is expected
not to cause such excitation eﬀects and therefore to be suitable for observing the
ground state structures. This is because the operation of the noncontact AFM isbased on very weak interactions due to attractive atomic forces, rather than the electric ﬁeld utilized in the STM.
Uozumi et al. [26] have experimentally investigated the ground state structure of
the Si(0 0 1) surface at 5 K by using noncontact AFM. As force sensors, a conductive
Si cantilever was used with a sharpened tip. Its mechanical resonant frequency was
170 kHz. The Si tips were cleaned by Ar-ion sputtering for 30 min, and the nativeoxide layer and any contamination on the tip apex were removed. Thus, there aredangling bonds out of the Si tip. The frequency modulation detection method wasused to measure the force between the Si tip and the Si(0 0 1) surface.
Fig. 2 shows a noncontact AFM image of the Si(0 0 1) surface measured at 5 K.
The frequency shift of the cantilever was set at 6 Hz, its vibration amplitude was 17

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Fig. 2. Noncontact AFM image of the Si(1 0 0) surface at 5 K [26]. The scan size is 18.8 nm · 18.8 nm.

nm, and the scan area was 18.8 nm · 18.8 nm. In this image, a bright spot expresses a
Si atom at the surface. More than 70% of surface shows the buckled dimers wherebright spots form a zigzag pattern. The c(4 · 2) structure with antiparallel zigzag pattern occupied 61% of all surface, and p(2 · 2) structure with parallel zigzag patternoccupied only 12% of all surface. This surface has a defect density of 8%. The

Fig. 3. Noncontact AFM image of the Si(1 0 0) surface at 5 K [26]. The scan size is 9.4 nm · 9.4 nm.

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observed fuzzy area is as large as 19% because the surface structure shows varieties
and becomes vague near defects.
Fig. 3 shows a magniﬁed image of the square area in Fig. 2. The scan area was 9.4
nm · 9.4 nm. Buckled dimers with the c(4 · 2) structure are conﬁrmed more clearlyin this ﬁgure. Thus the noncontact AFM study at 5 K indicates that the ground state
structure of the Si(0 0 1) surface is the c(4 · 2) structure.

5. Electron beam irradiation eﬀect in LEED measurements of Si(0 0 1) below 40 K
The STM measurements sometimes cause perturbation on the surfaces, and such
eﬀects were conﬁrmed in several experiments [28,30,32,39]. Therefore, it is unclear
whether these results reﬂect intrinsic properties or artifacts. The structure at lower
temperatures should be studied by other techniques that would not have a signiﬁcant
inﬂuence on the surface structures. LEED was expected to be one of such tools.

Fig. 4. (a) Spot intensities as a function of sample temperatures (EK = 50 eV). (b) Spot intensities as afunction of time after a shutter was opened (EK = 50 eV). (c) A c(4 · 2) pattern just after the electron beamirradiation (0.7 lA, EK = 50 eV) at 24 K. (d) A streaky pattern observed 50 s after the irradiation (0.7 lA,
EK = 50 eV) at 24 K [40].

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Matsumoto et al. measured LEED spot intensities as a function of temperature [29].
They obtained the intensity diminution of the quarter-order spots below 40 K. Theirresults suggested the occurrence of a new order-disorder phase transition at around40 K. The same change of LEED spot intensities was observed by Mizuno et al. as inFig. 4. It was concluded [40] that the disappearance of the c(4 · 2) pattern is causedby the electron beam as described below.
All measurements [40] after the ﬂashing of the surface have been done at pressureless than 3 · 1011 Torr. The following samples were used: (1) an Sb doped n-type
wafer(0.014 X cm), and (2) a B doped p-type wafer (0.017 X cm). Sharp c(4 · 2) patterns were observed at 80 K. The intensity of the streaks along half-order spots wasvery weak as observed in the previous LEED study [3]. The c(4 · 2) structure wasdetermined using LEED IV analysis at 80 K. The obtained structural parameters
were in excellent agreement with the previous theory [21]. There is no diﬀerence instructural parameters between samples (1) and (2).
The eﬀect of electron beam irradiation was demonstrated by the following two
procedures: (i) The sample position was changed quickly at 24 K during LEED
observation; (ii) a shutter between LEED optics and the sample was closed duringcooling down to 24 K, and was opened quickly. With both procedures, clearc(4 · 2) patterns were observed immediately after LEED observation as shown in
Fig. 4(c). However, the patterns changed into streaky ones after 50 s at 50 eV and
0.7 lA as shown in Fig. 4(d). The same LEED pattern changes were observed forboth the p-type and n-type samples.
The procedure (ii) was examined with several electron beam conditions. The
intensities of the (3/4 1/2) and (1/2 1/2) spots were plotted in a semi-logarithmic scalewith respect to the irradiation time as shown in Fig. 4(b) for sample (2) at 50 eV. The
intensities were normalized by the beam current. Initial intensity changes were very
rapid and almost completed within 20 s at 1 lA. Higher beam current resulted infaster changes of the intensities as shown in Fig. 4(b). Very slow changes after 100 s
are due to the contamination by residual gases. The slopes of the slow changes did
not depend on the beam current but depended on the pressure. The same slow
changes were observed at 80 K.
The intensities of some spots were plotted on a semi-logarithmic scale with respect
to the sample temperature at incident electron energy of 50 eV in Fig. 4(a). These
curves were obtained for sample (2) with increasing temperature by direct heating.
At the start of this measurement, the surface was irradiated by electrons for morethan 1 min at a sample temperature of 24 K. Therefore, the intensities of the quarter-order spots were already decreased. When the sample temperature rose above 40
K, the intensity of the quarter-order spots recovered and the streaks disappeared.
Similar curves were also obtained on cooling. The intensity change of the (3/4 1/2)
spot is consistent with the previous ones obtained by Matsumoto et al. [29]. Similarintensity changes were also conﬁrmed for sample (1) and at diﬀerent electronenergies.
We conclude that the most stable structure at 24 K is c(4 · 2). The intensitychanges at 40 K observed in previous LEED study [29] is not a new phase transition
but caused by the electron beam irradiation. With increasing irradiation time, the156

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surface got covered by small c(4 · 2) and p(2 · 2) domains at 24 K. This surface
quickly rearranged to the well-ordered c(4 · 2) above 40 K.

6. Evidence of asymmetric dimers of the Si(0 0 1) surface at low temperature by highresolution Si 2p photoelectron spectroscopy
Measurements by STM have larger tip–surface interaction than AFM imaging,and the observed image might diﬀer from the real structure. Therefore, informationon core level photoelectron spectroscopy (PES) is useful because it provides chemical
states and relative abundance. In addition, core level PES probes information aboutchemical environment of each atom with an instantaneous excitation.
Yamashita et al. have successfully demonstrated that the up and down dimer
atoms, and the subsurface atoms of the clean Si(0 0 1)-c(4 · 2) surface whose chemical environments are diﬀerent from that of the bulk produce separate peaks in highresolution Si 2p PES at low temperatures (from 140 to 30 K) [31,41,42]. On the basisof comparison of the Si 2p spectra with the results of STM, it can be clariﬁed
whether the symmetric or p(2 · 2) image in STM is induced by the tip–surface interaction or not.
Fig. 5(a) shows a Si 2p spectrum for the Si(0 0 1) surface at 140 K [41]. In the spectrum, we can decompose the spectrum into ﬁve components and assign them: thecomponents B is due to the bulk Si atoms; the components Su and Sd correspondto the up and down Si atoms of the asymmetric dimers, respectively; the component
SS is assigned to second-layer Si. The component X is still unidentiﬁed. The relative
binding energies for Su, X, Sd, and SS to the bulk Si energy position are 485, 200,
62, and 215 meV at 140 K, respectively. The split of 547 meV between the up anddown dimer components originates from a substantial charge transfer within the dimer atoms and a ﬁnal state eﬀect [43]. The peak positions and the angle dependence
of intensity ratios agree well with the previous results by Uhrberg group [10].
Fig. 5(a–d) show the Si 2p PES spectra for the Si(0 0 1) surface as a function oftemperature (hm = 129 eV and normal emission) [31,41,42]. As can be seen, the spectral shapes become sharper with decreasing the temperature owing to reduced thermal phonon broadening and/or reduced inhomogeneous broadening. However, thespectral shapes are basically similar, and an additional component is not required
for each Si 2p PES spectrum.
Yokoyama and Takayanagi [25] proposed that a dynamical ﬂipping could occur
due to the reduced force constant at a low temperature. ShigekawaÕs group has reported that c(4 · 2) and p(2 · 2) coexist on Si(0 0 1) by low temperature STM [27].
If they were intrinsic phenomena, the inhomogeneous broadening of Si 2p peakwould be observed. However, this is not the case in the present high resolution Si
2p PES results. Thus, the dimer ﬂipping and/or the formation of p(2 · 2) ordering
is most probably due to induced eﬀects by STM observation. The present Si 2p
PES investigation strongly suggests that the buckled dimer with the c(4 · 2) ordering
is stable below 40 K, and the ground state on Si(0 0 1). This is consistent with theresults of careful LEED and noncontact AFM studies.

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(a)

(b)

140 K

100 K

157

Sd

B

SS

Sd

B

Su

SS

Su

X

X

1
0
-1
Relative Binding Energy (eV)
(c)

1
0
-1
Relative Binding Energy (eV)

(d)

55 K

30 K
Sd
SS

Sd
SS

B

B
Su

Su
X
1
0
-1
Relative Binding Energy (eV)

X

1
0
-1
Relative Binding Energy (eV)Fig. 5. Si 2p PES spectra for the Si(0 0 1) surface (a) at 140 K, (b) 100 K, (c) 55 K, (d) 30 K [31,41,42]. The
emission angle is 0o (normal emission) and the photon energy is 129 eV. B: bulk, Su: up dimer, Sd: down
dimer, SS: subsurface, X: unidentiﬁed species.

7. Reversible and local transformation between c(4 · 2) and p(2 · 2) on a Ge(0 0 1)
surface
Reversible control of surface local structures is expected on the c(4 · 2) reconstructed surface of clean Ge(0 0 1) as well as Si(0 0 1) because the energy diﬀerence
between the ground state and the p(2 · 2) structure is estimated to be a few meV/
dimer [18,46]. On the both surfaces, the neighboring two atoms form a buckled
dimer, and their reconstruction is characterized by the ordering of the buckled
dimers. Takagi et al. have reported that the structure can be transformed by changing the sample bias voltage of STM below 80 K on Ge(0 0 1) surface [32,44,45].
The c(4 · 2) structure is observed with the sample bias Vb 6  0.7 V while p(2 · 2)
with Vb P 0.8 V at 80 K. Moreover, both structures can be maintained under scanning the surface with jVbj 6 0.6 V at 80 K after ﬁxing the local structure by scanning
there with a higher jVbj. The bias dependence of the surface reconstruction at 80 K is

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Fig. 6. A schematic showing the observed structures depending on the bias voltage and the direction of thevoltage change [32,44].

summarized in Fig. 6. The transformation rate from c(4 · 2) to p(2 · 2) at Vb = 0.8 V
is estimated to be 3 · 1011 dimer/electron.
Fig. 7 demonstrates a nanoscale memory eﬀect. These images were observed with
Vb = 0.2 V. After taking the image shown in Fig. 7(a), the area A in the ﬁgure wasscanned with Vb = 0.8 V to change from c(4 · 2) to p(2 · 2). The result is shown in
Fig. 7(b). The change along the dimer row continued to the outside of the scanningarea. Then the area B in Fig. 7(b) was scanned to form another p(2 · 2) area asshown in Fig. 7(c). The reverse change from p(2 · 2) to c(4 · 2) was done by scanning the area C in Fig. 7(c) with Vb = 0.7 V. In this case, all of the desiredp(2 · 2) area was scanned because the change to c(4 · 2) was limited nearby the areaof the scanning even along the dimer row. The annihilation of p(2 · 2) is shown in
Fig. 7(d).
It has been argued that the ground state energy of Ge(0 0 1) surface is determinedby the two competing energies between the electrostatic energy among the electric
dipole moments at the dimers and the subsurface strain energy. When the surface
is positively biased under the STM tip, the negatively charged upper-atoms of the
dimers are electro-statically pushed toward the subsurface by the tip, and theFig. 7. Successive STM images of the same area (22.5 · 10 nm2) of a Ge(0 0 1) surface at 80 K [32]. The
square areas ‘‘A’’ in (a) and ‘‘B’’ in (b) were scanned with Vb = 0.8 V to change the local structure fromc(4 · 2) to p(2 · 2) after taking each image. The surface after scanning ‘‘A’’ is shown in (b), and that afterscanning ‘‘B’’ is in (c). The rectangular area ‘‘C’’ in (c) was scanned with Vb = 0.7 V to change it fromp(2 · 2) to c(4 · 2). The surface after scanning the area ‘‘C’’ is shown in (d).

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lower-atoms of the dimers are pulled toward the vacuum side. Consequently, the dimer buckling becomes smaller. This makes the diﬀerence of the subsurface strain energy between c(4 · 2) and p(2 · 2) structures smaller than that of the dipole energy
among buckled dimers. Thus for the positively biased surface, the p(2 · 2) structure
is favored by the gain of the dipole energy, and can be the ground state. On the other
hand, under the negative Vb, the buckling of the dimers is increased by the electric
ﬁeld, and the c(4 · 2) structure is more favored.
The local and reversible restructuring of the Ge(0 0 1) surface is demonstrated between c(4 · 2) and p(2 · 2) by controlling the sample bias voltage of STM below 80
K. The ground state can be altered by electric ﬁeld from the STM tip, and the tunneling current induces the transformation of the structure. There should be the similar STM tip-eﬀect on the Si(0 0 1) surface. The structure change on the Si(0 0 1)
surface, however, is observed only when the tunneling current is small [39]. The
atomic force between the tip and the surface may inﬂuence the structure in the caseof the short tip–surface distance.

8. Vibration of the dimer on the Si(0 0 1) surface excited by STM current
The ground state of the Si(0 0 1) surface with the c(4 · 2) ordered structure of the
dimer arrangement turns into a disordered state at room temperature [18,20,21]. In
the disordered state, the symmetric images of the p(2 · 1) structure are observed by
STM, and have been attributed to the rapid repeat of the ﬂip-ﬂop motion. Even in
the ordered state, the symmetric STM images of the p(2 · 1) structure [24,25,27] arealso observed at some conditions of the tip bias voltages Vb and the STM currents
ISTM in STM observations at very low temperatures, for example, Vb = 1 V andISTM = 50 pA on a boron doped (B-doped) substrate at 5 K [25]. These observationsof the symmetric images in the ordered state are puzzling and have not been
explained so far.
Kawai and Narikiyo [47] have investigated theoretically the vibration of the dimer
excited by the STM current on the Si(0 0 1) surface of the p-type substrate, and have
solved the puzzle of the symmetric–asymmetric crossover in the dimer images. They
treated the case that Vb is positive and so large that the Fermi level in the conduction
band of the STM tip is below the bottom of the p-band. The Hamiltonian used by
Kawai and Narikiyo consists of the term of the electronic system describing the tunneling current of electrons from the p-band on the Si(0 0 1) surface to the conduction
band of the STM tip, and the electron–vibration coupling term. The latter is the key
ingredient. The electron–vibration coupling constant is obtained by the energy of thevibrational state and the model potential for the dimer system on the Si(0 0 1) surface [47,48].
The transition rates relas and rint
0!1 for the inter-band transition of electrons fromthe p-band to the conduction band of the tip are obtained for the elastic transition
without coupling to the vibration and for the inelastic transition with the excitationin the vibrational state from the vibrational number n = 0 to n = 1, respectively. relas
and rint
0!1 depend critically on ISTM and not on the temperature T of the substrate.

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The ratio of the rates of the inter-band transition W ¼ rint
0!1 =relas , however, is shown
not to depend on ISTM and is given dominantly from the intrinsic property of theSi(0 0 1) surface [47]. The key quantity W is obtained to be about 0.6 from the estimation of the electron–vibration coupling constant and the results of scanning tunneling spectroscopy [25].
At ﬁnite temperatures, the deexcitation of the vibrational number through the inner-band excitation of the electron–hole pair creation in the p-band can occur. The
rate of the deexcitation rinn
1!0 of vibration through the inner-band excitation is independent of ISTM and depends on T [47].
The total transition rates of the excitation R0!1 of the vibrational number n = 0 to
1 and the deexcitation R1!0 of that n = 1 to 0 are obtained selfconsistently with relas,inn
rint
0!1 , r1!0 , and ISTM [47]. The total transition rates R0!1 and R1 ! 0 for B-doped
substrate are monotonically increasing as a function of T and ISTM in highly nonlinear manner [47]. The distribution of the vibration is well characterized by the eﬀective temperature Tef of the dimer vibration; T ef ¼ hx=ðk B logðR0!1 =R1!0 ÞÞ. Tef for
B-doped substrate is shown in Fig. 8 [47]. Below 20 K, Tef scarcely depends on T and
increases steeply with ISTM. Tef becomes about 250 K at ISTM = 50 pA and reaches
about 400 K at ISTM = 130 pA. These high Tef appearing below 20 K, essentiallyexplain why the symmetric STM images are observed at low temperatures. When
T increases around 20 K, Tef starts to decrease steeply, because of steep increaseof R1 ! 0. Tef increases gradually with T, scarcely depends on ISTM, and takes thenearly same values as T. These low Tef explain why the asymmetric STM images recover in the temperature range higher than 50 K.
At temperatures much lower than 20 K, the fraction at the down-position of theatom beneath the STM tip is much larger than that at the up-position, because thetip current and the eﬀective temperature are expected to be much larger and higher atthe up-position than at the down-position. The tip height is tuned so that ISTM will

Fig. 8. The eﬀective temperature of the dimer vibration (Tef) on the B-doped substrate [47]. Tef reaches
about 400 K for the STM current ISTM = 130 pA at low substrate temperatures T < 20 K, and decreases
steeply around T  20–40 K as T increases.

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take the intended value at the down-position. As a result of the large fraction at the
down-position, the symmetric dimer images of p(2 · 1) structure is observed even in
the ordered state of c(4 · 2) at very low temperatures. The crossover behavior on the
STM images is semi-quantitatively understood by the nonlinear dependence of Tef
on T and ISTM [47].

9. Concluding remarks
It is now experimentally clear that the dimers on the Si(0 0 1) surface are buckled
at the ground state. The apparent symmetric dimers in STM images are attributed toelectronic or vibrational dynamical eﬀects by the tip. A theoretical model including
vibrational excitation/deexcitation could explain such phenomena. On the other
hand, the ground state ordering of the buckled dimers is experimentally still controversial. The result of the PES study suggests the c(4 · 2) structure is stable between
80 and 30 K while the change from c(4 · 2) to p(2 · 2) is observed in the STM study
below 50 K with decreasing temperature. Below 10 K, both the c(4 · 2) to p(2 · 2)
structures have been reported in the STM observations depending on the doping species and level. Moreover, the structure changes from one to the other by controllingthe bias voltage. This indicates that the tip–surface interaction through the current,
the electric ﬁeld and/or the atomic force plays an important role. Further studies arenecessary for the understanding of the ground state, the tip–surface interaction andthe mechanism of the newly found current eﬀect in the LEED observation below
40 K.

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