PHYSICAL REVIEW B 68, 033301 共2003兲

Characteristic intra- and interunit interactions of Kr atoms adsorbed on the Si„111…-7Ã7 surface
Yan Jun Li, Osamu Takeuchi, Don N. Futaba, Haruhiro Oigawa, Koji Miyake,* and Hidemi Shigekawa†
Institute of Applied Physics, 21st Century COE, University of Tsukuba, Tsukuba 305-8573, Japan

Young Kuk
Department of Physics and Center for Science in Nanometer Scale, Seoul National University, Seoul 151-742, Korea
共Received 9 September 2002; revised manuscript received 23 December 2002; published 3 July 2003兲
Adsorption of Kr atoms on the Si(111)-7⫻7 surface at 8 K was studied by scanning tunneling microscopy.
Despite similar electronic structures of noble gas atoms, the observed site-dependent adsorbed Kr structures
and their formation processes were different from those of Xe atoms. In comparison with the results ofsimulation, the existence of the characteristic intraunit and interunit interactions between Kr atoms was confirmed.
DOI: 10.1103/PhysRevB.68.033301

PACS number共s兲: 68.43.Fg, 68.37.Ef

In recent molecular devices, molecular layers are deposited on metal or semiconductor substrates. When they aredeposited on surfaces, we do expect a strong interaction between the molecular layers and substrates. Therefore, the understanding and control of the interaction between moleculesand substrate surfaces has become an important issue. Noblegas atoms on various substrates have been model systems forstudying the interaction because of their simple electronicstructure.
Recent scanning tunneling microscopy 共STM兲 studies
have revealed characteristic interaction mechanisms of raregases on metal and semiconductor surfaces.1– 6 For example,
Xe atoms on Pt共111兲 and Cu共111兲 surfaces show completelydifferent adsorption behaviors despite the similarity of thesubstrate geometries. The complicated interactions between
rare gases can be interpreted as follows. The adsorption ofrare gases influences the substrate electronic structures,
which then leads to a change in the electronic structure of theadsorbates, resulting in the observed adsorption processes. In
fact, recently, the dispersion of the Cu surface state wasfound to be modified by Xe adsorption.5 In addition, Xeatoms were found to form site-dependent adsorption structures on the Si(111)-7⫻7 surface. The I/V characteristic of
STM images and the stability of Xe atoms under STM scanning also showed a considerable site dependence, which is adirect indication of the occurrence of interactions between
Xe and Si substrate atoms.6 The observed characteristic
properties are difficult to explain, in consideration of thestable electronic structures of the rare gases and of the factthat they have been adopted as a model for analyzing theinteraction of ideal gases even on metal surfaces.
In order to clarify the point described above, we analyzed
the adsorption processes of another rare gas, Kr, on theSi(111)-7⫻7 surface by STM at 8 K. Despite similar electronic structures of noble gas atoms, the observed sitedependent adsorbed Kr structures and their formation processes were different from those of Xe atoms. In comparison
with the theoretical calculation, the existence of the characteristic intraunit and interunit interactions between Kr atoms
on Si(111)-7⫻7 surface was confirmed for the first time.
The samples used were As-doped, n-type Si共111兲 surfaces
with a conductivity of 0.37–0.625 ⍀ cm. The base pressure

was 7⫻10⫺9 Pa. After confirming a complete 7⫻7 structure, the sample was cooled to 8 K. The STM tip was retracted from the sample during gas exposure, and observation was carried out over the same area after adsorbing Kr.
An electrochemically etched tungsten tip was used. We observed various areas of the samples with different doses inorder to check the reproducibility. The coverage was determined from the observed STM images. The dosing rate of Krgas was controlled with an electronically controlled pulsevalve. The sample temperature was monitored using an Au⫹0.07%Fe-Cr thermocouple located near the sample.
Figure 1共a兲 shows a typical STM image of the Kr adsorbed surface. Although adsorbed Kr atoms still diffused
during STM observation, the stability was sufficient to observe the structures at this low coverage. Kr atoms are dominantly adsorbed in the faulted-half 共FH兲 units. In theunfaulted-half 共UH兲 units, three different structures were observed, the magnified images of which are shown in Figs.
1共b兲–1共d兲. As represented by the schematic models in Fig. 1,
these structures consist of the one dimer⫹one corner Kratom (1D⫹1C) structural unit which is the same structure
as that observed in the case of Xe.6 However, despite thesame final structure, 3D⫹3C, the adsorption processes weredifferent for Kr. Xe atoms first adsorb in a dimer form, resulting in the hexagonal shape formed by three dimers 共six
green circles in Fig. 1兲. The three corner sites 共three yellow
circles in Fig. 1兲 are then occupied one by one. However, theadsorption of Kr proceeds in units of Kr trimers, that is, the1D⫹1C structure in the notation used for Xe: 共1兲 one trimer, 共2兲 two trimers and 共3兲 three trimers. In detail, a onetrimer structure can also sometimes be found in the Xe casewhen the neighboring half-unit is occupied by Xe atoms. Inaddition, the 3D⫹2C structure can also be found in the Krcase. However, the major growth modes are clearly different;
that in the Xe case is based on dimer adsorption and that in
the Kr case is based on trimer adsorption.
In the FH units, the observed structures were even moredifferent from those of Xe. In the case of Xe, the same structure, 3D⫹3C, was also formed in the FH units. However, asshown in Fig. 2, four types of different adsorption structures
were dominantly observed for Kr: 共a兲 a base structure 共B兲
and 共b兲 one 共1Ce兲, 共c兲 two 共2Ce兲, and 共d兲 three adatoms

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FIG. 1. 共Color兲 共a兲 A typical STM image of Kr adsorbed
Si(111)-7⫻7 surface at 8 K (V s ⫽2 V, I t ⫽0.3 nA). 共b兲 1-trimer,共c兲 2-trimer, and 共d兲 3-trimer structures.

共3Ce兲 at the center adatom site. The base structure is rather
unclear at this bias voltage. Compared to the clean FH units
关yellow triangle in Fig. 2共a兲兴, however, the image of thisstructure is slightly brighter in the area between Si adatoms.
The difference is much clearer when the bias voltage ischanged from 2.0 to 3.0 V 关Fig. 3共a兲兴. In this figure the Kradatoms at the center adatom site diffuse across the surface,which appears in the image as horizontal bright streaks indicated by a white arrow. However, it is obvious that they arealways on the base structure. Thus, we concluded that when
Kr adatoms are observed at the center adatom site, the basestructure always exists below them, which is the reason for
the notation. Therefore, they are written as 共b兲 B⫹1Ce, 共c兲
B⫹2Ce, and 共d兲 B⫹3Ce in Fig. 2. The details of the basestructure are discussed later. In addition to these structures,
further Kr adsorption was sometimes observed on the corner
adatom sites, as shown in Fig. 2共e兲. Consequently, the finalstructure of adsorbed Kr atoms in the FH structure is expected to be six Kr atoms adsorbed on center and corner sites

FIG. 2. 共Color兲 STM images of Kr adsorbed Si(111)-7⫻7 FHunit at 8 K: 共a兲 base structure and structures with 共b兲 single 共c兲 two,and 共d兲 three Kr atoms at the center adatom sites. 共e兲 FH unit withsix Kr atoms at the center and corner adatom sites.

with the base structure existing below them 关Fig. 2共e兲: B⫹3Ce⫹3C].
To illustrate the difference between Xe and Kr in theiradsorption processes, a simple rigid ball model was built
similarly as in the case of Xe adsorption.6 When Kr atoms
that form dimers were located at the same positions as Xe
atoms, i.e., in contact with a rest atom, its neighboring centeradatom, and one of the Si atoms to which the center adatom
is bonded, the calculated distance between the two Kr atoms
is approximately 0.44 nm, which is significantly larger thanthe diameter of the Kr atom, 0.41 nm. This disagreement
might have caused the instability of the isolated dimer adsorbate, contrary to the Xe case, which results in the growthmode based on trimer units in UH units and a completelydifferent structure in FH units. Indeed, the completely different growth mode in the UH unit is quite noteworthy. Since
the calculated positions are almost the same for the twounits, the observed phenomenon indicates that Kr more sensitively reflects the difference in the electronic structures of
FH and UH units.
Figure 3 shows magnified images of the base structure at033301-2

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FIG. 3. 共Color兲 FH unit with the base structure observed atsample bias voltages of 共a兲 3 V, 共b兲 ⫺1.5 V, and 共c兲 ⫺2 V.

different sample bias voltages 共3, ⫺1.5, and ⫺2 V兲. First, at
higher voltages, the trimer Kr atoms in UH units and theupper center and corner Kr atoms in FH units became unstable under STM scanning, indicating their weaker interaction with the substrate compared to Kr atoms in the basestructure in the FH units. With the sample bias of 2 V, asmentioned above, the base structure is imaged with a fuzzy
outline 关Fig. 2共a兲兴. At 3 V, the contrast becomes clearer, but adetailed structure does not appear, as shown in Fig. 3共a兲. On
the other hand at negative sample bias voltages, the basestructure is imaged clearly even at ⫺1.5 V 关Fig. 3共b兲兴. In
particular, at ⫺2 V, the base structure is imaged separately
into three parts near corner adatom sites, as shown in Fig.
3共c兲. Moreover, only one or two of the three parts are sometimes observed in a FH unit cell 关an example is shown in Fig.
3共c兲兴. Although the details cannot be determined, a possible
origin of the base structure is three dimer Kr atoms 共threegreen atoms in the schematic model in Fig. 2兲 and additional
Kr atoms in the hexagonal Kr dimer structure. In any case,the adsorption of the structure modifies the center adatom
sites to be more attractive to the subsequent Kr atoms.
In order to understand intra- and inter-half-unit interactions of Kr gases in detail, we analyzed the distribution of Kratoms. First, the interaction in a half-unit, intra7⫻7-half-unit interaction, is investigated. Figure 4共a兲 shows
the distribution of the number of Kr atoms at center adatom
sits in a FH unit with base structure 共red line兲. Schematicadsorption structures of type-0 共B兲, type-1 (B⫹1Ce), type-2(B⫹2Ce), and type-3 (B⫹3Ce) are also shown below thegraphs. When the distribution of Kr atoms is completely random, the distribution will be N(1⫺ ␪ ) 3 , 3N ␪ (1⫺ ␪ ) 2 ,3N ␪ 2 (1⫺ ␪ ), and N ␪ 3 , where N represents the total numberof FH units where the base structure exists and ␪ is the coverage of Kr at the center adatom site in those FH units. The
calculated random distribution is shown by the black line.

FIG. 4. 共Color兲 共a兲 Number of Kr atoms at the center adatom
sites in a FH unit. Theoretical results are calculations obtained forthe distributions of similar types with the assumption of randomsite adsorption 共䊏兲 and a small attractive interaction 共夝兲, respectively. 共b兲 similar analysis performed for the number of Kr trimers
in a UH unit.

The difference between experimental and theoretical results
is clear, indicating the existence of a certain attractive interaction between adsorbates, despite their separate adsorption
form instead of clustering.
Next, the correlation between the rare gases in the neighboring 7⫻7 half-units is discussed. We selected all UH units
occupied by at least one Kr atom and classified them according to the number of neighboring FH units that contains atleast one Kr atom. A UH unit cell has three neighboring FH
unit cells. Thus, all UH units with Kr atoms are classified
into four types 共from type 0 to type 3兲, which are illustrated
in Fig. 5 below the graph. As in the case of intra-half-unit
interaction, distribution was plotted for these four types 共redline兲 and the random distribution was calculated using measured coverage 共black line兲. It is clear that the occurrence of033301-3

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FIG. 5. 共Color兲 Number of Kr adsorbed FH units which surround a UH unit.

type 0 is less frequent in the experiment, and vice versa fortypes 1, 2, and 3. This again indicates the existence of an
attractive interaction between Kr atoms even across the 7⫻7 units.
The complete understanding of an epitaxial system may
be difficult, unless an ab initio calculation is done. However,
it is very difficult to perform a full calculation on an adsorbate of high Z number with a large unit cell size. Therefore,
we performed a simulation assuming a small attractive interaction among Kr atoms. The interaction energies for each Kr
atom in a unit cell that includes one, two, and three Kr atoms
are defined as E 1 , E 2 , and E 3 , respectively, where E 3 ⬍E 2
⬍E 1 . Then, the total free energies are reduced by clustering
as dE⫽2(E 1 ⫺E 2 )⫽⫺2dE 12 and dE⫽3(E 1 ⫺E 3 )⫽⫺3dE 13 for a half unit cell with two and three Kr atoms,
respectively. The experimental distribution was reproduced
within 1% accuracy with the parameters of dE 12⫽⫺0.18
and dE 13⫽⫺0.57, here thermal energy k B T is used as the*Present address: Tribology group, AIST, Tsukuba, 305-8564,
Japan†
Corresponding author. Email address: hidemi@ims.tsukuba.ac.jp
http://dora.ims.tsukuba.ac.jp/
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unit. This indicates that an attractive interaction exists among
Kr atoms in the adsorption process, resulting in less frequent
occurrences of types 1 and 2. A similar analysis was performed for the number of Kr trimers in a UH unit 关Fig. 4共b兲兴.
For the case of trimers, the values are dE 12⫽⫺1.8 anddE 13⫽⫺2.8.
The value calculated by the Lennard-Jones potential using
the parameters of ␧⫽160 K and ␴ ⫽0.338 nm and the distance 0.77 nm is ⫺0.29k B T, which is close to the obtainedvalues. However, the noteworthy point is that Kr atoms do
not form clusters and are adsorbed separately. That is, theinteraction energy becomes larger in a cluster form at a distance of ⬃0.4 nm; however, even a dimer does not exist at
the center adatom sites, suggesting the existence of an interaction different from the simple van der Waals interaction.
The apparent temperature may be higher than ⬃10 K due tothe influence of a tip sample interaction. In such a case, theenergies we estimated become higher, and does the mechanism more comprehensive. Another remarkable point is thatthe energy is not a simple additional form.
As pointed out earlier by Lang et al. in the jellium model,
noble gas adsorbates on metallic or semiconducting substrates can be model systems for understanding a general
adsorption problem.7 Kr may not be a simple atom with vander Waals interaction but an atom interacting with substrate.
A similar tendency of the attractive interaction was also observed for Xe, as shown in Fig. 1 of Ref. 6. Since the energy
is not a simple additional form, a many body effect may need
to be taken into account even in such a case.8 Further study isnecessary to clarify the interaction in more detail.
The weak interaction may become an advantage for probing the subtle change in the surface electronic structure. In
fact, for example, alkali metals are known to induce a strong
charge transfer.9,10 In such a case, although site-dependentadsorption occurs, the change in the electronic structure cannot be clearly detected by the subsequent atoms. A complete
understanding of the adsorption mechanism will allow raregases to be used as a sensitive probe on the nanoscale.
This work was supported by Grant-in-Aid for Scientific
Research from the Ministry of Education, Science, Sportsand Culture of Japan.

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