PHYSICAL REVIEW B 86, 035423 (2012)√√
Charge transfer and structure of K/Si(111)-2 3 × 2 3-B surface studied
by reflection high-energy positron diffraction
Y. Fukaya,* I. Mochizuki, and A. Kawasuso
Advanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan(Received 21 February 2012; revised manuscript received 1 June 2012; published 16 July 2012)
√
√
using
The atomic coordinates and charge transfer of the K/Si(111)-2 3 × 2 3-B surface were investigated√√
reﬂection high-energy positron diffraction (RHEPD). Upon the adsorption of K onto the Si(111)- 3 × 3-B
surface, the position of the 111 Bragg reﬂection is shifted to a lower angle, thus suggesting that a change in
the inner potential arises from the charge transfer of 1.0e− per K atom to the surface. From RHEPD rocking
curves recorded at 113 K, we determined that the top K atoms and the Si adatoms are adsorbed 2.96 and 2.51 Å
from the ﬁrst Si√layer,√respectively. The Si adatoms are signiﬁcantly displaced upward compared to that found
for the Si(111)- 3 × 3-B surface. Furthermore, we found that the K atoms are adsorbed between the H3 andprediction that the Si adatoms are upwardly displaced
T4 sites. These are consistent with the recent theoretical√√and the K atoms form a trimer structure in the 2 3 × 2 3 unit cell at low temperature [Phys. Rev. Lett. 107,
187603 (2011)], although the ﬂat model where all the Si adatoms have the same height is also acceptable in therockingat room temperature, which is above√the surface√analyses.
√ However,√√ phase-transition temperature√ curvefor 2 3 × 2 3 to 3 × 3, the K atoms are randomly located in the 2 3 × 2 3 unit cell. This phase transitionis accompanied by the disordering of K atoms.
DOI: 10.1103/PhysRevB.86.035423

I. INTRODUCTION

PACS number(s): 68.35.Rh, 61.05.jh, 68.35.B−√√
The highly B-doped Si(111) surface possesses a 3 × 3
1–3
structure with the B√atoms√located at the S5 site (see Fig. 1).
When the Si(111)- 3 × 3-B surface√is saturated√ by K atoms
at room temperature, the K/Si(111)- 3 × 3-B surface isformed. This surface is known as √a Mott√ insulator.4 The
electronic structure of the K/Si(111)- 3 × 3-B surface has
been extensively investigated using angle-resolved photoemission spectroscopy.
√√However, the atomic conﬁguration of
the K/Si(111)- 3 × 3-B surface is still under debate. In
particular, the atomic positions of the K atoms have yet to be
conﬁrmed experimentally.5 Furthermore, it is argued that thesaturation coverage (ρ) of the K atoms is a third or a half of amonolayer (ML, 1 ML = 7.83 × 1014 cm−2 ).4,6√
3√×√√ Recently, it has been reported that the K/Si(111)3-B√ surface√ undergoes a phase transition from the 37 × 3
to 2 3 × 2 3 structure at temperatures below 270
From√ K. √
photoemission spectroscopy, the K/Si(111)-2 3 × 2 3-B
7,8
surface is considered to be a bipolaronic
insulator.
However,√√
the atomic conﬁguration of the 2 3 × 2 3 structure is also
unknown experimentally.9 From a structural point of √
view,
there
√ are two possible atomic conﬁgurations for the 2 3 ×
2 3 structures with the bipolaron. One is the “one-up andthree-down” (1U3D) model, where one Si adatom is locatedat a relatively higher position than the other three Si adatoms
in the unit cell. The other is the “three-up and one-down”(3U1D) model, where one adatom is located at a relatively
lower position than the other three atoms in the unit cell.
Reﬂection high-energy positron diffraction (RHEPD) is asensitive tool for the topmost surface because of the total
reﬂection. Since the positron has a positive charge and hence
the crystal potential acts as a potential barrier, the total
10,11
reﬂection occurs at grazing incidence.
In this study, we√√investigated the K/Si(111)-2 3 × 2 3-B surface structures
by RHEPD at both above and below the phase-transition
temperature. Shown are the atomic positions and disordering of1098-0121/2012/86(3)/035423(5)√ √√√the K atoms that result from the 3 × 3-2 3 × 2 3 phasetransition. Furthermore, we estimate the amount of chargetransfer from the K to Si atoms.
II. EXPERIMENT

Substrates (10 × 5 × 0.5 mm3 ) were cut from a highly Bdoped, mirror-polished Si(111) wafer.12 These were ﬂashed a
few times at 1470 K in an ultrahigh vacuum (UHV) chamberwith a base pressure of less√than 2√× 10−8 Pa. After annealing
at 1170 K, a well-ordered √ 3 × √ 3 structure was formed.13
Subsequently, the Si(111)- 3 × 3-B surface was saturated
by the K atoms at room temperature.
A well-collimated and highly parallel positron beam ofenergy 10 keV was irradiated onto the sample surface at
grazing incidence. The diffraction patterns were observed
using a microchannel plate with a phosphor screen and acharge-coupled-device camera. By rotating the sample, theglancing angle (θ ) of the incident positron beam was varied
from 0.3◦ to 6.0◦ in steps of 0.1◦ . Details of the positron beam
apparatus are described elsewhere.14
III. RESULTS AND DISCUSSION√ Figure√ 2 shows the RHEPD rocking curves for the Si(111)3 × 3-B surface at 295 K. The incident azimuth of thepositron beam is 7.5◦ away from the [112̄] direction (one-beamcondition15 ). Under this condition, the rocking curve mainly
depends upon the atomic positions that are perpendicular to thesurface. In the total reﬂection region (θ < 2.0◦ ), the specularintensity is high and a small dip in the curve is clearly observed
at 1.8◦ . In addition, distinct peaks for the 111 and 222 Bragg
reﬂections and weak 333 and 444 Bragg reﬂection peaks areclearly visible.
√ to verify the atomic conﬁguration of the Si(111)√ In order3 × 3-B substrate, we calculated the RHEPD intensities

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: cal

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Glancing angle (deg)√√FIG. 1. (Color online) Schematic drawing of the Si(111)-2 3 ×
2 3-B surface. Red, gray,√and black√ circles√ indicate√ K, Si, and B
atoms, respectively. The 2 3 × 2 3 and 3 × 3 unit cells areindicated by the black and red lines, respectively. rK and ϕK denotethe polar coordinates of the K atoms.

on the basis of the dynamical diffraction theory.16 In thecalculations, the thermal vibrational amplitude of the Si
and B atoms were assumed to be 7.84 × 10−2 Å.17 The
adsorption potentials resulting from the electronic excitations
were assumed to be a ﬁtting parameter for the surface layer and1.70 eV for the bulk layer.18 Two heights of Si adatoms (zad )and the ﬁrst layer (z1 ) of Si atoms were varied so as to minimize
the difference between the experimental and calculated curves.
The goodness of ﬁt was judged via the reliability (R) factor.19
The solid line in Fig.
the calculated rocking√ 2 represents√
curve for the Si(111)- 3 × 3-B surface using the optimized
atomic conﬁguration and it is shown that the calculated curve
is in good agreement with the measured curve. In the ﬁtting
procedure, with respect to the ideal Si bulk positions, we
obtained zad = +0.24 ± 0.10 Å and z1 = −0.46 ± 0.06 Å
(see Fig. 1). The structure parameters are summarized inTable I. The atomic displacements obtained here are in good
agreement with those previously obtained by experiment andcalculation.3,20–22
Figure 3(a)√ shows√ the RHEPD rocking curves for the
K/Si(111)-2 3 × 2 3-B surface at 113 K under the one-

FIG. √
2. RHEPD
rocking curves of the specular spot from the√Si(111)- 3 × 3-B surface under the one-beam condition. The incident azimuth of the positron beam is 7.5◦ with respect to the [112̄]
direction. The open circles denote the experimental curve at 295
K. The solid line indicates the curve calculated using the heights of
the optimum adatom and ﬁrst Si layer. The acceleration voltage ofthe incident positron beam is 10 kV. The critical angle of the total
reﬂection is estimated to be 2.0◦ via Snell’s equation.

beam
In the rocking curve for the K/Si(111)√ condition.
√
2 3 × 2 3-B surface, we observe intense 111 and 222 Bragg
reﬂection peaks and weak 333 and 444 Bragg peaks. In the
total reﬂection region, the dip in the curve that results from theadsorption of K atoms appears at 1.2◦ . Upon deposition of the
K atoms, the position of the 111 Bragg peak is dramaticallyshifted toangle compared to that found for the√ a lower√
Si(111)- 3 × 3-B surface (Fig. 2). This suggests that there
is a reduction in the inner potential due to the adsorption of K
atoms.
We ﬁrst estimate the change in the mean inner potentialfrom the shifts of the Bragg peaks in the RHEPD rocking
curves. The peak positions in the rocking curve obey the
Bragg equation. In the crystal, the glancing angles that satisfy
the Bragg condition are varied due to the refraction. The
refractive index√can be expressed using Snell’s equation ascosθc /cosθv = E/(E + eV0 ), where θv and θc denote theglancing angles of the incident positron before and after
refraction, respectively, and V0 and E are the mean innerpotential and accelerating energy of the incident positron,
respectively.10 Thus the peak position is ﬁnally determinedby the mean inner potential (V0 ). In √order to√estimate the mean
inner potential of the K/Si(111)-2 3 × 2 3-B surface, we√√√√
TABLE I. Structure parameters for the Si(111)- 3 × 3-B and the K/Si(111)-2 3 × 2 3-B surfaces.
zad√√Si(111)- 3 × 3-B√√
K/Si(111)-2√3 × 2√3-B (ρK = 1/2 ML)
K/Si(111)-2 3 × 2 3-B (ρK = 1/3 ML)

1.49 ± 0.10 Å
rK

ϕK

zK

zad(1) ρSi = 1/12 ML

zad(2) ρSi = 3/12 ML

2.31 ± 0.37 Å

43.4 ± 7.8◦

2.96 ± 0.10 Å
2.20 Å

2.51 ± 0.83 Å
1.15 Å

2.51 ± 0.23 Å
1.15 Å

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CHARGE TRANSFER AND STRUCTURE OF K/Si(111)- . . .

total reflection: exp (113 K): cal (1/2 ML):c al (1/3 ML)

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RHE
EPD intensity (aarb. units)

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Glancing angle (deg)total reflection: exp (112 K)
: cal
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-1/3 -1/3-2/3
2/3 -2/3
/3
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Glancing angle (deg)FIG. 3. (Color online)√(a) RHEPD
rocking curves of specular√spots for the K/Si(111)-2 3 × 2 3-B surface at 113 K under the
one-beam condition. (b) RHEPD rocking curves of the (0 0), (−1/3√−1/3),(−2/3 −2/3), and (1 1) spots from the K/Si(111)-2 3 ×√
2 3-B surface at 112 K along the [112̄] direction. The circles indicate
the experimental curves. In (a), the black and red lines denote thecalculated curves using the optimum heights of K atoms and the Si
adatoms at ρK = 1/2 ML and ρK = 1/3 ML, respectively. In (b), thesolid lines show the calculated curves when it is assumed that thesurface structure is composed of the K trimers.

varied V0 so as to reproduce the experimental peak positions.
As a result of ﬁnding the minimum √in R, we√ determined
V0 = 8.6 ± 0.5 eV for the K/Si(111)-2 3 × 2 3-B surface.
Therefore V0 changes from 12 to 8.6 eV as a result of the K
atom deposition.
The change in the mean inner potential corresponds to theformation of the surface dipole. The change in the potential
due to the dipole formation is given as V0 = end/0 , wheren, d and 0 are the number density of K ions, the distance
between charges, and the permittivity, respectively. For theadsorption position of the K atoms (d = 0.46 Å), comparisonof their number density to that of the K atoms in the unit cell−2−2(n = 0.041 Å , cf. 0.039 Å ) means that we can estimate
the amount of charge transfer from the K to Si atom as 1.0e−
per K atom at 113 K.

In considering V0 =√ 8.6 eV√ and the theoretical prediction
for the K/Si(111)-2 3 × 2 3-B surface with ρK = 1/2
ML,6,9 we optimized the height (zK ) of the K atoms andtwo independent heights (zad(1) with ρSi = 1/12 ML andzad(2) with ρSi = 3/12 ML) for the Si adatoms by meansof the R factor so as to minimize the difference between
the measured and calculated curves. For the calculations, thethermal vibrational amplitudes of the K atoms were assumed
to be 2.16 × 10−1 Å.17 As shown by the black line in Fig. 3(a),the calculated curve is in good agreement with experiment
if we assume that the positions of the K atoms and the Si
adatoms are zK = 2.96 ± 0.10 Å, zad(1) = 2.51 ± 0.83 Å, andzad(2) = 2.51 ± 0.23 Å from the ﬁrst Si layer, respectively (seealso Table I). As a result, we found that the K atoms andthe Si adatoms are farther away from the ﬁrst Si layer. In
considering the large error bar of zad(1) , both the 1U3D and
3U1D models are acceptable as well as the ﬂat model where
all the Si adatoms have the same height. In the case of the 3U1D
model, the averaged height of the Si adatoms is smaller than
2.51 Å. This indicates that the amount of charge transfer fromthe K to Si atom is less than 1.0e− per K atom. In the case of the
1U3D model, the amount of charge transfer is larger than 1.0e−
per K atom. However, the charge transfer larger than 1.0e−
per K atom is not physically acceptable. Thus, considering
the large error bar of zad(1) due to the lower coverage, thestructure model determined in this study is consistent with
the ﬂat model and the 3U1D model proposed by the recent
theoretical calculations.9 Since the saturation coverage of the
K atoms has not been conﬁrmed yet, we also calculated therocking curves taking into account the structure model with
ρK = 1/3 ML.4,5 As shown by the red line in Fig. 3(a), the calculated curve using ρK = 1/3 ML is inconsistent with the experiment, as compared to that for ρK = 1/2 ML. Thus thesaturation coverage of ρK = 1/2 ML is more plausible. In aprevious theoretical study,5 H3 or T4 are suggested as possible
adsorption sites. The positions of the K atoms are estimatedto be 2.36 and 2.49 Å for the H3 and T4 sites, respectively.5
The position of the K atoms determined in this study is higher
than these values, thus implying that the adsorption site of the
K atoms is shifted from the H3 or T4 sites.
To conﬁrm the adsorption site of the K atoms, we measured
the rocking curves along the [112̄] direction. The open circles
in Fig. 3(b)√show √the measured rocking curves for the
K/Si(111)-2 3 × 2 3-B surface along the [112̄] direction
at 112 K. On the basis of the theoretical results,9 we calculated
the RHEPD rocking curves assuming√ that√ the K atoms forma trimer structure on the Si(111)- 3 × 3-B surface. Then,
we optimized the length (rK ) and the rotation angle (ϕK )of the K trimer so as to minimize the difference between
the measured and calculated curves (see Fig. 1). The solidlines in Fig. 3(b)√ show√ the calculated rocking curves for
the K/Si(111)- 3 × 3-B surface using the optimum length(rK = 2.31 Å) and rotation angle (ϕK = 43.4◦ ) for the K trimer(see also Table I). The measured curves can be reproducedby the calculated curves using the trimer model. The bondlength between the K atoms determined here is estimated to be
4.00 Å, which is in good agreement with the average between
the metallic (4.70 Å) and ionic bondings (2.74–3.28 Å).
Therefore the adsorption site of the K atoms corresponds toan intermediate position between the H3 and T4 sites. Recent

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total reflection: exp (288 K)
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RHE
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Glancing angle (deg)total reflection: exp (289 K)
: cal
00

-1/3 -1/3-2/3 -2/3
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Glancing angle (deg)FIG. 4. √(a) RHEPD
rocking curves of specular spots from the√K/Si(111)- 3 × 3-B surfaces at 288 K under the one-beamcondition. (b) RHEPD rocking curves of the (0 0), (−1/3√√ −1/3),(−2/3 −2/3), and (1 1) spots from the K/Si(111)- 3 × 3-B
surface at 289 K along the [112̄] direction. The circles indicate theexperimental curves. In (a), the solid line denotes the calculated curveusing the optimum heights determined at 113 K. In (b), the solid lines
show the calculated curves when the K atoms are assumed to berandomly situated at the intermediate positions between the H3 andT4 sites.

theoretical studies suggested that the K atoms were locatedbetween the H3 and T4 sites.9 The present model is consistent
with the theoretical calculations.
Figure 4(a)the RHEPD rocking curves for the√√ shows
K/Si(111)- 3 × 3-B surface at 288 K under the one-beamcondition. The shape of the curveis √not changed from that√observed for the K/Si(111)-2 3 × 2 3-B surface at 113 K[Fig. 3(a)], which suggests that there are no displacements of
the K atoms√and the√ Si adatoms√√due to the phase transition
from the 2 3 × 2 3 to 3 × 3 structure. The positionof the 111 Bragg
peak√√ is nearly the same as that for the
K/Si(111)-2 3 × 2 3-B surface. This indicates that themean inner potential is almost unchanged upon the phasetransition.
The solid line in Fig.√4(a) shows
the calculated rocking√
curve for the K/Si(111)- 3 × 3-B surface using the optimum heights of the K atoms and the Si adatoms determinedat 113 K. The calculations are capable of reproducing theexperimental
data.
√ To verify the adsorption site of the K atoms√
for the 3 × 3 structure, we measured the rocking curves
along the [112̄] direction at 289 K, as shown by the open
circles in Fig. 4(b). As described above, the vertical atomic
positions remain unchanged above and below the phasetransition
the transformation from√ temperature.
√√ In considering√
the 2 3 × 2 3 to 3 × 3 periodicity, the lateral atomic
positions should be changed upon the phase transition. Above
the phase-transition temperature, it is considered√that √the Katoms are randomly distributed on the Si(111)- 3 × 3-B
surface. Thus we calculated the RHEPD rocking curves
assuming that the K atoms are randomly situated at theintermediate√√ positions between the H3 and T4 sites in the
2 3 × 2 3 unit cell. As shown by the solid lines in Fig. 4(b),the measured curve for each spot can be reproduced by
the calculated curve using the randomly distributed model.
Therefore the K atoms are disordered due to the phasetransition.
From photoemission spectroscopy data, the lowtemperature phase is considered to be the bipolaron phase.7,8
In this phase, it is suggested that three of four Si adatoms
are shifted to a higher position in the unit cell. Considering thecharge transfer of 1.0e− per K atom determined in this study, it
is likely that the atomic orbitals for the Si adatoms are changed
from sp2 like to sp3 like. Therefore three of four Si atoms are
expected to shift toward the vacuum region, in agreement witha previous photoemission study.8 The K atoms are situatedat the intermediate positions between the H3 and T4 sites,
giving rise to a higher adsorbed position. Hence the K atoms
that are shifted to higher positions are loosely
bound√√ to the Si
adatoms. Consequently, the K/Si(111)-2 3 × 2 3-B surface
at low temperature
for the bipolaronic phase and√√ is responsible
the K/Si(111)- 3 × 3-B surface at high temperature is in
the disordered state.

IV. SUMMARY

In summary, we investigated the√ atomic√ structures√ andchargetransfers of the K/Si(111)-2 3 × 2 3-B and 3 ×√
3-B surfaces using reﬂection high-energy positron diffraction. We found that
K atoms form a trimer structure on√ the √
the K/Si(111)-2 3 × 2 3-B surface with charge transferof 1.0e− taking place from the K to the Si atom. The Si
adatoms are signiﬁcantly shifted upward. When the temperature increases to above√270 K,√the surface√undergoesa phase√transition from the 2 3 × 2 3 to the 3 × 3 structure.
√
The K atoms are randomly distributed on the Si(111)- 3 ×√
3-B surface at room temperature. Therefore this surface
phase transition may be classiﬁed as an order-disorder phasetransition with charge transfer.

ACKNOWLEDGMENTS

We thank Yukichi Shigeta for supplying the samples usedin this study. The present work was partly supported by
a Grant-in-Aid for Young Scientists (B) 22740205 fromJSPS.

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