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Total reflection high-energy positron diffraction: An ideal diffraction technique for surface
structure analysis

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2014 Appl. Phys. Express 7 056601(http://iopscience.iop.org/1882-0786/7/5/056601)
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Applied Physics Express 7, 056601 (2014)
http://dx.doi.org/10.7567/APEX.7.056601

Total reﬂection high-energy positron diffraction:
An ideal diffraction technique for surface structure analysis
Yuki Fukaya1, Masaki Maekawa1, Atsuo Kawasuso1, Izumi Mochizuki2,
Ken Wada2, Tetsuo Shidara3, Ayahiko Ichimiya4, and Toshio Hyodo2*
1

Advanced Science Research Center, Japan Atomic Energy Agency, Takasaki, Gunma 370-1292, Japan
Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
3
Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
4
Nagoya University, Nagoya 464-8601, Japan
E-mail: toshio.hyodo@kek.jp
2

Received February 12, 2014; accepted March 19, 2014; published online April 9, 2014
It is shown that the reﬂection high-energy positron diffraction (RHEPD) pattern from a Si(111)-(7 ' 7) reconstructed surface for the total reﬂection
condition, that is, the total reﬂection high-energy positron diffraction (TRHEPD) pattern, does not contain contributions from atoms in the bulk. Now,a method of observing the diffraction pattern formed only by the atoms on the topmost surface by a straightforward measurement of a bulk sample
is available. © 2014 The Japan Society of Applied Physics

eﬁnitive knowledge of the crystal structure of materials is key to our understanding of their physical andchemical properties and their technological applications. X-ray diffraction has long been the standard techniquein materials research to elucidate the bulk structure. However,for the determination of the top and near-surface atomic
conﬁgurations, an equivalent single method is yet to beestablished. Here, we show that total reﬂection high-energy
positron diffraction (TRHEPD) is an ideal technique for thispurpose, where full use is made of the total reﬂection of thepositron beam from a solid surface in reﬂection high-energy
positron diffraction (RHEPD),1,2) the positron counterpart ofreﬂection high-energy electron diffraction (RHEED).3)
The positron, the antiparticle of the electron, has the same
properties as the electron except that it is positive in charge.
Its eventual annihilation with an electron into £-rays has been
employed in various applications based on the detection ofthese annihilation £-rays. Examples include positron emission tomography (PET) for locating cancers in the human
body, angular correlation of annihilation radiation (ACAR)
for the investigation of Fermi surfaces of metals and alloys,
and positron lifetime measurements for ﬁnding vacancy-type
defects in materials.
The way positrons are used in diffraction techniques differsfrom that in the applications listed above in that, here, thepositrons themselves are detected, having undergone elastic
collision, and coherently scattered back. Positron diffraction
has features different from those of the diffraction of electrons(which are quantum mechanically indistinguishable frommaterial electrons). It has been pointed out that these features
may lead to the positron diffraction method being superior
to the electron counterpart.1,2,4) Perhaps the only drawback
with using positrons is that, since it is an antiparticle, it istechnically more difﬁcult to obtain a beam of high intensity.
First proposed by Ichimiya1) in 1992, RHEPD uses
positrons of approximately 10 keV in energy and directs
them at a crystal surface with a glancing angle smaller thantypically 6°. The usefulness of this technique was proved by
Kawasuso and Okada2) in 1998 at JAEA, Takasaki, with anapparatus using a 22Na positron source providing a beam of
103–104 slow positrons/s.
This apparatus, which was the only one of its kind in theworld, and subsequent modiﬁcations of it, yielded fruitfulD

results for more than a decade in determining the structuresof metal-deposited surfaces of Si and Ge crystals,5) some ofwhich were impossible or very difﬁcult to characterize byother techniques. Some notable examples are as follows. It
was shown from the excellent ﬁt of the data of the RHEPD
rocking curves6) that the arrangement of In atoms on aSi(111)-(8 © 2)-In surface at low temperatures
waspﬃﬃﬃﬃﬃ p
ﬃﬃﬃﬃﬃ that of thehexagon model.7) The details of the ( 21  21p) ﬃﬃstructure
ﬃ pﬃﬃﬃ
of noble metals (Ag, Au) deposited on Si(111)-( 3  3)Ag were determined using RHEPD rocking curves and theintensity proﬁle along the 1/7 Laue zone.8) The structure
found was different from any of the models previously
proposed.9–12)
Recently, the RHEPD station has been moved to the Slow
Positron Facility at KEK where an intense slow positron
beam is produced using a dedicated linac (55 MeV, 600 W)
and a production (i.e., converter/moderator) unit consistingof a Ta target and a W foil moderator.13) The ﬁrst experiment
performed, prior to the brightness enhancement described
below, was a study of a Ge(001)-(4 © 2)-Pt surface.14) A
number of different models had been proposed15–17) for
the one-dimensional structure of this surface and, using the
RHEPD rocking curves obtained, we were able to determine
which of these models is correct.17)
The high intensity of the positron beam allowed theinstallation of a transmission-type brightness enhancement18)
unit upstream of the RHEPD chamber. Positrons, transported
at an energy of 15 keV, were focused onto a 100-nm-thickW foil remoderator at an electrostatic potential of 10 kV.
The positrons thus struck the foil at 5 keV, thermalizing
inside and were subsequently reemitted from the other sideat 10 keV with a brightness enhanced by about 1 © 103 times
over the initial magnetically guided beam. This reﬁned beam
has a diameter of ³0.5 mm (FWHM), an energy spreadof ³40 meV, an angular divergence of ³12 mrad, and anormalized emittance of ³0.01 cm rad eV1/2.19) The ﬁnal
positron intensity was 5 © 105 slow positrons/s. It yieldeda clear positron diffraction pattern from a crystal surface.
The sample is now oriented in real time while observing
the phosphor screen behind MCP. An RHEPD pattern canbe taken within 1 h and a set of those necessary for making
a specular-spot rocking curve within 3 h. The brightnessenhanced beam has recently been used to conﬁrm that

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Appl. Phys. Express 7, 056601 (2014)

Y. Fukaya et al.

(a)

(b)

(c)

(d)

Fig. 2. Schematic diagram of Si(111)-(7 © 7) structure. The circles are all
silicon atoms.
Fig. 1. Comparison between RHEPD (positron) and RHEED (electron)
patterns of Si(111)-(7 © 7) surface. A darker contrast shows a higher
intensity. The integer-order spots due to bulk diffraction are visible in the
periphery of the RHEED patterns but not in the RHEPD pattern for ª = 1.3°
(TRHEPD pattern). Kikuchi lines are much less prominent in the RHEPD
patterns.

silicene constructed on a Ag(111) surface has a buckling
structure20) unlike graphene.
The advantage of RHEPD over RHEED is that it is capableof undergoing total reﬂection1) owing to the positive crystal
potential and is therefore particularly sensitive to the topmost
atomic layer of the surface. The purpose of the present study
is to show that the RHEPD patterns from a Si(111)-(7 © 7)
surface for the total reﬂection condition do not contain contributions from atoms in the bulk. This surface was chosen to
be a suitable testing ground since its structural characteristics
are well known.21,22) The critical glancing angle for the total
reﬂection of 10 keV positrons from this surface is 2.0°. Notethat the total reﬂection range covers a considerable part of atypical RHEPD measurement range (6°).
A Si(111) sample was cut from a mirror-polished n-type
wafer with a resistance of 1–10 ³ cm. It was ﬂushed at
1200 °C in an ultrahigh-vacuum chamber to produce a(7 © 7) reconstructed structure. The azimuth was chosen to direction.
be in the ½112
Figure 1 shows the RHEPD patterns observed for glancing
angles ª of (1) 1.3° (within the total reﬂection condition,i.e., TRHEPD) and (2) 2.1° (slightly off the total reﬂection
condition). The results of RHEED at the same energy andª = 1.3° (3) and 2.1° (4) are also shown. The immediately
apparent differences are as follows: (i) the intensity distributions of the spots are different; (ii) the integer-order spots
due to bulk diffraction seen in the periphery of the RHEED
patterns (3) and (4) are barely visible in the RHEPD pattern
for ª = 1.3° (1); (iii) Kikuchi lines are noticeable only in the
RHEED patterns (3) and (4). Observation (ii) indicates that,while RHEED contains information from the bulk crystal
structure even at ª = 1.3°, RHEPD for the same glancing
angle gives information only from the surface. Observation(iii) is interpreted as follows. Because of the difference in thesign of the potential energy between the electron and thepositron in the crystal, the index of refraction is larger thanunity for the former and less than unity for the latter. Wheninjected at the same glancing angle, the electron penetrates
deeper and hence has more chance to undergo inelastic
scattering relevant to the formation of the Kikuchi patterns
than the positron.

To unambiguously show that the RHEPD patterns under
total reﬂection conditions give only information about theatoms on the surface and not those in the bulk, we calculated
the RHEPD patterns for the two glancing angles across thetotal reﬂection condition, together with the RHEED patterns
for the same angles. Figure 2 is a schematic drawing of
this surface in which the circles are all Si atoms. Shown are(a) the arrangement of adatoms (colored red), (b) the adatoms
and ﬁrst surface layer (colored green), and (c) down to thesecond surface layer (colored blue). Figure 2(d) shows across-sectional view of this surface structure.
Results of the calculations are shown in Fig. 3. The codedeveloped by Ichimiya for the analysis of RHEED patternson the basis of the dynamical electron diffraction theory3,23)
was adopted for RHEPD by changing the electric charge ofthe incident particle from negative to positive. Detailed positions of the atoms were taken from the ab initio calculation ofthis surface, i.e., the rumpling model, by Brommer et al.22)
Figure 3(1) shows the calculated RHEPD pattern forª = 1.3° (ﬁrst data set). It can be clearly seen that theagreement of Fig. 3(1-d), calculated for the whole crystal,with the experimental data for ª = 1.3° in Fig. 1(1) is good.
Figure 3(1-a) shows the RHEPD pattern for a two-dimensional single sheet of the Si(111)-(7 © 7) adatom conﬁguration [Fig. 2(a)] calculated using the same code. Such asheet cannot support itself in reality but it is possible toassume its existence for purposes of calculation. Interestingly,
this calculated pattern [Fig. 3(1-a)] already displays mostof the features shown in Figs. 3(1-d) and 1(1). This strongly
indicates that the main features of both the experimentallyobserved pattern and the theoretical pattern calculated for thebulk sample are essentially determined by the contribution
from the adatoms on the surface. If we look more closely at
Figs. 3(1-a), 3(1-b), and 3(1-d), inclusion of the contributions
from the atoms in the ﬁrst surface layer gives a better
agreement. This is reasonably understood if we note that the
distribution of the Si adatoms in the (7 © 7) superstructure israther sparse so that most of the atoms in the ﬁrst surface
layer (colored green) are also exposed, as can be seen in
Figs. 2(b) and 2(d). Figure 3(1-c) is indistinguishable from
Figs. 3(1-b) and 3(1-d), indicating that the atoms in thesecond surface layer have almost no contribution. The
conclusion is that the RHEPD pattern in the total reﬂection
condition for the Si(111)-(7 © 7) surface observed from abulk sample includes only the contributions from the atoms
exposed on the surface.

056601-2© 2014 The Japan Society of Applied Physics

Appl. Phys. Express 7, 056601 (2014)

Y. Fukaya et al.

Fig. 3. RHEPD patterns for (1) glancing angle ª = 1.3° (within the total reﬂection condition), (2) ª = 2.1° (slightly off the total reﬂection condition),
RHEED patterns for (3) ª = 1.3° and (4) ª = 2.1°, calculated on the basis of the dynamical diffraction theory. A darker contrast shows a higher intensity. For
each case, the results are shown for the assumed two-dimensional crystal sheet of the Si adatoms (a), as in Fig. 2(a); the set of sheets of adatoms and ﬁrst
surface layers (b), as in Fig. 2(b); the set of sheets of layers down to the second layer (c), as in Fig. 2(c); and for the whole crystal (d).

Figure 3(2) (second data set) shows similar results forª = 2.1°. In this data set also, Fig. 3(2-d) is the RHEPD
pattern calculated for the bulk sample; Figs. 3(2-a)–3(2-c)
are those for a single sheet of adatoms, and sheets down
to the ﬁrst and second layers, respectively. The effects of the
inclusion of the second layer are clearly seen in Fig. 3(2-c),which is essentially the same as Fig. 3(2-d) and similar to
Fig. 1(2). This indicates that the RHEPD pattern at thisglancing angle includes contributions from the second layer,
but almost no other contribution.
Results of the calculations for RHEED at ª = 1.3° areshown in Fig. 3(3) (third data set). The intensity distributionsof all the patterns in this set are different from each other.
This indicates that the pattern from the bulk sample by nomeans includes only the exposed atoms on the surface — afeature that is to be expected from the absence of the total
reﬂection condition for electrons due to the positive crystal
potential (negative potential energy for the electron). It isinteresting that the RHEPD and RHEED patterns for ª = 1.3°
are different for even the single sheet of adatoms. This
indicates the existence of multiple scattering within the layer;since the phase shift in the individual scattering of thepositron is different from that of the electron from a single
Si atom, the multiple scattering yields the difference in theintensity of the spots.
Figure 3(4) (fourth data set) shows a similar analysis forthe case of ª = 2.1°. It reveals that contributions from many
more layers are included at this glancing angle.
To quantify the above arguments, we introduce the residual
factor R+ as a measure of the goodness of the agreement
between the patterns calculated for a single sheet or a numberof sheets of surface atomic layers and that calculated for thewhole crystal:X
jfsheetðsÞ  fwhole j=ðfsheetðsÞ þ fwhole Þ;R ¼
where f is the calculated
the diffraction peak, after
Pintensity ofP
the normalization as
fsheetðsÞ ¼ fwhole for convenienceof comparison, with the summations extended over all the
peaks. A smaller R+ value indicates a closer agreement
between the two calculated patterns. Note that the inclusion ofa sufﬁcient number of sheets that contribute to the diffraction
pattern in the actual crystal will give R+ = 0. The results areshown in Fig. 4. It clearly shows that the RHEPD pattern forª = 1.3° is almost entirely determined by the contributions
from the adatoms and the atoms in the ﬁrst surface layer, andthat for ª = 2.1°, by the atoms down to the second surface
layer. In contrast, inclusion of the atomic layers down to thesecond surface layer in the case of RHEED is not enough to
reproduce the pattern for the whole crystal. In more detail,inclusion of layers down to the second surface layer, (c), forª = 1.3°, does not appear to lower the R+ value from that for(b). This may seem strange because the pattern in Fig. 3(4-c)
appears to resemble that in Fig. 3(3-d) more closely than thatin Fig. 3(3-b). However, if we inspect them carefully, it is not
the case, i.e., it so happens that some of the spots in the pattern
in Fig. 3(3-b), which have a similar intensity to thosein Fig. 3(3-d), reduce their intensities in Fig. 3(3-c), and in
turn, some other spots gain a similar intensity to those in
Fig. 3(3-d). This accidentally gives similar R+ values. Since
diffraction patterns result from interference, a step-by-stepinclusion of the surface layers does not necessarily improve
the resemblance to the full inclusion monotonically. In fact,

056601-3© 2014 The Japan Society of Applied Physics

Appl. Phys. Express 7, 056601 (2014)

Y. Fukaya et al.

diffraction has played in solid-state physics and molecularbiology.
Part of the present results were presented at SLOPOS-13(13th International Workshop on Slow Positron BeamTechnology and Applications).24)
Acknowledgments We thank the staff of the Photon Factory and theAccelerator Laboratory of KEK for their support in the operation of the Slow
Positron Facility. This work has been supported by a Grant-in-Aid for ScientiﬁcResearch (S) No. 24221007 and for Young Scientists (B) 25800182 from theJapan Society for the Promotion of Science.

(a)

(b)

(c)

Fig. 4. Values of residual factor R+, deﬁned in the text, for RHEPD or
RHEED patterns at glancing angles shown. This factor indicates the
goodness of agreement between the patterns calculated for an assumed twodimensional structure and the whole crystal; the smaller the value, the betterthe agreement. The assumed two-dimensional structures are as shown in(a) Fig. 2(a), (b) Fig. 2(b), and (c) Fig. 2(c). It is clearly seen that, in the caseof (1), inclusion of the adatoms and the ﬁrst surface layer reproduces very
well the pattern calculated for the bulk crystal.

we have checked that if we further include the contribution
from the third layer, R+ decreases to about 0.17.
In this study, we have demonstrated that RHEPD with abrightness-enhanced high-intensity positron beam has thepromise to be an ideal tool for the determination of surface
atomic conﬁgurations, where other more well-establishedmethods are limited by physical and technical characteristics.
This is the only technique that yields diffraction patterns
separating out the contributions from the atoms exposed on
the surface alone by simple measurements on a bulk sample.
Furthermore, it should be possible to determine accurately the
crystal structure of the surface region from the topmost layer
downward by analyzing the RHEPD patterns across the total
reﬂection range. Diminution of the Kikuchi patterns reduces
the diffuse background and makes the accurate determinationof the intensity of the spots easy. We propose to call thismethod using RHEPD data taken under the total reﬂection
condition, total reﬂection high-energy positron diffraction(TRHEPD). We expect the application of this techniqueto play as signiﬁcant a role in surface science as X-ray

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056601-4© 2014 The Japan Society of Applied Physics