VOLUME 86, NUMBER 16 PHYSICAL REVIEW LETTERS 16 APRIL 2001
Subsurface Dimerization in III-V Semiconductor (001) Surfaces
C. Kumpf,
1,
* L. D. Marks,
2
D. Ellis,
3
D. Smilgies,
1
E. Landemark,
1
M. Nielsen,
1
R. Feidenhans’l,
1
J. Zegenhagen,
4
O. Bunk,
5
J. H. Zeysing,
5
Y. Su,
5
and R. L. Johnson
5
1
Condensed Matter Physics and Chemistry Department, Risø National Laboratory, DK-4000 Roskilde, Denmark
2
Department of Material Science and Engineering, Northwestern University, Evanston, Illinois 60208
3
Department of Chemistry, Northwestern University, Evanston, Illinois 60208
4
European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex, France
5
II. Institut f ür Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany
(Received 21 September 2000; revised manuscript received 17 January 2001)
We present the atomic structure of the c8 3 2 reconstructions of InSb-, InAs-, and GaAs-(001)
surfaces as determined by surface x-ray diffraction using direct methods. Contrary to common belief,
group III dimers are not prominent on the surface, instead subsurface dimerization of group III atoms
takes place in the second bilayer, accompanied by a major rearrangement of the surface atoms above
the dimers to form linear arrays. By varying the occupancies of four surface sites the 001-c8 3 2
reconstructions of III-V semiconductors can be described in a unified model.
DOI: 10.1103/PhysRevLett.86.3586 PACS numbers: 68.35.Bs, 61.10.–i, 81.05.Ea
The (001) surfaces of III-V compound semiconductors
show a wealth of surface reconstructions that play an
important role in both homoepitaxial and heteroepitax-
ial growth. Knowledge of the atomic structure of these
surfaces is particularly important because a wide variety
of high-speed electronic and optoelectronic devices used
in communications technology and fundamental studies
(e.g., quantum transport) are fabricated on (001) wafers.
It is generally believed that the basic building blocks in
these reconstructions are dimers [1]. The presence of
group V dimers on V-rich surfaces has been clearly es-
tablished, e.g., Sb dimers on the InSb001-c4 3 4 sur-
face by scanning tunneling microscopy (STM) [2], and As
dimers on InAs001-b2-2 3 4 by surface x-ray diffrac-
tion (SXRD) [3]. It has been assumed that group III
dimers are the primary structural element on III-rich (001)
surfaces [4–10] as suggested in the early STM study by
Biegelsen et al. on in situ grown GaAs(001) surfaces [4].
However, on the Ga-rich surface it is difficult in STM to es-
tablish whether the features attributed to dimers are really
made up of one or two atoms. If dimers at the surface are
not the key structural element in III-rich surfaces, a sub-
stantial rethinking of the physics of III-V compound semi-
conductor surfaces would be required. Our surface x-ray
diffraction results presented here demonstrate that this is
indeed the case, since an essential part of the structure is
subsurface dimerization of group III atoms in the second
bilayer accompanied by the formation of linear chains of
the atoms in the topmost layer.
A fundamental difficulty in structure determination is to
identify whether the correct solution, i.e., the global mini-
mum, or a local minimum, of the goodness-of-fit function
has been found. For 3D structure determination with x-ray
diffraction the ambiguity has been largely removed by us-
ing what are called direct methods [11]. Direct methods
find probable values for the phases of the measured reflec-
tions, consistent with the atomicity of the crystal structure.
Combining the phases with the measured amplitudes al-
lows approximate charge density maps to be calculated,
and placing atoms at the peaks in these maps yields a
good approximation to the structure. Direct methods elimi-
nate the need to guess starting models for the structural
refinement. While direct methods have been used success-
fully on two-dimensional SXRD or transmission electron
surface diffraction data [12,13], extending them to three-
dimensional SXRD data is not simple. We have recently
shown that the mathematical approach of “feasible sets”
[14] developed for image restoration problems can be ap-
plied to crystallographic problems [15], permitting addi-
tional constraints to be introduced that enable full, ab initio
surface structure determination to be performed in three
dimensions [16]. Since this is a truly model-independent
approach, group III dimers will arise only in the data
analysis if they are an intrinsic part of the structure.
All samples, GaAs, InAs, and InSb, were prepared in
an ultrahigh vacuum (UHV) system by sputtering and an-
nealing cycles as described in the literature [7,8]. STM
images were measured prior to the SXRD measurements
and were consistent with the images in the literature [7,8].
After preparation the samples were transferred to a small
UHV chamber and brought to the BW2 wiggler beam line
at Hamburg synchrotron radiation laboratory (HASYLAB)
for the x-ray measurements. Extended in-plane and out-of-
plane data sets were measured on all three systems at
wavelengths between 1.24 and 1.42 Å. The intensity of
each reflection was measured in a rocking scan by rotat-
ing the sample about its surface normal (v scan). The
scans were integrated, background subtracted, and cor-
rected for the Lorentz factor, polarization factor, active
sample area, and rod interception [17]. In the zinc-blende
structure the III-terminated (001) surface has twofold rota-
tional symmetry so there was only a single rotational do-
main. By averaging equivalent reflections using a c2mm
symmetry, systematic errors in jFj
2
of 7.2%, 7.8%, and
3586 0031-9007 01 86(16) 3586(4)$15.00 © 2001 The American Physical Society