1. ,::c::>: ‘: :::.:-7.k.: .::.-,.
,.:. >::2:__..: .i.‘. .I.....’
.I
. . ...’ . . . . . . ....).
..,..:
....
i ::.: i:.;;: .I:.:.:.
:j _,,,:: :j
Surface Science 275 (1992) 190-200
kurface science
North-Holland
:>:.,:,::
:... .,..:.,,: ..‘. .:.
.. . ..:. >:..:I
::~.~~.:~i:::~.~:.:~~.:::.:::.~..:~,.~..~,:
“:‘-‘:..:~‘:::~,::~::~‘i ,,....
;i3:i ~ ,..:.
::..:
,::..,:,:
Asymmetrical dimers on the Ge( OOl>-2 x l-Sb surface observed
using X-ray diffraction
Martin Lohmeier, H.A. van der Vegt, R.G. van Silfhout, E. Vlieg
FOM Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, Netherlands
J.M.C. Thornton, J.E. Macdonald
Physics Department, Linkers&y of Wales College of CardifJ P. 0. Box 913, Cardiff CFI 3TH, UK
and
P.M.L.O. Scholte
Technische Unicersiteit Delft, Postbus 5046, 2600 GA Delft, Netherlands
Received 23 March 1992; accepted for publication 10 June 1992
The atomic structure of the 2 X 1 reconstruction induced by the adsorption of Sb on Ge(001) has been determined by X-ray
diffraction. Sb can be grown on Ge(001) in large ordered domains at elevated temperatures. Sb-Sb dimers replace the Ge dimers
of the0 clean Ge(001) surface and pick up all dangling bonds. The dimers have a bond length of 2.90 A and are midpoint-shifted by
0.16 A with respect to the substrate bulk unit cell. Such an asymmetric dimer is reported for the first time for a group IV/V
system. Relaxations of the four topmost substrate layers are measured as well, and these compare favourably to elastic strain
calculations.
1. Introduction Si(OO1) and Ge(001) has attracted much attention
in the past as well [ll-181, mainly driven by the
Clean Ge(001) and Si(OO1) surfaces have been large technological interest in III/V epitaxy on
investigated extensively both in experimental and group IV elements [17]. Both As and Sb are
theoretical studies [ 1,2]. The generally accepted reported to form symmetrical dimer type recon-
structure model for both surfaces is an asymmet- structions on Si(OOl), as seen by ARUPS [131,
rical dimer formed by two surface atoms on top STM [14,16,181 and by SEXAFS [12]. For the
of a slightly relaxed substrate [3-51. By forming As/Ge(OOl) system ARUPS also finds symmetri-
dimers, the number of dangling bonds per surface cal As-As dimers [15], suggesting that this type of
atom is reduced by a factor two. This number can reconstruction is a general rule for the IV/V
effectively be lowered further by a vertical buck- systems. The adsorbate atom (As/Sb) bonds to
ling of the dimer, leaving the dimer bond partially one other adsorbate atom and to the substrate
ionic [3,6]. Interactions between adjacent dimers dangling bonds, thereby chemically passivating
can lead to supersymmetrical phases (~(2 X 2), the substrate. The remaining two electrons of the
c(4 x 2)), observed experimentally by ARUPS/ As/Sb form a lone pair.
LEED [7,8] STM [1,2] and He diffraction [9,10]. We have used surface X-ray diffraction [19] to
The adsorption of group V elements on both investigate the growth behaviour and the struc-
0039.6028/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

2. M. Lohmeier et al. / Asymmefrical dimers on the Ge(OOl)-2 x I-Sb surface 191
ture of Ge(OOl)-2 x 1-Sb up to saturation cover- The sample was cleaned by repeated cycles of
age. To our knowledge, no structure study on this cold Ar* ion sputtering (900 eV, 1 PA, 15 min)
system has been published so far. Sb can be and annealing (980 K, 15 min). In order to obtain
grown on Get0011 in large ordered domains, and well-ordered surfaces, the sample was cooled
does indeed lead to a dimer-type reconstruction, down slowly (< 1 K/s) around the temperature
but, in contrast to the system mentioned above, of the order/disorder phase transition of the
the dimer is found to be asymmetric. Ge(OOl)-2 X 1 phase at 955 K [22]. After a small
number of cycles, a sharp two-domain 2 X 1 pat-
tern was observed by RHEED. From this point
2. Experimental on, the (5, 0) in-plane X-ray reflection was moni-
tored after every cleaning cycle. Due to the much
For the structure determination, we use the higher resolution of X-ray diffraction compared
following primitive real-space lattice with respect to RHEED, we could see considerable improve-
to a conventional fee lattice: ment in the measured peak full width at half
maximum AqFwHM with additional cleaning cy-
al = +[llo]cubic; a2== ~[l~Olcubic; cles, while the RHEED pattern remained essen-
tially unchanged. After about 15 cycles no further
*3 = ~oo~lc”bic~ (1) improvement could be obtained. By fitting the
giving the following lattice dimensions: I a, I = peak to a Lorentzjan we derived a correlation
1a2 I = ifia,; 1a3 I = a,, where a0 denotzs the length L of 1030 A, where L = 2/Aq~w~~ [231
germanium bulk Iattice constant (5.658 A). By (see fig. 1).
these definitions, a, and aZ are both parallel and Thereafter, antimony was deposited from a
a3 is perpendicular to the sample surface. Coor- Knudsen evaporation source, with a deposition
dinates of the jth atom in the unit cell are rate of _ 0.1 monolayers/min. During deposition
expressed by a set of real numbers {xi, yj, Zj} the specular X-ray reflectivity was monitored. The
with r-r= xjal + yja, + tju3 being the real-space reflected intensity first dropped, then after pass-
position of the atom. Reciprocal-space coordi- ing smoothly through a minimum increased again
nates are given in units of {bi} with a, - b, = 2~6,~ and finally saturated, whereupon the deposition
and I b, I = I b, I = t27r/aJ&; I b, i = 27r/u,,. was stopped after a tota time of - 9 min. In the
The momentum transfer vector q is denoted by investigated sampIe temperature range of 670-
the Miller indices (kkl) with q = hb, + kbz + lb,. 870 K during deposition, a 2 X 1 RHEED pattern
General reflections are thus labelled by (hkl), was seen after cooling down to RT before and
and in-plane reflections (I = 0) by (hk). after deposition of Sb. The best-ordered surfaces
The experiment was carried out at the station were obtained at a substrate temperature of 770
9.4 wiggler beamline at the Synchrotron Radia- K during deposition, followed by a slow cool-
tion Source (SRS) in Daresbury, UK. A focused down; These surfaces had a correlation length of
monochromatic X-ray beam [ZOJ with a wave- 630 A (see fig. lb). At 870 K the Sb started
length of 0.9 A was used. The incoming beam was desorbing, and the resulting surface had a corre-
defined by slits to be 1 mm horizontally (out-of- lation length of only 230 A. We therefore decided
plane) and 0.3 mm vertically (in-plane). A detec- nor to anneal the surface after deposition. The
tor was used whose angular acceptance was con- antimony coverage of the sample investigated in
straint by slits to be 0.37” along the surface nor- our structure determination was close to 1 mono-
mal and 0.15” in the in-plane direction. A single layer (ML) of atoms (- 6.25 X lOI atoms/cm2),
crystal Ge(OO1) sampIe with dimensions 8 X 10 X 3 as discussed in section 3.2.
mm3 was mounted in a UHV environmental The sample was optically aligned using a laser
chamber which was coupled to a 5-circle diffrac- beam. The crystallographic alignment was done
tometer 1211. The polished crystal had a miscut using two bulk Bragg peaks. Scans around the
smaller than 0.1”. diffractometer +-axis correspond to a rotation

3. 192 M. Lohmeier et al. /Asymmetrical dimers on the Ge(OOl)-2 x I-Sb surface
a possible surface degradation. No changes in
FWHM and intensity were observed. The UHV
chamber pressure was 2 x lo-’ Pa during deposi-
tion and data collection.
For the in-plane structure analysis a total of 52
fractional order reflections was measured, which
reduce to 14 non-symmetry-equivalent reflec-
tions. A few reflections were measured on the
90”-rotated 2 X 1 domains. These had the same
intensity as the 2 x 1 domains within the error
bar, indicating identical occupation of the do-
mains. The average agreement between symmetry
equivalent reflections was 5%, and the total error
for each reflection was calculated by squaring the
systematic and statistical errors [25]. The com-
plete in-plane data set was taken at p = 0.9”
(corresponding to I= 0.2), which is well above the
critical angle for total external reflection (0.18”
for Ge at A = 0.9 A>.
The out-of-plane data set consists of the crys-
tal truncation rod (CTR) [26] for h = 2, k = 1.
For this rod scan, the (2 1) and the (2i) rods were
measured and averaged afterwards, also with an
average agreement of approximately 5%.
3. Structure determination
The structure determination is performed in
Fig. 1. Transverse in-plane scans of the (2, 0) reflection (open
circles) together with Lorentzian fits (solid curves). From the two steps: First the in-plane projection of the
fitted FWHM’s, the correlation length L is derived (see text). structure is derived from the measured frac-
(a) Clean substrate, (b) substrate covered with 1 ML Sb. tional-order reflections at I= 0.2. These are pure
surface reflections, i.e. reflections free from inter-
fering contributions from the bulk crystal. Analy-
sis of these reflections provides the in-plane posi-
about the sample surface normal. Diffraction in- tions of the Sb atoms, and, due to a lateral
tensities were obtained by numerically integrating relaxation of the topmost substrate layers, also
such +-rocking curves after linear background resolves the registry of the surface unit cell with
subtraction [19]. Structure factors were calculated respect to the bulk. The intensity along the (2 1)
from the intensities by correcting for the illumi- integer-order CTR subsequently yields the atomic
nated area fraction (sin 28) and the Lorentz fac- coordinates along the direction perpendicular to
tor (sin 28. cos p) and taking the square root the substrate surface, resulting in a full threc-di-
[24]. Here, 28 specifies the in-plane scattering mensional model of the reconstructed Ge(OOl)-
angle and p is the angle and p is the angle of 2 x 1-Sb surface. The general method has been
incidence which was taken equal to the outgoing reviewed earlier [19,25]; here we introduce the
angle in our experiment. relevant symbols.
During the data collection the (2, O)-in-plane The scattering amplitude at a given momen-
reflection was scanned frequently as a monitor of tum transfer (hkl) is proportional to the corre-

4. M. Lohmeier et al. /Asymmetrical dimers on the Ge(OOli-2 x I-.% surface 193
spending structure factor, which is given by
[ 19,271:
I;hkt= Cfj e+B,rlz/t16~2)]
i
xexp[ -27ri(hxj + bj + Lzj)], (2)
with the sum extending over all atoms j in the
unit cell. Bj is the isotropic Debye-Waller factor,
{xi, yj, z;] are the positional coordinates and fj
is the atomic structure factor. The Debye-Waller
factor is given by Bj = 8r2( uf> with (u;) the
mean-square vibration amplitude.
The Patterson function for an in-plane data set
is given by [27]:
P(r) = c Ir;,,,l’ co+,,*+ (3)
h,k
with q,, = hb, + kb, and the sum extending over
the whole reciprocal space.
A given model is fitted to the experimentally
determined structure factors using a x2 minimi-
sation. Different models are compared on the
basis of the reduced x2 [28].
3.1. In-plane structure - P%t&c
Fig. 2. (al Patterson map Pfrac of the experimental structure
factors. Solid lines mark the irreducible part of the unit ceil,
The in-plane structure analysis employs the dashed lines the 2 X l-unit cell. The origin is labelled by x .
direct comparison of measured with calculated Peaks IV and V coincide, whereas peak I is broadened by II.
structure factors for a given model as well as the For clarity only positive peaks are shown. (b) Real space
model-independent Patterson map PrraCof the 14 in-plane structure model: Sb dimer atoms are shown as large
balls, first layer Ge atoms as small balls. Interatomic vectors
measured fractional-order reflections, from which
that correspond to peaks in the Patterson map are labelled I
interatomic vector lengths are obta‘ned. Though to V. The 2 X 1 unit cell is marked by dashed lines.
this map is incomplete, i.e. integer-order reflec-
tions are omitted and only a finite part of the
reciprocal space is used, the distortion of the map model that is derived from the Patterson map is
is predictable [29,19]. shown in fig. 2b, together with the interatomic
From the Patterson map we immediately see vectors that can be found in the Patterson map.
that the main structural element in the surface As mentioned above, these interatomic vectors
unit cell is a Sb-Sb dimer, and that other models are distorted, due to the omission of integer-order
such as a vacancy or a conjugated-chain model [4] reflections. If we assume the model to be sym-
can directly be excluded. The interatomic vector metric, the best fit yields x2 = 4.9. The fitting
of the Sb-Sb dimer corresponds to peak I in the parameters are a global scale factor, Debye-
Patterson map (fig. 2a). This is the strongest Wailer factors for Sb and Ge, one lateral dis-
peak, because it is the interatomic vector between placement parameter for the Sb atoms and one
the heaviest atoms. The fact that the Patterson for the two first-layer Ge atoms in the unit cell.
map has additional peaks directly shows that the From the Patterson map one cannot see
substrate is also reconstructed. The in-plane whether the Sb dimer is asymmetric. However,

5. 194 M. Lohmeier et al. /Asymmetrical dimers on the Ge(OOl)-2 x I-Sb surface
Table 1 table 2 (Ax,_ of layers 0 and 1). The asymmetry
Experimental in-plane structure factor amplitudes / Fl;;Xpwith
/ of the Sb dimer is significantly larger than the
uncertamttes q,zk and best-fit values for the symmetrical dimer
corresponding error bars of the fit parameters.
model 1 I as
FhydC’.S well as for the asymmetrical dimer model
Allowing an asymmetry in the lateral displace-
1J%odc’.a
, Fhmk(ldc1.s ,
ments of the first layer Ge atoms does not im-
k I F$’ 1 ahk
/ ,yydel,a ,
- prove the fit. The Ge displacements in that layer
1 8.3 0.5 9.2 X.6 are therefore taken to be equal but with opposite
2 10.0 0.7 29.5 10.0 signs. The best-fit Debye-Waller factors are 0.34
0 28.7 1.6 17.9 29.6
_t 0.30 and 0.40 i 0.30 A2 for Sb and Ge, respec-
1 17.9 1.0 10.0 17.2
tively. Though the error bars of the vibration
2 23.8 1.4 24.3 24.2
factors are rather large, the Ge value lies well in
0 24.6 1.4 21.‘) 22.2
the range of Ge bulk values, as reported in the
1 11.0 0.7 10.0 11.5
literature [301.
2 18.0 1.1 19.0 19.1
Other possibilities, such as an in-plane twisting
0 8.8 I.1 8. I 9.3
of the Sb-Sb axis, or Sb-Ge dimers, do not give
I 9.0 0.8 7.4 8.8
better fits and are therefore not considered any
2 9.1 1.1 7.1 x.2
0 8.7 1.2 4.8 8.3
further.
1 15.1 1.1 17.3 14.9 The conclusion for the in-plane structure is
2 8.0 1.3 4.6 7.6 that Sb forms asymmetrical dimers on top of a
slightly relaxed Ge substrate. The displacement
X 2: 4.9 0.93
of the midpoint of the Sb-Sb bond with respect
to the centre of the 1 x 1 bulk unit cell is 0.16 IL
0.01 A.
the quality of the fit improves drastically if one
allows for an asymmetry of the Sb dimer along
the a,-axis, as indicated in fig. 2b. The best-fit 3.2. Out-of-plane structure
yields x2 = 0.93. The experimental and best-fit
structure factors for the symmetrical and the For the calculation of the intensity along the
asymmetrical model are compared in table 1, and (2 1) crystal truncation rod, the scattering contri-
the best-fit displacement parameters are listed in butions from both bulk Ge and the surface layers
Table 2
Best-fit coordinates of the full Ge(OOl)-2 X 1 Sb structure model
Layer Atom Xbulk Yhulk Zhulk AX,,* ~Zcxp AX Kcat,ng JZKC‘!,,“~
0 Sb _ 0.5 _ + 0.177 (4) + 0.245 (12) _
0 Sb 0.5 _ + 0.902 (4) + 0.252 ( 6) _
1 Ge 0.0 0.0 0.0 + 0.046 (5) 0.000 * +0.046 * 0.000 *
1 Ge 1.0 0.0 0.0 - 0.046 (5) 0.000 * - 0.046 * 0.000 *
2 Ge 0.5 0.0 ~ 0.25 0.000 * -0.031 t 7) 0.000 * ~ 0.032
2 Ge 15 0.0 ~ 0.25 0.000 * + 0.037 (12) 0.000 * + 0.033
3 Ge 0.5 0.5 - 0.5 0.000 * -0.031 ( 7) 0.000 * - 0.025
3 Ge 1.5 0.5 - 0.5 0.000 * + 0.037 (12) o.ootl * + 0.023
4 Ge 0.0 0.5 - 0.75 ~0.012 (4) 0.000 * ~0.018 0.000 *
4 Ge 1.0 0.5 - 0.75 + 0.012 (4) 0.000 * +0.01x 0.000 *
5 Ge 0.0 0.0 - 1.00 0.000 * 0.000 * - 0.004 0.000 *
5 Ge 1.0 0.0 ~ 1.00 0.000 * 0.000 * + 0.004 0.000 *
AXCXPl Az,,n are best-fit atomic displacements, and ~~~~~~~~~~~ AzKcatln$ are Keating-energy minimising displacements. All values
are given in fractional coordinates, i.e. in units of 4.001 8, (x, y) and 5.658 A tz). with respect to the would-be bulk position of the
first Ge atom. Fixed values are indicated by an asterisk (* ).

6. M. Lohmeier et al. /Asymmetrical dimers on lhe Ge(OOl)-2 x I-Sb surface 195
are taken into account. The bulk is modelled in a FsurfC1) is the surface structure factor of a one-do-
hkl L
1 x 1 unit cell with plane group p4mm, and the main surface unit cell. Because the integrated
surface contribution is calculated in a 2 x 1 unit intensity is measured, the contributions of the
cell having plml symmetry. Both parts interfere four different surface domains are added inco-
coherently, hence the resulting structure factors herently [231. The square of the total structure
F$jk for the bulk and FiEif for the surface have factor is then calculated as follows:
to be added. FiIif is calculated using eq. (2),
whereas the bulk part is given by [23]:
p-bulk j= 1
Fbulk = hkl
hkl 1 _ ,-2ril e-c3/P (4)
+(1-B)IF,S,U;f,Ce+2FIPkU:k12. (6)
where .Fhyy denotes the structure factor of a
complete 1 x 1 bulk unit cell with four Ge layers The factor two in the second and the third term
and p is the penetration depth of the X-rays in accounts for the different unit cell sizes, whereas
Ge. F”“‘f,Ge describes the structure
hkl
factor of a clean
Because the unit cell is asymmetric and there Ge surface, which will contribute to the scattering
are 2 X 1 and 1 X 2 domains, the surface unit cell for a Sb coverage 0 smaller than one.
is present in four different orientational domains From the in-plane analysis, it is known that the
with respect to the bulk, as depicted in fig. 3. The Ge substrate is essentially bulk-like, but with
measured structure factor is the average over lateral relaxations extending at least to the first
these four possibilities. For computational pur- substrate layer. In order to obtain the perpendic-
poses, it is convenient to express the four differ- ular atomic coordinates in the surface region, we
ent surface structure factors in terms of only one allow different numbers of atoms to relax verti-
surface unit cell: cally with respect to the surface plane. The best-fit
is obtained for a model in which the vertical
FWf(2) = Fy;I’;) e2rrih
hkl 3 (5a) positions of the Sb atoms are fitted indepen-
F;;;f@) = F;;;f( 1) dently, the vertical positions of the first layer Ge
> (5b)
atoms are fixed to their bulk values, and the
FSUrf(4) = F,su_‘(;’ e2vik
hkl (5c) second and third layer vertical positions are de-
1)
Im 2)
liEI
Fig. 3. Schematic drawing of the four different orientational surface domains that need to be considered in calculating the intensity
of integer-order rods.

7. 196 M. Lohmeier et al. /Asymmetrical dimers on the Ge(OOl)-2 x I-Sb surface
0.71 A 0.31,.A
layer:
b) -----) f-
Fig. 4. Ball-and-stick perspective view of the best-fit Ge(OOl)-2 x 1-Sb structure model. (a) Top view, (b) side view. Sb atoms are
drawn as large balls, whereas the smaller balls represent Ge atoms. Layers are labelled by numbers, and arrows indicate the
displacement directions of the Ge atoms with respect to their bulk positions.

8. M. Lohmeier et al. /Asymmetrical dimers on the Ge(OOl)-2 X I-Sb surface 197
scribed by only two displacement parameters (see
table 2). This limits the number of fitting parame-
ters to four. For this model x2 = 6.5 is obtained.
Adding vertical displacements for layer 1 wors-
ens x2 and the corresponding displacements are
zero within the error bars. Fixing the third layer
and allowing only layer 2 to relax leads to a
similar x2, but with unrealistic Ge-Ge bond
lengths. Using independent displacements for the
second and third layers to slightly smaller dis-
placements in the third as compared to the sec-
ond layer and a larger x2 also. Including more
layers in the analysis worsens x2 even more.
With the vertical positions set to their best-fit
values, the in-plane fit can even be slightly im-
proved if a lateral relaxation of the fourth Ge- L”o.o 0.5 1.0 1.5 2.0 2.5 3.0
perp. momentum transfer 1 (r.1.u.)
layer is introduced. In this optimisedo geometry,
the Sb-Sb bond length is 2.90 f 0.03 4, which is Fig. 5. The (21) crystal truncation rod (CTR). The solid line
close to the Sb bulk bond length (2.87 A). Ge-Ge represents the best-fit for a model with 4 Ge layers relaxed,
with coordinates as given in table 2. The dashed curve depicts
bond lengths vary between 2.39 & 0.05 and 2.51 f
the best-fit for a model featuring a buckling of 0.2 A of the Sb
0.05 A, and the Sb-Ge bond lengths are 2.49 f dimer, and the dotted curve represents the best;fit for a
0.05 and 2.47 k 0.07 A, respectively. Table 2 lists model with Sb-Ge bond lengths fixed to 2.6 A.
the best fit coordinates for the model with 4
relaxed Ge layers and fig. 4 shows a perspective
view of the best-fit structure model. dinates given by Grey et al. [31]. For all models
The (2 1) CTR proves to be quite sensitive to discussed above, the best-fit x2 increases consid-
vertical buckling of the Sb dimer. The best-fit erably already for a Sb coverage 0 of 90% instead
buckling is 0.04 k 0.03 A, with the least displaced of the 1 ML saturation coverage used in the
Sb being the upper atom of the dimer. A buckling calculations previously discussed. The x2 values
as small as 0.2 A (equivalent to a tilt angle of 4”) are 9.3, 13.4 and 17.7 for 90%, 80% and 70%
more than doubles x2. We conclude that the surface fraction covered with Sb, respectively, as
buckling is less than 0.1 A. shown in fig. 6. From this, and from the fact that
Fig. 5 shows the experimental rod scan datt, the X-ray reflectivity saturates during Sb deposi-
the best-fit (solid line) and a curve with 0.2 A tion, we conclude that the Sb coverage must have
buckling (dashed line). While the Sb-Ge bond been close to 1 ML.
lengths seem small compared to the sum of the
covalent radii of Sb and Ge (2.62 A>, fixing the 3.3. Subsurface relaxation: elastic strain
Sb-Ge bond lengths to 2.6 A and allowing the
three topmost substrate layers to rearrange re- We have investigated whether the subsurface
sults in a large x2 as well (see fig. 5, dotted line). relaxations can be ascribed to elastic strain. Using
Including the effect of surface roughness the simple elastic energy model proposed by
(modelled after Robinson [26]) yields worse fits Keating [32], Appelbaum and Hamann [33] and
even for small roughness parameters, hence the Pedersen [34] have shown that covalent semicon-
surface must have been close to ideally flat. ductor subsurface relaxations can be well under-
Finally, we have tried to estimate the Sb cover- stood in terms of elastic strain minimisation.
age on the surface by allowing for a mixture of a While the model generally fails to predict heavily
Ge(OOl)-2 x 1-Sb and a clean Ge(OOl)-2 x 1 re- distorted bonds and changes in bond topology,
constructed surface, using for the latter the coor- the agreement between this model and total en-

9. 19s h4. Lohmeier et al. / Asymmetrical dimers on the tie(OOl)-2 x I-Sb surface
values obtained from the fits to our experimental
data, and all other layers are allowed to relax
along the dominant directions, as given in ref.
[33]. As model parameters, the short-wavelength
values LY 0.1614 and /3 = 0.0132 1361 have been
=
used.
Table 2 lists the results of the Keating-energy
minimisation for the topmost five layers. As a
general feature, the displacements “damp out”
with increasing distance from the surface by
roughly one order of magnitude per four layers.
Lateral displacements (layers 4, 5 and 8, 91 are
weaker than vertical displacements (layers 2, 3
and 6, 7) by about a factor three. The Keating-en-
/ /~__u_L_II__UJ ergy optimised structure is in good quantitative
l”“olomomentum
1 / I 1 I :
1.0 0.5 1.5 2.0 2.5 3.0 agreement with our best-fit for the experimental
perp. transfer 1 (r.1.u.)
data. In the fit the vertical displacements of lay-
Fig. 6. The (21) CTR with best-fit curves for different anti- ers 2 and 3 were taken equal, but the values are
mony coverages: the solid line represents lOO%, the dashed very close to those derived from the Keating-en-
line 9095, the dotted line 80% and the dash-dotted line 70%
ergy o~timisation. The x2 values obtained using
surface fraction covered with Sb dimers.
the best-fit parameters are essentially the same as
those obtained by using the Keating optimised
ergy calculations is good for the calculation of displacement parameters.
small subsurface relaxations, including those of
the Ge(OOl)-2 X 1 surface [34]. Elastic energy
minimisation schemes have previously been in- 4. Discussion
cluded in structure analyses by X-ray diffraction
In our proposed structure model, antimony
1351.
We have used the elastic energy in the form replaces the Ge-Ge dimers of the clean Ge(OOl)
given by [33]:
reconstructed surface and picks up the dangling
bonds associated with Ge-Ge dimer atoms. Since
E Keating = CYc (XI”; - rg2 Sb has completely filled valence orbitals in this
i,i bond topology, the surface is chemically passi-
vated by a full monolayer of Sb.
+ p t: ( xij * Xik + fq2, (7) The most remarkable feature of our proposed
i,j,k
structure model for the Ge(OOl)-2 X 1-Sb system
where the first sum extends over all bonds and is the asymmetry, i.e. the midpoint shift of the
the second sum over all bond angles in the crystal Sb-Sb dimer. Because of the absence of dangling
except for the Sb-Sb and the Sb-Ge bonds/ bonds bonds on the Ge(OOl)-2 x l-Sb surface, the driv-
angles. xlj is the real space vector between atom ing mechanism for the asymmetry must be differ-
i and atom j and r. the equilibrium distance ent from the one leading to the asymmetric dimers
between two crystal atoms. Note that the second on the clean Si(OOl)/Ge(OOl) surfaces. On the
term explicitly takes into account the tetrahedral latter surfaces the two remaining dangling bonds
bond geometry of bulk Ge. of the dimer atoms can lower their energies by
In our calculations we have minimised EKeating charge-redistribution along the dimer, pushing
for a substrate consisting of 10 Ge layers with the more negatively charged atom slightly up-
doubly periodic boundary conditions. The posi- wards and the more positively charged atom
tions of the first-layer atoms are fixed to the slightly downwards 13-51. The asymmetries con-

10. M. Lohmeier et al. /Asymmetrical dimers on the Ge(OOl)-2 x I-Sb surface 199
netted with the latter are rather large, e.g. Chadi seen by STM [18,421. We attribute this mainly to
predicts Jheoretically for Si(OO1) a midpoint0 shift the different ratio of covalent radii (1.15 for
of 0.31 A and a vertical buckling of 0.48 A [3], Sb/Ge and 1.26 for Sb/Si); possibly also the
confirmed by experiments by Jedrecy et al. [l l] larger difference in electronegativity (2% for
and Tromp et al. [37]. Sb/Ge and 8% for Sb/Si) plays a role. Both
The midpoint shift in our study is a factor two factors have been identified as stress inducing on
smaller than these values, and the vertical buck- semiconductor surfaces [43].
ling is less than 0.1 A. A charge transfer between
the dimer Sb atoms is unlikely to lower the total
energy of the surface. By introducing lateral 5. Summary / conclusions
asymmetry, the angles between the Sb-Sb dimer
and the backbonds to the substrate atoms change The results of our study on Ge(OOl)-2 x 1-Sb
from a 98.5” for a symmetrical (not midpoint- can be summarised as follows:
shifted) dimer to 94.5” and 102.6”, respectively. - Sb can be adsorbed on Ge(001) in large or-
We suggest that one of the dimer atoms under- dered domains. The domain size is largest for a
goes a sp3-rehybridisation, with three of the sp3 sample temperature of 770 K during deposition,
electrons taking part in bonds and the fourth corresponding to a correlation length of 630 A.
sp3-electron constituting a lone-pair orbital to- *The 2 x 1 pattern observed by RHEED and
gether with the remaining s-electron. The second X-ray diffraction at RT results from dimers,
dimer atom has p3-like bonds, with the two s- formed by Sb atoms which replace the Ge dimers
electrons not contributing to the bonding. Hereby, of the starting surface and thereby chemically
two bonds of one Sb atom can approximate closer passivate the surface. The Sb-Sb dimer bond
the ideal value of a sp3-hybrid configuration of length measures 2.90 A.
109”, and two bonds of the other dimer atom get *The dimers are laterally shifted by 0.16 A
closer to the ideal p3-value of 90” [38]. Theoreti- with respect to the centre of the bulk unit cell,
cal work on this point, specifically on the ques- but there is no significant buckling. The meas-
tion of whether this configuration is energetically ured bond angles are consistent with an elec-
favourable, is clearly needed. Antimony has been tronic configuration in which one of the dimer
found to occupy substitutional sites in delta-dop- atoms rehybridises to sp3 and the other dimer
ing of Si(OOl), showing that sp3-hybrides are gen- atom has p-type bonds.
erally possible [39]. On the other hand, p3-type *‘The relaxations of the subsurface layers due
bonds are reported for the Sb/Ge(lll) system to the dimer on top of the surface have been
[40] and for the surface Sb atoms of the InSb measured and are in good quantitative agreement
(1111-2 x 2 reconstruction [41]. In both these sys- with elastic energy minimisation calculations.
tems, however, the Sb bonding geometry is com-
pletely different from the dimer configuration
found here. Acknowledgements
A lateral asymmetry has not been found in the
comparable dimer system As/Si(OOl) by STM We would like to thank Dr. G.F. Clark, G.J.
[14], ARUPS [13,15] and X-ray diffraction [ll], Milne and the other Daresbury staff members for
but the sensitivity in these studies may not have their assistence during the measurements. Prof.
been high enough t$ detect a midpoint shift of Dr. J.F. van der Veen is thanked for helpful
the order of 0.16 A, e.g. Jedrecy et al. give a discussions and a critical reading of the manu-
sensitivity limit of 0.18 A [ll]. script. Dr. H.G. Muller is thanked for useful
The system Sb/Ge(OOll shows a much higher suggestions. R. Koper is gratefully acknowledged
correlation length (630 A) compared to Sb/ for polishing the crystal. This work is part of the
Si(OOl), where ordered dimer structures could not research program of the Stichting voor Funda-
be grown in domains larger than 30 x 30 A2, as menteel Onderzoek der Materie (FOM) and is

11. 200 M. Lohmeier et al. /Asymmetrical dimers on the Ge(OOl)-2 x I-Sb surface
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