1992 asymmetrical dimers on the ge(001) 2 × 1-sb surface observed using x-ray diffraction

$: 1992 asymmetrical dimers on the ge(001) 2 × 1-sb surface observed using x-ray diffraction$
Surface Science 275 (1992) 190-200

North-Holland

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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

Clean Ge(001) and Si(OO1) surfaces have been investigated extensively both in experimental and theoretical studies [ 1,2]. The generally accepted structure model for both surfaces is an asymmetrical dimer formed by two surface atoms on top of a slightly relaxed substrate [3-51. By forming dimers, the number of dangling bonds per surface atom is reduced by a factor two. This number can effectively be lowered further by a vertical buckling of the dimer, leaving the dimer bond partially ionic [3,6]. Interactions between adjacent dimers can lead to supersymmetrical phases (~(2 X 2), c(4 x 2)), observed experimentally by ARUPS/ LEED [7,8] STM [1,2] and He diffraction [9,10].

The adsorption of group V elements on both

Si(OO1) and Ge(001) has attracted much attention in the past as well [ll-181, mainly driven by the large technological interest in III/V epitaxy on group IV elements [17]. Both As and Sb are reported to form symmetrical dimer type recon- structions on Si(OOl), as seen by ARUPS [131, STM [14,16,181 and by SEXAFS [12]. For the As/Ge(OOl) system ARUPS also finds symmetrical As-As dimers [15], suggesting that this type of reconstruction is a general rule for the IV/V systems. The adsorbate atom (As/Sb) bonds to one other adsorbate atom and to the substrate dangling bonds, thereby chemically passivating the substrate. The remaining two electrons of the As/Sb form a lone pair.

We have used surface X-ray diffraction [19] to investigate the growth behaviour and the struc-

0039.6028/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

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 coverage. To our knowledge, no structure study on this system has been published so far. Sb can be grown on Get0011 in large ordered domains, and does indeed lead to a dimer-type reconstruction, but, in contrast to the system mentioned above, the dimer is found to be asymmetric.

2. Experimental

For the structure determination, we use the following primitive real-space lattice with respect to a conventional fee lattice:

al = +[llo]cubic; a2== ~[l~Olcubic;

*3 = ~oo~lc”bic~ (1) giving the following lattice dimensions: I a, I = 1 a2 I = ifia,; 1 a3 I = a,, where a0 denotzs the germanium bulk Iattice constant (5.658 A). By these definitions, a, and aZ are both parallel and a3 is perpendicular to the sample surface. Coor- dinates of the jth atom in the unit cell are expressed by a set of real numbers {xi, yj, Zj} with r-r = xjal + yja, + tju3 being the real-space position of the atom. Reciprocal-space coordinates are given in units of {bi} with a, - b, = 2~6,~ and I b, I = I b, I = t27r/aJ&; I b, i = 27r/u,,. The momentum transfer vector q is denoted by the Miller indices (kkl) with q = hb, + kbz + lb,. General reflections are thus labelled by (hkl), and in-plane reflections (I = 0) by (hk).

The experiment was carried out at the station 9.4 wiggler beamline at the Synchrotron Radia- tion Source (SRS) in Daresbury, UK. A focused monochromatic X-ray beam [ZOJ with a wavelength of 0.9 A was used. The incoming beam was defined by slits to be 1 mm horizontally (out-of- plane) and 0.3 mm vertically (in-plane). A detec- tor was used whose angular acceptance was con- straint by slits to be 0.37” along the surface normal and 0.15” in the in-plane direction. A single crystal Ge(OO1) sampIe with dimensions 8 X 10 X 3

mm3 was mounted in a UHV environmental chamber which was coupled to a 5-circle diffractometer 1211. The polished crystal had a miscut smaller than 0.1”.

The sample was cleaned by repeated cycles of cold Ar* ion sputtering (900 eV, 1 PA, 15 min) and annealing (980 K, 15 min). In order to obtain well-ordered surfaces, the sample was cooled down slowly (< 1 K/s) around the temperature of the order/disorder phase transition of the Ge(OOl)-2 X 1 phase at 955 K [22]. After a small number of cycles, a sharp two-domain 2 X 1 pattern was observed by RHEED. From this point on, the (5, 0) in-plane X-ray reflection was monitored after every cleaning cycle. Due to the much higher resolution of X-ray diffraction compared to RHEED, we could see considerable improvement in the measured peak full width at half maximum AqFwHM with additional cleaning cycles, while the RHEED pattern remained essentially unchanged. After about 15 cycles no further improvement could be obtained. By fitting the peak to a Lorentzjan we derived a correlation length L of 1030 A, where L = 2/Aq~w~~ [231 (see fig. 1).

Thereafter, antimony was deposited from a Knudsen evaporation source, with a deposition rate of _ 0.1 monolayers/min. During deposition the specular X-ray reflectivity was monitored. The reflected intensity first dropped, then after pass- ing smoothly through a minimum increased again and finally saturated, whereupon the deposition was stopped after a tota time of - 9 min. In the investigated sampIe temperature range of 670- 870 K during deposition, a 2 X 1 RHEED pattern was seen after cooling down to RT before and after deposition of Sb. The best-ordered surfaces were obtained at a substrate temperature of 770 K during deposition, followed by a slow cool- down; These surfaces had a correlation length of 630 A (see fig. lb). At 870 K the Sb started desorbing, and the resulting surface had a correlation length of only 230 A. We therefore decided nor to anneal the surface after deposition. The antimony coverage of the sample investigated in our structure determination was close to 1 monolayer (ML) of atoms (- 6.25 X lOI atoms/cm2), as discussed in section 3.2.

The sample was optically aligned using a laser beam. The crystallographic alignment was done using two bulk Bragg peaks. Scans around the diffractometer +-axis correspond to a rotation

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

Fig. 1. Transverse in-plane scans of the (2, 0) reflection (open

circles) together with Lorentzian fits (solid curves). From the

fitted FWHM’s, the correlation length L is derived (see text).

(a) Clean substrate, (b) substrate covered with 1 ML Sb.

about the sample surface normal. Diffraction intensities were obtained by numerically integrating such +-rocking curves after linear background subtraction [19]. Structure factors were calculated from the intensities by correcting for the illumi- nated area fraction (sin 28) and the Lorentz factor (sin 28. cos p) and taking the square root [24]. Here, 28 specifies the in-plane scattering angle and p is the angle and p is the angle of incidence which was taken equal to the outgoing angle in our experiment.

The structure determination is performed in two steps: First the in-plane projection of the structure is derived from the measured fractional-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 positions of the Sb atoms, and, due to a lateral relaxation of the topmost substrate layers, also resolves the registry of the surface unit cell with respect to the bulk. The intensity along the (2 1) integer-order CTR subsequently yields the atomic coordinates along the direction perpendicular to the substrate surface, resulting in a full threc-di- mensional model of the reconstructed Ge(OOl)- 2 x 1-Sb surface. The general method has been reviewed earlier [19,25]; here we introduce the 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-

a possible surface degradation. No changes in FWHM and intensity were observed. The UHV chamber pressure was 2 x lo-’ Pa during deposition 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 reflections. 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 domains. 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 complete 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 crystal 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

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+,,*+ h,k

(3)

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 minimisation. Different models are compared on the basis of the reduced x2 [28].

3.1. In-plane structure

The in-plane structure analysis employs the direct comparison of measured with calculated structure factors for a given model as well as the model-independent Patterson map PrraC of the 14 measured fractional-order reflections, from which interatomic vector lengths are obta‘ned. Though this map is incomplete, i.e. integer-order reflections are omitted and only a finite part of the reciprocal space is used, the distortion of the map is predictable [29,19].

From the Patterson map we immediately see that the main structural element in the surface unit cell is a Sb-Sb dimer, and that other models such as a vacancy or a conjugated-chain model [4] can directly be excluded. The interatomic vector of the Sb-Sb dimer corresponds to peak I in the Patterson map (fig. 2a). This is the strongest peak, because it is the interatomic vector between the heaviest atoms. The fact that the Patterson map has additional peaks directly shows that the substrate is also reconstructed. The in-plane

- P%t&c Fig. 2. (al Patterson map Pfrac of the experimental structure

factors. Solid lines mark the irreducible part of the unit ceil,

dashed lines the 2 X l-unit cell. The origin is labelled by x . Peaks IV and V coincide, whereas peak I is broadened by II.

For clarity only positive peaks are shown. (b) Real space

in-plane structure model: Sb dimer atoms are shown as large

balls, first layer Ge atoms as small balls. Interatomic vectors

that correspond to peaks in the Patterson map are labelled I to V. The 2 X 1 unit cell is marked by dashed lines.

model that is derived from the Patterson map is shown in fig. 2b, together with the interatomic vectors that can be found in the Patterson map. As mentioned above, these interatomic vectors are distorted, due to the omission of integer-order reflections. If we assume the model to be sym- metric, the best fit yields x2 = 4.9. The fitting parameters are a global scale factor, Debye- Wailer factors for Sb and Ge, one lateral displacement parameter for the Sb atoms and one for the two first-layer Ge atoms in the unit cell.

From the Patterson map one cannot see whether the Sb dimer is asymmetric. However,


Table 1

Experimental in-plane structure factor amplitudes / Fl;;Xp / with

uncertamttes q,zk and best-fit values for the symmetrical dimer

model 1 FhydC’.S I as well as for the asymmetrical dimer model

1 J%odc’.a

k I F$’ 1 ahk - , Fhmk(ldc1.s , / ,yydel,a ,

1 8.3 0.5 9.2 X.6

2 10.0 0.7 29.5 10.0

0 28.7 1.6 17.9 29.6

1 17.9 1.0 10.0 17.2

2 23.8 1.4 24.3 24.2

0 24.6 1.4 21.‘) 22.2

1 11.0 0.7 10.0 11.5

2 18.0 1.1 19.0 19.1

0 8.8 I.1 8. I 9.3

I 9.0 0.8 7.4 8.8

2 9.1 1.1 7.1 x.2

0 8.7 1.2 4.8 8.3

1 15.1 1.1 17.3 14.9

2 8.0 1.3 4.6 7.6

X 2: 4.9 0.93

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 yields x2 = 0.93. The experimental and best-fit structure factors for the symmetrical and the asymmetrical model are compared in table 1, and the best-fit displacement parameters are listed in

Table 2

Best-fit coordinates of the full Ge(OOl)-2 X 1 Sb structure model

table 2 (Ax,_ of layers 0 and 1). The asymmetry of the Sb dimer is significantly larger than the corresponding error bars of the fit parameters. Allowing an asymmetry in the lateral displacements of the first layer Ge atoms does not improve the fit. The Ge displacements in that layer are therefore taken to be equal but with opposite signs. The best-fit Debye-Waller factors are 0.34 _t 0.30 and 0.40 i 0.30 A2 for Sb and Ge, respectively. Though the error bars of the vibration factors are rather large, the Ge value lies well in the range of Ge bulk values, as reported in the literature [301.

Other possibilities, such as an in-plane twisting of the Sb-Sb axis, or Sb-Ge dimers, do not give better fits and are therefore not considered any further.

The conclusion for the in-plane structure is that Sb forms asymmetrical dimers on top of a slightly relaxed Ge substrate. The displacement 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.

3.2. Out-of-plane structure

For the calculation of the intensity along the (2 1) crystal truncation rod, the scattering contributions from both bulk Ge and the surface layers

Layer Atom

0 Sb

0 Sb

1 Ge

1 Ge

2 Ge

2 Ge 3 Ge

3 Ge 4 Ge 4 Ge

5 Ge 5 Ge

Xbulk

_

0.0

1.0

0.5

15 0.5

1.5 0.0 1.0

0.0 1.0

Yhulk Zhulk

0.5 _

0.5 _

0.0 0.0

0.0 0.0

0.0 ~ 0.25

0.0 ~ 0.25 0.5 - 0.5

0.5 - 0.5 0.5 - 0.75 0.5 - 0.75

0.0 - 1.00 0.0 ~ 1.00

AX,,* ~Zcxp AX Kcat,ng JZKC‘!,,“~

+ 0.177 (4) + 0.245 (12) _

+ 0.902 (4) + 0.252 ( 6) _

+ 0.046 (5) 0.000 * +0.046 * 0.000 *

- 0.046 (5) 0.000 * - 0.046 * 0.000 *

0.000 * -0.031 t 7) 0.000 * ~ 0.032

0.000 * + 0.037 (12) 0.000 * + 0.033 * * 0.000 -0.031 ( 7) 0.000 - 0.025

0.000 * + 0.037 (12) o.ootl * + 0.023 ~0.012 (4) 0.000 * ~0.018 0.000 * + 0.012 (4) 0.000 * +0.01x 0.000 *

0.000 * 0.000 * - 0.004 0.000 * 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 (* ).

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 1 x 1 unit cell with plane group p4mm, and the surface contribution is calculated in a 2 x 1 unit cell having plml symmetry. Both parts interfere coherently, hence the resulting structure factors F$jk for the bulk and FiEif for the surface have to be added. FiIif is calculated using eq. (2), whereas the bulk part is given by [23]:

Fbulk =

p-bulk hkl

hkl 1 _ ,-2ril e-c3/P (4)

where .Fhyy denotes the structure factor of a

complete 1 x 1 bulk unit cell with four Ge layers and p is the penetration depth of the X-rays in

Ge. Because the unit cell is asymmetric and there

are 2 X 1 and 1 X 2 domains, the surface unit cell is present in four different orientational domains with respect to the bulk, as depicted in fig. 3. The measured structure factor is the average over these four possibilities. For computational pur- poses, it is convenient to express the four different surface structure factors in terms of only one surface unit cell:

FWf(2) = Fy;I’;) e2rrih hkl 3 (5a)

F;;;f@) = F;;;f( 1) > (5b)

FSUrf(4) = F,su_‘(;’ e2vik hkl (5c)

1) Im

FsurfC1) is the surface structure factor of a one-do- hkl L

main surface unit cell. Because the integrated intensity is measured, the contributions of the four different surface domains are added inco- herently [231. The square of the total structure factor is then calculated as follows:

j= 1

+(1-B)IF,S,U;f,Ce+2FIPkU:k12. (6)

The factor two in the second and the third term accounts for the different unit cell sizes, whereas F”“‘f,Ge describes the structure factor of a clean hkl

Ge surface, which will contribute to the scattering for a Sb coverage 0 smaller than one.

From the in-plane analysis, it is known that the Ge substrate is essentially bulk-like, but with lateral relaxations extending at least to the first substrate layer. In order to obtain the perpendicular atomic coordinates in the surface region, we allow different numbers of atoms to relax vertically with respect to the surface plane. The best-fit is obtained for a model in which the vertical positions of the Sb atoms are fitted indepen- dently, the vertical positions of the first layer Ge atoms are fixed to their bulk values, and the second and third layer vertical positions are de-

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.


b) 0.71 A 0.31, .A -----) f-

layer :

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.

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 parameters to four. For this model x2 = 6.5 is obtained.

Adding vertical displacements for layer 1 worsens 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 displacements in the third as compared to the second 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- layer is introduced. In this optimisedo geometry, the Sb-Sb bond length is 2.90 f 0.03 4, which is close to the Sb bulk bond length (2.87 A). Ge-Ge bond lengths vary between 2.39 & 0.05 and 2.51 f 0.05 A, and the Sb-Ge bond lengths are 2.49 f 0.05 and 2.47 k 0.07 A, respectively. Table 2 lists 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.

The (2 1) CTR proves to be quite sensitive to vertical buckling of the Sb dimer. The best-fit buckling is 0.04 k 0.03 A, with the least displaced Sb being the upper atom of the dimer. A buckling as small as 0.2 A (equivalent to a tilt angle of 4”) more than doubles x2. We conclude that the buckling is less than 0.1 A.

Fig. 5 shows the experimental rod scan datt, the best-fit (solid line) and a curve with 0.2 A buckling (dashed line). While the Sb-Ge bond lengths seem small compared to the sum of the covalent radii of Sb and Ge (2.62 A>, fixing the Sb-Ge bond lengths to 2.6 A and allowing the three topmost substrate layers to rearrange results in a large x2 as well (see fig. 5, dotted line).

Including the effect of surface roughness (modelled after Robinson [26]) yields worse fits even for small roughness parameters, hence the surface must have been close to ideally flat.

Finally, we have tried to estimate the Sb coverage on the surface by allowing for a mixture of a Ge(OOl)-2 x 1-Sb and a clean Ge(OOl)-2 x 1 reconstructed surface, using for the latter the coor-

L”o.o 0.5 1.0 1.5 2.0 2.5 3.0 perp. momentum transfer 1 (r.1.u.)

Fig. 5. The (21) crystal truncation rod (CTR). The solid line

represents the best-fit for a model with 4 Ge layers relaxed,

with coordinates as given in table 2. The dashed curve depicts

the best-fit for a model featuring a buckling of 0.2 A of the Sb

dimer, and the dotted curve represents the best;fit for a

model with Sb-Ge bond lengths fixed to 2.6 A.

dinates given by Grey et al. [31]. For all models discussed above, the best-fit x2 increases consid- erably already for a Sb coverage 0 of 90% instead of the 1 ML saturation coverage used in the calculations previously discussed. The x2 values are 9.3, 13.4 and 17.7 for 90%, 80% and 70% surface fraction covered with Sb, respectively, as shown in fig. 6. From this, and from the fact that the X-ray reflectivity saturates during Sb deposition, we conclude that the Sb coverage must have been close to 1 ML.

3.3. Subsurface relaxation: elastic strain

We have investigated whether the subsurface relaxations can be ascribed to elastic strain. Using the simple elastic energy model proposed by Keating [32], Appelbaum and Hamann [33] and Pedersen [34] have shown that covalent semiconductor subsurface relaxations can be well under- stood in terms of elastic strain minimisation. While the model generally fails to predict heavily distorted bonds and changes in bond topology, the agreement between this model and total en-

19s h4. Lohmeier et al. / Asymmetrical dimers on the tie(OOl)-2 x I-Sb surface

/ 1 l”“olo / I /~__u_L_II__UJ 1 I :

0.5 1.0 1.5 2.0 2.5 3.0 perp. momentum transfer 1 (r.1.u.)

Fig. 6. The (21) CTR with best-fit curves for different antimony coverages: the solid line represents lOO%, the dashed line 9095, the dotted line 80% and the dash-dotted line 70%

surface fraction covered with Sb dimers.

ergy calculations is good for the calculation of small subsurface relaxations, including those of the Ge(OOl)-2 X 1 surface [34]. Elastic energy minimisation schemes have previously been in- cluded in structure analyses by X-ray diffraction 1351.

We have used the elastic energy in the form given by [33]:

E Keating = CY c (XI”; - rg2

i,i

+ p t: ( xij * Xik + fq2,

i,j,k (7)

where the first sum extends over all bonds and the second sum over all bond angles in the crystal except for the Sb-Sb and the Sb-Ge bonds/ bonds angles. xlj is the real space vector between atom i and atom j and r. the equilibrium distance between two crystal atoms. Note that the second term explicitly takes into account the tetrahedral bond geometry of bulk Ge.

In our calculations we have minimised EKeating for a substrate consisting of 10 Ge layers with doubly periodic boundary conditions. The positions of the first-layer atoms are fixed to the

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-energy optimised structure is in good quantitative agreement with our best-fit for the experimental data. In the fit the vertical displacements of layers 2 and 3 were taken equal, but the values are very close to those derived from the Keating-energy o~timisation. The x2 values obtained using the best-fit parameters are essentially the same as those obtained by using the Keating optimised displacement parameters.

4. Discussion

In our proposed structure model, antimony replaces the Ge-Ge dimers of the clean Ge(OOl) reconstructed surface and picks up the dangling bonds associated with Ge-Ge dimer atoms. Since Sb has completely filled valence orbitals in this bond topology, the surface is chemically passi- vated by a full monolayer of Sb.

The most remarkable feature of our proposed structure model for the Ge(OOl)-2 X 1-Sb system is the asymmetry, i.e. the midpoint shift of the Sb-Sb dimer. Because of the absence of dangling bonds on the Ge(OOl)-2 x l-Sb surface, the driv- ing mechanism for the asymmetry must be different from the one leading to the asymmetric dimers on the clean Si(OOl)/Ge(OOl) surfaces. On the latter surfaces the two remaining dangling bonds of the dimer atoms can lower their energies by charge-redistribution along the dimer, pushing the more negatively charged atom slightly up-

wards and the more positively charged atom slightly downwards 13-51. The asymmetries con-

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 predicts Jheoretically for Si(OO1) a midpoint0 shift of 0.31 A and a vertical buckling of 0.48 A [3], confirmed by experiments by Jedrecy et al. [l l] and Tromp et al. [37].

The midpoint shift in our study is a factor two smaller than these values, and the vertical buckling 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 asymmetry, the angles between the Sb-Sb dimer and the backbonds to the substrate atoms change from a 98.5” for a symmetrical (not midpoint- shifted) dimer to 94.5” and 102.6”, respectively. We suggest that one of the dimer atoms under- goes a sp3-rehybridisation, with three of the sp3 electrons taking part in bonds and the fourth sp3-electron constituting a lone-pair orbital together with the remaining s-electron. The second dimer atom has p3-like bonds, with the two s- electrons not contributing to the bonding. Hereby, two bonds of one Sb atom can approximate closer the ideal value of a sp3-hybrid configuration of 109”, and two bonds of the other dimer atom get closer to the ideal p3-value of 90” [38]. Theoreti- cal work on this point, specifically on the ques- tion of whether this configuration is energetically favourable, is clearly needed. Antimony has been found to occupy substitutional sites in delta-dop- ing of Si(OOl), showing that sp3-hybrides are generally possible [39]. On the other hand, p3-type bonds are reported for the Sb/Ge(lll) system [40] and for the surface Sb atoms of the InSb (1111-2 x 2 reconstruction [41]. In both these systems, however, the Sb bonding geometry is completely different from the dimer configuration found here.

A lateral asymmetry has not been found in the comparable dimer system As/Si(OOl) by STM [14], ARUPS [13,15] and X-ray diffraction [ll], but the sensitivity in these studies may not have been high enough t$ detect a midpoint shift of the order of 0.16 A, e.g. Jedrecy et al. give a sensitivity limit of 0.18 A [ll].

The system Sb/Ge(OOll shows a much higher correlation length (630 A) compared to Sb/ Si(OOl), where ordered dimer structures could not be grown in domains larger than 30 x 30 A2, as

seen by STM [18,421. We attribute this mainly to the different ratio of covalent radii (1.15 for Sb/Ge and 1.26 for Sb/Si); possibly also the larger difference in electronegativity (2% for Sb/Ge and 8% for Sb/Si) plays a role. Both factors have been identified as stress inducing on semiconductor surfaces [43].

5. Summary / conclusions

The results of our study on Ge(OOl)-2 x 1-Sb can be summarised as follows:

- Sb can be adsorbed on Ge(001) in large ordered domains. The domain size is largest for a sample temperature of 770 K during deposition, corresponding to a correlation length of 630 A.

*The 2 x 1 pattern observed by RHEED and X-ray diffraction at RT results from dimers, formed by Sb atoms which replace the Ge dimers of the starting surface and thereby chemically passivate the surface. The Sb-Sb dimer bond length measures 2.90 A.

*The dimers are laterally shifted by 0.16 A with respect to the centre of the bulk unit cell, but there is no significant buckling. The measured bond angles are consistent with an elec- tronic configuration in which one of the dimer atoms rehybridises to sp3 and the other dimer atom has p-type bonds.

*‘The relaxations of the subsurface layers due to the dimer on top of the surface have been measured and are in good quantitative agreement with elastic energy minimisation calculations.

Acknowledgements

We would like to thank Dr. G.F. Clark, G.J. Milne and the other Daresbury staff members for their assistence during the measurements. Prof. Dr. J.F. van der Veen is thanked for helpful discussions and a critical reading of the manu- script. Dr. H.G. Muller is thanked for useful suggestions. R. Koper is gratefully acknowledged for polishing the crystal. This work is part of the research program of the Stichting voor Funda- menteel Onderzoek der Materie (FOM) and is


made possible by financial support from the Ne- derlandse Organisatie voor Wetenschappelijk Onderzoek (NW01 and the Netherlands Tech- nology Foundation.

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1992 asymmetrical dimers on the ge(001) 2 × 1-sb surface observed using x-ray diffraction

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Transcript of 1992 asymmetrical dimers on the ge(001) 2 × 1-sb surface observed using x-ray diffraction