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


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

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
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