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Physica B 248 (1998) 1—8

   Epitaxial clusters studied by synchrotron X-ray diffraction and
2                                     M. Nielsen et al. / Physica B 248 (1998) 1—8

revealed that similar nanoclusters are...
M. Nielsen et al. / Physica B 248 (1998) 1—8                                               3

4                                             M. Nielsen et al. / Physica B 248 (1998) 1—8

Fig. 2. Measured and fitted ...
M. Nielsen et al. / Physica B 248 (1998) 1—8                                             5

Fig. 3. Diffraction results ...
6                                              M. Nielsen et al. / Physica B 248 (1998) 1—8

Fig. 4. Measured and fitted...
M. Nielsen et al. / Physica B 248 (1998) 1—8                                 7

translation of the whole wedge by half a n...
distance in the direction of the long axis 11 1 02 (see                  The vertical lattice spacing inside the huts foll...
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1998 epitaxial clusters studied by synchrotron x ray diffraction and scanning tunneling microscopy


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1998 epitaxial clusters studied by synchrotron x ray diffraction and scanning tunneling microscopy

  1. 1. Physica B 248 (1998) 1—8 Epitaxial clusters studied by synchrotron X-ray diffraction and scanning tunneling microscopy M. Nielsen *, R. Feidenhans’l , F. Berg Rasmussen , J. Baker , G. Falkenberg , L. Lottermoser , R.L. Johnson , A.J. Steinfort , P.M.L. Scholte Ris~ National Laboratory, DK-4000 Roskilde, Denmark ( II Institut fur Experimentalphysik, University of Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany Department of Applied Physics, Delft University of Technology, NL-2600 GA Delft, The Netherlands Abstract Nanoscale clusters are often formed during heteroepitaxial crystal growth. Misfit between the lattice parameter of the substrate and the adsorbate stimulates the formation of regular clusters with a characteristic size. The well-known “hut-clusters” formed during the growth of Ge on Si(0 0 1) are a good example of this type. Adsorbates can also produce another type of nanocluster; if the surface free energy of a particular crystallographic plane becomes lower than that of the geometrical surface of the substrate, then the entire surface will break up into regular arrays of small facets which look similar to the “hut clusters”. We demonstrate that X-ray diffraction in combination with scanning tunneling microscopy can be used to determine the fundamental properties of such clusters. 1998 Elsevier Science B.V. All rights reserved. Keywords: Nanoclusters; X-ray diffraction; STM 1. Introduction interface. In between these regimes a special type of small clusters are formed at substrate temperatures The lattice constant of Ge is 4% larger than that below 530 K. They are small regularly shaped dis- of Si. When Ge is grown on a Si(0 0 1) substrate location-free islands called “hut clusters” which are then the first 2—3 layers will form pseudomorphic depicted in Fig. 1a. All of the facets correspond to layers which accommodate the lateral compres- +1 0 5, planes and with the proper preparation sional strain. For thicker films nucleation of three conditions the huts are nearly monodisperse in dimensional islands sets in and the misfit is accom- width and height, but they have variable length. modated by dislocations at the island/substrate Apart from elastic strain relaxation their internal structure is a continuation of the Si-substrate lat- tice. For an effective coverage of 8 ML it is found that the huts almost cover the substrate entirely. * Corresponding author. Fax: (45) 42 37 01 15; e-mail: The hut clusters were first observed by Mo et al. [1], and since then STM measurements have 0921-4526/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 1 9 3 - 8
  2. 2. 2 M. Nielsen et al. / Physica B 248 (1998) 1—8 revealed that similar nanoclusters are common in spected by STM. Best results were obtained with other systems as well [2—9]. For example, depos- a deposition rate of 0.6 ML/min and a substrate ition of about a monolayer of In on a Ge(0 0 1) temperature of 430°C (see Fig. 1a). surface followed by heat treatment at 350°C pro- For the In/Ge(0 0 1) samples, In was evaporated duces the regular facetted surface shown in Fig. 1b. onto the clean Ge(0 0 1) surface at room temper- Here all the facets are +1 0 3, planes, the height and ature until at about 1 ML the RHEED spots of the width of the huts are about 11 and 65 A, respecti- fractional order (4;3) superstructure reached max- vely. The surface morphology can be varied to imum intensity. On annealing RHEED reflections some extent by altering the substrate temperature characteristic of the +1 0 3, facets appeared. Sys- and deposition conditions. By optimizing the con- tematic STM investigations revealed that the ditions, regular arrays of long huts can be produced shape, size, and density of the facets depend criti- [10]. This is an example of nanofacetting. cally on the temperature. The samples used in these The last system we will discuss are the internal measurements were annealed at 350°C for 5 min, facets which form when Cu films with thicknesses which produced a surface completely covered with up to 20 ML grow epitaxially on Ni(0 0 1). The long huts of uniform width as shown in Fig. 1b. model for the internal facets proposed by Muller ¨ Desorption of In beyond a critical coverage of et al. [11] on the basis of STM studies is shown in 0.5 ML at temperatures around 500°C causes the Fig. 1c. Here the Cu film is pseudomorphic with the clusters to decompose and the Ge(0 0 1) surface is Ni substrate except for the Cu atoms inside the reestablished. wedge-shaped clusters. These are bounded by The Cu/Ni(0 0 1) samples were prepared follow- +1 1 1, planes towards the surrounding Cu film and ing the prescription given by Muller et al. [11]. For ¨ by a +0 0 1, plane upwards. The atoms inside the Cu coverages from 1 to 20 ML the clusters appear wedges are translated half a nearest neighbour dis- with the same density, the clusters simply grow in tance along the axis of the wedges and about 0.5 A maximum width because the number of rows of upwards, thereby opening some space for strain atoms in the top layer of the wedge equals the relaxation. For the three systems illustrated in number of atomic layers in the Cu film. The wedge Fig. 1 we will show how synchrotron X-ray diffrac- shaped clusters have their long axis parallel to the tion can be used to measure the fundamental struc- 11 1 02 direction of the Ni crystal. At monolayer tural properties. coverage the “clusters” are single rows of atoms and at 20 ML the clusters start to merge. We have done diffraction measurements in the regime from 2. Measurements 5 to 20 ML [12]. All measurements were performed with the verti- cal scattering diffractometer on the BW2 wiggler 3. Analysis beam line at HASYLAB (DESY, Hamburg). The samples were prepared in the STM Laboratory at We will now discuss the results of the X-ray the nearby II. Institute fur Experimentalphysik, ¨ diffraction measurements. For the three systems University of Hamburg. After preparation and Ge/Si(0 0 1), In/Ge(0 0 1), and Cu/Ni(0 0 1) we have characterization with RHEED and LEED the sam- clusters bounded by +5 0 1,, +3 0 1,, and +1 1 1, ples were studied by STM. Subsequently the facets respectively. This provides us with a conve- sample was transferred into a portable small UHV nient method to selectively observe the diffraction chamber with a hemispherical Be window which signal from the clusters, namely by measuring the was mounted on the diffractometer for the X-ray crystal truncation rods (CTR) from these facets. As measurements. a first model we ignore scattering from the “end For preparing the Ge/Si(0 0 1) samples Ge was gables” of the huts (since the length is much larger deposited from a Knudsen cell onto a clean Si(0 0 1) than the width of the huts), and we assume the surface. After deposition the hut clusters were in- internal structure to be a simple continuation of the
  3. 3. M. Nielsen et al. / Physica B 248 (1998) 1—8 3 Fig. 1. (a) STM image of Ge hut-clusters on Si(0 0 1), the area shown is 1000;900 A. The samples were prepared by depositing 6 ML Ge on Si(0 0 1) at 430°C. (b) STM image of the In/Ge(0 0 1) sample after the formation of the +1 0 3,-facets. About 1 ML of In was deposited on Ge(0 0 1) at room temperature followed by 5 min annealing at 350°C. (c) A model of the buried Cu clusters in Cu/Ni(0 0 1) films. The large gray circles represent 5 layers of pseudomorphic Cu atoms on the Ni substrate which is indicated by small black circles. The large black circles represent the Cu atoms inside the wedge-shaped cluster, all displaced half a neighbour distance in the long cluster direction and a little upwards. substrate, except for Cu/Ni(0 0 1) which include gives a convenient reference frame and Figs. 2—4 also a uniform translation. As indicated in Figs. 2 show examples of measured diffraction results from and 3 the CTRs from the facets are straight lines scans in symmetry directions across CTRs, and as perpendicular to the facet planes extending from expected we get scattering peaks at the CTR posi- each Bragg point of the internal structure. In this tions. The important point now is that the relative picture we also ignore that the facets are not large intensities of the scattering groups from different compared to the wavelength. This simple model CTRs depend sensitively on the non-uniform strain
  4. 4. 4 M. Nielsen et al. / Physica B 248 (1998) 1—8 Fig. 2. Measured and fitted X-ray diffraction profiles for the Ge/Si(0 0 1) system around the (1 1 l), (2 0 l), and (4 0 l) reciprocal lattice points of Si. The panel on the right illustrates how the scans cut through the CTRs. The strong asymmetry of the intensity in the (4 0 l) scans is an effect of non-uniform strain relaxation. inside the huts, and this give us a first order duce a lattice parameter a (z) allowing a homogene- W measure of the strain relaxation [12,13]. ous expansion in each atomic layer z described by To analyze the data we assume a realistic model for the cluster including the inhomogeneous strain z a (z)a #(a !a ) , relaxation and calculate the diffraction response by W h summing the phase factor over all atomic positions. In this way we can take into account finite size where h is the height of the hut. The vertical lattice effects, surface structures, and interference scatter- parameter is determined using the Poisson ratio ing between different huts. In the following we 0.28. Fair agreement with the complete set of discuss the three systems in more detail. measured data is obtained with an onset relaxation Fig. 2 show examples of measured data for the at the bottom of the hut of 0.5% and full relaxation Ge/Si(0 0 1) system. The profiles have three (or five) (4% expansion) at the apex of the hut. This simpli- peaks corresponding to three (or five) CTRs cross- fied model does not include inhomogeneity within ed in the scans. The central peak is the CTR from each layer or bowing distortions of the lattice the (0 0 1) surface. This has contributions from the planes, but it has been sufficient for determining the hut/substrate interface and from the pseudomor- dominant parameters of the non-uniform strain. phic Ge layers between the huts, and interference The In/Ge(0 0 1) system was studied and ana- between these. We do not include the central peak lyzed in much the same way. The samples used in in the data analysis. In axial scans at high mo- the diffraction measurements were completely mentum transfer q the asymmetry of the intensity covered with clusters of nearly uniform width and is very pronounced (see the right-hand panel of with a high ratio of length to width. In Fig. 1b each Fig. 2 with scans through the CTR from the (4 0 0) stripe is a single hut cluster 65 A wide and 11 A Bragg point). This asymmetry is an effect of in- high. The volume of all clusters corresponds to homogeneous strain relaxation and the full curves a coverage of 4 ML and thus they cannot be built in the figure are the result of a fitted model consist- up of In atoms. The STM measurement showed ing of huts 300 A long and 130 A wide (9 atomic that the side of the clusters are +1 0 3, facets which layers high). Along the long axis we use no strain consist of narrow +0 0 1, terraces separated by relaxation but along the short (130 A) side we intro- single atomic steps. Fig. 3a show examples of the
  5. 5. M. Nielsen et al. / Physica B 248 (1998) 1—8 5 Fig. 3. Diffraction results from the In/Ge(0 0 1) system. (a) Measured profiles in scans through the CTRs from the (2 0 2) Bragg point of Ge. Notice the absence of the central peak and the relative symmetry of the intensities. (b Measured profiles near the Ge(4 0 0) reflection which illustrate the strong interference scattering. (c) sketch of the scans through the CTRs in panel (a). (d) model of the In covered 11 0 32 facets. The large open circles are In atoms, and the smaller grey shaded circles are Ge atoms at different heights. Each In atom saturates three dangling Ge bonds.
  6. 6. 6 M. Nielsen et al. / Physica B 248 (1998) 1—8 Fig. 4. Measured and fitted X-ray profiles for the Cu/Ni(0 0 1) system. Here LEED notation is used for (h k l) so that [1 0 0] is parallel to the long cluster axis. The left hand panel show transverse scans through (1 0 l) points, and the insert shows the small intensity in transverse scans through (h 0 l) when h is even. The right hand panel presents longitudinal (axial) scans through (1 0 l), and illustrates the strong asymmetry of the scattering intensity. diffraction results. The first point to observe here is An interesting aspect of the In/Ge(0 0 1) system is that there is no central peak corresponding to the the ordering of the huts. We observe, most dramati- CTR from a substrate/adsorbate interface and thus cally in the nearly in-plane scans, the interference the huts are simply a continuation of the Ge sub- scattering in the diffraction measurements. This is strate crystal. The role of the In atoms is to ener- shown in Fig. 3b. The single hut scattering provides getically stabilize the +1 0 3, surfaces. So, where a form factor for the scattering and this completely strain relaxation was the important mechanism for dominates the picture for Ge/Si(0 0 1). For understanding the growth of the Ge/Si(0 0 1) hut In/Ge(0 0 1) this form factor is multiplied with clusters, the surface energy is here the important a line spectrum given by the superlattice of the huts factor. Complete sets of diffraction scans were mea- and the width of each line is given by the range of sured through the CTRs within the instrumental ordering in the superlattice, which is around range and the measured profiles compared to 1000 A. For increasing vertical momentum transfer model calculations as above. Now, to a first ap- the effect become less important but it is noticeable proximation, the scattering intensity is symmetrical throughout the zone and is included in the model around the central position (the non-existing cen- calculations. tral rod) signaling little or no strain in the huts. The last system, Cu/Ni(0 0 1) is quite different However, the relative intensity of the two side again. Now we have huts of Cu buried in Cu peaks on each side is very sensitive to the occu- and they are upside down with the apex to- pancy of the In atoms. Combining the STM and wards the substrate. However, for the diffraction diffraction results we arrive at the model shown in measurements we have a quite analogous situation. Fig. 3d. Each In atom bonds to three Ge atoms and We use the CTRs from the clusters and analyze the saturates all of the Ge dangling bonds, [14—16]. By strain by fitting the measured scan profiles with fitting the diffraction results we determined the In model calculations. The clusters are conveniently coordinates. made visible in diffraction by the homogeneous
  7. 7. M. Nielsen et al. / Physica B 248 (1998) 1—8 7 translation of the whole wedge by half a neighbour b 1.0, 0.07, and n 7 in Ni lattice units.
  8. 8. distance in the direction of the long axis 11 1 02 (see The vertical lattice spacing inside the huts follow Fig. 1c). If the translation is r we have for the layer by layer that of the film outside the huts and it scattering function of the homogeneous film plus is 4% expanded relative to the Ni spacing. The wedges: homogeneous vertical translation of the wedges is determined to be 0.5 A and it is the same for all F(q)f (q)#f (q)(e q r!1) thicknesses. At film thicknesses around 20 ML the
  9. 9. lateral lattice spacing in the huts approaches that of where q is the momentum transfer, f the scatter-
  10. 10. the Ni lattice and this type of cluster formation ing function of a complete pseudomorphic film, and becomes ineffective in relaxing the strain energy. At f that of the wedges. This is like an antifer- the same time the wedges begin to merge and the romagnet and considering q components along r growth pattern changes. we have constructive (destructive) interference for It was observed in the data analysis that the odd (even) reciprocal lattice numbers. For this positions of the side peaks from the +1 1 1, facets argument we have neglected the small component do not follow closely the straight lines given by the of r in the vertical direction. CTRs of +1 1 1, surfaces, but instead the fitted Fig. 4 show examples of measured diffraction midpoints follow lines not going through the Bragg profiles for the Cu/Ni(0 0 1) system. They confirm points. This behaviour was duplicated nicely in the the essential points of the model proposed by calculation for the model cluster and is due to the Muller et al. [11]. The side peaks and their shift in ¨ finite size of the clusters [17]. position with the vertical momentum transfer l show the existence of the +1 1 1, facets and as illustrated by the insert the transverse scans with 4. Conclusions even indices have insignificant intensity confirming the half neighbour distance translation. The asym- We have proved that surface X-ray diffraction in metry of the scattering intensity around the central combination with STM is an effective technique for position is dramatic in the longitudinal (axial) measuring the internal structure of hut clusters. scans. Again this is an effect of the non-uniform The regular shape of these clusters allows the scat- strain inside the clusters. A good global fit to all tering from the huts to be distinguished from that of measured data is obtained with a model having the substrate and coexisting adsorbed films by fo- lateral strain relaxation of the atomic layers inside cussing on the scattering from the CTR from the the clusters only. The first few layers near the apex sloping facets. The intensity of this scattering is of the huts are fully laterally relaxed to the natural sensitively dependent on small deviations in the Cu spacing and the strain increases with height positions of the atoms in the clusters from the above the substrate. We have used extrapolated substrate lattice and is therefore n a good measure of non-uniform strains. The small b(n)b # ) exp! ! , size of the clusters makes it simple to compare the
  11. 11. n scattering with that from model clusters. A natural where b(n) is the lateral lattice parameter of layer n, extension of the present analysis would be to calcu- the extra relaxation at bottom (n0) and late the shape of the clusters by applying elasticity
  12. 12. theory or for the semiconductors the Keating n a fitted decay length. For a 9 ML film we find model [18], and comparing the calculated diffrac- tion signal with the measured X-ray data. Such an analysis would allow a more detailed descrip- tion of the huts including parameters not discussed Because the Cu clusters are aligned parallel to the axes of the (1;1) Ni surface structure we apply here LEED notation for the in this paper such as substrate deformation, be- in-plane q-component, which means that the (h, 0, l,) coordi- nding of the atomic layers, or nonuniformity within nates equals the (h, h, l,) of the 3D reciprocal lattice of Ni. individual layers, and altogether further improve
  13. 13. 8 M. Nielsen et al. / Physica B 248 (1998) 1—8 our understanding of the mechanisms controlling [6] L. Seehofer, S. Huhs, G. Falkenberg, R.L. Johnson, Surf. their growth. Sci. 329 (1995) 157. [7] R. Notzel, J. Temmyo, T. Tamamura, T. Fukui, ¨ H. Hasegawa, Europhys News 27 (1996) 148. [8] J.R. Heffelfinger, M.W. Bench, C.B. Carter, Surf. Sci. Lett. Acknowledgements 343 (1995) L1161. [9] J. Tersoff, C. Teichert, G. Lagally, Phys. Rev. Lett. 76 This work was supported by the Danish Nation- (1996) 1675. [10] M. Nielsen, D.-M. Smilgies, R. Feidenhans’l, E. al Science Foundation through DanSync and by Landemark, G. Falkenberg, L. Lottermoser, L. Seehofer, the German Bundesministerium fur Bildung, Wis- ¨ R.L. Johnson, Surf. Sci. 352—354 (1996) 430. senschaft, Forschung und Technologie (BMBF) un- [11] B. Muller, B. Fischer, L. Nedelmann, A. Fricke, K. Kern, ¨ der project no. 05 622GUA1. Phys. Rev. Lett. 76 (1996) 2358. [12] F. Berg Rasmussen, J. Baker, M. Nielsen, R. Feidenhans’l, R.L. Johnson, Phys. Rev. Lett. 49 (1997) 4413. [13] A.J. Steinfort, P.M.L.O. Scholte, A. Ettema, F. Tuinstra, References M. Nielsen, E. Landemark, D.-M. Smilgies, G. Falkenberg, L. Seehofer, R.L. Johnson, Phys. Rev. Lett. 77 (1996) 2009. [1] Y.-W. Mo, D.E. Savage, B.S. Swartzentruber, M.G. [14] L. Seehofer, G. Falkenberg, R.L. Johnson, Surf. Sci. Lagally, Phys. Rev. Lett. 65 (1990) 1020. 352—354 (1996) 425. [2] K. Kern, H. Niehus, A. Schatz, P. Zeppenfeld, J. Goerge, [15] Z. Gai, H. Ji, Y. He, C. HU, R.G. Zhao, W.S. Yang, Surf. G. Comsa, Phys. Rev. Lett. 67 (1991) 855. Sci. 358 (1995) L851. [3] J. Tersoff, R.M. Tromp, Phys. Rev. Lett. 70 (1993) 2782. [16] H. Ji, Y. Wang, R.G. Zhao, W.S. Yang, Surf. Sci. 380 (1997) [4] T.E. Madey, J. Guan, C.-H. Nien, C.-Z. Dong, H.-S. Tao, 507. R.A. Cambell, Surf. Sci. Lett. 3 (1995) 1315. [17] M. Nielsen, J. Baker, F. Berg Rasmussen, E. Feidenhans’l, [5] A.A. Baski, L.J. Whitman, Phys. Rev. Lett. 74 (1995) R.L. Johnson, to be published. 956. [18] J. Skov Pedersen, Surf. Sci. 210 (1989) 238.