Physica B 248 (1998) 1—8

Epitaxial clusters studied by synchrotron X-ray diffraction andscanning 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 fu( r 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 thesubstrate 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 produceanother type of nanocluster; if the surface free energy of a particular crystallographic plane becomes lower than that ofthe geometrical surface of the substrate, then the entire surface will break up into regular arrays of small facets which looksimilar to the “hut clusters”. We demonstrate that X-ray diffraction in combination with scanning tunneling microscopycan 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

The lattice constant of Ge is 4% larger than thatof Si. When Ge is grown on a Si(0 0 1) substratethen the first 2—3 layers will form pseudomorphiclayers which accommodate the lateral compres-sional strain. For thicker films nucleation of threedimensional islands sets in and the misfit is accom-modated by dislocations at the island/substrate

*Corresponding author. Fax: (45) 42 37 01 15; e-mail:Mourits.Nielsen@Risoe.dk.

interface. In between these regimes a special type ofsmall clusters are formed at substrate temperaturesbelow 530 K. They are small regularly shaped dis-location-free islands called “hut clusters” which aredepicted in Fig. 1a. All of the facets correspond toM1 0 5N planes and with the proper preparationconditions the huts are nearly monodisperse inwidth and height, but they have variable length.Apart from elastic strain relaxation their internalstructure is a continuation of the Si-substrate lat-tice. For an effective coverage of 8 ML it is foundthat the huts almost cover the substrate entirely.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

revealed that similar nanoclusters are common inother systems as well [2—9]. For example, depos-ition of about a monolayer of In on a Ge(0 0 1)surface followed by heat treatment at 350°C pro-duces the regular facetted surface shown in Fig. 1b.Here all the facets are M1 0 3N planes, the height andwidth of the huts are about 11 and 65 A_ , respecti-vely. The surface morphology can be varied tosome extent by altering the substrate temperatureand deposition conditions. By optimizing the con-ditions, regular arrays of long huts can be produced[10]. This is an example of nanofacetting.

The last system we will discuss are the internalfacets which form when Cu films with thicknessesup to 20 ML grow epitaxially on Ni(0 0 1). Themodel for the internal facets proposed by Mulleret al. [11] on the basis of STM studies is shown inFig. 1c. Here the Cu film is pseudomorphic with theNi substrate except for the Cu atoms inside thewedge-shaped clusters. These are bounded byM1 1 1N planes towards the surrounding Cu film andby a M0 0 1N plane upwards. The atoms inside thewedges are translated half a nearest neighbour dis-tance along the axis of the wedges and about 0.5 A_upwards, thereby opening some space for strainrelaxation. For the three systems illustrated inFig. 1 we will show how synchrotron X-ray diffrac-tion can be used to measure the fundamental struc-tural properties.

2. Measurements

All measurements were performed with the verti-cal scattering diffractometer on the BW2 wigglerbeam line at HASYLAB (DESY, Hamburg). Thesamples were prepared in the STM Laboratory atthe nearby II. Institute fur Experimentalphysik,University of Hamburg. After preparation andcharacterization with RHEED and LEED the sam-ples were studied by STM. Subsequently thesample was transferred into a portable small UHVchamber with a hemispherical Be window whichwas mounted on the diffractometer for the X-raymeasurements.

For preparing the Ge/Si(0 0 1) samples Ge wasdeposited from a Knudsen cell onto a clean Si(0 0 1)surface. After deposition the hut clusters were in-

spected by STM. Best results were obtained witha deposition rate of 0.6 ML/min and a substratetemperature of 430°C (see Fig. 1a).

For the In/Ge(0 0 1) samples, In was evaporatedonto the clean Ge(0 0 1) surface at room temper-ature until at about 1 ML the RHEED spots of thefractional order (4]3) superstructure reached max-imum intensity. On annealing RHEED reflectionscharacteristic of the M1 0 3N facets appeared. Sys-tematic STM investigations revealed that theshape, size, and density of the facets depend criti-cally on the temperature. The samples used in thesemeasurements were annealed at 350°C for 5 min,which produced a surface completely covered withlong huts of uniform width as shown in Fig. 1b.Desorption of In beyond a critical coverage of0.5 ML at temperatures around 500°C causes theclusters to decompose and the Ge(0 0 1) surface isreestablished.

The Cu/Ni(0 0 1) samples were prepared follow-ing the prescription given by Muller et al. [11]. ForCu coverages from 1 to 20 ML the clusters appearwith the same density, the clusters simply grow inmaximum width because the number of rows ofatoms in the top layer of the wedge equals thenumber of atomic layers in the Cu film. The wedgeshaped clusters have their long axis parallel to theS1 1 0T direction of the Ni crystal. At monolayercoverage the “clusters” are single rows of atomsand at 20 ML the clusters start to merge. We havedone diffraction measurements in the regime from5 to 20 ML [12].

3. Analysis

We will now discuss the results of the X-raydiffraction measurements. For the three systemsGe/Si(0 0 1), In/Ge(0 0 1), and Cu/Ni(0 0 1) we haveclusters bounded by M5 0 1N, M3 0 1N, and M1 1 1Nfacets respectively. This provides us with a conve-nient method to selectively observe the diffractionsignal from the clusters, namely by measuring thecrystal truncation rods (CTR) from these facets. Asa first model we ignore scattering from the “endgables” of the huts (since the length is much largerthan the width of the huts), and we assume theinternal structure to be a simple continuation of the

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

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 MLGe on Si(0 0 1) at 430°C. (b) STM image of the In/Ge(0 0 1) sample after the formation of the M1 0 3N-facets. About 1 ML of In wasdeposited 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 clusterdirection and a little upwards.

substrate, except for Cu/Ni(0 0 1) which includealso a uniform translation. As indicated in Figs. 2and 3 the CTRs from the facets are straight linesperpendicular to the facet planes extending fromeach Bragg point of the internal structure. In thispicture we also ignore that the facets are not largecompared to the wavelength. This simple model

gives a convenient reference frame and Figs. 2—4show examples of measured diffraction results fromscans in symmetry directions across CTRs, and asexpected we get scattering peaks at the CTR posi-tions. The important point now is that the relativeintensities of the scattering groups from differentCTRs depend sensitively on the non-uniform strain

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

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 latticepoints 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 ordermeasure of the strain relaxation [12,13].

To analyze the data we assume a realistic modelfor the cluster including the inhomogeneous strainrelaxation and calculate the diffraction response bysumming the phase factor over all atomic positions.In this way we can take into account finite sizeeffects, surface structures, and interference scatter-ing between different huts. In the following wediscuss the three systems in more detail.

Fig. 2 show examples of measured data for theGe/Si(0 0 1) system. The profiles have three (or five)peaks corresponding to three (or five) CTRs cross-ed in the scans. The central peak is the CTR fromthe (0 0 1) surface. This has contributions from thehut/substrate interface and from the pseudomor-phic Ge layers between the huts, and interferencebetween these. We do not include the central peakin the data analysis. In axial scans at high mo-mentum transfer q the asymmetry of the intensityis very pronounced (see the right-hand panel ofFig. 2 with scans through the CTR from the (4 0 0)Bragg point). This asymmetry is an effect of in-homogeneous strain relaxation and the full curvesin the figure are the result of a fitted model consist-ing of huts 300 A_ long and 130 A_ wide (9 atomiclayers high). Along the long axis we use no strainrelaxation but along the short (130 A_ ) side we intro-

duce a lattice parameter ay(z) allowing a homogene-

ous expansion in each atomic layer z described by

ay(z)"a

"0550.#(a

501!a

"0550.)A

z

hB2,

where h is the height of the hut. The vertical latticeparameter is determined using the Poisson ratiol"0.28. Fair agreement with the complete set ofmeasured data is obtained with an onset relaxationat the bottom of the hut of 0.5% and full relaxation(4% expansion) at the apex of the hut. This simpli-fied model does not include inhomogeneity withineach layer or bowing distortions of the latticeplanes, but it has been sufficient for determining thedominant parameters of the non-uniform strain.

The In/Ge(0 0 1) system was studied and ana-lyzed in much the same way. The samples used inthe diffraction measurements were completelycovered with clusters of nearly uniform width andwith a high ratio of length to width. In Fig. 1b eachstripe is a single hut cluster 65 A_ wide and 11 A_high. The volume of all clusters corresponds toa coverage of 4 ML and thus they cannot be builtup of In atoms. The STM measurement showedthat the side of the clusters are M1 0 3N facets whichconsist of narrow M0 0 1N terraces separated bysingle atomic steps. Fig. 3a show examples of the

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

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 ofGe. Notice the absence of the central peak and the relative symmetry of the intensities. (b Measured profiles near the Ge(4 0 0) reflectionwhich illustrate the strong interference scattering. (c) sketch of the scans through the CTRs in panel (a). (d) model of the In coveredS1 0 3T facets. The large open circles are In atoms, and the smaller grey shaded circles are Ge atoms at different heights. Each In atomsaturates three dangling Ge bonds.

M. Nielsen et al. / Physica B 248 (1998) 1—8 5

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 tothe long cluster axis. The left hand panel show transverse scans through (1 0 l) points, and the insert shows the small intensity intransverse scans through (h 0 l) when h is even. The right hand panel presents longitudinal (axial) scans through (1 0 l), and illustrates thestrong asymmetry of the scattering intensity.

diffraction results. The first point to observe here isthat there is no central peak corresponding to theCTR from a substrate/adsorbate interface and thusthe huts are simply a continuation of the Ge sub-strate crystal. The role of the In atoms is to ener-getically stabilize the M1 0 3N surfaces. So, wherestrain relaxation was the important mechanism forunderstanding the growth of the Ge/Si(0 0 1) hutclusters, the surface energy is here the importantfactor. Complete sets of diffraction scans were mea-sured through the CTRs within the instrumentalrange and the measured profiles compared tomodel calculations as above. Now, to a first ap-proximation, the scattering intensity is symmetricalaround the central position (the non-existing cen-tral rod) signaling little or no strain in the huts.However, the relative intensity of the two sidepeaks on each side is very sensitive to the occu-pancy of the In atoms. Combining the STM anddiffraction results we arrive at the model shown inFig. 3d. Each In atom bonds to three Ge atoms andsaturates all of the Ge dangling bonds, [14—16]. Byfitting the diffraction results we determined the Incoordinates.

An interesting aspect of the In/Ge(0 0 1) system isthe ordering of the huts. We observe, most dramati-cally in the nearly in-plane scans, the interferencescattering in the diffraction measurements. This isshown in Fig. 3b. The single hut scattering providesa form factor for the scattering and this completelydominates the picture for Ge/Si(0 0 1). ForIn/Ge(0 0 1) this form factor is multiplied witha line spectrum given by the superlattice of the hutsand the width of each line is given by the range ofordering in the superlattice, which is around1000 A_ . For increasing vertical momentum transferthe effect become less important but it is noticeablethroughout the zone and is included in the modelcalculations.

The last system, Cu/Ni(0 0 1) is quite differentagain. Now we have huts of Cu buried in Cuand they are upside down with the apex to-wards the substrate. However, for the diffractionmeasurements we have a quite analogous situation.We use the CTRs from the clusters and analyze thestrain by fitting the measured scan profiles withmodel calculations. The clusters are convenientlymade visible in diffraction by the homogeneous

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

translation of the whole wedge by half a neighbourdistance in the direction of the long axis S1 1 0T (seeFig. 1c). If the translation is Dr we have for thescattering function of the homogeneous film pluswedges:

F(q)"f&*-.

(q)#f8%$'%4

(q)(e2p*q >Dr!1)

where q is the momentum transfer, f&*-.

the scatter-ing function of a complete pseudomorphic film, andf8%$'%

that of the wedges. This is like an antifer-romagnet and considering q components along Drwe have constructive (destructive) interference forodd (even) reciprocal lattice numbers.1 For thisargument we have neglected the small componentof Dr in the vertical direction.

Fig. 4 show examples of measured diffractionprofiles for the Cu/Ni(0 0 1) system. They confirmthe essential points of the model proposed byMuller et al. [11]. The side peaks and their shift inposition with the vertical momentum transferl show the existence of the M1 1 1N facets and asillustrated by the insert the transverse scans witheven indices have insignificant intensity confirmingthe half neighbour distance translation. The asym-metry of the scattering intensity around the centralposition is dramatic in the longitudinal (axial)scans. Again this is an effect of the non-uniformstrain inside the clusters. A good global fit to allmeasured data is obtained with a model havinglateral strain relaxation of the atomic layers insidethe clusters only. The first few layers near the apexof the huts are fully laterally relaxed to the naturalCu spacing and the strain increases with heightabove the substrate. We have used

b(n)"b=#e

3%-) exp!C!A

n

n#B

2

D,where b(n) is the lateral lattice parameter of layer n,e3%-

the extra relaxation at bottom (n"0) andn#

a fitted decay length. For a 9 ML film we find

1Because the Cu clusters are aligned parallel to the axes of the(1]1) Ni surface structure we apply here LEED notation for thein-plane q-component, which means that the (h, 0, lN) coordi-nates equals the (h, h, lN) of the 3D reciprocal lattice of Ni.

b="1.0, e

3%-"0.07, and n

#"7 in Ni lattice units.

The vertical lattice spacing inside the huts followlayer by layer that of the film outside the huts and itis 4% expanded relative to the Ni spacing. Thehomogeneous vertical translation of the wedges isdetermined to be 0.5 A_ and it is the same for allthicknesses. At film thicknesses around 20 ML thelateral lattice spacing in the huts approaches that ofthe Ni lattice and this type of cluster formationbecomes ineffective in relaxing the strain energy. Atthe same time the wedges begin to merge and thegrowth pattern changes.

It was observed in the data analysis that thepositions of the side peaks from the M1 1 1N facetsdo not follow closely the straight lines given by theCTRs of M1 1 1N surfaces, but instead the fittedmidpoints follow lines not going through the Braggpoints. This behaviour was duplicated nicely in thecalculation for the model cluster and is due to thefinite size of the clusters [17].

4. Conclusions

We have proved that surface X-ray diffraction incombination with STM is an effective technique formeasuring the internal structure of hut clusters.The regular shape of these clusters allows the scat-tering from the huts to be distinguished from that ofthe substrate and coexisting adsorbed films by fo-cussing on the scattering from the CTR from thesloping facets. The intensity of this scattering issensitively dependent on small deviations in thepositions of the atoms in the clusters from theextrapolated substrate lattice and is thereforea good measure of non-uniform strains. The smallsize of the clusters makes it simple to compare thescattering with that from model clusters. A naturalextension of the present analysis would be to calcu-late the shape of the clusters by applying elasticitytheory or for the semiconductors the Keatingmodel [18], and comparing the calculated diffrac-tion signal with the measured X-ray data. Suchan analysis would allow a more detailed descrip-tion of the huts including parameters not discussedin this paper such as substrate deformation, be-nding of the atomic layers, or nonuniformity withinindividual layers, and altogether further improve

M. Nielsen et al. / Physica B 248 (1998) 1—8 7

our understanding of the mechanisms controllingtheir growth.

Acknowledgements

This work was supported by the Danish Nation-al Science Foundation through DanSync and bythe German Bundesministerium fur Bildung, Wis-senschaft, Forschung und Technologie (BMBF) un-der project no. 05 622GUA1.

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