VOLUME 77, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 2 SEPTEMBER1996

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Strain in Nanoscale Germanium Hut Clusters on Si(001) Studied by X-Ray Diffraction

A. J. Steinfort, P. M. L. O. Scholte, A. Ettema, and F. TuinstraDepartment of Applied Physics, Delft University of Technology,

P.O. Box 5046, NL-2600 G A Delft, The Netherlands

M. Nielsen, E. Landemark, D.-M. Smilgies, and R. Feidenhans’lRisø National Laboratory, DK-4000 Roskilde, Denmark

G. Falkenberg, L. Seehofer, and R. L. JohnsonII. Institut für Experimentalphysik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germa

(Received 28 May 1996)

Scanning tunneling microscopy and synchrotron x-ray diffraction have been used to investigatenanoscale Ge hut clusters on Sis001d. We have been able to identify the contributions to the scatteredx-ray intensity which arise solely from the hut clusters and have shown that x-ray diffraction can bevery sensitive to the strain field in the hut clusters. At the GeySi interface the Ge clusters are almostfully strained with a misfit of only 0.5% but towards the apex of the clusters the strain is relaxed and theatomic spacing is close to the natural Ge lattice spacing with a 4.2% misfit. [S0031-9007(96)01009-5]

PACS numbers: 68.35.Bs, 61.10.– i, 61.16.Ch, 68.55.Jk

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Electronic devices and many other technologies expthe properties of thin films of various materials with diffeent lattice constants deposited on top of each other.rently there is great interest in strained-layer superlattmade of III-V semiconductors for laser applications ain SiGe alloys because of their excellent high frequeperformance. The internal strain is a very importantrameter in these systems because it modifies the opand electronic properties of the materials. In this pawe address the problem of determining the strain inhut clusters grown on Sis001d substrates.

It is conventional to distinguish between three clacal growth modes: layer by layer growth (Frank–vanMerwe mode), 3D island growth (Volmer-Weber modand layer by layer followed by 3D island growth [StransKrastanov (SK) mode] [1]. These are simplified scenarand in practice the situation may be complicated by seffects as surface alloying and internal strain that canto nonplanar interfaces or interdiffusion. In heteroepitial growth misfit between the bulk lattice parametersthe substrate and the adlayer introduces strain in thterface, and pseudomorphic layers with misfit dislocatmay form. The surface morphology of films dependsboth the deposition temperature and the depositionsince the processes of nucleation and surface diffusiopend strongly on the temperature and crystallographicentation of the surface. The growth of smooth epitalayers usually takes place in the step flow mode at htemperatures, whereas 3D islands with a distributionsizes may form at lower temperatures [2–4]. Twoferent types of 3D islands can be formed in the SK moInitially, small regularly shaped dislocation-free islandsformed which are called hut clusters. At higher coveralarger islands form and strain relief occurs so the latparameter of the adlayer is closer to its bulk value.

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It is well established that the growth of Ge on Sis001dprogresses according to the following steps. For smcoverages up to 3 monolayer (ML) epitaxial growth ocurs—the layers are continuous and the surface has a2 3

N reconstruction (typically withN ­ 8 12) with missingdimer rows which allow some strain relaxation. As tgrowth continues the missing dimers are partially filleand if the temperature and deposition rate are chosenrectly then nanoscale hut clusters start to form. Eventuafter depositing the amount of Ge equivalent to a coverof about 6 ML most of the substrate surface is covered whut clusters. At higher coverages sometimes larger Glands are formed as described in Ref. [5]. It is importto note that the nanoscale clusters are metastable anformed only at growth temperatures below 530±C.

The name “hut cluster” was introduced by Moet al. [6]in the course of their scanning tunneling microsco(STM) investigations on the epitaxial growth of GeSis001d. The islands look like elongated huts all of similwidth, typically about 150 Å and with variable lengdepending on the deposition conditions. The extersurfaces are bounded byh105j facets, and at the interfacthe hut clusters are in registry with the Sis001d substrate;thus they are parallel to thek100l or the k010l directions.Two important characteristics of the hut clustersthe lack of dislocations at the interface and an eladeformation which partially relaxes the strain associawith the 4.2% misfit between the lattice parameters ofand Si [7].

The importance of hut clusters for the relaxation of strhas been studied by several authors [8–10]. Williaet al. [11] performed x-ray diffraction measurementsthe lattice parameters parallel to the substrate surfacewere able to distinguish a broad peak originating fromscattering from the sharp Si signal, and they concluded

© 1996 The American Physical Society 2009

VOLUME 77, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 2 SEPTEMBER1996

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the onset of strain relaxation coincided with the appearaof clusters. However, it is not clear to what extent tscattering they observed originated from the hut cluste

Scanning probe microscopy techniques have revealvast amount of information concerning thin film growand the shapes and size distributions of such islands [614]. However, it is difficult to determine the internatomic structure of the islands, the strain fields, andinterface structure of small islands. We report here wwe believe to be the first determination of the interstructure of hut clusters by combined STM and x-rdiffraction measurements. The strain distribution of smnanocrystals on a substrate, here Ge islands on Sis001d, hasbeen determined separately from the strain in the subsand in the layers between the islands. We find that thelayers are almost fully strained near the interface but reprogressively towards the apex of the hut clusters.

The samples were prepared in a UHV system with STreflection high energy electron diffraction (RHEED), loenergy electron diffraction (LEED), and controlled dposition facilities. The substrates were polished Sis001dwafers, cleaned by prolonged outgassing at 875 Klowed by flashing to 1425 K. STM measurements reveaclean well-ordered surfaces, and the step distribution icated that the miscut angle of the wafers was less than±.Germanium was evaporated from an effusion cell adeposition rate of about 0.6 MLymin. Different substratetemperatures were tried to optimize the growth of theclusters and the best results were obtained with a substemperature of 430±C. After deposition and allowing tocool to room temperature the sample was inspectedLEED and STM for the presence of hut clusters andabsence of macroclusters which have characteristich113jfacets. In the LEED pattern the hut clusters give riseextra reflections in thef100g bulk direction [15]. Figure 1shows a representative STM image from a sample prepby depositing the equivalent of 6 ML Ge at a substrate teperature of 430±C. The average height of the hut clusteis only 13 Å. After preparation and characterization welectron diffraction and STM the samples were transferunder ultrahigh vacuum to a small chamber with a he

FIG. 1. STM image with dimensions of2200 3 2200 Å ofa sample prepared by depositing 6 ML Ge on Sis001d at atemperature of 430±C.

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spherical Be window, which was mounted on the diffratometer for the x-ray measurements with synchrotradiation.

The x-ray measurements were performed on the vertscattering diffractometer at the BW2 wiggler beam lineHASYLAB (DESY Hamburg). The photon energy wa9.4 keV and slits limited the width of incident and scatterbeams to 1 and 1.5 mm, respectively, thus definingeffective diffracting area on the sample. The angle of gring incidence was kept constant and equal to the critangle of total external reflection for Si (0.2±). We use thecoordinate notation of the bulk Si crystal with thes001ddirection perpendicular to the sample surface. Scans wperformed parallel to the surface by varying eitherh ork, keeping the momentum transfer perpendicular tosurfacel constant. An extensive data set including sevesymmetry equivalent reflections was measured.

Figure 2 shows some representative examples ohscans through the crystal truncation rods (CTR) whichthrough thes111d, s202d, ands400d bulk Bragg points (theexperimental data points are indicated by open circleIn addition to the central peak, side peaks are obserwhich run alongh105j directions and have an asymmetcal intensity distribution around the central peak. Theside peaks originate from theh105j facets of the hut clus-ters. As will be shown below the strain distributionthe hut clusters can be deduced from the analysis of thprofiles.

The central peak in the measured scans is due tocrystal truncation rod arising from all of thes001d inter-faces and includes contributions from the surface ofGe layers between the huts and both the buried interfabeneath the huts and below the Ge layer in the areatween the huts. The STM images show that the2 3 Nreconstructed Ge layers between the hut clusters is rarough. There will be interference effects between the mtiple contributions from the variouss001d interfaces whichdepend on the detailed atomic geometry. Hence, thetral peak cannot be modeled readily and is excluded frthe data analysis. On the other hand, the intensities ofrods in thek105l directions are due solely to the hut clusteand by measuring them we can distinguish uniquelyscattering from the atoms in the hut clusters from all otcontributions. It should be noted that despite the graziincidence geometry the dimensions of the hut clusterssmall compared to the penetration depth of the x raysthe extinction length so it is permissible to apply kinemascattering theory.

In the model calculations we included contributiofrom all of the atoms in the hut clusters to determithe diffracted intensity. As a starting point we assumthat the hut cluster is laterally completely strained athus all the Ge atoms in the hut clusters are at in-plSi lattice sites. This model predicts theh105j rods, butthe asymmetric intensity distribution is not reproducas shown in Fig. 3(a). To account for the 4.2% mis

VOLUME 77, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 2 SEPTEMBER1996

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FIG. 2. Calculated and measured x-ray diffraction profiles arounds1 1 ld, s2 0 ld, and s4 0 ld. The circles represent thexperimental data points, and the solid lines are the calculated profiles using the model described in the text whichthe inhomogeneous strain field in the hut cluster.

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between the Ge and Si lattices we have to introduce strelaxation. As a first approximation we assume thatclusters are long and narrow and set the lattice paramin the direction along the long side of the hut clustto be equal to the Si lattice constant. Along the shside we allow the in-plane Ge lattice parameterayszdto expand laterally with a power-law dependence asfunction of heightz above the interface. We have triedifferent functional forms and have found that a quadradependence ofayszd gives the best fit to the experimentadata. The height variation of the lattice constant is givby

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whereh is the height of the hut cluster,atop and abottom

are the lateral lattice parameters at the top and botof the cluster. One expectsabottom to be close to the Silattice parameter and thatatop will tend towards the lat-tice parameter of bulk Ge. The vertical lattice paramters are calculated using the Poisson ratio (n ­ 0.277).As indicated schematically in Fig. 3 this strain profiallows the clusters to relax from a maximum strain nethe substrate to a minimum at the apex of the cluster. Tlower part of Fig. 3 indicates the effect of strain on thcalculated structure factors, and it can be seen that thehomogeneous strain produces an asymmetrical intendistribution. The effects are particularly pronounced flarge momentum transfer, so we have measured out aass5 0 ld. Although the model given above to describe tstrain profile is clear and plausible, it certainly represean oversimplification since it neglects a number of aspeThe strain field in the Si substrate, the bowing distortiof the Ge lattice planes, and the reconstruction of the s

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faces were not included in the model; such consideratigo beyond the scope of the present investigation [16].

The size distribution of the hut clusters is an esstial input parameter for the model calculations. From tSTM images of the samples investigated by x-ray diffration the average length of the clusters was determinebe 300 Å and the average width 130 Å with a surface cerage of 70%. By combining the information from STand x-ray diffraction a satisfactory fit to the measured dcould be obtained by varying only the in-plane lattice prametersabottom, atop, and a scale factor. Figure 2 showthe comparison between the experimental and calcul

FIG. 3. Schematic diagram illustrating the models of tstrained hut clusters. The upper part shows cross sectionclusters with and without inhomogeneous strain; the midsection shows the variation of the lattice parameterayszd asfunction of the heightz above the interface. At the bottom thcorresponding calculated structure factors forh scans throughthe s4 0 0.5d reciprocal lattice point are shown.

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VOLUME 77, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 2 SEPTEMBER1996

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h scans. The open circles indicate the measured proand the solid lines the profiles calculated using the stfield in the hut cluster given by the fit procedure. Frothe model calculations we find the onset relaxation atbottom of the hut cluster is 0.5% and the maximum strrelaxation at the apex of the cluster is 4.2%. This methat the strain is relaxed uniformly through the hut clusand that no dislocations are formed.

In conclusion, we have determined the strain field inssmall Ge hut clusters on Sis001d by performing model cal-culations using kinematic theory to simulate the measux-ray diffraction profiles. We find that the strain candescribed by a continuous relaxation from the almost fustrained Ge-Si interface towards the unstrained Ge atat the apex of the hut clusters. We have shown that Scombined with synchrotron x-ray diffraction is a sensititechnique for determining the nonuniform strain and thais possible to distinguish uniquely the scattering fromhut cluster atoms from all other contributions.

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