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the lattice mismatch, the size of the nanocrystal,      continuously rotated around the [OOl] axis at 0.2
and the chemical...
60                                    F. Tuinstra et al. /Surface   Science 317 (1994) 58-64

grown onto it. In addition ...
F. Tuinstra et al. /Surface   Science 317 (I 994) 58-64                                       61

them after transformati...
62                                      F. Tuinstra et al. /Surface   Science 317 (1994) 58-64

AC, is the anisotropy con...
F. Tu~~r~ ei al. /Surface Science 317 (1994) 58-64                            63

that only those atoms dimerize that hav...
64                                F. Tuinstra et al. /Surface   Science 317 (1994) 58-64

entations along the [lOO] and [...
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1994 the influence of dimerization on the stability of ge hutclusters on si(001)


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1994 the influence of dimerization on the stability of ge hutclusters on si(001)

  1. 1. :(.:I> ,... ..:. :: :.. :j. ..:.:.., . . . . . . . :.: . . . . .:.,., ,.. ,... ,:: ,~:::i:i’,:i~:.:::c’..... ” .,.. ” ” .,. : . ..., ‘.... :..,y:. “. surface science i :.,.... ,. . .....>....:),,., .......j “‘-‘.‘i>:... ....:_,j,:. ~ ,:..:,,.. ,.:.:i .:.x,,:,:.,.:.:, :) ~ :.:,; ..: ,,,. ,,:,.,:,,: ““.:‘.“::::.‘:::.::.:::jj ELSEVIER Surface Science 317 (1994) 58-64 The influence of dimerization on the stability of Ge-hutclusters on Si( 001) F. Tuinstra, P.M.L.O. Scholte *, W.I. Rijnders, A.J. van den Berg Department of Applied Physics, Solid State Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands Received 16 June 1993; accepted for publication 16 May 1994 Abstract The epitaxial growth of Ge on Si(OO1)initially proceeds two-dimensional. After a few monolayers, a large number of three-dimensional Ge nanocrystals are formed with well defined, highly anisotropic shapes and bounded by (105) facets. These facets are unstable in the morphology of macroscopic crystals. Apparently a different set of parameters governs the crystal stability, size, shape and orientation of nanocrystals. By applying elastic continuum theory we calculate the stability of Ge nanocrystals on Si(OOl), bounded by different facets. We show that (105)-faceted nanocrystals are indeed the most stable. The model identifies some of the principal parameters which control the stability of nanocrystals: the strain due to the lattice mismatch between substrate and nanocrystal, the size of the nanocrystal, and the surface energy (or the reconstruction) of the substrate and of the facets of the nanocrystal. 1. Introduction with well defined, highly anisotropic shapes (aspect ratios up to 1: 81, and bounded by (105) With the introduction of the scanning tunnel- facets. Upon annealing above 800 K, the hutclus- ing microscopy @TM) in the field of crystal ters are replaced by much larger crystals with growth, the initial stages of nucleation and mor- (113) facets; the {105} facets having disappeared phology of nanocrystals have become accessible [3]. The appearance of (10.5) facets is surprising to experimental investigation [1,2]. During the since according to the morphology of macro- epitaxial growth of Ge on Si(OO1) nanocrystals scopic crystals, 1105) facets are not stable. At the emerge with a morphology that is unexplained by same time the appearance of {113} facets after the morphology of macroscopic crystals 13-51. annealing is understood by macroscopic morphol- The epitaxial growth of Ge on Si(OO1) initially ogy 161. proceeds two-dimensional. After a few monolay- Apparently a different set of parameters gov- ers, a large number of three-dimensional Ge erns the stability, size, shape and orientation of nanocrystals (the so-called hutclusters) are formed nanocrystals. The object of this paper is to present a model for the morphology of the hutclusters, that identi- * Corresponding author. Fax: +31 15 783251. E-mail: fies some of the principal parameters which con- trol the stability of nanocrystals: the strain due to 0039-6028/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZ 0039-6028(94)00315-Z
  2. 2. the lattice mismatch, the size of the nanocrystal, continuously rotated around the [OOl] axis at 0.2 and the chemical surface energy of the substrate revolutions/s. RHEED images were taken at an and of the nanocrystal. acceleration voltage of 10 kV and an angle of By applying elastic continuum theory we calcu- incidence of 2.1& 0.2”. A CCD-camera was read late the stability of the Ge nan~~stals on SKOOl), out about one hundred times per sample-revolu- bounded by different facets. We show that {lOS}- tion with a video frame-grabber. The stored faceted nanocrystals are indeed the most stable. RHEED patterns were combined by a computer Recent work of Tromp and Tersoff corroborates program into a single pattern which has the same our model by identifying the size and strain as the features as a pattern obtained by low energy parameters that determine the shape of Ag clus- electron diffraction (LEED). The resulting dia- ters on Si@Ol) 171. gram displays the projected intensity of the This paper consists of two sections. In the first diffraction rods onto the U&O) plane in recipro- section of the paper a modified RHEED (reflec- cal space. tion high energy electron diffraction) technique is To illustrate the feasibility of the method, the introduced. We have used this technique to es- result for a clean Si(OO1)surface is shown in Fig. tablish the presence of hutclusters during the 1. The horizontal and vertical directions in this growth of Ge on Si, under the circ~stances as figure coincide with the [llO] and [liO] directions, described by MO et al. [3]. The principal advan- respectively. Clearly the diffraction pattern of the tage of this technique is that it gives a projection 2 X 1 reconstructed surface can be discerned. The of the reciprocal space along all azimuthal direc- splitting of some spots in Fig. 1 is an artefact of tions, while conventional RHEED uses one az- the method and is due to irregularities in the imuthal direction only. rotation speed of the sample during the recording In the main part of the paper a theoretical of the RHEED images. model for the morphology of hutclusters is pre- In Fig. 2a the transformed RHEED pattern is sented. First we will consider the respective con- shown of a Si(OO1)surface with 9 monolayers Ge tributions from the bulk and the surface to the total energy of a hutcluster separately. In the final section we will discuss how the corrobora- tive effect of all contributions stabilizes clusters bounded by (105) facets. 2. Experimental observation of the hutclusters The observation with STM of the evolution of the morphology during molecular beam epitaxy (MBE) growth, seems as yet beyond reach. Yet, diffraction techniques like RHEED and GIXD (grazing incidence X-ray diffraction) can be em- ployed without much interference with the depo- sition process. In particular the low incidence of the beam favors substantially the diffracted inten- sity of protrusions on the substrate, over the contribution of the smooth crystalline substrate. To observe the appearance of the hutclusters, RHEED diagrams have been recorded during the Fig. 1. Generated “LEED image” of clean Si(OO1) surface. deposition of Ge on Si(tOl) at 460°C. The deposi- The image has been constructed from approximately 60 tion rate was set at 1 A/s, and the sample was RHEED images.
  3. 3. 60 F. Tuinstra et al. /Surface Science 317 (1994) 58-64 grown onto it. In addition to the well pronounced function of the hutclusters appears as broad fea- spots of the Ge bulk structure and those of the tures. 2 x 1 surface reconstruction, a raster of weak Therefore the continuous and narrow appear- lines along the [lOO] and [OlO] direction is ob- ance of the lines in Fig. 2a can be attributed to served (Fig. 2b). protruding structures which have a large exten- The streaky radial pattern in the background sion in the [loo] and small dimension in the [OlO] of Fig. 2 is due to fluctuations of the background direction, and the other way around. According intensity of the RHEED patterns. In general to the diffraction pattern the ratio between length artefacts in the transformed image have a radial and width of these nanostructures is at least 100; nature due to the fact that the sample is rotated the width cannot be more than a few atomic around an axis perpendicular to the image. This distances. MO and Lagally observed an aspect is corroborated by computer simulations in which ratio of up to 1: 8. Due to the finite penetration we calculated the effect of experimental errors on depth of the RHEED electrons in Ge, the elec- the transformed image, such as wobbling of the trons skim only the tops of the protruding hut- wafer during the rotation and a non-constant clusters. Consequently the aspect ratio observed rotation speed. We conclude that the weak lines with RHEED is much larger than that observed in Fig. 2b, originate from a surface effect and with STM. cannot be attributed to an artefact of the trans- Also, the projection along the [OOl] direction formation method. that is used to transform the RHEED images In the kinematic approximation, the diffrac- gives an overestimation of the aspect ratio, since tion spots from the crystalline structure of the diffraction rods from the vicinal surfaces that nanocrystals are convoluted with the Fourier bound the hutcluster are not parallel to [OOll. transform of their shape. The transform of a long The weak lines appear in the transformed pat- narrow form is a thin flat slab, the normal of tern after growth of 6 monolayers of Ge. MO and which is parallel to the long dimension of the Lagally report the hutclusters to nucleate after crystallite. Thus in reciprocal space the shape 3-4 monolayers [3]. In order to be able to observe - [l -1 OJ Fig. 2. (a) “LEED image” of 9 monolayers Ge on Si(oO1) constructed from 100 RHEED images. (b) Schematic clarification of Fig. 2a, showing the diffraction spots from the crystalline surface and the lines due to the appearance of the hutclusters.
  4. 4. F. Tuinstra et al. /Surface Science 317 (I 994) 58-64 61 them after transformation of the RHEED im- of Ge on a Si substrate (Fig. 3). The strip is ages, enough hutclusters have to be present. bounded in the y- and the z-direction, respec- Therefore the appearance of the weak lines after tively parallel and perpendicular to the substrate. 6 monolayers corresponds very well with the ap- The complete strain tensor can be deduced pearance of the hutclusters as reported by MO straightforwardly from the symmetry of the Ge and Lagally. strip. The misfit of the epitaxial Ge adlayer intro- Aumann et al. have calculated the RHEED duces a compressive strain E of 4.2% at the pattern for hutclusters with a fixed azimuth of the interface between substrate and adlayer. At the incident beam along the [lOO] and [llO] directions Si-Ge interface the strain is uniaxial because of [8]. In our experiment we find the same patterns, the equivalence of the [RIO] principal axes. Along if we fix the azimuth of the incident beam. There- the long axis the strain cannot relax, since the fore we conclude that the raster of weak lines in strip is thought to be (infinitely) long. In the Fig. 2b, is due to the appearance of the hutclus- y-direction, however, a gradual elastic relaxation ters. over the height of the strip is possible. As a consequence the strain is anisotropic in the bulk of the cluster. Since the strip can freely expand 3. The morphology of hutclusters along the [OOll direction, the stress along the z-direction is zero. The morphology of a hutcluster is character- From these considerations we find up to first ized by a high aspect ratio and the orientation order in the strain E at the interface: along the [loo] and [OlO] directions. In the next sections a hutcluster is modelled by a long, nar- C,* &i =E, ,,=e;, Es= -$&i+E*), row cluster bounded by 4 facets. A Cartesian 11 coordinate system is attached to the cluster with Y the x-axis parallel to the long axis of the cluster, h the y-axis parallel to the short axis, and the z-axis where h is the height of the strip, and Cij are the perpendicular to the substrate (see Fig. 3). The elastic stiffness constants with respect to the sym- facets bounding the long ends of the cluster are metry axes xyz of the strip. Now the elastic taken to be parallel to the y-z plane, the other energy can be calculated straightforwardly: two facets are parallel to the x-direction. The azimuthal orientation of the hutcluster is given by E=/ dV $ ~C;E~&~ - AC,[ ( e1 - Q)’ Cluster id the angle 4 between the x-axis and the [lo01 direction of the substrate. We assume the hutcluster to be coherent with I -&6” cos2+sin24 i . the substrate for all azimuthal orientations, i.e. for all values of 4. This means that the principal axes of the crystallographic structure of the hut- cluster may not be parallel to the xyz-axes that describe the symmetry of the morphology. To calculate the total energy of a hutcluster, the energy is split into a term related to the bulk of the cluster, and a term related to the surface of the cluster. We will consider both contribu- tions separately in the next sections. 3.1. Elastic misfit energy Fig. 3. Infinitely long Ge strip on a Si substrate. The strip is The first stage in the nucleation of a hutcluster stressed at the interface with the Si substrate and relaxed at can be approximated by an (infinitely) long strip the top.
  5. 5. 62 F. Tuinstra et al. /Surface Science 317 (1994) 58-64 AC, is the anisotropy constant of the elastic (001) terraces, separated by equivalent monos- tensor of rank 4. For Ge we find [9]: teps. In a similar fashion it is also possible to construct the competing {lln} facets from (001) AC, = Cfi - CfZ - 2C& = - 53.2 GPa. terraces. In this case the terraces are separated Ct. are the (tabulated) elastic stiffness constants by monosteps and double steps. For the {lln} of Ge with respect to its principal axes. Since the facets the monosteps are inequivalent, since they Ge cluster is assumed to be coherent with the are alternatingly parallel and perpendicular to substrate, the symmetry axes of the Si coincide the dimer rows of the (001) terrace. The steps with the crystallographic principal axes of the and terraces on the (10n) vicinal facets on the cluster. contrary, are all equivalent; all of them are mak- The first term in the elastic energy is indepen- ing angles of 45” with the dimer rows on (001). dent of the azimuthal orientation of the Ge strip The atoms on the (001) terraces try to mini- on the Si substrate. The second term, however, mize the number of unsaturated dangling bonds. does depend on &Jand is minimal if 4 = 0, i.e. if One way to do that is by the formation of dimers. the strip is oriented along the principal axis of the Roberts and Needs have calculated the energy Si substrate and maximal if the strip is oriented gain due to the 2 x 1 reconstruction of SXOOZ)to along the Ill01 or [liOl direction. be approximately 2.08 eV per asymmetric dimer bond [lo]. This value compares reasonably well 3.2. Chemical surface energy with the strength of a single covalent Si-Si bond: 1.8 eV. Therefore we estimate the lowering of the The second contribution to the internal energy chemical surface energy by the Ge-dimer bonds that is considered, is the chemical surface energy to be approximately equal to the strength of a of the (10n) and (lln} facets. Ge-Ge bond in bulk Ge: 1.6 eV. {lOn} and {lln) facets can be considered as The chemical surface energy is calculated by vicinal (001) planes, especially if IZ is not too counting the number of dangling bonds that are small. In Fig. 4 this is illustrated for a (104) and a left, making sure that if possible the dimers are (1051 plane. It can be seen that they consist out of formed on the terraces. (See Fig. 4.) It is assumed (1051 {lo41 Fig. 4. Side view and top view of (104) and (105) vicinal planes. Possible dimers are indicated by connecting the atoms. The height of the atoms is indicated by their color: the lighter the atom, the deeper it lays.
  6. 6. F. Tu~~r~ ei al. /Surface Science 317 (1994) 58-64 63 that only those atoms dimerize that have at least surface energy of the SK000 interface that is two dangling bonds. In doing so we neglect re- covered by the cluster. bonding at the bottom of steps. Rebonding com- In Fig. 5 the excess surface energy is shown of pensates a number of dangling bonds that could a 100 nm long cluster of 10’ atoms. The cluster is not be removed by the dinner reconstruction of bounded by {10nf or {lln) facets, that make an the facets. But the bonds at the rebonded steps angle fi with the substrate. Generally a hutclus- are highly strained and therefore rather weak. ter is much longer than it is wide. Therefore in Chadi calculated the energy gain due to rebond- the calculation the contribution from the small ing to be 0.16 eV/bond [ll]. Although this can- facets at the end of the long axis has been ne- not be neglected compared to the energy of a glected. In Fig. 5 the excess surface energy has dangling bond (- 0.8 eV1, the only effect is that been normalized on the total number of atoms in the differences in surface energy of different the cluster. The figure shows a remarkable peri- facets are smoothened somewhat. odicity, due to the interference of the dimeriza- Depending on the width of a terrace, not all tion and the terrace structure of the facets. The atoms can dimerize, as is illustrated by the (104) periodic&y of n = 4 of the {lOn) line is related to plane in Fig. 4. In the case of the {lo51 facet an the atomic arrangement in the diamond struc- efficient dimer reconstruction is possible, leaving ture, the basis of which consists of two atoms, one only 1 dangling bond per atom on each terrace. shifted over (0.25, 0.25, 0.25) with respect to the On the {104} facet atoms are left with 2 dangling other. bonds, making the surface energy of this facet slightly higher than of (1051. To be able to quantify the effect of the mor- 4. discussion and conclusion phology on the surface energy of a cluster, an excess surface energy has been defined. The ex- As a Ge adlayer grows on the Si(OO1) sub- cess surface energy is calculated by subtracting strate, the elastic misfit energy stored in the from the total surface energy of a cluster, the adlayer increases. The adlayer may release this elastic energy partly by developing steps. Conse- quently if the elastic energy raises above a certain level, the layer starts to facet. This facetting in- creases the surface area, and consequently the total chemical surface energy increases. The layer finds an optimum by developing a facet that is as steep as possible, i.e. with as many steps as possi- ble, while at the same time has a lowest possible chemical surface energy. From Fig. 4 it can be seen that both (105) and {113) fulfil these criteria. a The azimuthal orientation of the hutcluster is determined by the elastic contributions to the total energy of the cluster. Tersoff and Tromp showed that highly anisotropic Ag islands are stabilized by the stress induced by the lattice mismatch between Ag and Si. By the same effect 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 a highly anisotropic Ge island will nucleate dur- aa ing the first stages of epitaxial growth of Ge on Fig. 5. Excess surface energy of a 100 nm long cluster of 10’ Si(OO1). If we consider the elastic energy that is atoms versus the angle B of the facets with the substrate. The stored in the bulk of a long Ge strip, we find that total energy has been divided by the number of atoms. Solid squares represent the clusters with {lOn} facets (tg 6 = l/n), it is oriented along the principal axes of the Si open squares the clusters with {lln) facets (tg 9 = .,‘2/n). substrate. The energy difference between the ori-
  7. 7. 64 F. Tuinstra et al. /Surface Science 317 (1994) 58-64 entations along the [lOO] and [llO] directions is been observed recently during the surfactant- approximately 1.0 meV/atom. Including the third mediated growth of Ge on Si(ll1) [12]. order term in the elastic energy raises the energy difference up to 1.4 meV/atom. Although this energy difference seems small, a 4 nm by 100 nm Acknowledgments Ge strip of 4 monolayers high contains lo4 atoms The authors gratefully acknowledge mr. K. already, making the energy difference between Werner and mr. 0. Schannen for the opportunity the two orientations 14 eV. to use the MBE system of the Delft Institute of We conclude that the elastic stress due to the Microelectronics and Submicron technology (DI- dimerization and the misfit favors the nucleation MES) for the RHEED experiments. of anisotropic islands along the principal axis of the Si substrate. When the growth proceeds, small crystals nucleate on top of the strips. The elastic References relaxation propagates to the growing nucleus, forcing it to be elongated along the strip. Adding [l] H. Neddermeyer, Crit. Rev. Solid State Mater. Sci. 16 (1990) 309. successively a few layers the islands start to de- [2] A.J. Hoeven, D. Dijkkamp, J.M. Lenssinck and E.J. van velop facets in order to allow further elastic re- Loenen, J. Vat. Sci. Technol. A 8 (1990) 3657. laxation. [3] Y.-W. MO, D.E. Savage, B.S. Swartzentruber and M.G. The trade-off between the step structure of Lagally, Phys. Rev. Lett. 65 (1990) 1020; the vicinal (10n) facets, and their dimer recon- Y.-W MO and M.G. Lagally, J. Ctyst. Growth 111 (1991) 876. struction stabilizes the (105) facets, because of [4] U. Kiihler, 0. Jusko, B. Miiller, M. Horn-von Hoegen the efficient removal of dangling bonds that is and M. Pook, Ultramicroscopy 42-44 (1992) 832. possible on these facets. [S] F. Iwawaki, M. Tomitori and 0. Nishikawa, Surf. Sci. 2.53 It must be stressed that this model proposes (1991) L411. that the strain in the hutcluster is relieved par- [6] J.G.E. Gardeniers, W.E.J.R. Maas, R.Z.C. van Meerten and L.J. Gihng, J. Cryst. Growth 96 (1989) 832. tially only. The strain at the base of the cluster 171 J. Tersoff and R.M. Tromp, Phys. Rev. Lett. 70 (1993) stabilizes the orientation of the long axis of the 2782. clusters, while the strain is relaxed elastically at [8] C.E. Aumann, Y.-W. MO and M.G. Lagally, Appl. Phys. the top of the clusters. If growth proceeds fur- Lett. 59 (1991) 1061. ther, the clusters starts to coalesce and they relax [9] Landolt and Barnstein, New Series Vol. III/11 (Springer, Berlin, 1979)~. 9. plastically by introducing dislocations at the inter- [lo] N. Roberts and R.J. Needs, Surf. Sci. 236 (1990) 112. face. The anisotropy in the elastic energy lessens [ll] D.J. Chadi, Phys. Rev. Lett. 59 (1987) 1691. and it becomes energetically favorable to form [12] M. Horn von Hoegen, M. Pook, A. Alfalou, B.H. Muller {113) facets. Plastic relaxation of Ge clusters has and M. Henzler, Surf. Sci. 284 (1993) 53.