Substrate-step-induced effects on the growth of CaF2 on Si (111)

158[111](a)(a)Si[112]D S T(b)[ 110]Si[112][ 110](b)[11 2]250nmFig. 3a,b. Model for a CaF island with B orientation grown at a Si substrate<strong>step</strong>. The Si substrate has miscut towards the [11¯2] direction. a Side view;b top viewterrace width w[nm]5002001005020crit. temperature T c [ 0 C]600 550 500 450<strong>step</strong>nucleation(<strong>step</strong> flow)terracenucleation1.1 1.2 1.3 1.4inv. crit. temperature 1000/T c [1/K]Fig. 4. Kinetic “phase diagram” of terrace and <strong>step</strong> nucleation. From theslope of the solid line and (1) a diffusion barrier at E D = 1.8 eV is proposedfor the diffusion of CaF on Si (111)shows the kinetic “phase diagram” we obtain from ourstudies. The larger the terrace size the larger the criticaltemperature to obtain pure <strong>step</strong> nucleation and subsequentgrowth in the <strong>step</strong>-flow growth mode. Obviously, the dependenceof w on the critical temperature, T c , exhibits anArrhenius behaviour (solid line in Fig. 4). From theoreticalconsiderations,w ∝ exp(−E D /2k B T c ). (1)(c)Fig. 5a,b. STM micrograph for the growth of CaF islands after depositionof 0.3-TL CaF 2 at 600 ◦ C. a Overview demonstrating the nucleation andgrowth of islands on defect-free terraces (T), at <strong>step</strong>s (S) and at anti-phasedomain boundaries (D). No individual island are at <strong>step</strong>s due to the progressivecoalescence. b Enlarged micrograph of the rectangular area in ademonstrating the material contrast between Si substrate and CaF decoratingthe Si substrate <strong>step</strong>. c Height profile of the line scan marked in b.CaF island heights are apparently higher than the Si <strong>step</strong>s due to materialcontrast.is predicted [41, 52, 53]. Here E D and k B denote the diffusionbarrier for the CaF molecule on the Si (111) surface andthe Boltzmann constant, respectively. Fitting the experimentalresults to (1), a diffusion energy of E D = 1.8 ± 0.2eV isobtained (solid line in Fig. 4). This value agrees very wellwith the diffusion barrier obtained from analysing the homogeneousnucleation on the defect-free terraces [53].After deposition of 0.3-TL CaF 2 the CaF film leaves thenucleation stage and enters the island growth stage. Duringthis stage the CaF islands are growing and the coalescenceof the island starts. For deposition at 600 ◦ C, this is demonstratedin Fig. 5. Here, the islands which are heterogeneouslynucleated at <strong>step</strong>s or at anti-phase boundaries form long CaFstripes.Figure 5b presents a closer inspection of the film close toa Si substrate <strong>step</strong>. One can distinguish easily Si and CaF dueto the electronic material contrast involved in the tunnelingcurrent used to record STM micrographs (cf. Fig. 5c).

Furthermore, Fig. 5b demonstrates that the growth oftype-D islands is stopped at the Si substrate <strong>step</strong>. The type-DCaF stripe is only on top of the upper Si terrace; no materialis on top of the type-S CaF stripe on the lower terracerunning perpendicular to the type-D stripe. This effect is observedalso for type-T islands (Fig. 5a). Therefore, it can beconcluded that Si substrate <strong>step</strong>s act as growth barriers. Thiswill be discussed in more detail below.(a)1593 Initial stages of growth on the CaF interface layerFigure 6 presents an STM micrograph of a 1.7-TL CaF 2 filmdeposited at 600 ◦ C on a Si substrate with very short terraces.The surface exhibits <strong>step</strong>s of both mono-atomic and bi-atomicheights.Clearly, one can distinguish two different kinds of terraces.On the one hand, type-R terraces are covered by“rough” films with many point defects. On the other hand,type-S terraces are extremely smooth and defect free. By investigatingvarious deposition amounts, it is clear that type-Rand type-S terraces are covered by the CaF interface layer andCaF 2 films, respectively.Point defects in CaF islands have been reported previously[33]. They are attributed to the ejection of Si atomsfrom the 7 × 7 reconstructed surface due to the transformationof the 1×1 Si interface layer underneath the CaF island.These Si atoms are incorporated into the CaF layer. For theadditionally deposited CaF 2 molecules diffusing on the interfacelayer, however, these defects do not act as strong bindingcenters since no nucleation occurs at these sites. At least thenucleation process is strongly suppressed, since there are noislands observed in the STM micrograph.Figure 7a presents a UHV–AFM micrograph recorded insitu after growth of 1.4-TL CaF 2 at 750 ◦ C. Obviously, thefilm covers the entire Si substrate and generally mimics theregularly <strong>step</strong>ped substrate structure.The normal force on the AFM cantilever was used torecord the film topography. Lateral forces are recorded sim-500nm(b)(c)RSFig. 7. a AFM micrograph obtained after deposition of 1.4-TL CaF 2 at750 ◦ C. The film covers entirely Si substrate terraces. In addition, very fewtriangular protrusions are observed. b Friction force micrograph of the areamarked in a. The friction contrast is used to distinguish CaF (strong frictionsignal, light colored terraces) andCaF 2 layers grown on top of the CaF interfacelayer (small friction signal, dark colored terraces). c Lateral frictionforce obtained from the line scan marked in b50nmRRFig. 6. STM micrograph obtained after deposition of 1.7-TL CaF 2 at600 ◦ C. The arrows indicate double <strong>step</strong>s. The residual <strong>step</strong>s are monoatomic.Two types of terraces can be distinguished: R – terraces coveredwith a rough CaF layer; S – smooth terraces covered with a CaF 2 film. TheCaF 2 film is grown with double layer thickness on top of the CaF interfacelayerultaneously. Figure 7b shows the lateral force for the areamarked by the white rectangle in Fig. 7a. Since, duringrecording, the normal force was kept constant by a feedbackloop, the contrast due to the lateral forces is caused by differentfriction forces between probe and film. The stronglypronounced signal (white lines) originates from the <strong>step</strong>s. Inaddition, there is a clear contrast between different terraces.Terraces with an exposed CaF interface layer have a largerfriction signal than terraces covered with CaF 2 multilayers[34]. At the moment it is not clear whether the increasedfriction is due to the <strong>induced</strong> dipole forces between the cantilevertip and the CaF interface layer or due to topological<strong>effects</strong>, e.g. the defects observed by STM (Fig. 6) which cannotbe observed by AFM due to its limited lateral resolution.

160As emphasized previously, no free-standing islands areobserved in either experiment. Therefore, it seems that theentire film grows in the <strong>step</strong>-flow growth mode. As shownabove, this growth mode is expected for the CaF interfacelayer for the terrace size of the Si substrate used here. For theCaF 2 layer, however, this cannot be true, since only very fewof the terraces are type-S terraces. Thus the CaF 2 does notform nuclei at every <strong>step</strong>. Consequently, the additional CaF 2double layer does not grow in the <strong>step</strong>-flow growth mode.This effect of very inhomogeneous CaF 2 multilayergrowth can be attributed to the B orientation of the CaF 2 film.After deposition of the CaF interface layer, the <strong>step</strong>s are nolonger preferential nucleation sites. For instance, at monoatomicSi substrate <strong>step</strong>s, additional CaF 2 molecules cannotbind strongly to the CaF molecules on the upper terrace, since(a)(b)(c)a filma <strong>step</strong>MM CaF[111]top Fbottom F[111][112][ 110]Si[112]M si[112]Fig. 8a–c. Models of second-layer CaF 2 molecules with B orientation adjacentto Si substrate <strong>step</strong>s. a Comparison of the bond length in [11¯2]direction for the binding at <strong>step</strong>s a <strong>step</strong> and within films projected a film formono-atomic <strong>step</strong>s. b Triangular B-oriented CaF 2 island in front of a CaFcovered mono-atomic <strong>step</strong>. c Comparison of the binding at double height<strong>step</strong>s for binding to the CaF film (M CaF ) and binding to the Si <strong>step</strong> (M Si )the lateral distance between the CaF 2 molecule on the regularsite on the lower terrace and the CaF molecule on the upperterrace is √ 7/3 of the regular bond length. The binding distanceis too large to have significant interaction between thetwo molecules.The same effect occurs also for multiple substrate <strong>step</strong>s,as demonstrated by Fig. 8b for a Si double <strong>step</strong>. The additionalCaF 2 molecule cannot be simultaneously on a regularsite with respect to the CaF monolayer (M CaF ) or with respectto the Si <strong>step</strong> atoms (M Si ).4 Film growthIn the preceding sections, it was established that the CaFinterface layer can grow in the <strong>step</strong>-flow growth mode at sufficientlyhigh temperatures (dependent on the terrace width).This mechanism does not work for the subsequent CaF 2 (double)layers, as will be demonstrated in this section.Figure 9 shows UHV–AFM micrographs recorded forCaF 2 films of various thicknesses deposited at 750 ◦ C. Duringthe first stages of film growth, the topography is governedby terrace-<strong>step</strong> structures <strong>induced</strong> by the Si substrate. In addition,however, one observes some triangular protrusions.They grow with increasing coverage and overgrow substrate<strong>step</strong>s.As reported in the previous section, the AFM topographysignal is not sensitive to different species of the CaF 2film, namely the CaF interface layer and the CaF 2 multilayergrown on top of the interface layer. Therefore, in addition, thefriction force signal is used to distinguish between the twospecies. Generally, all terraces are covered exclusively eitherby the CaF interface wetting layer or by thick CaF 2 ‘islands’.Thus, here, ‘islands’ denote CaF 2 stripes whose boundariesfollow substrate <strong>step</strong>s. The confining mechanism will be discussedbelow.Figure 10a shows the analysis of the friction force micrographsrecorded from CaF 2 films deposited at 500 and750 ◦ C. For the high-temperature deposition large parts of theinterface layer are exposed even after deposition of very thickfilms. For deposition at 500 ◦ C, the exposed interface layervanishes much faster with increasing film thickness. Practically,the interface layer is overgrown after deposition of10-TL CaF 2 .Combining both the deposited CaF 2 coverage and the exposedCaF interface coverage, one can estimate the averageheight, t, oftheCaF 2 ‘islands’. The result is presented inFig. 10b. The dashed line shows the height expected for perfectlayer-by-layer growth. On the one hand, the film grownat 500 ◦ C approaches this growth mode after deposition of10-TL CaF 2 , confirming the growth of a closed film for thiscoverage. On the other hand, the CaF 2 ‘islands’ grown at750 ◦ C are always thicker. Thus, CaF 2 grows in the Stranski–Krastanov growth mode at these high temperatures, and thelateral growth is strongly suppressed perpendicular to the<strong>step</strong>s.In the previous section, it was emphasized that substrate<strong>step</strong>s are not preferential nucleation sites for growth on topof the CaF interface layer. In addition, it is obvious from themorphology studies presented in this section that CaF 2 hasdifficulty in overgrowing the substrate <strong>step</strong>s (except for thetriangular protrusions). Again, the B orientation of the CaF 2

500nm(a)161(b)CaF 2CaFSi(111)tFig. 10. a Exposed CaF interface coverage as obtained from friction forcemicrographs. The interface layer is overgrown more difficultly at higher depositiontemperatures. b Average thickness of the CaF 2 islands obtainedfrom a and assuming that the CaF interface layer completely wets the Sisubstrate(c)Fig. 9a–c. AFM micrographs obtained after CaF 2 growth at 750 ◦ C: a 5TL,b 10 TL, and c 43 TL. With increasing coverage, the number of triangularprotrusions increases significantly. For the large coverage presented in c,the coalescence of the islands has startedfilm explains that substrate <strong>step</strong>s act as growth barriers. Thiseffect is demonstrated in Fig. 11. If the substrate has singleor double <strong>step</strong>s (Fig. 11a and b, respectively) the lattices ofboth ‘islands’ do not match. This is different if the substrate<strong>step</strong> has a TL height (or any integer multiple of it) as seen inFig. 11c. Here, the lateral shift due to the B orientation can becompensated. Since most of the substrate <strong>step</strong>s have heightsdifferent to (integer multiples of) the TL height, most of themact as growth barriers promoting the inhomogeneous growthof the CaF 2 film.Since CaF 2 islands cannot nucleate homogeneously at<strong>step</strong>s, nucleation on top of the underlying CaF interfacelayer and the pre-grown CaF 2 multilayer is the dominatingatomic process for the film growth. As soon as one islandhas been nucleated on a terrace it grows immediately intwo dimensions until its boundary touches the <strong>step</strong>s confiningthe terrace. Thereafter, the growth perpendicular to the<strong>step</strong>s is stopped and the island grows exclusively parallel tothem.This mechanism explains the strongly improved homogeneousgrowth at lower temperatures. The nucleus densityincreases with decreasing deposition temperature. Therefore,the film starts to grow simultaneously at more sites thanat higher temperatures, and more terraces (within the AFMscanning range) are covered by CaF 2 ‘islands’. This modelpredicts that the film grows homogeneously if the temperaturefalls below the critical temperature when the average islanddistance is less than the terrace width.For the terrace width of the substrates studied here(100–200 nm), this condition is fulfilled if the film is grownat 400 ◦ C, as demonstrated by the AFM micrograph presentedin Fig. 12a. The entire surface is covered by a homogeneousCaF 2 film. The observed multi-<strong>step</strong>s are due to theSi substrate. On top of the terraces, one obtains exclusivelymono-atomic islands. In addition, holes of mono-atomic (H)depth are observed. Therefore, the film grows almost perfectlyin the layer-by-layer growth mode.

HH162250nmHP P[111](a)[112](a)100nm(b)(b)[111][112]Fig. 12. a AFM micrograph obtained after deposition of 4-TL CaF 2 at400 ◦ C. The entire substrate is covered homogeneously by CaF 2 .Therearemono-atomic islands as well as substrate-<strong>induced</strong> <strong>step</strong>s. In addition, a fewtriangular protrusions (P) and holes (H) are present. b Enlarged area of a toshow more clearly the mono-atomic islands on the terraces. Islands withregular triangular shape and with irregular shape are obtained25(c)[111][112]Fig. 11a–c. Comparison of the structure of a 4-TL CaF 2 film grown on twoadjacent terraces with a single, b double, and c triple atomic <strong>step</strong> height.For a and b the lattices of both films do not match, due to the B orientationof the film. Coalescence without dislocation can be obtained only for tripleatomic height <strong>step</strong>s, as demonstrated in cThe amount of triangular protrusions (P) observed at substrate<strong>step</strong>s is strongly suppressed compared with that forgrowth at higher deposition temperatures (Figs. 9b and 12a).This points to kinetic <strong>effects</strong> for the nucleation of triangularprotrusions.At the moment the origin for the formation of the triangularprotrusions is not clear. Probably, defects of substrate <strong>step</strong>s(e.g. kinks) support the nucleation of the protrusions, sinceprotrusion area [%]protrusion density/10 8 cm 22015105500 o C750 o C(a)01502 3 5 10 20 30 502010521(b).51 2 3 5 10 20 30 50CaF 2 coverage [TL]Fig. 13. a Dependence of the surface fraction covered by triangular protrusions.The fraction increases with increasing CaF 2 coverage, since theprotrusions often overgrow <strong>step</strong>s. b Density of triangular protrusions. Afterdeposition of 5-TL CaF 2 the nucleation is almost constant

163the protrusions are not distributed homogeneously. Figure 9band c demonstrate clearly that some <strong>step</strong>s are decorated by seriesof triangular protrusions, while other <strong>step</strong>s are completelyprotrusion-free. In all cases, however, these protrusions arein front of CaF 2 -covered terraces, which has been proved byFFM. Therefore, the lateral growth of CaF 2 on the terrace hasto be previous to the formation of the triangular protrusionsin front of it. This may be explained by the necessity of triplesubstrate <strong>step</strong>s which can be overgrown by protrusions. Thisassumption, however, cannot be proved strictly because onecan investigate only the <strong>step</strong> heights of the film, which maydiffer from the height of the underlying substrate <strong>step</strong>.The analysis of the protrusion densities is presented inFig. 13. First, the density and coverage of these protrusionsincrease with increasing coverage. In later growth stages thedensity of protrusions is almost constant, while the surfacefraction covered with protrusions increases further. This effectis due to the overgrowth of substrate <strong>step</strong>s.5 Relaxation at <strong>step</strong>sSome of the largest triangular protrusions show hole-likestructures. Figure 14 shows a typical example for a film depositedat 630 ◦ C. The large twin protrusion has rims at thefree-standing edges which do not point to the upper terraceof the vicinal substrate. The small triangular protrusion on theback side of the twin protrusion, however, does not show thiseffect. In addition, there are small gaps (arrows in Fig. 14)running preferentially parallel to substrate <strong>step</strong>s. Unfortunately,the sample must be at room temperature for the AFMmeasurement. Therefore, one has no information on whetherthese cracks are formed during growth or during the coolingfrom growth to room temperature.The AFM micrograph shown in Fig. 14 is recorded underambient conditions. One can distinguish smooth CaF 2 layersand areas covered by small clusters. In a previous report, wehave shown that the clusters are formed due to the transfer ofthe sample from UHV conditions to ambient conditions [54].The clusters are formed by transformation of the unstable CaFinterface layer under the influence of air.Rim-like structures of long CaF 2 stripes are also formedclose to some of the CaF 2 film <strong>step</strong>s. Figure 15a shows thiseffect for an 8-TL film grown at 630 ◦ C. CaF 2 stripes coverthe entire <strong>step</strong>s (arrows). The edge of the stripes pointing tothe upper terrace is smooth while the other edge pointing tothe lower terrace is rough. In addition, some small protrusionsare formed at the rough edge. Unfortunately, it cannot be determinedusing AFM whether the CaF 2 stripe is formed onthe lower or on the upper terrace. The shape of the stripe,however, suggests that it is more likely that the CaF 2 stripeis formed on the lower terrace since the edge pointing in thisdirection is rough.A line scan (Fig. 15b taken from the white line in Fig. 15a)shows the typical height a and width b of the CaF 2 stripe. Thegeometric dimensions of the CaF 2 stripes have been analysedfrom various micrographs. The result of the analysis is shownby Fig. 16. Although the scattering of the data is not negligible,there is a tendency that the stripe height a seems to beindependent from the <strong>step</strong> height h while the stripe width bincreases with increasing height of the <strong>step</strong>. CaF 2 stripes areobtained exclusively if the <strong>step</strong> height h is larger than 1 nm(equivalent to <strong>step</strong>s of triple-layer height). Thus triple-layerhigh<strong>step</strong>s seem to be critical <strong>step</strong> heights for the onset of thisphenomenon.One has to consider the small (but not negligible) latticemismatch between CaF 2 and Si at these growth temperaturesto explain the growth of the CaF 2 stripes. Since CaF 2 hasa larger lattice constant than Si the pseudomorphic CaF 2 filmis compressed laterally. At <strong>step</strong>s, however, the film on theupper terrace can relax easily since neighbour molecules are(a)250nmbah(b)Fig. 14. Rim formation at the edges of a big triangular twin protrusiongrownbyCaF 2 deposition at 630 ◦ C (AFM micrograph). The clusters observedon the terraces close to the triangular protrusion are formed after thetransfer of the sample from UHV to ambient conditions due to the instabilityof the CaF interface layer. Partially, there are cracks in the CaF 2 film(see arrows)Fig. 15. a AFM micrograph obtained after deposition of 8-TL CaF 2 at630 ◦ C and transfer to ambient conditions. The arrows mark CaF 2 stripes.b Height profile of the line scan marked in a showing the typical geometriclengths to characterize the stripes: <strong>step</strong> height, h, stripe height, a, and stripewidth, b

164a(nm)b(nm)2.01.51.00.500602 4 6402000 2 4 6h(nm)(a)(b)Fig. 16a,b. Analysis of the stripe geometry for an 8-TL CaF 2 film grown at630 ◦ C. a Stripe height, a, andb stripe width, bdiffusingparticleCaF 2Si(111)missing at the <strong>step</strong> (see Fig. 17). In addition, if the Si substrateexhibits multi-<strong>step</strong>s the CaF 2 film on the lower terracecan relax, too, due to the B orientation (see Fig. 17).The (partially) relaxed parts of the CaF 2 films are preferentialnucleation sites for the additional deposited CaF 2molecules (self-decoration). Since the relaxation increaseswith increasing (local) film thickness it is expected that theself-decoration effect is bigger for thicker films. This explainsthat one does not observe CaF 2 stripes due to self-decorationfor extremely thin films. Assuming that the <strong>step</strong> height h reflectsthe (local) CaF 2 film thickness the critical thickness forthe onset of self-decoration is more than 1 nm (see Fig. 16).Therefore, at higher deposition temperatures both the increasedlattice mismatch (enhancing the film relaxation forthinner films) and the increased diffusion length proliferatethe self-decoration effect. A model for this self-decorationprocess at <strong>step</strong>s is shown in Fig. 17.From this model one expects decoration of both films onthe upper and on the lower terrace. Surprisingly, the decorationof the lower terrace seems to be preferred due to theB orientation (see Fig. 17). This may explain that the decorelaxedfilmpreferentialgrowth onrelaxed filmFig. 17. Model of the self-decoration effect. The CaF 2 film relaxes laterallyclose to the underlying substrate <strong>step</strong>. The diffusing CaF 2 moleculesreaching the relaxed part of the film form stripesration of upper terraces is favoured for the triangular protrusionswhich have high edges with bigger relaxation <strong>effects</strong>while the substrate <strong>step</strong>-<strong>induced</strong> film <strong>step</strong>s are decorated atthe lower terrace.Figure 17 explains also the formation of cracks (see alsoFig. 11). The higher the substrate <strong>step</strong> the larger is the gapbetween the film grown on the lower and the upper terrace,respectively. For thicker films, however, the film can coalescedue to the progressive relaxation of these parts of thefilm. Therefore, one would obtain a homogeneously closedbut strained film, as expected due to interface dislocations.6 Discussion and conclusionsThe study presented here shows clearly that Si substrate <strong>step</strong>sact differently for the submonolayer range where the CaF interfacelayer is formed and the subsequent growth of the CaF 2layers.Si <strong>step</strong>s are preferential nucleation sites in the submonolayerrange. Therefore, the growth mode can be driven fromthe growth of islands which are homogeneously nucleatedon terraces to the <strong>step</strong>-flow growth mode, where the CaFmolecules migrate to the substrate <strong>step</strong>s before they are capturedby other CaF molecules and form nuclei. The criticaltemperature for the transition from terrace to <strong>step</strong> nucleationdepends on the terrace width of the Si substrate.Previous annealing experiments have shown a similar effect[23]. CaF islands which have been grown at lower temperaturescan be dissolved, and the material is transportedto the Si substrate <strong>step</strong>s. In addition, the 3 × 1 reconstructionwas formed by annealing at very high temperatures(> 700 ◦ C).The experiments reported here are performed at lowertemperatures. Therefore, on the one hand, the analysis ofthe transition from terrace to <strong>step</strong> nucleation is not complicatedby the formation of the 3 × 1 reconstruction. On theother hand, however, the low deposition temperature has thedisadvantage that SiF x species do not desorb from the surface[10, 35]. Thus, the CaF diffusion may be influenced bythe existence of F on the Si substrate. Therefore, the diffusionbarrier of E D = 1.8 ± 0.2 eV received from the critical temperaturefor the transition from terrace to <strong>step</strong> nucleation isprobably an effective barrier for CaF diffusion on the partiallyF-covered Si (111) surface. Both the STM study presentedhere and STM studies by other authors [20–23, 33], however,do not show any evidence for the existence of SiF x specieson the surface. One possible explanation for this discrepancybetween STM experiments and XPS studies is that theelectron-stimulated desorption of F from the Si (111) surface(see [55] for this effect) is due to the tunneling current. Nostructural changes, however, are observed at high tunnelingvoltages such as 9 V and low tunneling currents, in contradictionto this assumption [56].Further growth beyond the nucleation stage does not showany nucleation on top of CaF islands before completion ofthe layer although the CaF has many point defects. Therefore,it can be concluded that the diffusion of CaF 2 on the CaFinterface layer is much faster than the diffusion of CaF onSi(111). This agrees well with the diffusion barrier of 1.4eVfor CaF 2 /CaF calculated by Denlinger et al. [40] which has tobe compared to 1.8eVforCaF/Si(111).

165The AFM investigations presented here are in very goodagreement with previous results for CaF 2 films grown onthe CaF interface layer obtained using XPS, XPD andTEM [38, 40, 41]. One obtains laminar growth at low temperatures.The film becomes more inhomogeneous when thedeposition temperature is increased. The application of a microscopictechnique, however, offers deeper insight into thelocal morphology. For instance, the AFM study demonstratesthat the substrate-<strong>induced</strong> <strong>step</strong>s of the CaF interface layer arenot preferential nucleation sites, since only very few of theCaF-covered terraces are overgrown by CaF 2 . This effect isattributed to the B orientation of the CaF 2 film on top of theCaF interface layer which suppresses heterogeneous nucleationat <strong>step</strong>s. Therefore, the film cannot grow either by <strong>step</strong>flow or by nucleation and growth of 3D islands at <strong>step</strong>s. Theonly pathway for CaF 2 nucleation is the homogeneous nucleationon terraces, since the point defects observed in the CaFlayer are also not preferential nucleation sites.Therefore, on the one hand, the model presented by Hessingeret al. that 3D islands at <strong>step</strong>s induce the growth of inhomogeneousfilms cannot be applied to the inhomogeneousgrowth of CaF 2 on the CaF interface layer at high depositiontemperatures [52]. On the other hand, the result that thelaminar growth at low temperature is due to homogeneousnucleation on terraces is in good agreement with the studypresented here.The model of inhomogeneous CaF 2 film growth via homogeneousnucleation includes the necessity of preferentialnucleation of CaF 2 on CaF 2 layers compared to nucleationon the CaF interface layer. The driving force for this maybe a smaller surface energy of the CaF layer compared tothe CaF 2 film. In addition, there may be some instability ofthe CaF 2 film on the CaF layer. A similar effect has beenobserved by LEEM, although the authors attributed the instabilityto a CaF 2 interface layer which is less strongly bound tothe Si surface than the CaF layer [57].A comparison of the various proposed growth models ispresented in Fig. 18.In a previous study, we assumed also that the inhomogeneousgrowth at high temperatures is due to <strong>step</strong> nucleation.We deduced from the critical temperature for the transitionfrom homogeneous to inhomogeneous growth that the diffusionbarrier for CaF 2 molecules on CaF 2 films is 1.4eV.Hessinger et al. concluded a similar barrier height from theirexperimental data. This result, however, is quite problematicin the light of the data and the model presented here. Therefore,one has to study the (homogeneous) nucleation of CaF 2on both (probably pre-grown) CaF and CaF 2 films in moredetail. In addition, the entire suppression of <strong>step</strong> nucleationfor the growth of CaF 2 on the CaF interface layer has tobe proved by appropriate scanning probe microscopy experiments.We will perform these studies in the near future.The formation of triangular or trapezoidal protrusionshas been reported previously by various groups [46–48].Kim et al. [47] assumed that CaF 2 grows exclusively via theseprotrusions. This is probably due to the higher depositiontemperature during these experiments.By comparing growth on vicinal and well-aligned Si (111)surfaces, it has been proposed that the formation of protrusionsis due to the formation of coreless dislocations at substrate<strong>step</strong>s [47]. It is assumed that the film can solve theproblem of overgrowing substrate <strong>step</strong>s due to the B orien-increasing coverage(a)(b)(c)CaF 2CaFSiFig. 18a–c. Comparison of growth models for various temperatures. Everypanel shows subsequent phases – from top to bottom: submonolayer nucleationphase, deposition of 1-TL CaF 2 , phase directly after deposition of1-TL CaF 2 , deposition of 2-TL CaF 2 . a Low-temperature growth. The filmgrows homogeneously due to homogeneous nucleation on many terraces.b High-temperature growth due to <strong>step</strong> nucleation proposed by Hessingeret al. [41]. Islands nucleate at all <strong>step</strong>s and grow as 3D islands. c Hightemperaturegrowth mode proposed here. On very few terraces are islandsnucleated. Laminar growth is suppressed by substrate-<strong>induced</strong> <strong>step</strong>s of theCaF interface layertation of this mechanism. The good agreement between theprotrusion density and the expected dislocation density wasthe main argument. The results presented here do not sustainthis model, since the protrusion density depends on both temperatureand coverage. Only for the high temperatures studiedin [47] did the protrusion density saturate very quickly with

166increasing coverage. Therefore, kinetic <strong>effects</strong> play an importantrole in protrusion growth.The self-decoration of CaF 2 films on the upper part ofsubstrate <strong>step</strong>s has been reported previously for CaF 2 monolayersdeposited on the CaF interface layer after annealing[43]. The authors explain the decoration of the upperterrace by the steric effect due to the B stacking of the film.They used vicinal surfaces with miscuts towards the [¯1¯12]azimuth where the CaF 2 film grows towards the <strong>step</strong>. Thesubstrates in our experiments, however, had the miscut towardsthe [11¯2] azimuth where the film starts to grow at the<strong>step</strong> on the lower terrace. A critical <strong>step</strong> height for the onsetof the self-decoration effect is observed in the experimentsreported here. It is not completely clear whether this is duea minimum <strong>step</strong> height of the Si substrate or whether thisis a film property (relaxation of the film close to the <strong>step</strong>).The linearly increasing CaF 2 stripe width with the <strong>step</strong> height,however, points to relaxation <strong>effects</strong> as expected from elasticproperties and the self-decoration of relaxed parts of thickerfilms.In conclusion, it has been demonstrated that Si substrate<strong>step</strong>s are advantageous for the homogeneous growth of theCaF interface layer. At sufficiently high temperatures CaFnucleates preferentially at substrate <strong>step</strong>s and the CaF layergrows via <strong>step</strong> flow. The critical temperature to obtain thiseffect depends on the terrace width (or <strong>step</strong> density) of theSi substrate. The CaF 2 film subsequently grown on the CaFinterface layer cannot nucleate at <strong>step</strong>s due to its B orientation.In addition, substrate-<strong>induced</strong> <strong>step</strong>s are growth barriers.Therefore, CaF 2 films grow very inhomogeneously athigh temperatures via terrace nucleation on the CaF interfacelayer. Homogeneous films via laminar growth are obtained atlow temperatures with a sufficiently high terrace nucleation.A preferred nucleation close to <strong>step</strong>s (self-decoration) is observedfor thicker CaF 2 film and multi-substrate <strong>step</strong>s (miscuttowards the [11¯2] azimuth) due to film relaxation close to substrate<strong>step</strong> <strong>effects</strong> and B orientation.Acknowledgements. Sincere thanks are given to M. Bierkandt, A. Klust andH. Pietsch for their tremendous contributions to the results presented here,performing, analysing and discussing the experiments. Financial supportfrom the Deutsche Forschungsgemeinschaft (DFG) is acknowledged.References1. L.J. Challis, Contemporary Physics 33, 111 (1992)2. G.A. Toombs, F.W. Sheard: In Electronic Properties of Multilayers andLow Dimensional Semiconductor Structures, ed. by J.M. Chamberlainet al. (New York, Plenum Press 1990) p. 2573. T.C.L.G. Sollner, W.D. Goodhue, P.E. Tannenwald, C.D. Parker,D.D. Peck: Appl. Phys. Lett. 43, 588 (1983)4. T.J. Shewchuk, P.C. Chapin, P.D. Coleman, W. Kopp, R. Fischer,H. Morkoc: Appl. Phys. Lett. 46, 508 (1985)5. M. Watanabe, T. Suemasu, S. Murakte, M. Asada: Appl. Phys. Lett. 62,300 (1993)6. T. Suemasu, M. Watanabe, J. Suzuki, Y. Kohno, M. Asada, N. Suzuki:Jpn. J. Appl. Phys. 33, 57 (1994)7. T. Suemasu, Y. Kohno, W. Saitho, N. Suzuki, M. Watanabe, M. Asada:Jpn. J. Appl. Phys. 33, L1762 (1994)8. L.J. Schowalter, R.W. Fathauer: CRC Crit. Rev. in Solid State Mater.Sci. 15, 367 (1989)9. C. Strahberger, P. Vogl: Phys. Rev. B 62, 7289 (1999)10. M.A. Olmstead: In Thin Films: Heteroepitaxial Systems (World ScientificPublishing, Singapore 1999) p. 21111. D. Rieger, F.J. Himpsel, U.O. Karlsson, F.R. McFeely, J.F. Morar,J.A.Yaramoff:Phys.Rev.B34, 7295 (1985)12. M.A. Olmstead, R.I.G. Uhrberg, R.D. Bringans, R.Z. Bachrach: J. Vac.Sci. Technol. B 4, 1123 (1986)13. F.J. Himpsel, F.U. Hillebrecht, H. Hughes, J.L. Jordan, U.O. Karlsson,F.R. McFeely, J.F. Morar, D. Rieger: Appl. Phys. Lett. 48, 596 (1986)14. M.A. Olmstead, R.I.G. Uhrberg, R.D. Bringans, R.Z. Bachrach: Phys.Rev. B 35, 7526 (1985)15. F.J. Himpsel, U.O. Karlsson, J.F. Morar, D. Rieger, J.A. Yaramoff: Mat.Res. Soc. Proc. 94, 181 (1987)16. M.A. Olmstead, R.D. Bringans: J. Electron. Spectrosc. Relat. Phenom.51, 599 (1990)17. J. Wollschläger, A. Meier: J. Appl. Phys. 79, 7373 (1996)18. G.C.L. Wong, C.A. Lucas, D. Loretto, A.P. Payne, P.H. Fuoss: Phys.Rev. Lett. 73, 991 (1994)19. C.A. Lucas, D. Loretto, G.C.L. Wong: Phys. Rev. B 50, 14 340 (1994)20. T. Nakayama, M. Katayama, G. Selva, M. Aono: Phys. Rev. Lett. 72,1718 (1994)21. T. Sumiya, T. Miura, S. Tanaka: Jpn. J. Appl. Phys. 34, L1383 (1995)22. T. Sumiya, T. Miura, S. Tanaka: Surf. Sci. 357–358, 896 (1996)23. T. Sumiya: Appl. Surf. Sci. 156, 85 (2000)24. R. Wolkow, Ph. Avouris: J. Microscopy 152, 167 (1988)25. Ph. Avouris, R. Wolkow: Phys. Rev. Lett. 55, 1074 (1989)26. H. Ishiwara, T. Asano: Appl. Phys. Lett. 40, 66 (1982)27. T. Asano, H. Ishiwara, N. Kaifu: Jpn. J. Appl. Phys. 22, 1474 (1983)28. R.M. Tromp, M.C. Reuter: Phys. Rev. Lett. 61, 1756 (1988)29. J. Zegenhagen, J.R. Patel: Phys. Rev. B 41, 5313 (1990)30. K.G. Huang, J. Zegenhagen, J.M. Phillips, J.R. Patel: Phys. Rev. Lett.72, 2430 (1994)31. K.G. Huang, J. Zegenhagen, J.M. Phillips, J.R. Patel: Physica B 221,192 (1996)32. C.A. Lucas, G.C.L. Wong, D. Loretto: Phys. Rev. Lett. 70, 1826 (1993)33. T. Nakayama, M. Aono: Phys. Rev. B57, 1855 (1998)34. A. Klust, H. Pietsch, J. Wollschläger: Appl. Phys. Lett. 73, 1967(1998)35. A. Klust, M. Bierkandt, J. Wollschläger, J. Falta, Th. Schmidt,B.H. Müller: in preparation36. N.S. Sokolov, J.C. Alvarez, Y.V. Shusterman, N.L. Yakovlev,R.M. Overney, Y. Itoh, I. Takahashi, J. Harada: Appl. Surf. Sci.104/105, 402 (1996)37. N.S. Sokolov, J.C. Alvarez, S.V. Gastev, Y.V. Shusterman, I. Takahashi,Y. Itoh, J. Harada, R.M. Overney: J. Crystal Growth 169, 40 (1996)38. J.D. Denlinger, E. Rotenberg, U. Hessinger, M. Leskovar, M.A. Olmstead:Appl. Phys. Lett. 62, 2057 (1993)39. G.C.L. Wong, D. Loretto, E. Rotenberg, M.A. Olmstead, C.A. Lucas:Phys. Rev. B 48 5716 (1993)40. J.D. Denlinger, E. Rotenberg, U. Hessinger, M. Leskovar, M.A. Olmstead:Phys. Rev. B51, 5352 (1995)41. U. Hessinger, M. Leskovar, M.A. Olmstead: Phys. Rev. Lett. 75, 2380(1995)42. J. Wollschläger, H. Pietsch, A. Klust: Appl. Surf. Sci. 130–132, 29(1998)43. J. Viernow, D.Y. Petrovykh, F.K. Men, A. Kirakosian, J.L. Lin,F.J. Himpsel: Appl. Phys. Lett. 74, 2125 (1999)44. J. Viernow, D.Y. Petrovykh, A. Kirakosian, J.L. Lin, F.K. Men,M. Henzler, F.J. Himpsel: Phys. Rev. 59, 10 356 (1999)45. A. Li, F. Liu, D.Y. Petrovykh, J.L. Lin, J. Viernow, F.J. Himpsel,M.G. Lagally: Phys. Rev. Lett. 85, 5380 (2000)46. B.M. Kim, C.A. Ventrice, T. Mercer, R. Overney, L.J. Schowalter:Appl. Surf. Sci. 104/105, 409 (1996)47. B.M. Kim, S.R. Ross, R. Overney, L.J. Schowalter: Mat. Res. Soc.Proc. 399, 177 (1996)48. V. Mathet, F. Nguyen-Van-Dau, J. Olivier, P. Galtier: J. Crystal Growth148, 133 (1995)49. A.L. Aseev, A.V. Latyshev, A.B. Krasilnikov: Surf. Rev. Lett. 4, 551(1997)50. A. Ishizaka, T. Doi, M. Ichikawa: Appl. Phys. Lett. 58, 902 (1991)51. G. Meyer, N.M. Amer: Appl. Phys. Lett. 53, 1045 (1988)52. A. Myers-Beaghton, D.D. Vvedensky: Phys. Rev. B 42, 9720 (1990)53. M. Bierkandt, J. Wollschläger, M.I. Larsson: in preparation54. J. Wollschläger, A. Klust, H. Pietsch: Appl. Surf. Sci. 123–124, 496(1998)55. K. Miura, K. Sugiura, H. Sugiura, Surf. Sci. 253, L407 (1991)56. M. Bierkandt, private communication57. R.M. Tromp, M.C. Reuter: Phys. Rev. Lett. 73, 110 (1994)