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

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