PACS: F, 68.55, J, A, C. Keywords: Kinetics of nucleation; Kinetics of growth; Vapor growth technique by magnetron sputtering

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1 DIFFUSION MEDIATED FILM GROWTH ON POLYCRYSTALLINE SUBSTRATES C. Eisenmenger-Sittner, Technische Universität Wien, Institut für Angewandte und Technische Physik, Wiedner Hauptstrasse 8-0, A-040 Wien, Austria, Europe Mechanisms of island formation and growth are central issues in thin film deposition. The shape and size as well as the spatial distribution of stable islands in the first phases of growth determine a wide variety of film properties. In an earlier work the growth mode of sputter deposited Tin (Sn) and Lead (Pb)-films on polycrystalline Al-substrates was analyzed in the framework of the rate equation theory. This analysis yielded Stranski-Krastanov growth with the size of the critical nucleus in the range from 6 to 20 monomers. The present study is devoted to a detailed experimental investigation of the mechanisms involved in the formation of Sn and Pb islands on polycrystalline Aluminium (Al). All thin-film systems treated in this work were deposited on glass substrates by DC magnetron sputtering. They consist of a polycrystalline Al-underlayer covered with a 00 Å thick Sn or Pb-films. The variation of the mean Sn and Pb island distance for was determined in dependence on the deposition temperature and on the underlayer thickness. It varied from 0.5 to 20 µm and showed an Arrhenius dependence on the deposition temperature. A rateequation analysis yielded activation energies for surface diffusion of single Sn and Pb atoms of approximately 0.5 ev. Island Size Distributions (ISD's) were determined for different deposition temperatures and were mostly found to be monomodal with a global maximum at the mean island size. All these facts indicate that the mechanism of island formation is mediated by surface diffusion of the Sn or Pb monomers on the Al surface in a wide range of deposition temperatures. PACS: F, 68.55, J, 8.5.A, 8.5.C Keywords: Kinetics of nucleation; Kinetics of growth; Vapor growth technique by magnetron sputtering. Introduction: The formation of clusters and islands from the vapor phase by diffusion and aggregation of monomers on surfaces has been extensively studied both experimentally [-4] and theoretically [, 5-7]. Also the Island Size Distribution (ISD) has been subject of considerable interest [8-] because of its distinct dependence on different mechanisms of condensation, aggregation and growth. The emergence of scanning microscopy techniques has given new impulses to the field [2,3], enabling the direct observation of the atomic processes involved in the formation of a stable island. Finally the increase in computer-power as well as the formulation of scaling concepts [8,9,4-6] stimulated the research and provided adequate tools for the theoretical analysis. A technological demand for arrays of equal sized micro- and nano-crystalline islands arises from the new developments in the field of quantum-electronic devices. A method for

2 the production of such systems is the diffusion mediated island growth on single crystalline substrates by vapor phase epitaxy [7-9]. Polycrystalline substrates have not been considered in this respect up to now because of the argument that the high defect density would prevent a sufficiently narrow Island Size Distribution. This paper investigates the general possibility of diffusion mediated growth on polycrystalline substrates. The motivation for this investigation results from earlier work [20] where it was found that Tin (Sn) and Lead (Pb) - layers deposited on polycrystalline Aluminium (Al) exhibit pronounced island growth. The growth mode of the Sn and Pb-films was determined to be of the Stranski-Krastanov-type with a size of the critical nucleus in the range from 6 to 20 Atoms for both materials. Preliminary investigations showed that the island density indeed varied strongly with the deposition temperature. Modification in the roughness and the crystallinity of the Al-underlayer surface achieved by different underlayerthicknesses on the other hand had little effect on the island density. It is the aim of this paper to quantify these statements by a systematic investigation of the dependence of the Sn and Pb island density on the deposition temperature and on the Al underlayer thickness. If the island density shows Arrhenius behavior upon the variation of the substrate temperature this would indicate that the mechanism of island formation is indeed surface diffusion mediated despite of the high defect density of the Al-underlayer. In addition the ISD's and their dependence on the deposition temperature are investigated in respect to their general shape and to their scaling properties to further support or to reject the possibility of diffusion mediated growth. The paper is structured as follows: Section 2 gives details about the experimental set-up and about the tools used for determining the island densities. In section 3 the experimental results are presented. Section 4 discusses the results in respect to the possibility of diffusion mediated growth on polycrystalline surfaces. Special attention is given to the existence of similarities of the Systems Al-Sn and Al-Pb. In section 5 a brief summary is presented and the consequences of the investigations in respect to island growth on polycrystalline substrates are discussed. 2. Experimental Set-Up All experiments were carried out in an Alcatel SCM 45 sputter plant. Technical and geometrical data of the equipment are given in Table I. The material combinations Al/Sn and Al/Pb were deposited from two planar magnetron targets with their surface normals tilted against each other by an angle of 52. Recipient diameter/height: Pumping speed (diffusion pump) Base pressure: Working gas/pressure/measurement: Magnetron target diameter Target voltage during operation: Target Power during operation: Distance Source/Substrate Table I: Technical data of the sputter equipment 450 mm/300 mm 250 l/s 0-5 Pa Ar/0.4 Pa/Baratron gauge 80 mm 500 V (Al); 500 V (Sn); 450 V (Pb) 400 W (Al); 60 W (Sn); 30 W (Pb) 30 mm 2

3 All samples were deposited on glass substrates (0x25 mm) attached to a heatable substrate holder. The temperature of the substrate holder was controlled by a Pt-000 temperature dependent resistor located approximately 3 mm apart from the substrate. The temperature reading proved to be very close to the actual substrate temperature since Sn and Pb deposited at nominal temperatures slightly above their melting points were found to be molten. The deposition temperature could be kept constant within a range of ± 2 C. The samples could be extracted from the deposition chamber together with the substrate holder through a load-lock-system. This prevented the deposition chamber from being vented after each deposition run. One deposition run comprised the following steps: First the Al-underlayer was deposited at the desired temperature. Thereafter the Al-source was switched off and Sn or Pb were deposited immidiately on the fresh Al-surface. Deposition rate and film thickness were measured by a carefully calibrated quartz microbalance (QMB). The data relevant to the deposition process are given in Table II. Substrate material glass, 0x25 mm RMS-roughness of glass substrate: < 5nm Deposition rate at the substrate: Al/Sn/Pb: nms - /0. nms - /0. nms - Deposition Temperature Al/Sn: C Deposition Temperature Al/Pb: C Deposition Temperatures of Sn on Al-underlayers of different thickness 00 C, T S /T Sn M = C, T S /T Sn M = 0.85 Deposition Temperatures of Pb on Al-underlayers of different thickness 60 C, T S /T Pb M = C, T S /T Pb M = 0.85 Underlayer thickness 0nm nm Table II: General deposition parameters for all samples. Special deposition conditions are indicated in the text whre necessary. All samples were investigated in a Scanning Electron Microscope (SEM) by element specific Backscatter Electron Imaging (BEI). Thus the Sn or Pb islands could well be distinguished from the Al-background and subsequently be counted. 3. Experimental Results 3a. General Properties of the Al Underlayer The two experimental parameters of this study were the deposition temperature and the thickness of the Al-underlayer. Fig. gives Atomic Force Microscopic (AFM) micrographs of the surfaces of µm thick underlayers. The Al-film in Fig. a was deposited at 00 C, while Fig. b shows a film deposited at 240 C. One immediately notices the highly structured surfaces of both films, and the increase in the lateral dimension of the surface features with increasing deposition temperature. 3

4 Fig..: AFM micrographs of Al-underlayer surfaces at different deposition temperatures. The underlayer thickness is µm (a) deposition temperature = 00 C (a) deposition temperature = 240 C The Root Mean Square (RMS) roughness of the Al underlayer depends on the deposition temperature in a roughly linear manner. Fig. 2a shows this relation for underlayers of µm thickness. Fig. 2b shows the dependence of the RMS-roughness on the underlayer thickness for films deposited at room temperature and at 280 C respectively. From Fig. 2 one can deduce that the roughness of the underlayer ranges from nm for very thin films deposited at low temperatures to about 60 nm for thick films (2 µm) deposited at high substrate temperatures RMS-Roughness [nm] RMS-Roughness [nm] 0 Room Temperature T = 280 C Deposition Temperature [ C] Underlayer Thickness [nm] Fig. 2.: (a) (b) Dependence of the RMS-roughness of the Al-underlayer (a) on the deposition temperature (thickness = µm) and (b) on the thickness at two different deposition temperatures It has to be mentioned that also the crystallite size of the polycrystalline underlayer depends on the deposition parameters. According to Lita and Sanchez [2] it is possible to determine the mean crystallite size of polycrystalline films from the one dimensional Power Spectral Densities (d PSD s) of AFM micrographs. A systematic study of this point will be the subject of further work. From preliminary measurements it can be concluded that the mean crystallite diameter ranges from some nanometers for thin underlayers at low substrate temperature to some µm for thick films deposited at elevated temperatures. The above statements together with Fig. illustrate the high complexity of the surface on which Sn and Pb are deposited. It is thus surprising to see how little influence this complex surface morphology has on the island formation in the Sn and Pb films as will be shown the next sections. 4

5 3b. General Remarks on the Morphology of the Sn and Pb Films: All Sn and Pb films investigated in this paper had a nominal thickness of 00 Å. Independent of the deposition temperature Energy Dispersive x-ray (EDX) analysis yielded a constant composition of all samples on µm thick underlayers within a relative error of approximately 0%. This indicates that the condensation of Sn and Pb on the Al-surface is complete. Both materials exhibit pronounced island growth on Al [20]. Nonetheless the morphologies of the islands are significantly different. Figs. 3a,b show element specific SEM micrographs of Sn and Pb-films on a µm thick Al underlayer, respectively. The enlarged areas in Figs. 3a,b are AFM micrographs of the underlayer surface between the islands. Fig. 3.: SEM-micrographs of the general appearance of 00 Å Sn or Pb on µm thick Al-underlayers (a) Sn on Al, deposition temperature 60 C (b) Pb on Al, deposition temperature 240 C The enlarged regions are AFM-micrographs of the underlayer surface to give an impression of the lateral extension of the underlayer surface features. The shape of the Sn islands varies from extremely anisotropic, elongated islands to compact triangular morphologies which is presumably due to the highly anisotropic tetragonal crystal structure of Sn. The fcc lattice of Pb on the other hand leads to the formation of compact and basically hemispherical islands. Figs 4a, b show AFM micrographs of these samples to give a 3d-impression of the islands. From the line scans in Figs. 4a, b it becomes apparent that in both cases the heights of the islands are approximately equal for either Sn or Pb. This fact will be important for the determination of the ISD's in section 3e. Fig. 4.: AFM micrographs of Sn-islands (a) and Pb-islands (b). The inserted line-scans across the islands show that the islands have approximately equal heights. 5

6 3c. Dependence of the Mean Island Distance l on the Deposition Temperature: It is obvious from Fig. that the mean surface feature extension of µm thick Alunderlayers deposited at 240 C is in the 0.5 µm-range. On the other hand the mean island separation of a 00Å Pb-film deposited on a similar surface is some 0 µm as the element specific SEM-micrograph in Fig. 3b shows. Therefore the actual surface morphology and defect structure seems to play a minor role in the nucleation processes for Sn or Pb. A single logarithmic plot of the mean Sn or Pb island separation l versus the inverse deposition temperature is given in Fig. 5. For both materials a typical Arrhenius-behavior is observed for deposition temperatures ranging from room temperature to C below the melting points of both materials. The slope of the Arrhenius plot is in the range of ev in both cases. These facts indicate that the formation of the Sn and the Pb-islands is an activated process. Further details concerning the Arrhenius-plots will be discussed in section 4. Mean island distance [µm] 0 E A =0.22 ev E A =0.25 ev Sn on µm Al Pb on µm Al Fig. 5.: 0,002 0,003 - Inverse Deposition Temperature [K ] Dependence of the mean island distance l on the inverse deposition temperature (underlayer thickness = µm). The solid lines are Arrhenius-fits to the data. The activation energies represent a combination of the activation energies for surface diffusion and island formation. At temperatures close to the melting points of Sn or Pb a significant deviation from the Arrhenius-behavior can be observed: At about 280 C the mean island separation levels off in the case of Pb. For Sn one observes a drastic reduction of l at about 20 C and approximately constant l above this temperature. The reasons for this behavior are yet unknown and can possibly be attributed to a change in the growth mode of the Sn or Pb-films. 3d. Dependence of the Mean Island Distance l on the Underlayer Thickness As discussed in section 3a the crystallite size of the Al-underlayers is closely correlated to its thickness: The mean lateral crystallite extension can be varied from < µm to about 5 µm by varying the underlayer thickness from 00 Å to 5 µm. Fig. 6 shows the influence of the underlayer thickness on the mean island distance at deposition temperatures of 00 and 60 C for Sn and 60 and 240 C for Pb. These temperatures correspond to equal reduced temperatures in respect to the melting points of Sn and Pb, respectively (Tab. II, Fig. 6). The importance of the reduced deposition temperature will become apparent in Section 4. 6

7 Mean Island Distance [µm] 0 S n Sn on Al, 60 C, T /T = 0.85 S M P b Pb on Al, 240 C, T /T = 0.85 S M S n Sn on Al, 00 C, T /T = 0.73 S M P b Pb on Al, 60 C, T /T = 0.73 S M Fig. 6.: Underlayer Thickness [nm] Dependence of the mean island distance l of Sn and Pb on the underlayer thickness d for two different deposition temperatures. Changing d over two orders of magnitude does not influence l significantly. Compared to the significant influence of the deposition temperature on l (Fig. 5) the underlayer thickness and therefore the crystallite size of the underlayer has only a minor influence on l (Fig. 6). 3e. Mean Island Size and Island Size Distribution All Island Size Distributions (ISD's) were determined from SEM-micrographs which, however, do not provide information about the effective island volume. Therefore Fig. 7 shows the dependence of the mean projected island area σ (and not the island size) on the deposition temperature. But based on the fact of approximately equal island heights for Sn and Pb (Fig. 4a,b) the island area is proportional to the island volume and can be used to represent the ISD Mean island area [µm ] 0 0, 0,0 Sn on µm Al Pb on µm Al Fig. 7.: E-3 0,002 0,003 - Inverse Deposition Temperature [K ] Dependence of the mean island area σ on the underlayer thickness. The error bars represent the mean square deviation of the island size distribution from the mean island size. Bold error bars refer to the data for Sn Similar to l the average island area shows an Arrhenius-behavior over a wide range of deposition temperatures and then again deviates from the Arrhenius-form in the vicinity of the melting point of the respective material. The ratio of the mean square deviation of the island 7

8 area, σ A, to the mean island area, σ, σ / A σ, hardly exceeds 0.3 for all deposition temperatures in the case of Al-Pb. For Al-Sn it can be considerably larger than.0 in the vicinity of the melting point and at deposition temperatures below 00 C. This indicates a much wider ISD for Sn. Finally, Fig. 8 shows ISD's for Al-Sn (Fig. 8a) and Al-Pb (Fig. 8b) at various deposition temperatures. Area Frequency [normalized to maximum],0 0,8 0,6 0,4 0,2 deposition temperature = 60 C deposition temperature = 00 C deposition temperature = 50 C,0 0,8 0,6 0,4 0,2 deposition temperature = 240 C deposition temperature = 60 C deposition temperature = 00 C Fig. 8.: 0, Island Area/Mean Island Area 0, Island Area/Mean Island Area (a) (b) Island area distributions for Sn (a) and Pb (b) on µm thick Al-underlayers at various deposition temperatures. The data are normalized to the maximum and scaled by the mean island size. All distributions are plotted over σ/ σ and are normalized to their maximum to check if the ISD's show some sort of scaling behavior. One immidiately notices the much sharper ISD's of Pb (Fig. 8b) in comparison to Sn (Fig. 8a). Additionally the ISD's of Pb coincide on a single curve for all deposition temperatures investigated. On the other hand, the ISD's of Sn only coincide at elevated deposition temperatures. At a deposition temperature of 50 C small islands dominate the ISD (Fig. 8a, diamond shaped icons). At 00 C the lower end of the ISD still has a secondary maximum of about 80% of the primary one (Fig. 8a, open squares) again indicating the presence of many small islands. 4. Discussion The experimental results presented in the previous section can be summarized in three points which are valid for both systems, Al-Sn and Al-Pb: the complete condensation of Sn and Pb on Al in a wide range of deposition temperatures the Arrhenius dependence of the mean island distance l and the mean island area σ on the deposition temperature the independence of l on the surface structure of the Al-underlayer These findings support the hypothesis that the nucleation and growth processes of Sn and Pb on polycrystalline Al are diffusion mediated. The detailed morphological and crystallographic structure of the Al-underlayer is of minor importance. Diffusion mediated growth can be treated in the framework of the rate equation theory [, 5-7]. The basic observable quantity to describe island nucleation and growth is the number of stable islands per unit area, or island density, n s. The mean island distance, l, is related to n s by l ( / ) = n s 2 /. For complete condensation the theory of rate equations yields the following expression for l if the nucleation of islands involves the formation of a critical nucleus containing i atoms and island growth is purely surface diffusion mediated [, 5-7]: 8

9 i+ 2 / R 2( i+ 2) 3i+ 2 2( i+ 2) l = [ ns( R, TS, i) ] Ω N0 exp Ei + ied N ( ) kbts i+ 0ν 2 2 i R l [ n R T i ] + 2 / 2i 5 2 2i+ 5 2i+ 5 = s(, S, ) Ω N0 exp Ei + ied N ( ) kbts i+ 0ν i + Ω = atomic volume N 0 = number of adsorption sites per unit area R = deposition rate (particles per second and unit area) T S = deposition temperature i = number of atoms in the critical nucleus E i = energy of formation of the critical nucleus E d = activation Energy of surface diffusion i (a) (b) Eqn. (a) is valid for two-dimensional island growth. Eqn. (b) is the analogous expression for three-dimensional islands. Expressions (a,b) allow the determination of i by monitoring the dependence of l on the deposition rate at constant deposition temperature. This was done in [20] and yielded sizes of the critical nuclei from 6 to 20 atoms dependent on the material (Sn or Pb) and on the dimensionality of the critical nucleus (2d or 3d). Since the observed islands are clearly three dimensional the following considerations will focus on the three dimensional case (Eqn. (b)) in which i ranges from 8-20 [20]. Expression (b) allows to extract informations about E i and E d from the dependence of l on the deposition temperature, T S. Unfortunately the two energies cannot be determined independently. With the measured slope ϕ of the Arrhenius-plots (Fig 5) one obtains: ϕ= ( Ei + ied ) 2a 2i + 5 E = ( 2i+ 5) ϕ ie 2b i [ i] d Ed = ( 2i+ 5) ϕ E / i 2c ϕ = measured slope of the Arrhenius-plot Under the assumption that neither E i nor E d can be smaller than zero Eqns. (2a-c) allow to confine E i and E d to the intervals given in Eqns. (3a,b): [ ( 2 i 5) ] [ ( 2 5)/ ] E i ϕ +, 3a E d ϕ i i 3b A value of E i = 0 means that E d has its maximum value and vice versa. Additionally Eq. (3) shows that the maximum energy of island formation, E max i, diverges for large values of i while the activation energy of monomer diffusion is limited to a minimal value of E min d = 2ϕ for i. Inserting the values of ϕ determined from Fig. 5 yields the following results: 9

10 Sn: E Pb: E min d min d = 044. ev = 05. ev It has to be emphasized that the above values of the surface diffusion energy are only valid in the case of small E i and large i. Since no limiting case exists for E max i the number of atoms in the critical nucleus, i, has to be taken into account. A detailed calculation of E i in dependence of i by a molecular static or dynamic approach is beyond the intention of this work, but E i can be estimated by the following energetic considerations: Classical nucleation theory states that the energy of island formation is basically the surface energy of the critical 2 3 nucleus. For compact hemispherical nuclei the surface area is given by ( / 2) [ 36( i V )] / at where V at is the volume of a single atom. With an atomic diameter of approximately 3 Å for Sn and Pb, V at is 4 Å 3. With i = 8-20 the surface area of the 3d critical nucleus ranges from approximately 9 Å 2 (i=8) to 26 Å 2 (i=20). The macroscopic surface energy of Sn is 0.02 ev/ Å 2 and that of Pb is ev/å 2 [22]. The formation energies of the critical nuclei therefore assume the following values: Sn: E i = 0.23 ev (i=8) E i = 0.3 ev (i=20) Pb: E i = 0.67 ev (i=8) E i = 0.9 ev (i=20) E d results from Eqn. (2c) and with the above values of E i one obtains Sn: E d = 0.54 ev (i=8) E d = 0.48 ev (i=20) Pb: E d = 0.57 ev (i=8) E d = 0.52 ev (i=20) It is worth noting that the activation energies of surface diffusion are remarkably similar for Sn and Pb despite the big differences in E i, resulting from the similarity of ϕ for both materials. In addition they are close to E d min even in the case of small i. The second important point presented above is the independence of l on the underlayer thickness (Fig. 6). As previously stated this fact indicates the unimportance of the detailed structure of the underlayer surface on the island formation process. But Fig. 6 also shows an additional effect: Sn and Pb-films deposited at the same homologous temperatures on different Al-underlayers show very similar l. Therefore the question arises if this is a general feature for every set of reduced temperatures. Surprisingly this is definitely valid, as a plot of l versus ( T/ T M ) in Fig. 9 shows. 0

11 Mean Island Distance [µm] 0 Sn on µm Al Pb on µm Al Fig. 9.:,0,2,4,6,8 2,0 Inverse Reduced Deposition Temperature Scaling of the mean island distance l in respect to the inverse homologous good data collapse is temperature ( / ) achieved T T M. When l is plotted over ( T/ T M ) Even the temperature where the Arrhenius-law is no longer fulfilled roughly coincides for both materials. The dependence of the mean island size, σ, on ( T/ T M ) shows the same coincidence (Fig. 0). 2 Mean Island Area [µm ] 0 0, Sn on µm Al Pb on µm Al,0,2,4,6,8 2,0 Inverse Reduced Deposition Temperature Fig. 0.: Scaling of the mean island area σ in respect to the inverse homologous. temperature ( T/ T M ) The reason for this surprising scaling behavior is yet unclear. A possible explanation is the existence of the wetting layer which was detected between the islands [20]. Sn and Pbatoms would therefore not diffuse on pure Al but on a thin layer formed by the respective material thus leaving only the relative temperature difference to the melting point as parameter entering the Arrhenius law. The last remaining point is the discussion of the ISD's. Recent work by Bales, Mulheran, and Amar [8, 0,, 23] used scaling arguments for the interpretation of the ISD: If one plots the ISD over σ/ σ (Figs. 8a,b) the data should collapse on a single curve when either coverage, deposition rate or deposition temperature are changed [8].This is roughly the case for the primary maxima of the ISD's of Sn at elevated temperatures (Fig. 8a) and well fulfilled for Pb (Fig. 8b). Mulheran and Blackman [0, ] developed an elegant method of generating the ISD by correlating the size of a single island to the extension of the monomer capture zone around this island. The capture zone can be identified as the Voronoi zone (the equivalent of the

12 Wigner-Seitz cell for random arrangements of points) surrounding the island. The sizedistribution of Voronoi Zones, s Vor can be expressed by functions of the form β β β svor ( y) = y exp( βy) Γ( β) with y= σ/ σ. β is an adjustable parameter which basically defines the "sharpness" of the ISD. The higher β the smaller is the deviation of the ISD from the mean island size. In Figs. a,b functions generated by Eq. (4) for different β values are compared to the observed ISD's of Sn (Fig. a) and Pb (Fig. b). (4) Area Frequency [normalized to maximum],0 0,8 0,6 0,4 0,2 deposition temperature = 60 C deposition temperature = 00 C deposition temperature = 50 C β = 6 β = 2 0, Island Area/Mean Island Area 2,0 0,8 0,6 0,4 0,2 deposition temperature = 240 C deposition temperature = 60 C deposition temperature = 00 C β=2 β=8 0, Island Area/Mean Island Area (a) (b) Fig..: Comparison of the island size distributions of Sn (a) and Pb (b) with theoretical curves resulting from Eq. (4) Reasonable agreement is obtained if β is chosen to be higher than 6. Especially Pb has an extremely sharp, monomodal ISD with β between 2 and 8. The high values of β in comparison to those obtained in [0,] can have four (possibly correlated) reasons: heterogeneous nucleation mechanisms as it was assumed in [0] the islands considered in [0,] were two-dimensional while they are three-dimensional in this work a large depletion zone (i. e. a zone around an island where no new nuclei can form) as argued in [] critical nuclei which contain significantly more than one atom as proposed by Amar [23]. The third point is supported by the estimates of i as given in [20] but the existence of extended depletion zones cannot be ruled out because of the high uniformity of island distances, especially in the case of Pb (Figs. 3, 6). The author tends to rule out the possibility of heterogeneous nucleation because no evidence of any correlation of the island positions with some special features of the Al-underlayer was found. All evidence presented above leads to the conclusion that the elementary processes of monomer diffusion, island nucleation and island growth are decoupled from the morphology of the underlayer to a high degree. They are only dependent on the reduced deposition temperature of Sn and Pb and can be described by the simple model of homogenous nucleation as it is comprised by the rate equations. The ISD's can be described reasonably well by a model based on the Voronoi-Zone construction. 5. Summary and Conclusion It was shown that Sn and Pb deposited on polycrystalline Al underlayers exhibit the typical behavior of diffusion mediated island growth despite the complex morphology of the underlayer surface. The variation of the mean island distance with the deposition temperature

13 yielded an Arrhenius-behavior over a wide temperature range. Only in the vicinity of the melting points of Sn and Pb there are significant deviations from the Arrhenius-law. An investigation of the island size distributions in respect to their scaling with the mean island area had the following results: the ISD's for Sn were broad and showed scaling only at elevated deposition temperatures. This can be attributed to the various shapes of the Sn islands. Pb, on the other hand, has very narrow island size distributions and shows good data collapse for a wide range of deposition temperatures. This makes the system Al-Pb an interesting candidate for the production of equally sized, equally spaced particles on a polycrystalline substrate. To produce Pb-islands with sizes and distances in the nm-range the deposition temperatures have to be below room temperature. Further work is planned into this direction by deposition on cooled substrates and by characterizing the Pb-islands by vacuum- AFM. Special interest shall be devoted to the question whether the Pb islands maintain their sharp monomodal ISD at low temperatures. If this is the case then the production of nanometer sized particles with a narrow size distribution on polycrystalline substrates will be possible. An analysis by the rate-equation theory yielded activation energies of surface diffusion of 0.44 ( E i min ) (i = 8) ev for Sn and 0.5 ( E i min ) (i = 8) ev for Pb. The values of the activation energies are very similar for both materials and are not correlated to the energies of island formation ( ev for Sn and ev for Pb). Furthermore it was found that the dependencies of the mean island distance on the deposition temperature for both materials collapsed to a single curve when the deposition temperature was scaled to the melting temperature. This scaling by the homologous temperature is rather surprising and adds an additional confirmation to the conclusion that the morphological features of the underlayer surface have no influence on the island formation process. The decoupling of the island formation process from the substrate morphology is possibly connected with the existence of a wetting layer of Sn or Pb on Al. Such a layer was reported in [20] and is suspected to uniformly cover the Al-surface. In this case the single Sn or Pb atoms would not diffuse on Al but rather on a film of their own kind, thus explaining the dependence of the mean island distance on the reduced deposition temperature alone. Future work shall be devoted to the detection and characterization of the wetting-layer. It is expected that the conventional mechanisms of the transition from layer to island growth on single-crystalline substrates (strained pseudomorphic layer/formation of misfit dislocations/island nucleation) cannot be valid on a polycrystalline substrate. With a joint effort of experimental techniques like Atomic Force Microscopy, Transmission Electron Microscopy and Scanning Auger Electron Analysis a detailed characterization of the wetting layer is planned. Its role in the remarkable independence of the island formation process on the morphological features of the underlayer and its responsibility for the scaling of the island distance with the homologous temperature shall be clarified. Acknowledgements: The Author would like to thank A. Bergauer for the AFM-measurements to determine the underlayer roughness and the morphology of the islands, and H. Bangert for stimulating discussion. This work was supported by the Austrian "Fonds zur Förderung der Wissenschaftlichen Forschung" (FWF) under Grant No. P-22 8-PHY 3

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