EPFL Lecture #5 (Venables)

Notes for EPFL Lecture 5 (Venables)

Lecture notes by John A. Venables. Lecture given 23 Oct 97. Latest version 2 April 09.

The references for this lecture are here.

5. Experimental and Model Studies of Specific Systems

This lecture (and maybe the next also) gives a historically based description of the use of microscopic techniques to study nucleation and growth processes, and the use of the models described in Lecture 4 to understand such systems quantitatively. The examples chosen are necessarily a bit arbitrary, and a fuller account can be found in recent multi-author research compilations. The latest one I have been involved with is Growth and Properties of Ultrathin Epitaxial Layers, edited by D.A. King and D.P. Woodruff (Elsevier, 1997) where my chapter 1 comments on the following systems, among others. I am also drawing on other articles in this volume for specific examples.

5.1 Ex-situ observations of metal/insulator growth by TEM

  • Noble metals on alkali halides
  • An example of the use of non-UHV TEM is shown in diagram E7 from the Robins' group. The deposition (of Au/NaCl(001)) is done in UHV, but the micrographs are obtained by 1) coating the deposit with carbon in UHV; 2) taking the sample out of the vacuum; 3) dissolving the substrate in water; 4) examining the Au islands on the carbon by TEM. By this means island densities, growth, coalescence and nucleation on defect sites can all be observed.

    By performing many experiments at different deposition rates R, and temperatures T, as a function of coverage, their group and others have produced quantitative data of island growth and rate equation models have been tested. It is clear that this type of technique is destructive of the sample: it is just as well that NaCl is not too expensive, and that gold/ silver etc are relatively unreactive, or the technique would not be feasible (see Venables and Price, 1975)

    The work on noble metals Ag and Au deposited onto alkali halides constitutes a long story which I summarize roughly as follows. A full review of early work has been given by Venables et al. (1984) and by Robins (1988), including an extensive tabulation of energy values deduced from experiment. For silver and gold, the adsorption energy, Ea, of the atoms is in the range 0.5 - 0.9 eV, with the Au values somewhat higher than the Ag values, and errors for particular deposit- substrate combinations < 0.1 eV. Typically, these values were deduced by first showing that the initial nucleation rate J at high temperatures varied as R2, and so corresponded to i = 1.

    In this regime, we can see that because J varies as Dn12 this is proportional to R2exp{(2Ea - Ed)/kT}, so the T-dependence of the nucleation rate yields (2Ea - Ed). This information can be combined with the low temperature (complete condensation) nucleation density, which for i = 1 yields Ed, as can be seen from diagram E6. An alternative piece of data is the island growth rate at high temperature, which is determined by the width of the BCF diffusion zone around each island. The growth rate thus has a T-dependence given by (Ea - Ed) via an equation which depends on the 2D or 3D shape of the islands.

    Examples of deducing the adsorption stay time taua for Au/KCl (001) and the mean square diffusion distance Dtaua for Au/NaCl (001) is shown in diagram E12 (Stowell 1972, 1974). The energies deduced depend a little on the exact mode of analysis, but are in the region Ea = 0.65-0.70 and Ed = 0.25-0.30 eV for Au/KCl. The corresponding quantities deduced for Au/NaCl were similar; for Ag/KCl they were around 0.5 and 0.2 eV, and for Ag/NaCl 0.65 and 0.2 eV respectively (Donohoe and Robins, 1976, Venables et al. 1984, Table 2).

    These Ea and Ed values are much lower than the binding energy of pairs of Ag or Au atoms in free space, which are accurately known, having values 1.65 ± 0.06 and 2.29 ± 0.02 eV respectively (Gringerich et al. 1985). We can therefore see why we are dealing with island growth, and why the critical nucleus size is nearly always one atom. The Ag or Au adatoms re-evaporate readily above room temperature, but if they meet another adatom they form a stable nucleus which grows by adatom capture. This type of behaviour is observed for all metal/ alkali halide combinations. It is helpful to get from diagram E12 not just the activation energies, but also the absolute magnitude of both taua and the BCF length (Dtaua)1/2; these quantities combined with the distance between the islands in diagram E7 make the distinction between complete and incomplete condensation more concrete.

  • Complications: defects and cluster mobility
  • The combination of experiment and model calculations presented above is satisfying, but is it correct? What do I mean by that? Well, the experiment may not be correct, in that there may be defects on the surface which act as preferred nucleation sites. It is very difficult to tell, simply from looking at TEM pictures such as diagram E7, whether the nuclei form at random on the terraces, or whether they are nucleated at defect sites; only nucleation along steps is obvious to the eye. We have described the classic way to distinguish true random nucleation, with i = 1. But there are several other ways to get J ~ R2, including the creation of surface defects during deposition. In this case we might have nucleation on defects (i = 0), but with the defects produced in proportion to R by electron bombardment. Alkali halides are very sensitive to such effects, which were subsequently shown to have played a role in the early experiments (Robins, 1988).

    As substrate preparation and other experimental techniques improved, lower nucleation densities which saturated earlier in time were observed (Velfe et al. 1982). This has been associated with the absence of impurities/ point defects, and the mobility of small clusters. From detailed observations as a function of R,T and t, some energies for the motion of these clusters have been extracted. Qualitatively, it is easy to see that if all the stable adatom pairs move quickly to join pre-existing larger clusters, then there will be a major suppression of the nucleation rate. An example is seen in diagram E12b; here the value of Dtaua apparently increases as the temperature increases, contrary to expectations. However, in this case it is the model which is incomplete, and the inclusion of some cluster mobility is needed to fix the problem. This results in a much lower coverage, Z1 at which the nucleation density is a maximum or saturates as indicated in diagram E13 (Venables 1973, Stowell 1974, Robins, 1988).

    This was then studied intensively for Au/NaCl(001) by Gates and Robins (1982, 1987), who found that a model containing several more mobility parameters was needed to explain the more recent results.

  • Further experiments and energy values
  • There are several further interesting possible experiments. The first is the study of alloy deposits, which has now been performed for three binary alloy pairs, formed from Ag, Au and Pd on NaCl(001) (Anton et al. 1990, Schmidt et al. 1990). In such experiments the atoms with the higher value of Ea, namely Au in Ag-Au, or Pd in Pd-Ag and Pd-Au, form nuclei preferentially, and the composition of the growing film is initially enriched in the element which is most strongly bound to the substrate. The composition of the films was measured by X-ray fluorescence and energy dispersive X-ray analysis, and only approached that of the sources only at long times, or under complete condensation conditions.

    These experiments can be analysed to yield energy differences dE, where dE = dEx - dEy, and dEx, dEy = (Ea-Ed)x,y for the two components. Values of dE have been obtained for the pairs, namely Au-Ag: 0.11 ± 0.03; Pd-Au: 0.12 ± 0.03; Pd-Ag: 0.25 ± 0.05 eV. These experiments measure, very accurately, differences in integrated condensation coefficients, alphax,y(t), which are determined by the diffusion distances of the corresponding adatoms. Coupled with nucleation density measurements, the data give particular values for Ea and Ed for these three elements on NaCl(001), as given in the following Table.

    Table 5.1: Values (in eV) of Ea and Ed of Ag, Au and Pd adatoms on NaCl(001)

    Values without errors are derived from data combinations (Robins 1988 and Anton et al. 1990)
    Element	    dE		(Ea-Ed)		Ea		Ed
    Ag    			0.22		0.41 		0.19
    	0.11 ± 0.03
    Au        		0.33 ± 0.02 	0.49 ± 0.03 	0.16 ± 0.02 
    	0.12 ± 0.03
    Pd         		0.45		0.78		0.33
    	0.25 ± 0.05
    As you may imagine, the low values of Ea make these and other insulating substrates very prone to have nucleation on defects, both steps and point defects. This topic also has a long history which I have reviewed for the MRS Fall meeting in 1996 (Venables, 1997). I am also working, with colleagues John Harding and Marshall Stoneham of University College London on the models to explain the values of Ea, Ed and other energies, such as binding to steps. I talked around these topics informally in the lecture.

    5.2 Metals studied by SEM, FIM, STM, and other (UHV) Microscopies

    UHV techniques (SEM, FIM and more recently STM, plus diffraction techniques including Helium scattering) examine the deposit/ substrate combination in-situ, without breaking the vacuum. This gives extra power to the experiment, at the cost of rather less convenience to the experimenter; but nevertheless a much wider set of substrates and deposits have been observed in recent years, not least at EPFL.

  • In-situ UHV SEM of metals on metals
  • My Sussex group developed UHV-SEM and related techniques, and used them to study Stranski-Krastanov growth systems at elevated T, where, as seen in diagram E8 for Ag/Mo(100), diffusion distances of the adatoms can be many micrometers (see e.g. Venables et al. 1984). The SEM is good for visualizing strongly 3D objects, such as the (001) oriented Ag islands seen on Mo(001) in this diagram.

    The systems Ag/W(110) and Ag/Fe(110) have been examined in detail with students and colaborators. In these systems, 2ML of Ag form first, and then flat Ag islands grow in (111) orientation. The nucleation density N(T) is a strong function of substrate temperature, and the results of several Ag/W(110) experiments are shown in diagram E14, in comparison with a nucleation calculation of the type outlined in lecture 4.3.

    The calculation arises in the following way. We assume that the energy of the critical nucleus Ei can be expressed in terms of lateral pair-bonds of strength Eb, and that the important clusters, on top of the 2ML intermediate layer, are 2-dimensional, compact and quasi-hexagonal. Then, Ei can be expressed in terms of Eb by counting bonds. The critical nucleus size i is obtained self-consistently, by assuming a given value, calculating nx for that value, and repeating the calculation for all possible i-values. The value which gives the lowest nx, or equivalently the lowest nucleation rate, is the actual critcal nucleus size, since the cluster size with the lowest density (i.e. highest free energy) in equilibrium with the adatom population, then constitutes the ‘nucleation barrier’.

    Condensation is complete in this system, except at the highest temperatures studied, and the critical nucleus size is in the range 6-34, increasing with substrate temperature. Energy values were deduced, Ea = 2.2 ± 0.1, and the combination energy (Ed +2Eb) = 0.65 ± 0.03 eV, within which Ed = 0.15 ± 0.1 and Eb = 0.25 -/+ 0.05 eV (Jones et al 1990).

    What, however, makes these values interesting is that they can be compared with the best available calculations of metallic binding. Comparison has been made with Effective Medium theory calculations, and the agreement is striking, as shown in the Table below. In particular, the results demonstrate the non-linearity of metallic binding with increasing coordination number. In the simplest nearest neighbour ‘bond’ model, the adsorption energy on (111) corresponds to 3 bonds, or half the sublimation energy for a fcc crystal. So for Ag, with L = 2.95 eV, such a model would give Ea = 1.47 eV, whereas the actual value is much larger. The same effect is at work in the high binding energy of Ag2 molecules, quoted in sect 5.1 in connection with island growth experiments. However, the last bonds to form are much weaker, so that in this case Eb is much less than L/6 = 0.49 eV. This is a general feature of ‘Effective Medium’ or ‘Embedded Atom’ calculations on metals.

    The comparison between Ag/W and Ag/Fe(110) shows that the first two layers are different crystallographically, with two distorted Ag(111)-like layers on W(110), compared to a missing row c5x1 structure for the first layer, followed by an Ag(111)-like second layer on Fe(110); but adatom behaviour on top of these two layers is very similar, and the values deduced from annealing experiments: Ea - Ed = 2.09 eV ± 0.05 eV for Ag/Ag/Fe(110) is essentially the same as deduced for Ag/Ag/W(110) from nucleation experiments (Noro et al, 1996).

    There are still some curious features of these systems, including how the transition from 2D nucleation to 3D growth occurs, and the precise role of surface defects, including steps on such surfaces. The evidence to date is that the 2D-3D transition occurs after nucleation is essentially complete, and that steps have a big effect on atomic motion within the first silver layers, but much less on top of these stable layers. The more perfect the substrate, the flatter the islands are. This is probably related to the difficulty of islands growing in height, without threading dislocations which may be generated at steps (Bermond and Venables, 1983). Some effects in the first ML’s of the related, but rather more reactive systems Cu and Au deposited onto W and Mo(110) have been studied by LEEM [Bauer 1997].

  • FIM studies of surface diffusion on metals
  • At the other end of the length scale, the Field Ion Microscope (FIM) has been used to study individual atomic jumps and the formation and motion of small clusters. These observations are made at low T, with annealing at higher T for given times to effect the jumps. FIM works best for refractory metals, and high quality information has been obtained on diffusion coefficients in systems such as Re, W, Mo, Ir and Rh on tungsten, as shown in diagram E9 for the W(211) surface (Ehrlich 1991, 1994). Diffusion on this surface is highly anisotropic, essentially moving along 1D channels parallel to the [01bar1] direction, and avoiding jumps between channels. On higher symmetry surfaces, e.g. diffusion on (001) is observed to be isotropic, as it should be.

    A particularly elegant application of FIM is to distinguish the ‘hopping’ diffusion (pictured schematically in diagram E3 and often assumed implicitly as the adatom diffusion mechanism) from ’exchange’ diffusion. Draw a (001) surface of an fcc crystal such as Pt(100). We know from problem 1.4.1 where an adatom will sit on this surface. So you can convince yourself that hopping diffusion will proceed in <110> directions. By contrast, the exchange process consists of displacing a nearest neighbor of the adatom, and exchanging the adatom with it. The substrate atom ‘pops out’ and the adatom becomes part of the substrate. In this case you can convince yourself that the direction of motion during diffusion is along <100>, at 45 degrees to hopping diffusion and with root-2 times the jump distance. By repeated observation of adatom diffusion over a single crystal plane, FIM is able to map out the sites which the adatoms visit, and thus to distinguish exchange and hopping diffusion. Such measurements taken at different annealing T can show the cross-over from one mechanism to the other (Kellogg 1994).

  • In-situ UHV STM studies of metal nucleation and growth
  • In my ASU lectures, we considered Surface and Microscopic Techniques in section 3 but only gave a short mention of STM and FIM in section 3.1, and section 3.5. To make definitive statements about the use of STM is almost bound to lead to failure; new applications and new configurations emerge at such a rate that it is more than a full time job just to keep up with them: so I won't try. At the risk of offending other authors, friends and colleagues recommend Chen's book as an introduction, and refer to multi-author texts and review articles for more specialist information. I would like to know which book you think is most useful for a beginner. Books that may be helpful in the present context include J. Stroscio and E. Kaiser Scanning Tunelling Microscopy (1993), Guntherodt and Weisendanger, vols 1-3 (1991 onwards), and also R. Weisendanger Scanning Probe Microscopy and Spectroscopy (1994). Despite the immense amount of work described in these books, I find it difficult to get a perspective on it, since it is all so recent.

    In the last few years, UHV-STM has become the main technique for studies of this type, with a variable (low) temperature instrument the most powerful for quantitative studies. The sub-ML sensitivity over large fie lds of view, and the large variations in cluster densities with deposition T, have provided detailed checks of the kinetic models of nucleation and growth described in lecture 4. In particular, STM has enabled the experiments to be done at high density, which occurs at low T, and so typically i = 1. In this limit the only energy parameter is Ed, which has been measured with high accuracy.

    An example is shown in diagram E10, from the work of Bott et al (1996) on Pt/Pt(111). Several other studies on similar systems have now made it possible to do detailed comparisons with (effective medium) theories of metal-metal binding. One illuminating comparison is that of Ag/Ag(111) with Ag on 2ML Ag on Pt(111), and with Ag/Pt(111). The systematic variations that are found reflect small differences in the lattice parameter (strain) and in strength of binding between these closely similar systems (Brune et al. 1995, Brune and Kern 1997).

  • Energy values from nucleation and diffusion experiments
  • Some comparisons betweeen the various experiments are made in the tables which follow. Table 5.2 is for (111)-like substrates and Table 5.3 for (100) surfaces.

    Table 5.2: Ea , Ed and Eb for fcc (111)-like metal substrates

    Deposit/Subs	Ea  (eV)	Ed (eV)	    Tech   Ed +2Eb (eV)
    Pt/Pt(111)			0.26 ± 0.02 (STM)
    				0.25 ± 0.02 (FIM)
    Cu/Cu(111)			0.04 ± 0.01 (He scattering)
    			(note experimental procedure may give low value)
    Ag deposited onto 2ML Ag/W(110) 2.20 ± 0.10 0.15 ± 0.10 (SEM) 0.65 ± 0.03 (Values in brackets are theoretical calculations) Ag(111) (2.23) 0.10 ± 0.01 (STM) (0.68) Pt(111) (2.94) 0.16 ± 0.01 (STM) 1ML Ag/Pt(111) 0.06 ± 0.01 (STM)

    We are at early stage of understanding these values in detail, but it is already clear that (001) fcc metal surfaces are very different from the (111)-like surfaces of table 5.2. The values found are quite a bit higher, and it is possible that several of these values correspond to exchange, rather than hopping diffusion. Some values abstracted from the literature are given in Table 5.3.

    Table 5.3: Ea , Ed and Eb for fcc (001) metal substrates

    Deposit/Subs	Ea  (eV)	Ed (eV)	    Tech      Eb (eV)
    Pt/Pt(001)			0.47        (FIM, Exchange)
    Fe/Fe(001)			0.45 ± 0.05 (STM)
    Ni/Ni(001)			0.47        (STM)
    Cu/Cu(001)			0.40        (STM)
    Ag deposited onto 2ML Ag/Mo(001) 2.5 0.45 ± 0.05 (SEM) 0.125 -/+ 0.125 (Values in brackets are theoretical calculations) Pd(001) (2.67) 0.37 ± 0.03 (He scatt)
    Cu deposited onto Ni(001) 0.35 ± 0.02 (STM) 0.46 -/+ 0.19

    In the last case, Cu/Ni(100), Müller et al (1996) observed the transition from i = 1 to i = 3, which is expected for the (001) surface, and so could deduce Eb in addition to Ed. They also observed both the rate dependence, and the size distributions, showing that this formed a consistent story, as illustrated in diagrams E15 and E16. You can notice that the temperature dependent region labelled i = 3 also shows the corresponding rate dependence power law, p = i/(i+2) = 3/5, supplementing the lower T regimes of i = 1 and i = 0. The last case arises at the lowest T where nucleation happens after rather than during deposition, so that the final nucleation density may depend on the amount condensed, but doesn't depend on how fast it was deposited. The size distributions found for i = 0, as well as other i-values have been calculated, inter alia by Amar and Family (1995). These distributions are compared with the experimental distributions in diagram E17.

    Some other work, e.g. on Cu/Cu(001) has failed to see the i = 1 to 3 transition but instead observed direct transitions to higher i-values. While this work remains preliminary and controversial, we note that no particular sequence of i-values is required by the nucleation model itself; what actually happens is the result of the (lateral and vertical) binding energy of the clusters. On the (001) surfaces, the role of second-nearest neighbors is particularly important, since all clusters only have either 1 or two nearest neighbor bonds. Thus there may not be any particularly 'magic' 2D sizes beyond 4-clusters.