5.4 Metal deposition studied by UHV microscopies	169

and with Î2 times the jump distance. By repeated observation of adatom diVusion over a single crystal plane, FIM has been able to map out the sites which the adatoms visit, and thus to distinguish exchange and hopping diVusion. Such measurements taken at diVerent annealing temperature can show the cross-over from one mechanism to the other (Feibelman 1990, Kellogg & Feibelman 1990, Chen & Tsong 1990, Kellogg 1994, 1997, Tsong & Chen 1997). Although the (001) surface presents particularly clear-cut examples of exchange diVusion, it is interesting to remember that the ®rst studies were actually done a decade earlier on f.c.c. (110) surfaces of Pt and Ir (Bassett & Webber 1978, Wrigley & Ehrlich 1980). DiVusion in the (cross-channel) [001] direction was found to proceed by an exchange process; this early work is reviewed by Bassett (1983) and Ehrlich (1994).

Many such interesting results have been obtained by the relatively few groups working in this ®eld. In particular, observations of linear rather than close-packed clusters, cluster diVusion, and adatom incorporation at steps by displacement mechanisms were all surprises when they were ®rst discovered, and warn against us making oversimple assumptions. Another use of FIM is for direct observation of the probability of diVerent spacings of pairs of adatoms within the ®rst ML. Applying Boltzmann statistics to these observations enables the lateral binding energy to be mapped in 2D as a function of spacing and direction. These interactions for Ir on W(110) are found to be in the range 30±100 meV, but can have either sign (Watanabe & Ehrlich 1992, Einstein 1996); thus the model introduced in this chapter, where a single pair binding energy Eb is used to describe lateral interactions, and nearest neighbor binding and directional isotropy are assumed, would be a serious oversimpli®cation if applied uncritically to such systems.

The same statistical methods have been used to identify the proportion of `long jumps' and/or `alternative paths' in surface diVusion, both by FIM and more recently by STM. Although these are typically a small proportion of the total, they could be important in particular circumstances, and are an important test of our understanding of rate processes at surfaces (Jacobsen et al. 1997, Lorensen et al. 1999). The full detail of these FIM and STM results are however very speci®c to each system; this is a reminder that the amazing complexity of dynamical cluster chemistry is involved in particular surface systems, but that we also need simple models to categorize broad classes of behavior.

5.4.3Energies from STM and other techniques

Until the advent of the STM, it was very diYcult to observe monolayer thick nuclei, except in special cases by REM and TEM, where high atomic number deposits were used (Klaua 1987, Yagi 1988, 1989, 1993). In the past few years UHV STM, with a variable low temperature stage, has become the most powerful technique for quantitative work on nucleation and growth. The sub-ML sensitivity over large ®elds of view, and the large variations in cluster densities with deposition temperature, have provided detailed checks of the kinetic models described in section 5.2. In particular, STM has enabled the experiments to be done at high density, which occurs at low T, and so typically i51. In this

170 5 Surface processes in epitaxial growth

Figure 5.15. STM pictures of a Pt(111) surface after deposition of 0.0042 ML at sample temperatures of (a) 23 K, (b) 115 K, (c) 140 K and (d) 160 K. Each picture is 48 nm wide and was taken at 20 K (after Bott et al. 1996, reproduced with permission).

limit the only energy parameter is Ed, which has been measured with high accuracy in several cases.

An example of the data obtained is shown in ®gure 5.15, from the work of Bott et al. (1996) on Pt/Pt(111); it is clear that nucleation densities, size and position distributions can be extracted from such (digitally acquired) images. This study, and several other studies on similar systems, have now made it possible to do detailed comparisons with eVective medium and related density functional calculations of metal±metal binding. One illuminating comparison is that of Ag/Ag(111) with Ag on 1 ML Ag on Pt(111), and with Ag/Pt(111). The systematic variations that are found re¯ect small diVerences in the lattice parameter (strain) and in strength of binding between these closely similar systems (Brune et al. 1994, 1995, Brune & Kern 1997); these features are also reproduced, more or less anyway, by the calculations (Ruggerone et al. 1997, Brune 1998). In Ag on 2 ML Ag on Pt(111), an interesting example of pattern formation was

5.4 Metal deposition studied by UHV microscopies						171
Table 5.4. Ea, Ed and Eb for f.c.c. (111)-like metal substrates
Deposit/Substrate	Ea	Ed		Ed12Eb	L2 Ea 2 Ed *	Technique
Pt/Pt(111)		0.26	6 0.02			STM [a]
		0.26	6 0.003			FIM [b]
Cu/Cu(111)		0.035 6 0.01				HAS [c]
					0.76 6 0.04	STM [d]
Ni/Cu(111)		0.08	6 0.02			HAS [c]
Ag/2MLAg/W(110)	2.20 6 0.10	0.15	6 0.10	0.65 6 0.03		SEM [e]
Ag/1MLAg/Fe(110)					0.86 6 0.05	SEM [e]
Ag/Ag(111)		0.10	6 0.01		0.71 6 0.03	STM [f, h]
	(2.23) [e]	(0.12) [e, g]		(0.68) [e]		Calculation
Ag/Pt(111)		0.16	6 0.01			STM [f]
	(2.94) [g]	(0.15) [g]				Calculation
Ag/1MLAg/Pt(111)		0.06	6 0.01			STM [f]
		(0.06) [g]				Calculation

Notes: * For a discussion of values in this column see section 5.5.2

Values in eV; those in brackets are theoretical calculations.

Sources: see table 5.5 on p. 172.

found in which mis®t dislocations provided a barrier to diVusing Ag adatoms (Brune et al. 1998); this example has much in common with the defect nucleation examples discussed in section 5.3.3.

Several groups are producing results in this ®eld, and as a result a data base is being accumulated as we write, albeit somewhat complicated by slight diVerences in techniques and analysis methods. Some comparisons between the various experiments are made in the tables which follow, and in a comprehensive review by Brune (1998). We are at an early stage of understanding these values in detail, but it is already clear that (001) f.c.c. metal surfaces are very diVerent from the (111)-like surfaces of table 5.4. The diVusion energies on (001) are quite a bit higher than on (111), and it is possible that several of these values correspond to exchange, rather than hopping diVusion. Some values abstracted from the literature are given in table 5.5.

In the last entry in table 5.5, Cu/Ni(100), Müller et al. (1996) observed the transition from i51 to i53, 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 ®gures 5.16 and 5.17. One can see that the temperature dependent region labelled i53, shows the corresponding rate dependence power law, p5i/(i12)53/5, supplementing the lower temperature regimes of i51 and i50. The last case arises at the lowest temperature where nucleation happens after rather than during deposition, so that the ®nal nucleation density may depend on the amount condensed, but does not depend either on how fast it was deposited, or on the difusion coeYcient.

At higher temperatures, work on the homoepitaxial system Cu/Cu(001) has failed to

172	5 Surface processes in epitaxial growth
	Table 5.5. Ea, Ed and Eb	for f.c.c. (001) metal substrates
	Deposit/Substrate	Ea (eV)	Ed (eV)	Eb (eV)	Technique
	Pt/Pt(001)		0.47 exchange		FIM [b]
	Fe/Fe(001)		0.45 6 0.05		STM [j]
	Cu/Cu(001)		0.36 6 0.03		SPA [k]
	Ag/Ag(001)		0.40 6 0.05		LEIS [l]
	Ag/1MLAg/Mo(001)	2.5	0.456 0.05	0.1257 0.125	SEM [m]
	Ag/Pd (001)	(2.67)	0.37 6 0.03		HAS [n]
	Cu/Ni(001)		0.35 6 0.02	0.467 0.19	STM [p]

Note: Values in eV; those in brackets are theoretical calculations.

Sources for tables 5.4 and 5.5.

Techniques: STM5scanning tunneling microscopy; FIM5®eld ion microscopy; HAS5 helium atom scattering; SEM5(UHV) scanning electron microscopy; SPA5SPA-LEED; LEIS5low energy ion scattering.

References: [a] Bott et al. (1996); [b] Feibelman et al. (1994), Kyuno et al. 1998; [c] Wulfhekel et al. (1996, 1998), Brune (1998); [d] Giesen & Ibach (1999); [e] Jones et al. (1990), Noro et al. (1996); [f] Brune et al. (1994, 1995); [g] more calculations (and more experiments) can be found via Brune (1998); [h] Morgenstern et al. (1998); [j] Stroscio et al. (1993), Stroscio & Pierce (1994); [k] Dürr et al. (1995), see also Swan et al. (1997); [l] Langelaar & Boerma (1996); [m] Venables (1987); [n] Félix et al. (1996); [p] Müller et al. (1996).

Figure 5.16. Arrhenius plot of the island density of Cu/Ni(001) measured by low temperature STM at coverage 0.1 ML, for a deposition rate 0.00134 ML/s (from Müller et al. 1996, reproduced with permisison).

5.4 Metal deposition studied by UHV microscopies	173

(a)

3x10±2 T = 145 K

2x10±2 post-nucleation

		i = 1
	10±2
units]	3x10±3	T = 215 K
	2x10±3	i = 1
[ML
x
N	10±3
	3x10±4	T = 345 K
	2x10±4		i = 3
	10±4
		10±4	10±3
			F [M L /s]

	(b)
	1.2					T = 160 K
						©i = 0©
	0.8				<S> = 5.5 atoms
	0.4
	0
	1.2					T = 215 K
Q/						©i = 1©
					<S > = 37 atoms
2	0.8
>
S<·	0.4
s
N
	0
	1.2					T = 345 K
						©i = 3©
	0.8
	0.4
	0	0.5	1	1.5	2	2.5	3	3.5
	0
				S /< S >

Figure 5.17. (a) Double logarithmic plot of the island density of Cu/Ni(001) versus deposition ¯ux for diVerent temperatures at coverage 0.1 ML; (b) scaled island size distributions deduced from the STM images of Cu/Ni(001) at coverage 0.1 ML, compared with KMC calculations of the corresponding distributions for i50 and 1 (after Amar & Family 1995, Müller et al. 1996, and Brune 1998, reproduced with permission).

see the i51±3 transition but instead observed direct transitions to higher i-values (Swan et al. 1997). However, 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 (001) surfaces, the role of second-nearest neighbors is particularly important, since all clusters only have either one or two nearest neighbor bonds. Moreover, it has been suggested that vacancy, in addition to adatom, migration is involved in coarsening (Hannon et al. 1997); this is certainly the case at high enough temperatures. Again, one can see that rather careful experimentation and analysis is required to keep the number of parameters in the models at a manageable level.

The cluster size distributions found for i50 as well as other i-values have been calculated, among others by Amar & Family (1995) and Zangwill & Kaxiras (1995). These distributions are compared with the Cu/Ni(001) STM experiments in ®gure 5.17(b). Note that the case for i50 has a maximum at small sizes. This is also a feature of