Venables J. Introduction to Surface and Thin Film Processes

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(Bauer 1997). Although one might attempt to extract detailed binding parameters from

such kinetic observations, this has not been emphasized, possibly because of their com-

plexity, including quite marked crystallographic anisotropy. Several of the adsorption

energies are however known from older thermal desorption and other thermodynamic

measurements (Bauer 1984).

5.4.2 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

5.4 Metal deposition studied by UHV microscopies 167

Figure 5.13. Arrhenius plot of nucleation density for silver islands on 2MLAg/W(110) with

nucleation model superimposed. Full line: E

52.1, E

50.25, E

50.135 eV, compared to data

on the ﬂattest, cleanest samples; dashed line: E

50.185 eV, other parameters unchanged,

compared to data on stepped and/or slightly contaminated samples. Deposition rate R5

0.3 ML/min (from Spiller et al. 1983, and Jones et al. 1990, reproduced with permission).

800 750 700 650 600 550 500 450

(K)

9.0

8.5

8.0

7. 5

7. 0

6.5

6.0

5.5

1.2 1.4 1.6 1.8 2.0 2.2

1000/

(1/K)

Log (

/cm

)

i = 34

i = 22

i = 17

i = 9

i = 6

Ag/W (110) Jones

et al

. (1990)

Triangles, two samples ‘clean’

Squares, ‘contaminated, stepped’

Diamonds, Spiller

et a

l. (1983)

observations are made at low temperature, with annealing at higher temperature for

given times to eﬀect the jumps; the imaging ﬁeld is of course switched oﬀ during the

annealing periods. FIM works best for refractory metals, and high quality information

has been obtained on diﬀusion coeﬃcients of individual atoms and small clusters in

systems such as Re, W, Mo, Ir and Rh on tungsten, as shown in ﬁgure 5.14 for the

W(211) surface (Ehrlich 1991, 1995, 1997). Diﬀusion on this surface is highly aniso-

tropic, essentially moving along 1D channels parallel to the [011

] direction, and avoid-

ing 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 ﬁgure 5.3 and often assumed implicitly as the adatom

diﬀusion mechanism) from exchange diﬀusion. If we draw a (001) surface of an f.c.c.

crystal such as Pt, we know from chapter 1, problem 1.2, where an adatom will sit on

this surface. So you can convince yourself that hopping diﬀusion will proceed in the

close-packed 冓110冔 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 see

that the direction of motion during diﬀusion is along 冓100冔, at 45° to hopping diﬀusion

168 5 Surface processes in epitaxial growth

Figure 5.14. FIM measurements of surface diﬀusion of individual adatoms at a function of

temperature on W(211), measured on the same sample. Note that energies E

are quoted in

kcal/mol (23.06 kcal/mol51 eV/atom). Errors in D

are the factors in brackets (from Ehrlich

1991, after Wang & Ehrlich 1988, reproduced with permission).

and with 冑2 times the jump distance. By repeated observation of adatom diﬀusion 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 diﬀusion. Such measurements taken at

diﬀerent 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 diﬀusion, it is interesting to remember that the ﬁrst studies were

actually done a decade earlier on f.c.c. (110) surfaces of Pt and Ir (Bassett & Webber

1978, Wrigley & Ehrlich 1980). Diﬀusion 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 ﬁeld. In particular, observations of linear rather than close-packed clus-

ters, cluster diﬀusion, and adatom incorporation at steps by displacement mechanisms

were all surprises when they were ﬁrst discovered, and warn against us making over-

simple assumptions. Another use of FIM is for direct observation of the probability of

diﬀerent spacings of pairs of adatoms within the ﬁrst ML. Applying Boltzmann sta-

tistics 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 E

is used to describe lateral interactions, and nearest neighbor binding and

directional isotropy are assumed, would be a serious oversimpliﬁcation 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 diﬀusion, 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 understand-

ing 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 speciﬁc 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.

5.4.3 Energies from STM and other techniques

Until the advent of the STM, it was very diﬃcult 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 ﬁelds 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 experi-

ments to be done at high density, which occurs at low T, and so typically i51. In this

5.4 Metal deposition studied by UHV microscopies 169

limit the only energy parameter is E

, which has been measured with high accuracy in

several cases.

An example of the data obtained is shown in ﬁgure 5.15, from the work of Bott et

al. (1996) on Pt/Pt(111); it is clear that nucleation densities, size and position distribu-

tions 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 eﬀective 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 reﬂect small

diﬀerences 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

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).

found in which misﬁt dislocations provided a barrier to diﬀusing Ag adatoms (Brune

et al. 1998); this example has much in common with the defect nucleation examples dis-

cussed in section 5.3.3.

Several groups are producing results in this ﬁeld, and as a result a data base is being

accumulated as we write, albeit somewhat complicated by slight diﬀerences in tech-

niques 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 diﬀerent from the (111)-like surfaces of table 5.4.

The diﬀusion 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 diﬀusion.

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 transi-

tion from i51 to i53, which is expected for the (001) surface, and so could deduce E

in addition to E

. They also observed both the rate dependence, and the size distribu-

tions, showing that this formed a consistent story, as illustrated in ﬁgures 5.16 and 5.17.

One can see that the temperature dependent region labelled i53, shows the corre-

sponding rate dependence power law, p5i /(i12)53/5, supplementing the lower tem-

perature regimes of i51 and i50. The last case arises at the lowest temperature where

nucleation happens after rather than during deposition, so that the ﬁnal nucleation

density may depend on the amount condensed, but does not depend either on how fast

it was deposited, or on the difusion coeﬃcient.

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

5.4 Metal deposition studied by UHV microscopies 171

Table 5.4. E

and E

for f.c.c. (111)-like metal substrates

Deposit/Substrate E

12E

L2 E

2 E

* 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.

172 5 Surface processes in epitaxial growth

Table 5.5. E

and E

for f.c.c. (001) metal substrates

Deposit/Substrate E

(eV) E

(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; FIM5ﬁeld 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).

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 nucle-

ation 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 neigh-

bor bonds. Moreover, it has been suggested that vacancy, in addition to adatom, migra-

tion 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 anal-

ysis 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 cal-

culated, among others by Amar & Family (1995) and Zangwill & Kaxiras (1995). These

distributions are compared with the Cu/Ni(001) STM experiments in ﬁgure 5.17(b).

Note that the case for i50 has a maximum at small sizes. This is also a feature of

5.4 Metal deposition studied by UHV microscopies 173

Figure 5.17. (a) Double logarithmic plot of the island density of Cu/Ni(001) versus deposition

ﬂux for diﬀerent 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).

= 145 K

post-nucleation

= 215 K

= 345 K

= 1

= 3

= 1

–

[ML/s]

–

2x10

–

3x10

–

2x10

–

3x10

–

2x10

–

3x10

–

(a)

[ML units]

•

0 0.5 1 1.5 2 2.5 3 3.5

1.2

0.8

0.4

1.2

0.8

0.4

1.2

0.8

0.4

= 160 K

' = 0'

<S> = 5.5 atoms

= 215 K

' = 1'

< > = 37 atoms

= 345 K

' = 3'

(b)

nucleation in the presence of steps (Bales 1996). The role of steps is introduced in the

following section 5.5, along with ripening and interdiﬀusion; further aspects of nuclea-

tion and growth of thin ﬁlms are deferred to the remaining chapters where they are con-

sidered via models of bonding and electronic structure in metals and semiconductors.

5.5 Steps, ripening and interdiffusion

5.5.1 Steps as one-dimensional sinks

Steps often act as one-dimensional sinks, as illustrated schematically in ﬁgure 5.10(b).

Most interest has historically centered on incomplete condensation in island growth

systems. In this case, when both E

and E

are typically quite small, the mean diﬀusion

length before desorption is the BCF length x

, introduced in section 1.3, and given by

5(D

)

1/2

5(a/2)(

)

1/2

exp{(E

– E

)/2kT}. (5.20)

At moderate deposition temperatures, steps (statistically) capture atoms arriving in a

zone of width x

either side of the step, as was shown in problem 1.4. Alkali halides

show the classic example of step decoration (Kern et al. 1979, Mutaftschiev 1980,

Keller 1986) where strongly bound pairs of metal atoms nucleate at steps, but nuclea-

tion is unlikely on a perfect terrace. In a few cases, step decoration eﬀects have been

studied quantitatively. The binding energy, E

50.23 6 0.025 eV, for Au atoms to steps

on NaCl(100) has been measured by comparison with a detailed step nucleation model

(Gates & Robins 1982, 1987b), and this value is borne out by a recent calculation

(Harding et al. 1998). The case of Cd/NaCl(100) has also been studied by modulated

mass spectrometry techniques, resulting in the much higher step binding energy of Cd

atoms, 1.1 6 0.15 eV (Henry et al. 1985).

There is also a large literature devoted to such clusters at steps, including their posi-

tion relative to the step, which involves long range elastic interactions in addition to

other atomic level forces. The ‘double decoration’ technique is an elegant method of

demonstrating such eﬀects, which has been used extensively in TEM experiments over

many years (Bassett 1958, Bethge 1962, Kern et al. 1979, Kern & Krohn 1989, Bethge

1990). The decoration technique is best known for demonstrating 2D island and pit

nucleation, oscillatory nucleation and growth and dislocation spiral growth (and evap-

oration) of the alkali halides themselves, as reviewed by Mutaftschiev (1980) and

Venables et al. (1984). As seen in ﬁgure 5.18, single height steps are rounded, double

height steps square, and dislocation spirals are easily recognized.

The eﬀect of adatom capture by steps can be treated using an extension of (5.13) in

one of two ways. Either, we can look on a scale between the steps, in which case the

steps provide the boundary conditions for a rate–diﬀusion equation of the form

/dt5R2n



x(D



x). (5.21)

Or, we can average over many steps, in which case adatom capture by steps adds an

additional loss term to (5.13) with a characteristic time

. We can show from the

174 5 Surface processes in epitaxial growth

5.5 Steps, ripening and interdiffusion 175

Figure 5.18. Steps on KCl(001) revealed by the decoration technique: (a) single height pits;

(b) single height and (c) double height dislocation spirals (from Venables et al. 1984,

reproduced with permission, after Métois et al. 1978 and Meyer & Stein 1980).

(b)

(c)

equivalence of these two viewpoints in complete condensation that the average

adatom density n

, (5.22)

where n

is the concentration in equilibrium with the steps, and

/12D, (5.23)

where d is the distance between steps; this expression is readily derived on the basis that

the adatom concentration n

(x) is an inverted parabola for complete condensation, as

in problem 1.4.

This simple expression may be modiﬁed if evaporation, nucleation or the

Ehrlich–Schwoebel (ES) barrier are allowed, as can be explored via project 5.3. The

name, adopted relatively recently, stems from two papers in which the eﬀect was ﬁrst

discussed (Ehrlich & Hudda 1966, Schwoebel & Shipsey 1966). TEM and FIM

methods have demonstrated the ES eﬀect, where diﬀusing adatoms have diﬃculty in

surmounting a downward step. At low temperatures the barrier is eﬀective, and nuclei

are formed on the upper terrace right up to the down-step. An early TEM example was

obtained by Klaua (1987), who observed Au ML islands decorating steps, and also

nucleating on the terraces of a Ag(111) sample, as shown in ﬁgure 5.19.

5.5.2 Steps as sources: diffusion and Ostwald ripening

Steps, in addition to being sinks, can also act as sources of adatoms. Emission of

adatoms is part of sublimation, which we studied in section 1.3 via problem 1.2(b), and

in the context of adsorption in section 4.2; this happens if n

.0 in (5.22). In this case,

adatoms are created at kink sites and can diﬀuse over the terrace and become incorpo-

rated in other steps. When the adatom concentration is low, this process has an eﬀective

diﬀusion constant

D, where n

5K exp{2(L 2E

)/kT}, (5.24)

so that the activation energy Q5(L2E

), with K an entropic constant. At high

temperatures, other mechanisms may be active, including surface vacancies; indeed one

of the diﬃculties of studying surface diﬀusion is that there are so many mechanisms

which may need to be considered (Bonzel 1983, Gomer 1983, 1990, Naumovets &

Vedula 1985, Naumovets 1994). However, during annealing at moderate temperatures

(5.24), or a variant which allows for small amounts of clustering, is likely to be a good

approximation. Such issues can be explored via project 5.4.

Noro et al. (1996) analyzed Ag patches deposited on Fe(110), following the anneal-

ing of the 3 ML of deposited Ag as shown in ﬁgure 5.20. The broadening of the ﬁrst

and second ML could be followed separately, by biased secondary electron imaging as

described in section 3.5; D

values were deduced for Ag motion on the ﬁrst ML, giving

an activation energy 0.86 6 0.05 eV. Using (5.24) and assuming that L for the second

ML is close to the bulk Ag value of 2.95 6 0.01 eV, they found (E

)52.0960.06

eV. This is to be compared with that deduced for Ag on 2 ML Ag/W(110) from the

176 5 Surface processes in epitaxial growth