Venables J. Introduction to Surface and Thin Film Processes

Подождите немного. Документ загружается.

i.e. on spatial correlations which develop during nucleation and growth. Many authors

(e.g. Myers-Beaghton & Vvedensky 1991, Bartelt & Evans 1992, 1994, Amar & Family

1995, Mulheran & Blackman 1995, 1996, and Zangwill & Kaxiras 1995) have evaluated

size distributions during simulations, and shown that they are characteristic both of the

critical cluster size, i, and of the spatial correlations. Brune et al. (1999) have made a

detailed comparison of the various approximations, including coalescence terms, for

the case of 2D sub-monolayer growth.

5.3 Metal nucleation and growth on insulating substrates

Some results of atomistic nucleation and growth models are described in the context

of speciﬁc experimental examples for the remainder of this chapter. We concentrate on

metal deposition, on insulators in this section and on metals in section 5.4. These exam-

ples illustrate the kinds of experimental tests to which atomistic models have been sub-

jected over almost 30 years.

5.3.1 Microscopy of island growth: metals on alkali halides

An example of the use of non-UHV TEM to study nucleation and growth is shown in

ﬁgure 5.8 from the Robins group (Donohoe & Robins 1972, Venables & Price 1975).

The deposition of Au/NaCl(001) was done in UHV, but the micrographs were obtained

by (1) coating the deposit with carbon in UHV; (2) taking the sample out of the

vacuum; (3) dissolving the substrate in water; and (4) examining the Au islands on the

carbon by TEM. By this means island densities, growth, coalescence and nucleation on

defect sites could all be observed. By performing many experiments at diﬀerent depo-

sition 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.

The work on noble metals Ag and Au deposited onto alkali halides constitutes quite

a long story which can be summarized roughly as follows. A full review of early work

has been given by Venables et al. (1984) and by Robins (1988), including extensive tab-

ulation of energy values deduced from experiment using the models described in

section 5.2. Typically, these values were deduced by ﬁrst showing that the initial nucle-

ation rate J at high temperatures varied as R

, and so corresponded to i51 in (5.11).

In this regime where n

we can see that

J5dn

/dt5

which is proportional to R

exp{(2E

2 E

)/kT}, (5.15)

so the T-dependence of the nucleation rate yields (2E

2 E

). This information can be

combined with the low temperature (complete condensation) nucleation density, which

for i51 yields E

, as can be seen from table 5.1. An alternative piece of data is the island

growth rate at high temperature, determined by the width of the BCF diﬀusion zone

5.3 Metal nucleation and growth on insulating substrates 157

around each island, which leads to (5.12) for the capture numbers. The growth rate thus

has a T-dependence given by (E

2 E

) via an equation which depends on the 2D or 3D

shape of the islands.

The energies deduced depended a little on the exact mode of analysis, but were in

the region E

50.65–0.70 and E

50.25–0.30 eV for Au/KCl. The corresponding quan-

tities deduced for Au/NaCl were similar; for Ag/KCl they were around 0.5 and 0.2 eV,

158 5 Surface processes in epitaxial growth

Figure 5.8. TEM micrographs of Au/NaCl (001) formed at T5250 °C, R51310

atoms cm

and deposition times of (a) 0.5, (b) 1.5, (c) 4, (d) 8, (e) 10, (f) 15, (g) 30 and (h) 85 min

(from Donohoe & Robins 1972, reproduced with permission).

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

and for Ag/NaCl 0.65 and 0.2 eV respectively (Stowell 1972, 1974, Venables 1973,

Donohoe & Robins 1976, Venables et al. 1984, Table 2). These E

and E

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 6 0.06 and 2.29 6 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 behavior was observed

for all metal/alkali halide combinations.

5.3.2 Metals on insulators: checks and complications

The combination of experiment and model calculations presented in the previous

section 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 nucle-

ation sites. It is very diﬃcult to tell, simply from looking at TEM pictures such as ﬁgure

5.8, 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. In the previous section

we described the classic way to distinguish true random nucleation, with i51. But there

are several other ways to get J⬃R

, including the creation of surface defects during

deposition. In this case we might have nucleation on defects (i50), but with the defects

produced in proportion to R by electron bombardment. Alkali halides are very sensi-

tive to such eﬀects, which were subsequently shown to have played a role in early experi-

ments (Usher & Robins 1987, Robins 1988, Venables 1997, 1999).

As substrate preparation and other experimental techniques improved, lower nucle-

ation densities which saturated earlier in time were observed (Velfe et al. 1982). This

has been associated with the reduction in 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 (Venables 1973, Stowell 1974). This

was studied intensively for Au/NaCl(001) by Gates & Robins (1987a), who found that

a model involving both defect and cluster mobility parameters were needed to explain

the results of Usher & Robins (1987). The revised values of E

and E

for this system

are given in table 5.2; in particular, (E

2 E

) has been determined in several indepen-

dent experiments to be 0.33 6 0.02 eV (Robins 1988, Venables 1994).

There are several further interesting experiments, including the study of alloy depos-

its, which has now been performed for three binary alloy pairs, formed from Ag, Au and

Pd on NaCl(100) (Schmidt et al. 1990, Anton et al. 1990). In such experiments the atoms

with the higher value of E

, 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 at long times, or under complete condensation conditions.

5.3 Metal nucleation and growth on insulating substrates 159

These experiments can be analyzed to yield energy diﬀerences dE, where

dE5dE

2dE

, and dE

, dE

5(E

2 E

)

x,y

for the two components. Values of dE have

been obtained for the pairs, namely Au–Ag, 0.11 6 0.03; Pd–Au, 0.12 6 0.03; Pd–Ag,

0.256 0.05 eV. These experiments measure, very accurately, diﬀerences in integrated

condensation coeﬃcients,

x,y

(t), which are determined by the BCF diﬀusion distances

of the corresponding adatoms, as explored in problem 5.1. Coupled with nucleation

density measurements, the data give accurate values for E

and E

for these three ele-

ments on NaCl(100), as given in table 5.2.

More recently, eﬀorts have been made to understand some of these energy values in

terms of metal–ionic crystal bonding. Earlier estimates maintained that a considerable

part of the binding was of van der Waals type, but recent work has shown that this con-

tribution was almost certainly overestimated. In particular, Harding et al. (1998)

calculated the pairwise ion–ion interactions within the relativistic Dirac–Fock approx-

imation, the metals Ag and Au being most attracted to the halide ion; the van der Waals

energy was reduced, due to overlap and better values of dispersion constants, from 0.5

to around 0.15 eV/atom. Atomic polarization within the shell model was included, and

the whole assembly relaxed to equilibrium, with a claimed accuracy of 6 0.1 eV. Some

results are given in table 5.3. The results suggest that the calculated values of E

are

within the quoted accuracy, but that E

seems to be systematically underestimated, pos-

sibly because of the neglect of charge transfer in the calculation. A Hartree–Fock

cluster calculation (Mejías 1996) also obtains very low values, ⬃0.1 eV for E

; so this

160 5 Surface processes in epitaxial growth

Table 5.2. Values (in eV) of E

and E

of Ag, Au and Pd adatoms on NaCl(001)

Alloy dE Element (E

2 E

Ag–Au: 0.11 6 0.03 Ag 0.22 0.41 0.19

Au–Pd: 0.12 6 0.03 Au 0.33 6 0.02 0.49 6 0.03 0.16 6 0.02

Pd–Ag: 0.25 6 0.05 Pd 0.45 0.78 0.33

Note: Values without errors are derived from data combinations (Robins 1988, Anton et al.

1990).

Table 5.3. Calculated values of E

and E

of Ag and Au on alkali halide(001) surfaces

Parameter (eV) Ag/NaCl Au/NaCl Ag/NaF Au/NaF

0.27 [0.27] 0.15 [0.69] 0.26 0.18 [0.59]

(0.41) (0.49) (0.63)

0.15 [0.09] 0.07 [0.22] 0.24 0.14 [0.08]

(0.19) (0.16) (0.08)

2 E

) 0.12 [0.18] 0.08 [0.47] 0.02 0.04 [0.51]

(0.22) (0.33 6 0.02)

Source: From Harding et al. 1998, with experimental values (round brackets) and previous

calculations [square brackets].

method presumably also gives very small values of E

, which must by deﬁnition be less

than E

What survives from previous work (Chan et al. 1977, Gates & Robins 1988) is that

the metal–metal binding energies E

are high, close to free space values, and that the

diﬀusion energies of dimers and small clusters are very low, often as low as E

itself.

This arises because one can ﬁt the ﬁrst atom of a pair on the surface optimally, but the

second one is constrained by being a member of a pair; the resulting energy surface,

while quite complex, is less corrugated.

Extension of these calculations to point defects has been attempted (Harding et al.

1998), with the result that the noble metal adatoms are generally attracted to surface

cation, but not anion, vacancies. This is especially the case if the adatom size is

suﬃciently small to ﬁt inside the surface vacancy, the attractive energies increasing as

the height of the adatom above the surface plane decreases. The role of surface charges,

and their eﬀect on the charge state of vacancies, could be very important, as has been

found for the case of Ag and other metals, particularly Pd, on MgO(001) (Ferrari &

Pacchioni 1996).

5.3.3 Defect-induced nucleation on oxides and ﬂuorides

There are many examples in the literature where defect nucleation seems to be needed

(Harsdorﬀ 1982, 1984, Venables 1997, 1999). The transition from i50 to 1 was

observed for Au/mica (Elliott 1974). In this case defect sites were used up initially, and

nucleation then proceeded on the perfect terraces in the initially incomplete condensa-

tion regime. A more recent example is furnished by high resolution UHV-SEM obser-

vations of the growth of nanometer-sized Fe and Co particles on various CaF

surfaces, typically thin ﬁlms on Si(111), as indicated in ﬁgure 5.9. In this work (Heim

et al. 1996) the nucleation density, for Z

⬵0.2 close to the maximum density, was inde-

pendent of temperature over the range 20–300°C. At 400 °C and above the substrate

itself is unstable. This behavior is not understandable if nucleation occurs on defect-

free terraces, but may be understood if defect trapping is strong enough.

Defects of various types can be incorporated into either analytical treatments or

simulations, at the cost of at least two additional parameters, the trap density n

, and

the trap energy E

, or the binding energy of adatoms to steps E

, as indicated schemat-

ically in ﬁgure 5.10. The nucleation density of islands on defective substrates can be

derived by considering the origin of the various terms in (5.14). The right hand side of

this equation is proportional to the nucleation rate (via the term in exp(E

/kT)), which

is enhanced by a ratio B

511A

with defects present (Heim et al. 1996, Venables 1997).

We start by considering the point defect traps shown in ﬁgure 5.10(a), constructing

a suitable diﬀerential equation for the number of adatoms attached to traps, n

/dt5

2 n

exp(2(E

)/kT), (5.16)

where n

is the number of empty traps5n

2 n

. In steady state, this equation is

zero, and inserting (1.15) for D, we deduce

/(n

2 n

)5A/(11A), with A5n

exp(E

/kT), (5.17)

5.3 Metal nucleation and growth on insulating substrates 161

where C

is an entropic constant, which has been put equal to 1 in the illustrative calcu-

lations performed to date. Equation (5.17) shows that the traps are full (n

2 n

)in

the strong trapping limit, whereas they depend exponentially on E

/kT in the weak trap-

ping limit, as expected. This equation is a Langmuir-type isotherm (section 4.2.2) for

the occupation of traps; the trapping time constant (

, in analogy to 5.13) to reach this

steady state is very short, unless E

is very large; but if E

is large, then all the traps are full

anyway.

The total nucleation rate is the sum of the nucleation rate on the terraces and at the

defects. The nucleation rate equation becomes, without coalescence, analogously to

(5.11),

/dt5

, (5.18)

where the second term is the nucleation rate on defects, and n

is the density of critical

clusters attached to defects,

i t

being the corresponding capture number. In the sim-

plest case where the traps only act on the ﬁrst atom which joins them, and entropic

eﬀects are ignored, we have

5 n

5 (n

2 n

)A/[n

(11 A)]. (5.19)

162 5 Surface processes in epitaxial growth

Figure 5.9. Nucleation and growth of small Fe crystals on CaF

(10 nm)/Si(111) at (a) room

temperature, (b) 140 °C, (c) 300 °C and (d) 400°C, observed by in situ high resolution SEM.

The average thickness is between 3.1 and 3.6 ML, and the coverage of the substrate, Z⬃20%

(from Heim et al. 1996, reproduced with permission).

(a)

20nm

(b)

20nm

(c)

20nm

(d)

20nm

A high value of A gives strong trapping, in which almost all the sites unoccupied by

clusters will be occupied by adatoms; in the simplest model we assume that clusters

cannot leave the traps.

However, even the simplest behavior ensures that the defect processes are not

linear. The clusters which form on the defect sites get established early on and thereby

deplete the adatom density on the terraces. As a result, the overall nucleation density,

which appears in the left hand side of (5.14), grows only as a fractional power [typi-

cally 1/(i12.5) for complete condensation, see table 5.1] of the trap density. In this

weak trapping limit, the main eﬀect is the reduced diﬀusion constant D due to the

time adatoms spend at traps (Frankl & Venables 1970). Nucleation on terrace sites is

strongly suppressed, due to adatom capture by already nucleated clusters. But when

, there is little eﬀect on the overall nucleation density. These eﬀects result in the

s-shaped curves shown in ﬁgure 5.11, illustrated for n

50.01 ML, E

50.5 and 1.0 eV,

and Fe/CaF

(111) parameters. If the trapping is very strong, and the diﬀusion

energy is low, there is a large regime where n

; conversely, weak trapping will lead

only to a point of inﬂection at, and a change of slope above and below, the trap

density.

Comparison with experiments puts bounds on the energies E

, E

and E

, all

⬵1 eV, and suggests a low value, 0.1–0.3 eV, for E

. Note that the reason why a low

value of E

is needed is so that the adatoms can migrate far enough at low tempera-

tures to reach the defect sites. The high values of the other energies are needed, so

that something else doesn’t intervene at high temperatures. For example, if E

is as low

as 0.5 eV, the density does not reach n

over a large enough temperature range; if E

is too small, condensation becomes incomplete too early. Note also that the transi-

tion from i51 to 2 is observed for E

50.1–0.3 eV at the highest temperature; this

5.3 Metal nucleation and growth on insulating substrates 163

Figure 5.10. (a) Model for nucleation at attractive random point defects, which can be

occupied by adatoms, density n

, clusters, density n

, or can be empty; (b) schematic diagram

of line defects (steps), with adatom density n

(x) and nucleation density n

(x) for position x

from up-steps (with attractive forces) and down-steps (maybe repulsive forces).

(b)

–n

(x)n (x)

(x)n

(x)

(

means that the limiting process can become breakup of the cluster (on a trap), rather

than removal of the adatom from the trap; E

is not then itself important, provided

it is high enough.

This type of model thus contains several sub-cases, depending on the values of the

parameters. A remarkable example is Pd/MgO(001), studied with AFM by Haas et al.

(2000); this data also requires a high trapping energy E

, in agreement with the calcu-

lations of Ferrari & Pacchioni (1996) and Venables & Harding (2000) for trapping of

Pd in surface vacancies, and a low value of E

. Models involving point defects are typ-

ically indicative, rather than truly quantitative, because of the possibility of other

eﬀects, such as cluster mobility and cluster detaching from defects, and the possibility

of a range of defect binding energies. One can see qualitatively that if E

is moderate

and dimer motion is easy, then the traps may become reusable at high enough temper-

ature; this further complication, needing even more parameters, has been thought nec-

essary on occasion (Gates & Robins 1987a, Usher & Robins 1987). This is an ongoing

tension between science and technology; both need conditions to be reproducible; tech-

nology can be successful even if complicated, but science needs the models to be rela-

tively simple: we cannot sensibly deal with too many parameters at once.

164 5 Surface processes in epitaxial growth

Figure 5.11. Nucleation density on point defects predicted with trap density n

50.01 ML, trap

energy (a) E

50.5 eV, and (b) 1.0 eV, parameter E

, with E

51.16 eV and E

51.04 eV

(recalculated after Heim et al. 1996, and Venables 1999).

2.0 2.5 3.0 3.5 4.0 4.5 5.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

14.0

14.5

= 1

= 2

0.3

0.1

0.6

0.5

0.4

(a)

= 0.5 eV

Parameter:

(eV)

Log

(

/cm

)

1000/T (K

–1

)

300200 100 0

(

2.0 2.5 3.0 3.5 4.0 4.5 5.0

11.5

12.0

12.5

13.0

13.5

14.0

14.5

= 2

0.3

0.1

0.6

0.5

0.4

Parameter:

(eV)

(b)

= 1.0 eV

1000/T (K

–1

)

300200 100 0

(

5.4 Metal deposition studied by UHV microscopies

UHV microscope-based techniques (SEM, STEM, FIM and more recently STM,

AFM, LEEM) plus diﬀraction techniques (including X-ray, SPA-LEED and helium

scattering) examine the deposit/substrate combination in situ, without breaking the

vacuum; we have discussed procedures for speciﬁc cases in chapters 2 and 3. Compared

to ex situ TEM described in section 5.3.1 and 5.3.2, a wider set of substrates and depos-

its have been observed in recent years; some examples for metals on insulators were

given in section 5.3.3.

In situ studies of metal deposition on metals are described in this section. These

results are illustrative, in order to give a feel for the work; this is not a review article.

Many review articles start with a statement: this is not an exhaustive treatment . . .!

Perhaps this is just as well, no-one wants to be exhausted; but it means that one often

has to go back to the original literature to be sure what went on. There are many exam-

ples where the primary literature represents a progress report, updated and maybe actu-

ally negated by subsequent work. Attempting to ﬁnd out what happened is often hard,

but is preferable to repeating the work in ignorance of the original!

5.4.1 In situ UHV SEM and LEEM of metals on metals

Ultra-high vacuum SEM and related techniques were developed by our group in

Sussex, and used to study Stranski–Krastanov growth systems at elevated temperature.

The SEM is good for visualizing strongly 3D objects, such as the (001) oriented Ag

islands seen on Mo(001) in ﬁgure 5.12. Since adatoms must diﬀuse across the substrate

to form the islands, we can see very directly that diﬀusion distances can be many

micrometers (Hartig et al. 1978, Venables et al. 1984).

The systems Ag/W(110) and Ag/Fe(110) have been examined in detail with research

students and other collaborators over a span of several years (Spiller et al. 1983, Jones

& Venables 1985, Jones et al. 1990, Noro et al. 1995, 1996, Persaud et al. 1998). In these

systems, 2ML of Ag form ﬁrst, and then ﬂat Ag islands grow in (111) orientation. The

experimental nucleation density N(T) is a strong function of substrate temperature,

and the results of several Ag/W(110) experiments are shown in ﬁgure 5.13, in compar-

ison with a nucleation calculation n

(T) of the type outlined in section 5.2. In practice

this proceeds by solving (5.14) iteratively, using the complete condensation solution as

the starting point.

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, E

52.260.1, and the combination energy (E

12E

0.6560.03 eV, within which E

50.1560.1 and E

50.2570.05 eV (Jones et al. 1990).

Note the errors are anti-correlated, since the combination energy is quite well deter-

mined by the absolute values of the data. What, however, makes these values interest-

ing is that they can be compared with the best available calculations of metallic binding.

Comparison has been made with eﬀective medium theory, and the agreement is

5.4 Metal deposition studied by UHV microscopies 165

striking, as shown in table 5.3 with other values later. In particular, the results demon-

strate the non-linearity of metallic binding with increasing coordination number. In

the simplest nearest neighbor bond model which we explored in chapter 1, the adsorp-

tion energy on (111) corresponds to 3 bonds, or half the sublimation energy for a f.c.c.

crystal. So for Ag, with L52.95 eV, such a model would give E

51.47 eV, whereas the

actual value is much larger. The same eﬀect is at work in the high binding energy of

molecules, quoted in section 5.3.1 in connection with island growth experiments.

However, the last bonds to form are much weaker, so that in this case E

is much less

than L/650.49 eV. This is a general feature of eﬀective medium or embedded atom cal-

culations on metals, discussed further in section 6.1.

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) (Bauer

et al. 1977), compared to a missing row c531 structure for the ﬁrst layer, followed by

an Ag(111)-like second layer on Fe(110) (Noro et al. 1995). But adatom behavior on

top of these two layers is very similar. UHV SEM methods can visualize the ﬁrst and

second MLs, and the islands on top of these MLs in ﬁnite deposits, using biased sec-

ondary electron imaging described in chapter 3. Diﬀusion in these systems is discussed

in section 5.5.2. Some eﬀects in the ﬁrst MLs of the related, but rather more reactive

systems Cu and Au deposited onto W and Mo(110) have been studied by LEEM

166 5 Surface processes in epitaxial growth

Figure 5.12. In situ UHV SEM pictures of nucleation and growth of Ag on Mo(001), shown

after 20 ML was deposited at T5550°C (from Hartig et al. 1978, reproduced with

permission).