Martin P.M. Handbook of Deposition Technologies for Films and Coatings, Third Edition: Science, Applications and Technology

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Thin Film Nucleation, Growth, and Microstructural Evolution 591

Figure 12.31: Upper ﬁgure: schematic illustration of the nucleation of a new {105} facet with

length s and height h on a Ge pyramid grown on Si(001). Lower ﬁgure: schematic cross-section of

a facet consisting of individual steps. A partly covered facet is completed up to the kth step.

(Adapted from [79].)

the facet will be completed very rapidly (note also that the step length s(k) decreases with k).

Thus, there is a large activation barrier G*. Estimates of G* as a function of s and ε have

been carried out using kinetic calculations incorporating step formation energy, facet surface

energy, and elastic and dipole step–step interaction energies [83].

The strain energy per unit interface area associated with the deposition of one monolayer of Ge

on Si(001) can be estimated using the classical equation E

elas

=2μ

(1 + ν

)ε

/(1 − ν

) which

assumes growth of a cubic structure material in the [001] direction and that the strain ε is

within the Hooke’s law limit [17]. The terms μ

and ν

are the shear modulus and Poisson ratio

of the ﬁlm. Inserting (bulk) Ge values for μ

and ν

, E

elas

∼ 0.021 eV/atom = 1.4 × 10

eV-cm

−2

= 0.16 GPa. Thus, it should not be surprising that relaxation of the large interfacial

strain associated with the growth of Ge/Si(001)2×1 manifests itself long before the

observation of QD formation above the 3 ML-thick wetting layer.

At Ge coverages θ

< 1 ML, the surface (2×1) reconstruction evolves to (2×N) via the

formation of dimer vacancy lines (DVLs) orthogonal to the 2×1 dimer rows, in which N is the

average number of dimers separating DVLs. In situ STM measurements of MBE Ge layers

grown at 300

◦

C with R = 0.05 ML/s show that the (2×N) periodicity decreases from N ∼ 17 at

= 0.8 ML toward N = 8, limited by trench–trench repulsion, at 2 ML [21]. The strain is

reduced, at the cost of the trench formation energy, as Ge atoms adjacent to the trenches relax

outwards into the trench. At θ

greater than ∼ 2 ML, dimer row vacancies (DRVs) form along

the rows to further decrease the strain and the (2×N) reconstruction becomes (M×N)inan

orthogonal quasi-periodic grid pattern. M is the DRV width, the number of vacant dimer rows.

A few representative DVLs and DRVs are labeled in Figure 12.32, an in situ STM image of a

2.8 ML thick Ge/Si(001)2×1 ﬁlm deposited by GS-MBE from Ge

at T

= 650

◦

C (well

above the H

desorption temperature) with R = 0.03 ML/s [22]. DVLs and DRVs are also

visible in the wetting layer in Figures 12.28 and 12.30.

592 Chapter 12

Figure 12.32: In situ STM image of a Ge(001)M×N layer grown on Si(001)2×1 by GS-MBE

from Ge

at T

= 650



C with R = 0.03 ML/s to a coverage θ

= 2.8 ML. A few representative

dimer vacancy lines (DVLs) and dimer row vacancies (DRVs) are highlighted by arrows. (Adapted

from [22].)

12.6 Structural Evolution of Polycrystalline Films

at the Nanoscale and Microscale

Polycrystalline thin ﬁlms have found diverse applications ranging from metallization and

dielectric layers to optical, magnetic, and tribological coatings, to diffusion and thermal

barriers, to catalytic and bioactive layers. The ﬁlms exhibit a wide variety of microstructures

characterized in terms of grain size and crystallographic orientation, lattice defects, phase

composition, and surface morphology.

Atomic scale control of thin ﬁlm microstructure during kinetically-limited low-temperature

deposition, crucial for a broad range of industrial applications, has been a leading goal of

materials science during the past few decades. Industrial demands for ever lower processing

temperatures in device and product manufacturing mean that ﬁlms are often deposited at

≤ 0.2–0.3. Thus, ﬁlm synthesis takes place far from thermodynamic equilibrium. As a

consequence, grain shape and orientation often evolve in a competitive fashion and the kinetic

limitations induced by low-temperature growth allow for the controlled synthesis of

metastable phases and artiﬁcial structures such as multilayers and self-organized

nanocomposites.

Among the determinant atomic processes controlling structure evolution during ﬁlm growth

are surface and bulk diffusion. In addition to T

, energetic particle bombardment can be used to

enhance adatom mobilities and manipulate nucleation rates. The presence of alloying or

Thin Film Nucleation, Growth, and Microstructural Evolution 593

impurity elements and their segregation to surfaces and grain boundaries also strongly

inﬂuences the ﬁnal result.

Extensive studies of the correlation between polycrystalline ﬁlm structure and deposition

parameters have been carried out over the past ﬁve decades. From an understanding of ﬁlm

formation follows the possibility for structural engineering at the microscale and nanoscale in

order to design materials for speciﬁc technological applications. This spawned the

development and reﬁnement of structure zone models (SZMs) which systematically categorize

self-organized structural evolution during ﬁlm growth as a function of ﬁlm growth parameters

[84–90]. The history of SZMs has been reviewed by Thornton [91], Barna and Adamik [92],

and Mahieu et al. [93]. In 1969, Movchan and Demchishin [84] observed that the

microstructural evolution of evaporated Ti, Ni, W, ZrO

, and Al

coatings can be

systematically represented by a single SZM diagram plotted as a function of ﬁlm thickness h

and the homologous growth temperature T

The ﬁrst SZMs were based on relatively low-resolution optical and scanning electron

microscopy observations. Later, cross-sectional transmission electron microscopy (XTEM),

STM, and AFM were employed to provide more detailed structural characterization, and in

situ analyses began to reveal the rich dynamics of ﬁlm growth. This, together with

computational materials science, has provided atomistic insights into microstructural evolution

during polycrystalline ﬁlm growth. The use of amorphous substrates is beneﬁcial for isolating

the effects of individual deposition variables on texture development. Polycrystalline

substrates bias texture through local pseudomorphic epitaxy. Nevertheless, the overall

microstructure will still evolve toward a ﬁnal state driven by the extant deposition conditions.

It is important to note, however, that if surface diffusion rates are signiﬁcant, once the substrate

is covered, ﬁlm growth will still proceed via local epitaxy on individual grains, even with

amorphous substrates.

12.6.1 Elemental Polycrystalline Films and Structure-Zone Models

The nucleation barrier for low-temperature deposition on amorphous substrates is generally

quite small, leading to randomly oriented islands [94, 95]. This has been demonstrated in a

wide variety of materials. Early in situ TEM investigations included Au/SiO

[96, 97] and

In/a-C [55, 98]. During island coalescence, there is a strong driving force for coarsening

through surface atom diffusion and grain boundary motion. Islands with lower energy per

atom E

consume their neighbor(s) during coalescence and this process can result in large

single-crystal islands as the system attempts to minimize the overall surface and interface

energy. Thus, coarsening during coalescence is the ﬁrst and most active phenomenon leading

to selection of preferred orientation [99–101]. Absenting other kinetic constraints (see

following sections), islands with the densest atomic planes are typically selected: (111) for fcc,

(0002) for hcp, and (110) for bcc.

594 Chapter 12

Figure 12.33: SZM schematically representing microstructural evolution of pure elemental ﬁlms as

a function of the reduced temperature T

, where T

is the deposition temperature and T

the melting point of the material, both expressed in K. (From [8].)

Depending on T

and island size (due to melting point depression for nanoscale clusters)

[56], coarsening can be very fast, often termed liquid-like coalescence, occurring either by

rapid surface diffusion or by melting upon contact followed by crystallization. The driving

force is the release of edge and surface energy. Rapid coalescence also results in new open

substrate area for secondary nucleation, as shown in the in situ TEM image sequence

(Figure 12.15) obtained during coalescence of In/a-C. At lower temperatures or larger island

sizes, coarsening is slower and proceeds through grain boundary migration. Grain coarsening

during coalescence of the contacting crystals is repeated until the local grain size becomes

sufﬁciently large that grain boundary mobility is low on the timescale of coalescence.

The SZM in Figure 12.33, characterizing microstructure evolution in pure elemental ﬁlms,

consists of three regions [8]: zone I corresponds to very low deposition temperatures for which

adatom diffusion is negligible; surface diffusion becomes signiﬁcant in the transition zone T;

and zone II represents ﬁlm growth at deposition temperatures for which both surface and bulk

diffusion are operative. The boundaries between zones are diffuse and transitions occur

gradually over wide ranges in T

During ﬁlm growth in the low-T

zone I regime (Figure 12.33), an underdense structure with a

ﬁne ﬁber texture is formed. Initial in-plane grain sizes are set by the saturation nucleation

density N

sat

. Adatom mobilities are low and columns preserve the random orientation of the

nuclei as predicted by ballistic deposition models [102, 103]. The columns are generally not

single grains, but composed of smaller more equiaxed grains, or completely amorphous.

Surface roughness, which develops owing to atomic shadowing and limited surface diffusion,

leads to extensive porosity. The wide angular distribution of the incident ﬂux during sputter

deposition, especially at pressures corresponding to non-ballistic transport, exacerbates these

effects.

Thin Film Nucleation, Growth, and Microstructural Evolution 595

At higher ﬁlm growth temperatures (zone T), grain coarsening occurs during coalescence of

small islands with large surface to volume ratios, while grain boundaries are immobile in

continuous ﬁlms. Orientation selection during coarsening is incomplete, thus crystallites are

nearly random or only weakly textured, and there is a wide distribution of initial grain sizes.

The orientation and size of individual crystallites determine their behavior during subsequent

growth processes characterized by competition among neighboring grains. In this T

range,

adatom surface diffusion is signiﬁcant, resulting in local epitaxial growth taking place on

individual grains. Pronounced columnar structure develops in which the columns are actually

elongated grains.

The primary features of zone T competitive grain growth are illustrated by the kinetic Monte

Carlo simulations of Gilmer et al. [104, 105] for sputter-deposited Al growth as shown in

Figure 12.34(a). While there are initially equal distributions of 111 and 001 islands, the latter

orientation eventually dominates, even though 111 is the low-energy surface, owing to

anisotropies in surface diffusivities and adatom potential energies. That is, the average adatom

residence time is signiﬁcantly higher at lattice sites on low diffusivity (low potential energy)

001 surfaces versus high diffusivity (high potential energy) 111 surfaces. Therefore, during the

Figure 12.34: (a) Kinetic Monte Carlo simulation of competitive texture evolution during

low-temperature sputter deposition of an Al ﬁlm. Islands (and later columns) with lighter contrast

are 001 oriented, while darker islands/columns are 111 oriented (from [104, 105]).

(b) Schematic cross-section.

596 Chapter 12

early stages, 111 islands tend to expand more two-dimensionally and thus ﬁll more surface

area (see upper panel in Figure 12.34a), while 001 grains favor more 3D growth. Following

coalescence, however, adatoms which are stochastically deposited near grain boundaries and,

through surface diffusion, can sample sites on both sides of the boundary, have a higher

probability of becoming incorporated at the low-diffusivity surface which provides more

stable, lower potential energy sites. Conversely, adatoms on high diffusivity planes have longer

mean free paths with correspondingly higher probabilities to move off the plane and become

trapped on adjacent grains. Thus, 001 grains become favored. Atomic shadowing enhances the

difference, as protruding surfaces capture more off-normal ﬂux. Thus, the low-diffusivity 001

grains slowly expand, overgrow the high-diffusivity grains, and become bounded by 111 facets.

This leads to considerable surface roughness which scales with the average in-plane grain size.

The consequence of competitive growth is a continuous change in morphology, texture, and

surface topography (hence, ﬁlm properties) as a function of ﬁlm thickness. Near the substrate,

the microstructure consists of randomly oriented small grains, out of which V-shaped columns

(Figure 12.34b) with favored orientations slowly emerge and overgrow kinetically

disadvantaged columns. This gives rise to preferred orientation. The faceted column tops

result, as noted above, in surface roughness which increases with thickness resulting in open

column boundaries due to atomic shadowing.

At still higher T

(zone II), bulk diffusion becomes signiﬁcant. Grain boundary migration

takes place not only during coalescence, but throughout the ﬁlm growth process. Orientation

selection during the coalescence stage is more pronounced and is driven by a decrease in the

total grain boundary area as well as minimization of interface and surface energy [99]. Large

grains with low surface and interface energy grow at the expense of smaller or unfavorably

oriented grains. Normal grain growth is impeded if the grains have a strong texture, i.e. if the

orientation selection was completed during coalescence, or the mean in-plane grain diameter

reaches several times the ﬁlm thickness [106]. Secondary recrystallization, also called

abnormal grain growth, may follow in which the grain size distribution is transformed from

monomodal, through bimodal, to a new monomodal distribution (unless grain growth is halted

due to solute drag and/or grain boundary grooving) [106, 107] with much larger in-plane grain

size. During secondary recrystallization, the degree of texture is further enhanced.

An example of grain boundary migration is shown in Figure 12.35, a series of STM topographs

from a 300

A thick polycrystalline Au ﬁlm deposited by MBE on SiO

(0001) at room

temperature with R = 0.0028

A/s and then annealed using a very slow linear temperature ramp

/dt

=20

◦

C/h [107]. X-ray diffraction (XRD) measurements of as-deposited samples reveal

a 111 texture: approximately 84% of the grains are 111, ∼ 16% 001, with no detectable 011

grains. The degree of 111 preferred orientation increases rapidly with annealing temperature.

The as-deposited polycrystalline Au ﬁlm in the upper panel in Figure 12.35 has a highly

irregular surface in which the roughness is controlled by grains with high-energy boundaries.

Thin Film Nucleation, Growth, and Microstructural Evolution 597

Figure 12.35: Typical STM topographical proﬁles from a 300

A thick Au ﬁlm deposited by MBE

with R = 0.0028

A/s on SiO

(0001) and subsequently annealed at 20



C/h: (a) immediately after

deposition, (b) at T

= 395



C, and (c) at T

= 475



C. Each dome is an individual grain. Vertical

lines indicate the grain boundary locations. Note the different height scales. Individual steps and

terraces are visible in panels (b) and (c). The topographs are from a video ﬁle obtained during

annealing. (Adapted from [107].)

The grain boundary line tension γ

is related to the surface tension γ

through the relationship

= 2γ

cos(ϕ/2) (12.29)

where ϕ is the dihedral angle as deﬁned in Figure 12.36. Grains with high-energy boundaries

have small dihedral angles, resulting in tall islands, and thus a rough surface. However, the

Figure 12.36: Schematic illustration of grain boundary grooving which occurs in order to minimize

the total system energy. γ

is the grain boundary line tension, γ

is the surface tension, and ϕ is

the dihedral angle.

598 Chapter 12

Figure 12.37: Surface roughness w of the polycrystalline Au ﬁlm, corresponding to Figure 12.35,

as a function of the average grain size d during annealing from room temperature to 475



Cat



C/h. (Adapted from [107].)

high-energy grain boundaries tend to anneal out as T

is increased and the remaining lower

energy boundaries have larger ϕ values, yielding a smoother surface. This is illustrated in the

in situ STM topographs Figures 12.36(b) (T

= 395

◦

C) and 12.36(c) (T

= 475

◦

C). Over the

entire range of temperatures, surface adatom diffusion is sufﬁciently fast to maintain the

surface shape at (or very close to) equilibrium with the evolving grain boundary conﬁguration,

as demonstrated by the fact that only very small shape changes are observed if the thermal

ramp is halted and T

maintained constant.

Figure 12.37 shows that the surface roughness w decreases by a factor of ∼ 3× over the

temperature range from 20

◦

Cto∼ 325

◦

C, remains approximately constant with T

until

∼ 400

◦

C, and then increases again at higher T

. Over the full annealing range, 20–475

◦

C, the

average grain size d increases by an order of magnitude and XRD results show that the ﬁlm

texture transforms to essentially complete 111. In the ﬁrst region, over which w decreases

rapidly and d increases, the high-energy grain boundaries become mobile as T

is increased

and quickly reorient themselves in lower energy conﬁgurations (corresponding to cusps in the

orientation vs grain boundary energy diagram). Thus, the average grain boundary energy

decreases giving rise to an increase in the average dihedral angle ϕ (Eq. 12.29), and therefore a

corresponding decrease in w from ∼ 23

Ato8

A while d increases from ∼ 300

A to 1000

As T

is raised further, the lower-energy grain boundaries also become mobile resulting in a

continued gradual coarsening of the grain boundary network. This mechanism, by itself, has

no signiﬁcant effect on the average dihedral angle ϕ since the average grain boundary energy

remains constant. However, as a given grain diameter increases, the height variation across

the grain also increases due to a self-similar scaling behavior. Over the intermediate regime in

Thin Film Nucleation, Growth, and Microstructural Evolution 599

Figure 12.37,asd increases from ∼ 1000

A to 1750

A, the surface roughness w remains

essentially constant owing to the competition between grain boundary reorientation (and

texture development) which decreases w, and the growth of grains with low-angle boundaries

which increases w. The third regime (T

∼ 400–475

◦

C) is dominated by the continued growth

of highly textured grains with low-energy boundaries as d increases from ∼ 1750

A to 3000

causing the average surface roughness w to increase from ∼ 8

Ato15

A. The maximum grain

size at the highest temperature, T

= 475

◦

C, is ∼ 3000

A, a factor of 10× larger than the Au

ﬁlm thickness. Prolonged annealing at 475

◦

C had no further signiﬁcant effect on d.

The grain growth history just described occurred through a combination of ‘normal’ and

‘abnormal’ mechanisms. During primary or normal grain growth, the grain size distribution

remains monomodal as individual grain boundaries move toward their centers of curvature in

order to reduce boundary curvature, total boundary length, and, thus, the total grain boundary

energy. That is, grains larger than the average size grow, while smaller grains shrink. In

columnar grain systems, grains with ﬁve or fewer sides tend to shrink, while those with seven

or more sides grow [108]. Secondary (or abnormal) grain growth results initially in a bimodal

grain size distribution which, if allowed to proceed to completion, leads again to a monomodal

distribution, but with a lower density of larger grains. Driving forces for abnormal grain growth

include local epitaxy [109], anisotropic surface and/or interfacial energies [110], anisotropic

strain [111], and/or kinetic competition [112–114]. For example, since surface energy is

strongly dependent on crystallographic orientation, those grains with orientations that lead to

low surface energies have an energetic advantage during growth. In the polycrystalline Au ﬁlm

experiments, the entire grain distribution moved toward a complete 111 texture.

12.6.2 Multicomponent and Multiphase Film Growth

Polycrystalline thin ﬁlms synthesized by reactive deposition provide additional pathways for

microstructure control while yielding enhanced thermal and process stability. Here, the term

reactive deposition encompasses the purposeful incorporation of dopants as well as

unintentional atmospheric contaminants such as water vapor, oxygen, and hydrocarbons since

even low concentrations of reactive elements (sometimes below the detection limits of modern

analytical techniques) can have strong effects on microstructural development [92, 115, 116].

Consider the case of O-containing polycrystalline Al ﬁlms deposited at room temperature,

= 0.32, corresponding to zone II in the pure Al SZM [117]. Changes in ﬁlm structure and

orientation as a function of increasing oxygen concentration, observed via in situ TEM

investigations, are summarized in Figure 12.38 [8, 92]. Oxygen has low solubility in Al and

segregates to surfaces and grain boundaries where it forms 2D oxide layers (oxide tissue

phases) which greatly reduce Al adatom surface and grain-boundary mobilities. These layers

modify all ﬁlm formation processes, limiting grain coarsening during coalescence and ﬁlm

growth. They also periodically interrupt the local epitaxial growth of individual crystallites and

600 Chapter 12

Figure 12.38: XTEM images, with corresponding schematic diagrams, showing the microstructure

of Al ﬁlms deposited by thermal evaporation on amorphous SiO

at room temperature as a

function of the incident O to Al ﬂux ratio J

. (From [8, 92].)

cause renucleation [55, 98]. By exploiting such phenomena, new microstructures and

nanostructures can be controllably synthesized.

At low O/Al arrival rate ratios, J

∼ 10

−3

, oxygen is incorporated into the grain boundaries

and further accumulates during boundary migration, eventually inhibiting grain coarsening

though solute drag. The resulting texture remains zone II with columns extending through the

ﬁlm, but with a lesser degree of preferred orientation and a smaller grain size, as shown in

Figure 12.38(b).