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Annu. Rev. Mater. Sci. 2000. 30:15990Copyright c by Annual Reviews. All rights reserved

STRUCTURE EVOLUTION DURING PROCESSINGOF POLYCRYSTALLINE FILMS

C. V. ThompsonDepartment of Materials Science and Engineering, Massachusetts Institute of Technology,

Cambridge, Massachusetts 02139; e-mail: [email protected]

Key Words thin films, grain growth, texture processing

s Abstract Polycrystalline films have wide variety of applications in which theirgrain structures affect their performance and reliability. Thin film growth techniquesand growth conditions affect grain shapes, the distribution of grain sizes, and the dis-tribution of the crystallographic orientations of grains. Variations in these structuralproperties are affected by the conditions under which grain nucleation, growth, coars-ening, coalescence, and thickening occur. General trends in structural evolution inpolycystalline films, as a function of processing conditions and materials class, arediscussed in terms of these fundamental kinetic processes.

INTRODUCTION

The microstructural characteristics of polycrystalline films control their proper-

ties, performance, and reliability in applications in a wide variety of electronic,

magnetic, photonic, chemical, and micromechanical devices and systems. Poly-

crystalline metallic films are used to interconnect devices in integrated circuits

(61, 92), as magnetic storage media, as elements in magnetic devices, as cat-alytic elements, as thermal sensing elements (80), and as protective and decorative

coatings (79). Polycrystalline semiconductor films are also used as conducting

elements in circuits and devices (35), as well as as optical interconnects (15), and

as active device elements in thin film transistors, solar cells, and detectors (35,

79, 80). Piezoelectric ceramic films are used in surface acoustic wave transducers

(80); ferroelectric ceramic films are being investigated foruse in nonvolatile memo-

ries [MRS Bulletin June 1966], and ceramic films are being investigated for use

as high-dielectric constant interlevel insulators for integrated circuits. Ceramic

high Tc films are also often polycrystalline, although preferably not composed ofrandomly oriented crystals (12). Polycrystalline materials from all classes of mate-

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160 THOMPSON

(a)

coalescence

(b)

thickening

lowTdep

highTdep

anneal

Type 1e.g. Ta, W, Cr, Fe, Si ...

(c)

Type 2e.g. Ag, Al, Au, Cu

(d)

nucleationand

growth

Figure 1 Overview of grain structure evolution during deposition of polycrystalline thin

films.

In all these applications the properties of polycrystalline films must be repro-ducibly controlled in order to control their performance and reliability. This, in

turn, requires the control of their microstructure, through manipulation of the

atomic scale processes that define their structures. Although often complex and

materials-specific phenomena affect the structures of polycrystalline films, there

are also known trends of behavior for materials in general, and for specific materi-

als classes, and these trends can be understood in terms of the fundamental kinetic

processes through which the structures must evolve. It is the purpose of this brief

review to outline the current understanding of these materials and process-generic

trends in structure development and evolution during processing of polycrystallinethin films.

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POLYCRYSTALLINE FILMS 161

(a) (b)

Figure 2 Nucleation,

growth, and coalescence to

form a continuous thin film.

on a substrate surface. This process is discussed in terms of condensation of asolid film from a vapor phase, the most common case, but similar phenomena occur

during film formation by electrodeposition or other methods involving growth from

liquid solutions, as well as for films grown from their melts. The evolution outlined

in Figure 1 also applies to for film formation through reactions at interfaces with

external vapor, liquid, and solid phases (6) and for crystallization of amorphous

films (99). Once formed, nuclei grow into the external phase, as well as laterally in

directions lying in the plane of the interface. Lateral growth leads to impingement

and coalescence of crystals, resulting in the formation of grain boundaries and

defining at least the initial grain-structure characteristics of the newly formed film.This nucleation, growth, impingement, and coalescence process is schematically

illustrated in cross-sectional sketches in Figure 1a and b and Figure 2.

Nucleation (discussed in more detail below) in most thin film formation pro-

cesses is copious, thus nuclei spacings and therefore the grain size at impingement

are of order 10 nm or less. In the absence of coarsening phenomena, the thickness

of the film at coalescence is also of order 10 nm or less. For most applications,

further thickening of the film is required. Grain structure evolution during thick-

ening occurs in two fundamentally different ways, as schematically illustrated in

Figure 1c, d. If the grain boundaries formed through island impingement are im-mobile, the grain structure resulting from the nucleation, growth, and coalescence

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162 THOMPSON

to as the in-plane grain size) becomes small compared with the average grain size

as measured in the direction normal to the plane of the interface (henceforth re-

ferred to as the through-thickness grain size). Often though, as the grains at the

base of the film grow into the parent phase, competitive growth processes lead toan increasing in-plane grain size at the top surface of the thickening film.

If grain boundaries are mobile, the grain structure of a film evolves during the

coalescence process and continues to evolve during film thickening. This often

results in a more equiaxed structure in which the in-plane grain size tends to be

approximately the same as and scale with the film thickness, resulting in structures

in which most grain boundaries traverse the thickness of the film, as schematically

illustrated in Figure 1d, so that the average in-plane grain size is uniform through

the thickness of the film.

Microstructural characteristics of importance include grain shapes, grain sizes,the distribution of grain sizes and the distribution of grain orientations. The in-

plane grain size di can be defined as (4A/ )1/2, where A is the area of the grain

in the plane of the interface (or a plane parallel to it). It is often useful to consider

the degree to which the grains are equiaxed, one measure of which is the grain

aspect ratio ai = dp/di, where dp is the through-thickness grain size. The aspect

ratio can vary from approximately 1, as in Figure 1d, to much larger values that

increase with increasing film thickness, as illustrated in Figure 1c. In general, it is

important to not only know and control the average in-plane grain size and aspect

ratio, but to also know and control the distribution of grain sizes and shapes. Thesecan vary widely with processing conditions. For example, the distributions of in-

plane grain sizes can range from narrow monomodal distributions to multimodal

distributions in which subpopulations can have average sizes that differ by orders

of magnitude (26, 62).

Knowledge and control of the distribution of grain orientations is also im-

portant in most applications of polycrystalline thin films. Whereas, by defini-

tion, the grains or crystals from which a polycrystalline film is formed do not all

have the same crystallographic orientations, rarely do they have fully randomly

distributed crystallographic orientations. Very often polycrystalline films havewhat is referred to as a crystallographic texture, in that the crystals from which

they are composed tend to have specific crystallographic directions normal to the

plane of the film. For example, it is common, although not required (see below),

for films of fcc metals to have crystallographic orientations with (111) planes

parallel to the plane of the film. In this case the films are said to have a (111)

texture. Whereas polycrystalline films often have a sharp texture, meaning that

the vast majority of grains have surface normals within a small deviation of a spe-

cific crystallographic direction, the grains often have random in-plane orientations

relative to rotations about axes normal to the plane of the film. The distribution ofgrain orientations is affected by all the processes that affect grain size and is also

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In the sections that follow, the nucleation, growth, coalescence, thickening and

grain growth processes are discussed in more detail in order to illustrate some of

the ways in which processing techniques and conditions affect the evolution of

grain sizes, shapes and orientations.

NUCLEATION, GROWTH, ANDCOALESCENCE

The following discussion focuses on film formation via condensation from a vapor

phase. However, as noted above, it should be borne in mind that analogous phe-

nomenology and analyses apply to film formation from other media.

Consider, for simplicity, nuclei which grow as islands that maintain the con-

stant shape of a spherical cap, as shown in Figure 3. This shape would result if theenergy of the free surface of the film, f, is isotropic, and if the particle maintains

its equilibrium shape. The equilibrium shape would be characterized by an angle

of contact between the free surface of the particle and the substrate surface , given

by the force balance f cos( ) + i = s, where i is the energy per unit area of

the island-substrate interface, and s is the energy per unit area of the substrate

surface. As deposition is carried out, atoms arrive at the substrate surface with a

flux R, which is the number of atoms arriving per unit area of the substrate surface

per unit time. It is assumed, again for simplicity, that the depositing atoms are

arriving at normal incidence to the substrate surface. Arriving adatoms adsorb on

f

r

i

s

(a)

rs

Figure 3 (a) An island with isotropic surface

energy s and film/substrate interface energy

i, on a substrate with energy s has an equi-

librium contact angle , and a circular area of

contact with radius rs. (b) A growing island

will incorporate atoms deposited directly and

by addition of adatoms, which are deposited

within a distance on the substrate surface.

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164 THOMPSON

the substrate surface and remain adsorbed for a mean residence time , which is a

function of the desorption rate (which is in turn a function of the binding energy).

Nucleation occurs when stable clusters of adatoms form and continue to grow

rather than dissolving back to smaller clusters and single adatoms. The nucleationrate can be analyzed using classical methods based on the capillarity approxima-

tion or, more appropriately in the current context, based on an atomistic analysis

(45, 56). Both approaches have been treated in exhaustive detail in the literature,

with an apparent consensus that the nucleation rate as indicated by atomistic anal-

yses, is given by

I = I0Rn exp

Gn

kT

, 1.

where I0 is a temperature and deposition-flux-independent constant, k isBoltzmans constant, and T is the temperature of the substrate. Gn is the en-

ergy of formation of a cluster of size n, where n is the critical cluster size.

For physical vapor deposition processes, n has a low integer value, often only 1

(so that the minimum stable cluster size is 2). Because the degree of supersatura-

tion decreases with increasing T, as T increases, n increases (e.g. from 1 to 2 to 3)

and Gn increases, so that the temperature dependence of the nucleation rate

becomes incrementally stronger with increasing T. It is generally found that the

nucleation rate decreases with increasing temperature (56).

When critical cluster sizes are sufficiently large that the crystallography ofthe nucleating phase is defined, specific nuclei crystallographic orientations will

minimize surface and interface energies (60), with nucleation rates higher for

nuclei with energy minimizing orientations. In this case, nucleation is orientation

selective, and the nucleation process can play an important role in determining the

distribution of orientations in the resulting film. When critical cluster sizes are

as small as they usually are in vapor deposition processes, the nucleation process

can still be orientation selective in that dimers and trimers etc will have specific

low-energy configurations relative to the configurations of the substrate atoms;

however, these energy-minimizing orientations may not be those that minimizethe macroscopic surface and interface energies so these initial orientations may

not persist during subsequent structure evolution.

As nuclei grow into islands of the sort illustrated in Figure 3, islands of a given

volume will have total energies that vary with their crystallographic orientations

relative to the plane of the interface and relative to the atomic level structure and

symmetry of the substrate surface. Iff is not isotropic, the energy-minimizing

island orientation will be a function of the anisotropy of f as well as of the

magnitude off, in addition to depending on the magnitude and anisotropy ofi (81,

100, 106). During island growth and competitive coarsening processes, growthof islands with specific surface and interface energy-minimizing crystallographic

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surface from which adatoms are more likely to be added to the growing island

than to desorb or become part of another island or critical cluster. The width of

this zone, , is a function of and of the difussivity for adatoms, both of which

have an Arhenius dependence on temperature [i.e. proportional to a Boltzman termof the form exp(E/kT)]. Whether increases or decreases with T depends on

the relative magnitudes of the energy of desorption and the activation energy for

surface diffusion. If the absolute value of the latter is lower, decreases with

increasing T, as has often been inferred from experimental observations (45).

Considering the radius rs of the circle of intersection of an island and the

substrate, as illustrated in Figure 3, the rate of in-plane growth of a particle has the

form

G =

drs

dt = G0

1+

rs, 2.

where G0 is proportional to R and independent of T, but depends on and on the

atomic volume of the particle (88).

If it is assumed that grain boundaries formed when islands impinge are immo-

bile, the grain size at impingement can be determined as a function of, I, and G,

and therefore as a function of R and . When (G0/I)1/3 , a Johnson-Mehl grain

structure results (18), for which the average in-plane grain diameter is

di = 1.203G

0I1/3

,

G0

I1/3

. 3.

When (G0/I)1/3 , a grain structure for which

di = 1.351 .

G0

I

1/34.

results. This structure, which we refer to as the -dominated structure, can be

described by a Vornoi construction for points defined by the centers of disks of

radius , which have been randomly place on a plane, with maximum final density(18). The distributions of grain sizes for Johnson-Mehl and-dominated structures

have been determined through simulations. The distribution of grain sizes in the

-dominated structure is found to be much narrower than that of the Johnson-Mehl

structure, resulting in a greater initial stability against the grain coarsening which

occurs when grain boundaries become mobile.

The grain size at impingement can be approximated for all , G0, and I by (88)

di 1.351 + 1.203G0

I 1/3

. 5.

When, as is generally the case, I and decrease with increasing temperature, the

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166 THOMPSON

deposition flux R. It should be noted that the film thickness at which coalescence

occurs should, under conditions discussed above, scale with di, so that the film

thickness at coalescence should also increase with increasing T and remain un-

changed or decrease with increasing R. When islands grow with more complexgeometries, the specific results given above will be modified, but it is expected

that the trends for the dependence of the grain size at impingement, di, on R and

T will be preserved.

Nucleation experiments often show that a saturation in the number of nuclei

per unit area Nmax is reached when the zones of width completely cover the

substrate surface. Nmax is expected to scale with the inverse of the square root

of di. Measurements ofNmax suggest that even for high mobility materials (such as

fcc metals) deposited at relatively high temperatures (several hundred degrees C),

the grain size at impingement is, or would be inferred to be, of order 10 nm orless (45). Low-mobility materials, such as semiconductors or refractory metals, or

materials deposited at still lower temperatures, are expected to have still smaller

grain sizes impingement.

COARSENING

In the preceding discussion it has been implicitly assumed that the exchange of

atoms between islands does not significantly impact the overall structure evolutionprocess. However, the average island size within a system of isolated islands can, in

principle, increase through a coarsening process, even if deposition is interrupted.

This can occur through detachment of atoms from islands and diffusion of atoms

on the substrate surface to attach to other islands, resulting in the shrinkage and

even disappearance of some islands and the growth of other islands, so that the

average island size increases (10, 85, 111). Such a coarsening processes would be

driven by differences in the average energy per atom for islands of different sizes.

For islands with the same surface and interface energies, the energy per atom will

scale with the island surface to volume ratio, so that the atoms in small islands willhave high energies relative to those in larger islands. In the more general case, the

free energy per atom in an island will be a function of the island size and of the

total surface and interface energies of the island.

Because the surface and interface energies are a function of the crystallographic

orientation of the lattice of the island relative to the orientations of the substrate

lattice and the interface plane, the energy differences driving coarsening processes

include contributions that depend on the crystallographic orientation of an island

as well as on its size relative to that of its neighbors. Pre-coalescence island coars-

ening should therefore lead to an evolution in the distributions of island orientationsand well as islands sizes, favoring islands with orientations with minimum surface

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once islands impinge, island coarsening can occur through exchange of atoms via

grain boundary motion or via diffusion of atoms on the surfaces of the islands.

Observations of coarsening during and after coalescence are more common (64).

COALESCENCE

Consider two islands of the same size that have grown just to the point of contact,

as schematically illustrated in Figure 4. Once the islands make contact, there

is an energetic driving force for formation of a grain boundary that eliminates

the energies of the free surfaces of the two contacting islands, 2f, in exchange

for the lower energy of the newly formed grain boundary gb. This can happen

without diffusive processes, through elastic distortion of the islands as they arebrought together through grain boundary formation which initiates at the base of

the islands where they first make contact. If there is no sliding at the island/substrate

interfaces, the resulting strain in the islands can be substantial. Nix & Clemens (58)

have recently shown that the energy per volume released by boundary formation

increases with decreasing island size and, for island sizes of order 10 nm, can be

sufficiently high to drive development of stresses in the islands on the order of

GPas. This provides a possible explanation for the high tensile stresses that often

develop during deposition under conditions for which, and of materials for which,

surface diffusivities are expected to be low (1, 31, 32). Low diffusivities lead tosmall grain sizes at coalescence and to little stress relief via diffusive processes

during the coalescence process.

Figure 4 Coarsening resulting from the coa-

lescence of two islands.

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168 THOMPSON

If surface self-diffusivities and grain boundary self-diffusivities are such that

pairs of contacting islands can adopt fixed volume equilibrium shapes, the island

pairs will evolve as shown schematically in Figure 4af. Islands first form a grain

boundary either through elastic straining or through diffusion of material to theboundary. In the former case, the centers of mass of the islands will move toward

each other. If the energy per atom is exactly the same for the two islands, the islands

will be in an unstable equilibrium, and coarsening will not occur until a fluctuation

leads to an energy difference between the islands. When energy differences exist

due to a size difference and/or differences in surface or interface energies, one

island will grow and the other island will shrink, as shown in Figure 4cf. As this

coarsening occurs, there are equilibrium shapes for the island pairs for any given

relative volume and surface and grain boundary energies. However, coarsening

continuously leads to lower energy configurations. Coarsening requires diffusiveprocesses in the grain boundary including grain boundary motion. As a result of

this coarsening process small islands can shrink and eventually disappear, and the

centers of mass of the remaining islands can move from their original positions.

This coarsening process therefore results in an evolution in the grain size distribu-

tion, and, because it is also orientation selective, might also lead to an evolution

in the grain orientation distribution.

If coarsening occurs during island coalescence, the fraction of the substrate

surface covered by islands and by their surrounding nucleation exclusion zones

can decrease. This can lead to a situation in which relatively late in the process ofcovering the substrate surface, for example after Nmax has been reached, new areas

are exposed in which nucleation can again occur. This phenomenon is known as

secondary nucleation and has been observed during deposition in metallic systems

(64). Therefore, while coarsening during coalescence can lead to a decrease in the

final grain size due to decreases in the number of nuclei that survive the coalescence

process, secondary nucleation, can, in principle, lead to an increase in the number

of surviving nuclei, at least partially compensating for the loss of nuclei.

The rate of coarsening during coalescence depends on the surface and grain

boundary diffusivities and also on the initial distribution of island sizes. In thesequence shown in Figure 4, the coarsening is relatively slow at first, but then

speeds up as the size difference (and therefore the driving force) becomes larger.

Islands that first make contact when their sizes are substantially different coarsen

quickly. Coarsening during coalescence leads to the rapid elimination of small

islands, and might therefore be expected to lead to structures with more uniform

grain sizes, such as the -dominated structures discussed above.

It should be noted that elastic distortion to create a grain boundary is rapid

compared with the diffusive processes required for the islands to adopt their fixed

volume equilibrium shapes. However, if diffusion is relatively fast, the islandpairs will adopt fixed volume equilibrium shapes, and the coalescence strain will

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complete stress relief requires dislocation generation and motion (23, 57) or sliding

at the film/substrate interface (95). If the deposition rate is high and the island

growth process is fast relative to the rate of surface self-diffusion, coalescence

stresses will not be relieved.Whether coarsening during coalescence results in the elimination of a signifi-

cant number of islands depends on the overall growth rate of all the islands, which

is a function of the deposition rate R. If R is high, only the smaller islands will

be eliminated. In this context, R must be high relative to the surface and grain

boundary self-diffusivities. These self-diffusivities increase with the substrate tem-

perature as exp(-Q/kT), so that coarsening during coalescence leads to an increase

in the grain size with increasing substrate temperature (assuming that secondary

nucleation does not compensate for the coarsening effects). The dependencies of

the grain size on R and T is therefore similar to that expected without coarsening.The grain structure characteristics resulting from coarsening processes occurring

during coalescence and their dependence on the relative magnitudes of the relevant

kinetic and energetic parameters are not quantitatively well understood. However,

coarsening processes that continue after coalescence, grain growth processes, have

been studied extensively and quantitatively modeled.

GRAIN GROWTH

Consider a fully coalesced polycrystalline film with an equiaxed grain structure,

such as the one shown in Figure 5. Grain coarsening can occur through motion of

grain boundaries resulting in the shrinkage and elimination of small grains which,

in turn, results in an increase in the average size of the remaining grains. This is a

well known phenomenon called grain growth. Grain growth has been the subject

of several reviews (4, 33, 77), and grain growth in polycrystalline thin films has

been the subject of a review in this series (86). Only the key characteristics of

grain growth in films are reviewed here, with a focus on improved understandings

since the earlier article in this series.Grain growth in pure defect-free bulk materials is driven by the reduction in

the total grain boundary area and in the corresponding reduction in the total grain

boundary energy that accompanies the area decrease. At a more microscopic scale

this is accomplished when individual boundaries move toward their centers of

curvature in order to reduce boundary curvature and therefore boundary energy.

When grain boundary energy reduction alone drives grain growth, it is expected

that (4)

dr

dt

mgb

r= mgb, 6.

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170 THOMPSON

(a)

(b)

Figure 5 Grain growth in a continuous film with an in-plane grain size, which is constant

through the film thickness, and with an average in-plane grain size similar to the film

thickness.

m = m0 exp(Qgb/kT), where m0 is a temperature-independent constant, and Qgbis the activation energy for the rate-limiting atomic process involved in boundary

motion. From Equation 6 it is expected that the average grain radius will increase

with t1/2. It is also expected that the shape of the grain size distribution will be

time-invariant, indicating self-similar growth in that the function describing the

distribution of normalized grain sizes (the grain sizes divided by the median grainsize) is time independent. Grain growth with these characteristics is called normal

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The number of sides of a grain changes through switching events is of two ba-

sic types (71, 77). The first type occurs when two new grain boundary triple

junctions combine to eliminate a grain boundary, forming an unstable quadru-

ple point that immediately decomposes into two triple junctions connected by anew grain edge. The second kind of switching event occurs when triple junctions

are eliminated through disappearance of grains. Approximate analytic models for

two-dimensional grain growth, which combine analyses of grain growth within

topological classes (number-of-sides classes) as well as analyses of the rates of

topological transitions, have been shown to be successful in modeling the time

evolution of the statistical geometric and topological characteristics of soap froths

evolving between glass plates, when the bubble size is roughly equal to or larger

than the plate spacing (24, 77). Froth evolution is thought to be similar to idealized

normal grain growth.Several techniques have been developed for computer simulation of grain

growth, including Monte Carlo Potts models (76), front-tracking models (19),

and so-called vertex models (21, 39). In front-tracking models, points on grain

boundaries are moved a distance and direction consistent with

= mgb, 7.

in time steps, where the boundary velocity and the curvature are vector quan-

tities. Force balances are maintained at the grain boundary triple junctions in each

time step. Using this approach, as well as the other modeling approaches, behaviorconsistent with the expectations for two-dimensional normal grain growth can be

demonstrated, i.e. average geometric dimensions of the grain structure scale with

t1/2, and the normalized grain size distributions and number-of-sides distributions

are time invariant (14, 77). It has been shown that the time-invariant or steady-state

grain size distribution is well fit by a Weibull distribution function (14).

A film with the structure shown in Figure 5a can, in principle, undergo a

grain growth process that is two dimensional in character, e.g. the directions of

boundary motion will generally lie in the plane of the film, and boundary motion

will largely occur to reduce the in-plane curvatures of the boundaries. However,true two-dimensional normal grain growth rarely if ever occurs in thin films. Grain

structures of films that are known to have undergone grain growth do not have grain

size distributions that are well fit by Weibull distribution functions (or similar

distribution functions such as the Gamma distribution), but are instead well fit

by lognormal grain size distribution functions (62, 97, 98, 109). Also it is often

found that these grain structures are resistant to further evolution through grain

growth when the average in-plane grain size is about three times the film thickness

(7, 20, 54, 62). This is known as the specimen thickness effect (7). The Weibull

and lognormal distributions can be readily distinguished. When grain growth doeslead to grain sizes significantly larger than the film thickness, it usually involves the

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172 THOMPSON

These departures from ideal two-dimensional behavior arise for a number of

reasons. First, consider a film with the as-deposited structure shown in Figure 1c.

Heating of such a film will increase the boundary mobility and eventually lead to

observable grain growth, which will ultimately lead to structures such as the onesschematically illustrated in Figure 1d and Figure 5. However, because the initial

structure has a grain size that is not uniform through the film thickness, there will

be an important three-dimensional component to the grain growth until the vast

majority of boundaries traverse the thickness of the film. Also, as highly non-

equiaxed columnar grains disappear, they are likely to do so by first collapsing to a

triple junction line in the interior of the film, which connects two three-dimensional

grains (96). The three-dimensional grains will rapidly shrink through motion of

boundaries in directions out of the plane of the film. The higher the average aspect

ratio of the grains, the more important this three-dimensional component will bein governing the overall structure evolution.

It is therefore only after structures of the type shown in Figures 1dand Figure 5

develop that the conditions for two-dimensional normal grain growth might, in

principle, be approximated. However, at this point the top and bottom surfaces

of the films begin to play important roles affecting further evolution. First, it is

important to recognize that a balance of the surface energies of neighboring grains

with the energy of the boundary between the grains leads to the formation of

grooves where boundaries intersect the surfaces of the film. Groove formation has

been treated by a number of authors (54, 78). Mullins (54) discusses the effectsthat groove formation have on grain growth in metallic sheets. Grooving and grain

growth are competing kinetic processes. To a first approximation, grooves will not

form on rapidly moving boundaries. However, as grain growth proceeds and the

velocity of a boundary decreases, grooves eventually form and suppress or stop

further boundary motion. Mullins showed that this effect can lead to the speci-

men thickness effect. This has also been demonstrated using a two-dimensional

simulation which assumes that boundary velocities drop discontinuously to zero

when the boundary curvature (and therefore the boundary velocity) falls below

a critical value (20). Frost et al also show that under these conditions not onlydoes grain growth stagnate when the average in-plane grain size is about three

times the film thickness, but also that the grain size distributions of the resulting

stagnant structures are well fit by a lognormal distribution function, as is observed

experimentally. It should be noted, however, that solute drag (29) can also lead

to transient regimes in which the grain size distribution is well fit by a lognormal

function.

The energies of the top surface of the film and the film substrate interface also

affect grain growth in films in other ways. Once structures of the type shown

in Figure 1d and Figure 5 develop, a significant fraction of the total energy of agrain is associated with the energies of the free surface and the interface. The

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s

i

2rs

2r

h

Figure 6 The energetics of grain structure evolution in thin films on substrates are affected

by the surface energy s, the interface energy i, and the strain energy density, all of which

vary with the crystallographic orientation of a grain.

not necessarily the same orientations, one energy will dominate so that there will

be grain orientations that minimize the sum of the surface and interface energy.

Therefore the growth of grains with these orientations is favored (see Figure 6).

This has several important consequences. First, there is a subpopulation of grains

for which growth is favored so that steady-state normal grain growth can not occur

until or unless only the favored grains are left. Second, since grains in the favored

subpopulation have restricted crystallographic orientations, grain growth in films

necessarily leads to an evolution in the distribution of grain sizes toward a uniform

or restricted texture unless the texture of the film is already uniform.

Two-dimensional front-tracking simulations can be modified to account for

surface and interface energy minimization by modifying Equation 7 to be

= mgb + s/i, 8.where

s/i =(s +i)

gbh, 9.

and where s and i are the differences of the surface and interface energies,

respectively, of the grains meeting at the boundary, and h is the film thickness.

s/i then becomes a measure for the out-of plane curvature of the boundary, and

the effect of surface and interface energy differences become more important in

thinner films.It is thought that surface energy minimization during grain growth is responsible

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174 THOMPSON

minimization does not favor growth of grains with specific in-plane orientations.

However, for polycrystalline films on single-crystal substrates, i depends on the

in-plane orientation of the grain, and grain growth is expected for films composed

of grains with three-dimensionally constrained or epitaxial orientations, as hasbeen observed in metallic films on various single crystals, including single-crystal

metallic films (91), and ceramic films (52).

Another important aspect of the energetics of grain growth in thin films is

that they are often under high intrinsic or extrinsic stresses. High intrinsic tensile

stresses can arise during coalescence, as described above, and in sputter-deposited

films, high intrinsic compressive stresses are sometimes observed, presumably

the result of shot peening effects (60). In addition, when films are heated or

cooled on substrates, differential thermal expansion can lead to significant ten-

sile or compressive extrinsic strains. In continuous films, these strains are largelybiaxial, thus the associated strain energy density in different grains is given by

E = 2Mhkl, 10.

and depends on the magnitude of the strain and the effective biaxial modulus

Mhkl. Mhkl depends on the crystallographic direction (hkl), which is normal to

the plane of the film and therefore normal to the plane of the strain (57, 89, 90).

The biaxial modulus for grains with arbitrary (hkl) texture can be calculated using

equations given by Murikami & Chaudhari (55). For fcc metals the effective

biaxial modulus is found to have a minimum value for grains with (100) texture

and a maximum value for grains with (111) texture.

It can be seen, then, that in biaxially strained films, grains with different orien-

tations have different strain energy densities and that these energy differences can

contribute to the driving force for grain growth, favoring grains with strain energy

density minimizing orientations (16, 68, 87, 110). This effect has been accounted

for in simulations (9) by modification of Equation 8 to become

= mgb + s/i + , 11.where is an upper bound for the effects of differences in strain energy density

and is given by 2 M/gb, where M is the difference in the biaxial moduli of

the two grains meeting at the boundary under consideration.

The effects of strain energy minimization are qualitatively similar to those of

surface and interface energy minimization in that normal grain growth can not

occur until the subpopulation of grains favored by strain energy minimization

has consumed all grains with other orientations. Strain energy minimization also

drives the evolution of the distribution of grain orientations, favoring strain energy-

minimizing textures. It is important to note, however, that the contribution ofstrain energy differences to the energetics of grain growth does not scale with film

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surface and interface energies generally appear to be minimized for grains with

(111) texture, whereas strain energies are minimized for grains with (100) texture

(16, 89, 90, 102). Other materials have energy minimizing textures. For example,

it has been suggested that for TiN, (100) texture minimizes the surface energy,whereas (111) is known to minimize the strain energy (59, 65).

It has been observed in a number films of mechanically anisotropic fcc metals

that annealing-induced grain growth can promote the development or enhancement

of pre-existing (111) texture or strengthening instead of an initially weak (100)

texture, depending the film thickness and the temperature at which the film was

deposited. This can be understood in terms of energy minimization by recognizing

that surface and interface energy minimization and strain energy minimization

compete in defining the texture that is, on average, favored during grain growth.

The average driving force for grain boundary motion arising from surface andinterface energy minimization is

Es/i =(s +i)

h, 12.

where s is the difference in the average surface energy of the film and the

minimum surface energy, and i is similarly defined for the interface. The

average driving force arising from strain energy minimization is

E = 2M, 13.

where, M is the difference in the average biaxial modulus of the film and the

minimum modulus. A transition in dominant texture will occur when Es/i = E,

with surface and interface energy minimization dominating when Es/i > E, i.e. in

films with low h and , and strain energy minimization dominating when Es/i


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176 THOMPSON

surfaceenergy

minimizatione.g. (111)

strainenergy

minimizatione.g. (100)

film thickness

Figure 7 A texture map

showing the expected texture

favored by grain growth as

a function of the elastically

accommodated strain and the

film thickness.

defects is partially recovered through grain growth and also contributes to texture

evolution (69).

When there is a subpopulation of grains whose growth is favored, e.g. by surfaceand interface energy or strain energy minimization, abnormal growth grain growth

results because the normalized grain size distribution and the grain orientation

distribution evolve during grain growth. If there is a favored subpopulation and

grain boundary grooves have formed favored grains may preferentially avoid stag-

nation (54). This can lead to strikingly bimodal grain size distributions as favored

grains grow by consuming grains with otherwise stagnant boundaries. This mode

of grain growth in thin films is commonly observed (62, 86, 93, 109) and has been

referred to as secondary grain growth. Secondary grain growth can also result from

precipitate-induced stagnation coupled with growth of preferred subpopulations(22, 48, 104). In secondary grain growth, the final grain size of the film depends

on how many grains are able to grow. This, in turn, depends on the degree of the

selectivity and on how many grains in the initial grain structure have the favored

orientation (84). A small initial grain size in initially randomly oriented films fa-

vors a smaller grain size resulting from the impingement of secondary grains. As

secondary grains impinge and completely consume the smaller stagnant grains, the

resulting grain structure is likely to be stagnant and characterized by a monomodal

distribution of sizes. In at least one case this has been characterized, and the dis-

tribution of grain sizes appears to be well fit by a lognornmal function (41). Thein-plane grain size resulting from secondary grain growth can be many times the

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defect energy, such as the energy from dislocations, as well as the energy of grain

boundaries. Strain energy and surface and interface energy minimization can also

contribute to the driving force for recrystallization, thus recrystallization can also

lead to texture evolution, bimodal grain size distributions, and final in-plane grainsizes many times the film thickness. Recrystallization and secondary grain growth

are not readily distinguishable.

GRAINGROWTHDURING FILM COALESCENCE

AND THICKENING

It has been shown that grain growth during the late stages of coalescence can

lead to the (111) texture observed in as-deposited Au (34, 64, 107), Ag (34), Cu(34) and Al (67) films, even when they are deposited at room temperature. In the

case of Au, room temperature is only about 20% of the absolute melting tempera-

ture. Continued grain growth during film thickening, schematically illustrated in

Figure 1bd, is expected in these metals and has been directly demonstrated in

experiments on Al (47). This behavior is also suggested by the stress evolution

characteristic of this mode of structure evolution observed during deposition of Ag,

Au, and Cu at room temperature (1) and Fe and Cr at elevated temperatures (1, 2).

If grain growth proceeds during thickening, but is subject to grooving-induced

stagnation, it is expected that the average in-plane grain size in the as-depositedfilms should scale with the film thickness, as has been observed for Al films (47).

In this case the as-deposited grain size distribution should be lognormal, as has

also been observed in Al (47, 97). The texture and the lognormal grain size dis-

tribution observed in as-deposited Al films is probably the result of grain growth

processes occurring during film coalescence and thickening. These microstruc-

tural characteristics observed in other as-deposited metallic films may have similar

origins. In general, the mode of structure evolution illustrated in Figure 1bd,

which we refer to as type 2 evolution, is expected in materials with high atomic

mobilities (and therefore high grain boundary mobilities) at low temperatures andin other materials at higher temperatures at which their atomic mobilities are

high.

It should be noted that impurities in films can lead to grain boundary drag and

even grain growth stagnation (17, 49). For this reason, improved vacuums with

lower pressures of background gases can lead to larger as-deposited grain sizes

in films that undergo grain growth during coalescence if solute drag effects are

reduced or absent. This is probably the reason that films of Al, Au, Ag, and Cu

tend to have larger as-deposited grain sizes when they are deposited under UHV

conditions (34, 67). Gettering of sputtering gases also leads to larger grain sizesin sputter-deposited Al films. On the other hand, introduction of impurities dur-

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178 THOMPSON

Impurity-induced suppression of grain growth during deposition can lead to an

increase in the grain boundary energy per volume, which can drive secondary

grain growth and recrystallization. Processes such as electrodeposition, which of-

ten lead to significant impurity incorporation, can therefore result in as-depositedfilms with very fine grain sizes in materials that would have larger grain sizes

if deposited via cleaner vapor deposition techniques. These films would be more

prone to undergo recrystallization, as in room-temperature so-called self annealing

of electroplated Cu films (28, 46).

COMPETITIVE GRAIN GROWTH PROCESSES AT THE

SURFACESOFGROWING FILMS

Once a continuous film has formed through nucleation, growth, and coalescence

processes, thickening is normally expected to occur via epitaxial growth on pre-

existing grains, even at quite low temperatures. Exceptions are possible if the

surface composition of the growing grains changes sufficiently to require renu-

cleation. For example, even during growth of nominally pure films, if impurities

absorb and accumulate on the surface of the growing grains, due for example to re-

jection from the growing crystals, the surface will periodically become sufficiently

coated with impurities to require nucleation of new grains of the pure material.

Under clean and well-controlled growth conditions, thickening is expectedto proceed as schematically illustrated in Figure 1c, d. As discussed above, in

cases in which grain boundaries are mobile during deposition, type 2 thickening

(Figure 1bd) occurs and the grain size of the film increases as the film thick-

ens. Adatoms join the grain on which they are deposited but may become incor-

porated in neighboring grains through motion of boundaries in the bulk or volume

of the film. The grain aspect ratios in the as-deposited films have an average value

of order 1 if grain growth proceeds to stagnation as the film thickens.

When the grain boundaries in the bulk of a film are immobile, type 1 thickening

(Figure 1bc) occurs and results in films with high-aspect-ratio columnar grains.Even in this case the grain size and texture at the top of the film can still evolve

through competitive grain growth processes restricted to the surface of the growing

film. At very low temperatures at which surface self-diffusivities for adatoms

are very low, surface topography present at coalescence can become accentuated

during thickening as atoms arrive and remain at their arrival site. It has been

shown that roughness on the surface of even thickening amorphous films can

become accentuated under conditions of severely limited adatom mobility, and this

stabilized roughness can result in a columnar growth mode and columnar structures

(5). This phenomenon is known as kinetic roughening (36, 51). When adatomsarrive at normal incidence to the films surface, perturbations are stabilized and

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minimum-sized perturbations that are stabilized increases. If adatoms arrive with a

range of angles off the normal to the film surface, as they do in sputter deposition,

shadowing can also occur (5, 38, 42). Perturbations that reach farther into the

vapor phase than others tend to collect more of the atoms arriving at angles otherthan normal incidence. Shadowing can lead to competitive growth of columns

with structures similar to those shown in Figure 1c but with the grain boundaries

replaced by walls of low density or voided material. It should also be noted that

surface corrugation to relieve strain can lead to growth of columnar structures,

even in the absence of polygranular or even crystalline structure (3, 27, 73, 75).

Ballistic aggregation models in which atoms are added to growing film surfaces,

and hence subject to severe limitations on their repositioning based on constrained

arrival directions, show features on an atomic scale similar to those expected by

analytic treatments of kinetic roughening (30).Although kinetic roughening and shadowing effects may contribute to the for-

mation of structures of the type shown in Figure 1c for polycrystalline films, given

that the columns in polycrystalline films are defined by grain boundaries, it is rea-

sonable to believe that some form of competition for incorporation of adatoms in

different grains is primarily responsible for the evolution of these structures. Also,

the spatial scales associated with kinetic roughening and shadowing effects are

generally smaller than those of the grain structures of polycrystalline films. This

has recently been nicely demonstrated in experiments on TiN grown on Al films

(13). In this case the Al films had grain sizes on the order of one micrometer andTiN grains grew epitaxially on the Al grains so that the TiN film had a grain size

of the same order as that of the Al film, even under growth conditions in which

the grain size of TiN grown on an amorphous SiO2 layer would have been much

smaller. However, a small-scale columnar structure as highlighted by microvoids

at column walls was observed within the TiN grains, demonstrating the effects

of kinetic roughening and shadowing on this smaller size scale. In this case the

columnar structure resulting from kinetic roughening and shadowing was smaller

than, and independent of, the size scale of the columnar grain structure associated

with the films polycrystallinity.The competitive polycrystalline growth illustrated in Figure 1c can be best un-

derstood by considering the action of adatoms with finite mobility, which, upon

arriving in the vicinity of a grain boundaries diffuse to attach to grains and thus

minimize the boundary curvature. Thus the competition among grains at the sur-

face of the film can be viewed as a two-dimensional grain growth process in

which the boundaries are mobile only at the surface of the film, and the mobil-

ity of the boundaries is related to the adatom diffusivities as well as to the time

during which adatoms can move before being buried by newly arriving adatoms.

This diffusion time is related to the deposition rate. If this simple picture applies,then simulations of two-dimensional grain growth run to different times would

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180 THOMPSON

t1/2 (74), and the grain size distribution should be well fit by a Weibull distribution

function (14). If surface energy minimization contributes to the driving force for

grain boundary motion at the surface of the film, the crystallographic texture of

the grains at the surface of the film will evolve as grains with high energy sur-faces are eliminated or occluded during thickening (43, 44). The texture evolution

and grain size evolution could then also be understood using two-dimensional

simulations (74). Similarly, if strains and strain energies are high, strain energy

minimization might also significantly contribute to the evolution of the surface

grain structure, driving the development of strain energy minimizing textures dur-

ing film thickening (59, 65, 88).

For films whose stress state is affected most strongly by the tensile stress that

develops during coalescence, the magnitude of the strain, and therefore of dif-

ferences in strain energy densities, will depend on the island size at coalescencewhich, under the conditions discussed above, increases with increasing deposi-

tion temperature and decreases with increasing deposition rate. In this case strain

energy minimizing textures might be expected in films deposited at lower tem-

peratures and higher rates, whereas surface energy minimizing textures might be

expected otherwise (88). This argument is qualitatively consistent with observa-

tions of texture as a function of deposition rate and temperature in a variety of

evaporated metallic films (25).

As mentioned earlier, sputtered films can be deposited with high compressive

stresses when the energies of arriving atoms and other bombarding species aresufficiently high to cause shot peening effects. Minimization of compressive strains

may also drive the evolution of strain-minimizing textures. This hasbeen suggested

as the origin of (111) textures in TiN films deposited under conditions leading to

high stresses, as opposed to the development of (100) texture, which is speculated

to minimize the surface energy of TiN (59, 65).

In addition to strain and surface energy minimization, growth velocity anisotro-

pies can also lead to competition of grains at the surface of the thickening film

and a through-thickness evolution of the in-plane grain size and the average crys-

tallographic texture of the grains at the surface. This is most simply illustrated inFigure 8, as originally described by van der Drift (101). Consider two-dimensional

crystals that grow with a square facetted morphology bound by faces with Miller

indices of type (01), which are assumed to grow only in the (01) directions so

that the square morphologies are retained. In this cases the maximum rate of ex-

tension or growth of the crystals is in the (11) directions. Even if these crystals

nucleate on a line (the analog of a surface for three-dimensional crystals) with

random orientations, thickening will result in the eventual occlusion of crystals

with textures near (01) by crystals with textures near (11). This happens because

the crystals with (11) texture are oriented to have fast growth directions lying notonly normal to the plane of the film but also in the plane of the film. This results

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Figure 8 van der Drift construction illustrating through-thickness grain-size and grain-

orientationevolution resulting fromgrowth velocity anisotropy during film thickening(101).

Thijssen (83) has termed this type of model a 1+1D model to capture thefact that the competition is occurring only in directions parallel to the line that

represents the surface as the film thickens in another dimension. Thijssen shows

that such a model also results in an average in-plane grain size at the surface of the

film (average grain width along a line parallel to the surface line), which scales with

h1/2. Thijssen later reported a model for 2+1D growth (82) in which competition

occurs on a two-dimensional surface of a growing film and argued that in this case

the average in-plane grain size at the surface of the film scales at h5/2. Paritosh et al

(63) have also treated the 1+1D case, again confirming that the average surface

grain size scales with h1/2, but also quantitatively analyzing the evolution of thedistribution of grain sizes and orientations. Models of this type have been invoked

to explain grain size and texture evolution in diamond films (105).

It should be noted that a number of experiment report grains with specific

in-plane orientations that are favored during thickening, which result in three-

dimensionally constrained surface textures and in-plane orientations (50, 72, 108).

A number of models for this behavior have been proposed (11, 37, 66).

For through-thickness in-plane grain size and surface texture evolution caused

by growth velocity anisotropy or driven by surface or strain energy minimization,

the rate of grain size evolution will diminish once grains with the favored texturehave occluded all other grains and the surface texture becomes uniform. This can

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182 THOMPSON

Figure 9 If surface grain growth during film thickening is driven by growth velocity,

surface energy, or strain energy anisotropy, when all unfavored grains are occluded, furtherevolution may lead to grains with parallel boundaries, uniform through-thickness sizes, and

uniform or restricted textures. (This could lead to zone 2 structures in the Movchan &

Demchishin scheme.)

e.g. when adatom mobilities are high, the competitive growth phase may transpire

in the very early stages of film growth, so that the columnar parallel-boundary

structure dominates the character of the film, especially in thick films.

ZONEMODELS REVISITED

In all the structure-governing phenomena described above, temperature is the crit-

ical effect in controlling the relative importance of various thermally activated

processes. Adatom diffusion on the substrate surface, the rate of adatom desorp-

tion, and the rate of nucleation control the grain size at impingement and are all

exponentially dependent on temperature. Pre-coalescence coarsening is controlled

by adatom diffusion on the substrate surface, and coarsening during and after co-alescence is controlled by self-diffusion on the island or film surfaces and by self-

diffusion along and across grain boundaries. Coarsening confined to the surface of

the growing film is also governed by the rates of surface self-diffusion of adatoms.

When adatom mobilities are low, grain boundary mobilities are also low, and

initial grain sizes are small and tend to change only through coarsening at the

surface of the growing film. Bulk, grain boundary and surface self-diffusivities

for a material at given temperature, tend to be lower the higher the melting tem-

perature of that material. This leads to the tendency to observe similar structural

evolution for materials within the same materials class at similar homologous tem-peratures, Th, where the homologous temperature is defined as the temperature in

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structures are expected when the deposition temperature is below a homologous

temperature of about 0.5, and the effects of bulk grain boundary motion are not

expected unless deposition temperatures above homologous temperatures of 0.5 K

are used. Thornton (94) noted that in sputter deposition, effective adatom mobili-ties are affected by the energy with which the atoms arrive at the film surface. The

energy is affected by the number of collisions the arriving atom has with sputter-

ing gas atoms, which scales with the pressure of the sputtering gas. This leads to

an increase in the homologous temperatures associated with structural transitions

with decreasing sputtering gas pressure for sputtered films. Thornton illustrated

this by adding another dimension and axis to Movchan & Demchishins diagram,

along which the sputtering gas pressure was tracked.

The zone diagrams of Movchan & Demchishin and Thornton are useful tools

for semi-quantitatively capturing and illustrating the expectations for structuralevolution as a function of the process parameters, deposition temperature, and

pressure. However, it is important to note that the such diagrams are developed for a

specific material or class of materials (typically refractory bcc metals) and are based

on assumptions about the deposition technique (typically sputter deposition) and

specific processing conditions, such as deposition rates and background impurity

gas pressures, both of which affect the purity of the deposited films. As has been

nicely illustrated by Brown & Ashby (8), while materials within the same class

tend to have similar diffusivities at similar homologous temperatures, diffusivities

for materials from different materials classes can have widely varying diffusivities,even at the same homologous temperature. As a class, materials with diamond

cubic structures such as Si, Ge, and C in the diamond form have among the

lowest diffusivities at a given homologous temperature of any materials class. The

diffusivities of diamond cubic materials are particularly low in comparison with

bcc materials, for which zone models are usually discussed (94) and are even lower

still than those of fcc materials. Adatom mobilities for Si are so low that deposited

films are amorphous up to homologous temperatures of 0.5 K. Grain boundary

mobilities of undoped diamond cubic materials are also anomalously low, thus bulk

grain boundary motion does not affect the as-deposited grain structures of thesematerials unless deposition temperatures are above homologous temperatures of

about 0.9 K (86). These observations are illustrated in a Movchan & Demchishin-

type zone map for diamond cubic materials (Figure 11b).

As discussed above, bulk grain boundary motion during coalescence and thick-

ening of films of Ag, Cu, Al, and Au clearly plays an important role in defining

the grain sizes, grain shapes, and grain orientations in films deposited even at

homologous temperatures as low as 0.2 K. Clearly the zone diagram for these

materials should be more like the ones schematically illustrated in Figure 11a,

than the one shown in Figure 10. Part of the reason for this is the higher atomicmobilities characteristic of fcc materials compared with bcc materials. However,

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184 THOMPSON

0.3 0.5

SUBSTRATETEMPERATURE (T/Tm)

ZONE 1 ZONE 2 ZONE 3

Figure 10 Movchan & Demchishin zone model (94).

minimized. The mole fraction of impurities in a film is expected to scale with the

background partial pressure of impurities so that films deposited under ultra-high-

vacuum conditions should have higher purities than films deposited with higher

background pressures. It is well known that very minor levels of impurities can

suppress grain boundary motion due to grain boundary drag effects (49). Impurity

absorption probably also affects adatom mobilities. It is usually expected thatthe homologous temperatures associated with the transitions in structural zones

will increase with decreasing film purity. It should be noted, however, that in

Si electron doping with electron donors leads to enhanced atomic and boundary

(a)

0.5 Tm 0.9 Tm

0.2 0.3 Tm

Figure 11 (a) Movchan

& Demchishin-type map

for Si, (b) Movchan &

Demchishin-type map for

fcc metals deposited under

ultra-high vacuum condi-

tions.

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mobilities impurities (40, 103), so that in this special case, and perhaps in others,

impurity additions might lower the homologous temperatures for zone transitions.

In general, it is important to recognize that film purity, whether impurities are

intentionally added or not, can significantly affect the homologous temperaturesassociated with transitions in growth modes in a particular materials class, and so

can affect the transitions shown in Figures 10 and 11a, b.

SUMMARY

Table 1 summarizes the kinetic factors and process parameters that affect the

evolution of the structure of polycrystalline films. The relative rates of island

nucleation and growth govern the grain size at impingement (see also Figure 1).The nucleation rate depends on the substrate temperature and the deposition rate,

and the rate of island growth also depends on the deposition rate as well as the

rate of adatom diffusion on the substrate surface and the adatom desorption rate,

both of which are strongly temperature dependent. The grain size at impingement

increases with increasing substrate temperature and is unaffected or decreases with

increasing deposition rate.

Competitive coarsening processes occurring before, during, and after coales-

cence can also affect the grain size of films. Pre-coalescence competitive coars-

ening can occur by diffusion of adatoms on the substrate surface, but evidence for

TABLE 1 Factors affecting structure evolution in polycrystalline films

Kinetic factors affecting structure evolution

Adatom diffusivities on the substrate surface

Adatom self-diffusivities on island surfaces

Self-diffusivities in grain boundaries

Grain boundary mobilities

Adatom cluster nucleation rates

Adatom desorption rates

Process parameters

Deposition rate (affects adatom arrival rate, affects adatom diffusion time before

cluster nucleation or desorption, affects film purity)

Substrate temperature (affects all kinetic processes, increasing rates with increasing

temperature

Background pressure (affects film and surface purity)

In sputter deposition: sputtering gas pressure and substrate bias (affect the angular

distribution and energies of arriving adatoms)

Factors affecting zone models

Materials class

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186 THOMPSON

strong affects of such coarsening is not known. Coarsening has been observed

as islands coalesce, at which point islands can exchange material via atomic self-

diffusion on the island surfaces and by diffusion along and across grain boundaries.

Coarsening processes are faster at higher temperatures. Coarsening through grainboundary motion (grain growth) can occur during or after film coalescence, during

film thickening (type 2 thickening), or as a result of post-deposition annealing. The

rate of grain growth is higher at higher temperatures. The rates of grain growth

and other coarsening processes are generally (though not always) reduced by the

presence of impurities from either solute or precipitate drag. Precipitates can sup-

press normal grain growth and lead to abnormal grain growth in which the final

grain size of a film can be many times larger than the film thickness.

When bulk grain boundaries are immobile during film growth, both the grain

size at impingement and the corresponding grain size distribution are preservedat the base of a film, and in the absence of impurity effects, films thicken through

epitaxial growth on the as-impinged grains at the base of the film. This type 1

thickening mode results in films with high-aspect-ratio columnar grains. Even

without bulk grain boundary motion, the grain size at the surface of the grow-

ing film can increase due to competition among the growing grains at the surface

of the film. This competition can be driven by grain boundary curvature reduc-

tion and by surface energy and/or strain energy minimization. Through-thickness

grain size evolution may also result from growth velocity anisotropies. The amount

of through-thickness grain structure evolution that occurs depends on the intrin-sic anisotropies of the growing materials and on the adatom surface diffusivities

and the deposition rate. High-growth temperatures promote this competition, as

do conditions leading to shadowing effects. When anisotropies are responsible

for through-thickness grain growth, through-thickness evolution stops when only

those grains with favored orientations remain.

The texture of as-deposited polycrystalline films is also affected by the pro-

cesses that control grain size and shape evolution as (schematically illustrated and

summarized in Figure 12). The texture of as-coalesced films can be affected by the

nucleation and pre-coalescence growth process, because the energetics of theseprocesses are affected by surface and interface energy anisotropies. These ener-

getic anisotropies as well as mechanical anistropies can also cause texture evolution

to result from coarsening processes occurring before, during and after coarsening.

Surface, interface, and strain energy minimization can drive grain growth, lead-

ing, in principle, to different textures. These energies as well as growth velocity

anisotropies can also drive texture evolution during type 1 thickening. The differ-

ent modes of structure evolution can be schematically summarized as a function

of substrate temperature and other process parameters in zone-model maps. How-

ever, such maps apply only for a specific material or a class of materials, depositedusing specific techniques under specific conditions. The homologous temperatures

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atomic mobility materials (such as fcc metals). The transition temperatures are also

strongly dependent on factors such as the background pressure during deposition

that affect film purity.

Many factors affect the structures of polycrystalline films, and polycrystallinefilms can have widely varying grain shapes and distributions of grain sizes and ori-

entations. The relationships between materials selection, processing techniques,

and processing conditions, and the structural characteristics of the resulting films

are qualitatively understood, and, increasingly, semi-quantitatively understood.

These understandings can provide the bases for materials selection, process se-

lection, and process design to tailor microstructures for optimized performance of

polycrystalline films in their wide range of specific engineering applications.

nucleation

pre-coalescencecoarsening

coarseningduring coalescence

coarseningafter coalescence

(grain growth)

coarsening

duringthickening

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188 THOMPSON

ACKNOWLEDGMENTS

The authors research on this topic has been primarily supported by the National

Science Foundation. During preparation of the bulk of this paper, the author was

a visitor at the Max-Planck Institute fur Metallforschung where he was supportedthrough an Alexander von Humboldt research prize for senior U.S. scientists. The

author also thanks Steven Seel for a critical review of the manuscript.

Visit the Annual Reviews home page at www.AnnualReviews.org

LITERATURE CITED

1. Abermann R. 1990. Vacuum 41:1279

2. Abermann R. 1992. MRS Soc. Symp. Proc.239:25

3. Assaro RJ, Tiller WA. 1972. Met. Trans.

3:1788

4. Atkinson HV. 1988. Acta Metall. 36:

469

5. Bales GS, Zangwill AJ. 1991. Vac. Sci.

Technol. A9:145

6. Barmak K, Rickman JM, Michaelson C.

1997. J. Electron. Mater. 26:1009

7. Beck PA, Holtzworth ML, Sperry PR.

1949. Trans. Am. Inst. Min. (Metall.) Eng.

180:163

8. Brown AM, Ashby MF. 1980.Acta Metall.

28:1085

9. Carel R, Thompson CV, Frost HJ. 1996.

Acta Metall. Mater. 44:2479

10. Chakraverty BK. 1967. J. Phys. Chem.

Solids 28:2401

11. Dong L, Srolovitz DJ. 1998. J. Appl. Phys.84:5261

12. Dimos D, Chaudhari P, Mannhart J,

LeGoues FK. 1988. Phys. Rev. Lett. 61:219

13. Eaglesham DJ, Bower JE, Marcus MA,

Gross M, Merchant S. 1997. Appl. Phys.

Lett. 71:219

14. Fayad W, Thompson CV, Frost HJ. 1999.

Scr. Mater. 40:1199

15. Fitzgerald EA, Kimerling LC. 1998. MRS

Bull. 23:3916. Floro JA, Thompson CV, Carel R, Bris-

PD 1994 J M R 9 241

18. Frost HJ, Thompson CV. 1987. Acta Met-

all. 35:52919. Frost HJ, Thompson CV, Howe CL, Whang

J. 1988. Scr. Metall. 22:65

20. Frost HJ, Thompson CV, Walton DT. 1990.

Acta Metall. Mater. 38:1455

21. Fullman RL. 1952. In Metal Interfaces,

p. 179. Cleveland, OH: Am. Soc. Metals

22. Gangulee A, dHeurle F. 1972. Thin Solid

Films 12:399

23. Gao H, Zhang L, Nix WD, Thompson CV,

Arzt E. 1999. Acta Mater. 47:2865

24. Glazier JA, Weaire D. 1992. J. Phys.: Con-

dens. Matt. 4:1867

25. Grantscharova E. 1993. Thin Solid Films

224:28

26. Greiser J, Muller D, Mullner P, Thompson

CV, Arzt E. 1999. Scr. Mater. 41:709

27. Grinfeld MA. 1987. Sov. Phys. Dokl.

31:1831

28. Harper JME, Cabral C Jr, Andricacos PC,Gignac L, Noyan IC, et al. 1999. J. Appl.

Phys. 86:2516

29. Hayashi Y, Frost HJ, Thompson CV, Wal-

ton DT. 1994. MRS Symp. Proc. 317:

431

30. Henderson D, Brodsky MH, Chaudhari P.

1974. Appl. Phys. Lett. 25:641

31. Hoffman RW. 1976. Thin Solid Films

34:185

32. Hoffman RW. 1981. Surf. Interface Anal.3:62

33 H h FJ H th l M 1998 R

byU




31/33


34. Kakati KK, Wilman H. 1973. J. Phys. D:

Appl. Phys. 6:1307

35. Kamins T. 1998. Polycrystalline Silicon for

Integrated Circuits and Displays. Boston:

Kluger. 2nd ed.

36. Karder M, Parisi G, Zhang YC. 1986. Phys.

Rev. Lett. 56:889

37. Karpenko OP, Bilello JC, Yalisove SM.

1997. J. Appl. Phys. 82:1397

38. Karunasiri RPU, Bruinsma R, Rudnick J.

1989. Phys. Rev. Lett. 62:788

39. Kawasaki K, Enomoto Y. 1988. Physica

150A:462

40. Kim H-J, Thompson CV. 1986.Appl. Phys.Lett. 48:399

41. Kim H-J, Thompson CV. 1990. J. Appl.

Phys. 67:757

42. Krug J. 1997. Adv. Phys. 46:139

43. Kynut G, Quaeyhaegens C, DHaen J, Stals

LM. 1995. Thin Solid Films 258:159

44. Kynut G, Quaeyhaegens C, DHaen J, Stals

LM. 1996. Phys. Status Solidi B159:179

45. Lewis B, Anderson JC. 1978. Nucleation

and Growth of Thin Films. New York:Academic

46. Lingk C, Gross ME. 1998. J. Appl. Phys.

84:5547

47. Lita AE, Sanchez JE. 1999. J. Appl. Phys.

85:876

48. Longworth H, Thompson CV. 1991. J.

Appl. Phys. 69:3929

49. Lucke K, Stuwe HP. 1963. InRecovery and

Recrystallization, ed. L Himmel, p. 171.

New York: Interscience50. Malhotra AK, Yalisove SM, Bilello JC.

1997. Thin Solid Films 286:196

51. Mazor A, Srolovitz DJ, Hagan PS, Bukiet

BG. 1988. Phys. Rev. Lett. 60:424

52. Miller KT, Chan C-J, Cain MG, Lange FF.

1993. J. Mater. Res. 8:169

53. Movchan BA, Demchishin AV. 1969. Fiz.

Met. 28:83

54. Mullins WW. 1958. Acta Metall. 6:414

55. Murikami M, Chaudhari P. 1977. Thin

Solid Films 46:109

Glang, Chpt. 8. New York: McGraw-Hill

57. Nix WD, 1989. Met. Trans. 20A:2217

58. Nix WD, Clemens BM. 1999. J. Mater.

Res. 14:3467

59. Oh UC, Je JH. 1993.J. Appl. Phys. 74:1692

60. Ohring M. 1992. The Materials Science of

Thin Films. New York: Academic

61. Ohring M. 1998. Reliability Failure of

Electronic Materials and Devices. New

York: Academic

62. Palmer JE, Thompson CV, Smith HI. 1987.

J. Appl. Phys. 62:2492

63. Paritosh, Srolovitz DJ, Battaile CC, Li X,

Butler JE. 1999. Acta Mater. 47:226964. Pashley DW, Stowell MJ, Jacobs MH, Law

JT. 1964. Philos. Mag. 10:127

65. Pelleg J, Zevin LZ, Lungo S, Croitoru N.


66. Ressler KG, Sonnenberg N, Cima MJ.

1997. J. Am. Ceram. Soc. 80:2637

67. Roberts S, Dobson PJ. 1986. Thin Solid

Films 135:137

68. Sanchez JE, Arzt E. 1992. Scr. Met. Mater.

27:28569. Seel SC, Carel R, Thompson CV. 1996.

MRS Symp. Proc. 403:63

70. Shen Y, Wong BY, Laughlin DE. 1994. J.

Appl. Phys. 76:8174

71. Smith CS. 1952. InMetal Interfaces, p. 65.

Cleveland, OH: Am. Soc. Metals

72. Sonnenberg N, Longo AS, Cima MJ,

Chang BP, Ressler KG, et al. 1993.J. Appl.

Phys. 74:1027

73. Spencer BJ, Voorhees PW, Davies SH.1993. J. Appl. Phys. 73:4955

74. Srolovitz DJ. 1986. J. Vac. Sci. Technol.

A4:2925

75. Srolovitz DJ. 1989. Acta Metall. 37:621

76. Srolovitz DJ, Anderson MP, Sahni PS,

Grest GS. 1984. Acta Metall. 32:793

77. Stavans J. 1993. Rep. Prog. Phys. 56:733

78. Suo Z. 1997. Adv. Appl. Mech. 33:193

79. Sze SM, ed. 1985. Semiconductor Devices

Physics and Technology. New York: Wiley

& Sons

byU




32/33

190 THOMPSON

81. Taylor JE, Cahn JW. 1988. J. Electron.

Mater. 17:443

82. Thijssen JM. 1995. Phys. Rev. B51:

1985

83. Thijssen JM. Knops HJF, Dammers AJ.

1992. Phys. Rev. B45:8650.

84. Thompson CV. 1985. J. Appl. Phys.

58:763.

85. Thompson CV. 1988.Acta Metall. 36:2929

86. Thompson CV. 1990. Annu. Rev. Mater.

Sci. 20:245

87. Thompson CV. 1993. Scr. Met. Mater.

28:167

88. Thompson CV. 1999. J. Mater Res.14:3164

89. Thompson CV, Carel R. 1995. Mater. Sci.

Eng. B 32:211

90. Thompson CV, Carel R. 1996. J. Mech.

Phys. Solids 44:657

91. Thompson CV, Floro J, Smith HI. 1990. J.

Appl. Phys. 67:4099

92. Thompson CV, Lloyd JR. 1993. MRS Bull.

17:19

93. Thompson CV, Smith HI. 1984. Appl.Phys. Lett. 44:603

94. Thornton JA. 1977. Annu. Rev. Mater. Sci.

7:239

95. Thouless MD. 1995.Annu. Rev. Mater. Sci.

25:69

96. Townsend SJ, Nichols CS. 1994. MRS

Symp. Proc. 343:43

97. Tracy BW, Davies PW, Fanger D, Gartman

P. 1988. In Microstructural Science for

Thin Film Metallizations in Electronics

Applications, ed. J Sanchez, DA Smith, N

DeLanerolle TMS

98. Tracy DP, Knorr DB, Rodbell KP. 1994.

J. Appl. Phys. 76:2671

99. Tu KN, Smith DA, Weiss BZ. 1987. Phys.

Rev. B36:8948

100. Uwaha M. 1987. Jpn. J. Appl. Phys.

26:1592

101. van der Drift A. 1967. Philips Res. Rep.

22:267

102. Vinci RP, Zielinski EM, Bravman JC.


103. Wada Y, Nishimatsu S. 1978. J. Elec-

trochem. Soc. 125:1499104. Weiss D, Mullner P, Thompson CV, Arzt

E. 1998. Grain Growth in Polycrystalline

Materials III Proc. 3rd Intl. Conf. Grain

Growth, ed. H Weiland, BL Adams, AD

Rollet, p. 537. Warrendale, PA: Min. Met.

Mater. Soc.

105. Wild C, Herres N, Koidl P. 1990. J. Appl.

Phys. 68:973

106. Winterbottom WL. 1967. Acta Metall.

15:303107. Wong CC, Smith HI, Thompson CV.

1986. Appl. Phys. Lett. 48:335

108. Yu LS, Harper JME, Cuomo JJ, Smith

DA. 1986. J. Vac. Sci. Technol. 4:443

109. Zielinski EM, Vinci RP, Bravman JC.

1994. J. Appl. Phys. 76:15

110. Zielinski EM, Vinci RP, Bravman JC.

1995. Appl. Phys. Lett. 67:1078

111. Zinke-Allmang M. 1999. Thin Solid

Films 346:1byU




33/33

Annual Review of Materials Science

Volume 30, 2000

CONTENTS

The Theory of Real Materials,Marvin L. Cohen 1

Tribochemical Polishing, Viktor A. Muratov, Traugott E. Fischer 27

High-Tc Superconductivity in Electron-Doped Layered Nitrides, ShojiYamanaka

53

Holographic Polymer-Dispersed Liquid Crystals (H-PDLCs), T. J.

Bunning, L. V. Natarajan, V. P. Tondiglia, R. L. Sutherland83

Optical Generation and Characterization of Acoustic Waves in Thin

Films: Fundamentals and Applications,John A. Rogers, Alex A. Maznev,

Matthew J. Banet, Keith A. Nelson

117

Structure Evolution During Processing of Polycrystalline Films, C. V.

Thompson159

Mechanical Behavior of Metallic Foams,L. J. Gibson 191

Copper Metallization for High-Performance Silicon Technology,R.

Rosenberg, D. C. Edelstein, C.-K. Hu, K. P. Rodbell229

The Properties of Ferroelectric Films at Small Dimensions, T. M. Shaw,

S. Trolier-McKinstry, P. C. McIntyre 263

IC-Compatible Polysilicon Surface Micromachining,J. J. Sniegowski, M.

P. de Boer299

SiGe Technology: Heteroepitaxy and High-Speed Microelectronics, P. M.

Mooney, J. O. Chu335

Ultrathin Diffusion Barriers/Liners for Gigascale Copper Metallization,

A. E. Kaloyeros, E. Eisenbraun363

Magnetocaloric Materials, K. A. Gschneidner Jr., V. K. Pecharsky 387

Advances in In Situ Ultra-High Vacuum Electron Microscopy: Growth of

SiGe on Si,Ruud M. Tromp, Frances M. Ross431

Layered Magnetic Manganites, T. Kimura, Y. Tokura 451

The Electronic Structure of Semiconductor Nanocrystals, Al. L. Efros, M.

Rosen 475Mechanisms for Enhanced Formation of the C45 Phase of Titanium

Silicide Ultra-Large-Scale Integration Contacts,J. M. E. Harper, C.

Cabral Jr.,, C. Lavoie

523

Synthesis and Characterization of Monodisperse Nanocrystals and Close-

Packed Nanocrystal Assemblies, C. B. Murray, C. R. Kagan, M. G.

Bawendi

545

Extremely High Density Longitudinal Magnetic Recording Media,Dieter

Weller, Mary F. Doerner611

Low Dielectric Constant Materials for ULSI Interconnects,Michael

Morgen, E. Todd Ryan, Jie-Hua Zhao, Chuan Hu, Taiheui Cho, Paul S.

Ho

645

Device Innovation and Material Challenges at the Limits of CMOSTechnology, P. M. Solomon

681

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