Review of the fundamentals of thin-film growth

Norbert Kaiser

The properties of a thin film of a given material depend on the film’s real structure. The real structure
is defined as the link between a thin film’s deposition parameters and its properties. To facilitate
engineering the properties of a thin film by manipulating its real structure, thin-film formation is
reviewed as a process starting with nucleation followed by coalescence and subsequent thickness growth,
all stages of which can be influenced by deposition parameters. The focus in this review is on dielectric
and metallic films and their optical properties. In contrast to optoelectronics all these film growth
possibilities for the engineering of novel optical films with extraordinary properties are just beginning to
be used. © 2002 Optical Society of America
OCIS codes: 310.0310, 310.1620, 310.1860, 310.3840, 310.6860, 310.6870.

1. Introduction extrinsic defects. Intrinsic defects are those that are

The dependence of optical properties on deposition caused by atoms’ not changing the stoichiometry of
conditions is a severe constraint in reproducing thin the crystal. Defects that produce nonstoichiometry
film’s performance. There is a significant conflict are called extrinsic defects. Defects generally can
between performance models based on ideal- and have a major influence on the physical properties of
real-structure films. Models are required that re- the solid, for instance, on the transmission of light
late real-film structure to desired optical properties. and on electrical conductivity.
This knowledge would permit the design and manu- The growth of thin films by physical-vapor deposi-
facture of coatings based on more-realistic production tion is an extremely nonequilibrium process that
conditions than are now possible. In this review as- takes place at high supersaturations and at compar-
pects of thin-film growth in various dimensions, from atively high concentrations of impurity atoms. Con-
isolated nanoclusters to continuous macroscopic sequently the number of extrinsic and intrinsic
films, are treated. The focus is on dielectric and defects in thin films may exceed that in bulk solids by
metallic films and their optical properties. ⬃5 orders of magnitude. As a result of the usual
Investigations of process parameters, real struc- deposition conditions in optics and of the surface
tures, and film properties have been in progress for structure of optical components, optical films are gen-
many years, starting in 1938 with the classic re- erally polycrystalline. This means that the real film
search of Hass.1 Perusal of Refs. 2–7 is recom- consists of defect-rich crystalline grains, which are
mended as an introduction to the structure-related separated by impurity-enriched grain boundaries.
optical properties of thin films. This is the reason why film properties differ signifi-
cantly from bulk properties. Figure 1 shows this
2. Real Structure fact schematically. The real structure of thin films
The ideal structure of solids is either ideally ordered is a metastable nonequilibrium state that is far away
single-crystalline or ideally disordered amorphous. from its energetic minimum. Real structure tends
But there is no ideal crystalline or amorphous struc- to change whenever enough energy is available.
ture in the real world. The real structure of single Real structure is the link between thin-film depo-
crystals always has a certain number of intrinsic and sition parameters and thin-film properties 共Fig. 2兲.
In engineering electronic and optical properties it is
vital to control stoichiometry, mean grain size, and
N. Kaiser 共kaiser@iof.fhg.de兲 is with the Fraunhofer Institute of
grain size distribution of the thin-film structure.
Applied Optics and Precision Engineering, Schillerstrasse 1, 07741 For engineering of film properties through real struc-
Jena, Germany. ture, models are indispensable. In what follows,
Received 14 August 2001. thin-film formation is described as a kinetic adsorp-
0003-6935兾02兾163053-08$15.00兾0 tion and diffusion process starting with nucleation,
© 2002 Optical Society of America coalescence, and subsequent thickness growth,

1 June 2002 兾 Vol. 41, No. 16 兾 APPLIED OPTICS 3053

 Fig. 4. Initial states of film growth 共after Ref. 9兲. ⌰, substrate
surface coverage in monolayers 共ML兲.

Fig. 1. Left, ideal single-crystalline substrate coated with ideal

of atoms that are different from those of the vapor.
single-crystalline films. Incoming light with intensity I0 is split Figure 3 shows the various stages of thin-film growth.
into reflected and transmitted parts IR and IT, respectively. Con- Nucleation takes place at high supersaturations S,
servation of energy is given by I0 ⫽ IR ⫹ IT. Right, real substrate defined as
with real coatings. Part of incoming intensity I0 is absorbed 共IA兲
or scattered 共IS兲. Conservation of energy is given by I0 ⫽ IR ⫹ S ⫽ p兾p e, (1)
I T ⫹ IA ⫹ I S .
where p is the vapor pressure of the deposit material
evaporated from the source at temperature T and po
whereby all states can be influenced by deposition is the equilibrium vapor pressure of the substrate
parameters. material at temperature TS. Deposition rate R is
related to p as
3. Growth of Thin Films
R ⫽ p兾共2␲mKT兲 1兾2, (2)
A. Nucleation K is Boltzmann’s constant, m is the molecular weight
The production of thin films by vapor deposition is a of the deposit material, and T is the temperature of
classic case of heterogeneous nucleation, i.e., the con- the evaporation source. Because S is extremely
densation of adatoms at a substrate that is composed high, S ⫽ 105–1050 共S ⬇ 4 in a Wilson chamber兲,
nucleation is a nonequilibrium process, which can
best be described by the mean-field nucleation theo-
ry.8
As for all phase transitions, the formation of thin
films is characterized by the formation of nuclei and
their growth. Depending on the interaction ener-
gies of substrate atoms and film atoms, any of three
Fig. 2. Factors that control the properties of thin films. growth modes 共Fig. 4兲 can occur:

Fig. 3. TEM micrographs of antimony film formation 共nucleation, growth of nuclei, coalescence, channels, holes, homogeneous film兲.
Here 共as is special for Sb兲 at percolation an amorphous– crystalline phase transition 共change of contrast兲 takes place.

3054 APPLIED OPTICS 兾 Vol. 41, No. 16 兾 1 June 2002

 trons through the network and conductivity rises
steeply by several orders of magnitude. Obviously,
a phase transition takes place at the percolation
threshold, with optical film properties changing ex-
ponentially. It is shown that this phenomenon is
crucial when it comes to engineering thin semitrans-
parent metal films.
C. Thickness Growth
Fig. 5. Wetting angle ␸ of a liquid nucleus on a substrate is
described by Young’s equation: ␥B ⫽ ␥* ⫹ ␥A cos ␸, where ␥B is The mean percolation thickness for many films is
the surface energy of substrate, ␥A is the surface energy of film 1–20 nm. The thickness required for producing
material, and ␥* is the interface energy film–substrate. metal mirror layers or dielectric quarter-wave sys-
tems is, however, larger than that value. Further
material deposition does not simply increase thick-
• Layer by Layer In the two-dimensional ness; moreover, the real structure is determined by
Frank–van der Merwe mode, layers of material grow the following four processes:
one on top of another. Interaction between sub-
strate and film atoms is greater than between adja- • Shadowing A geometric interaction between
cent film atoms. the arriving admolecules and the roughness of the
• Island In the Volmer–Weber mode, separate growing surface. This effect is dominant at low sub-
three-dimensional islands form on the substrate. strate temperatures TS. It occurs because the vapor
Interaction between film atoms is greater than be- beam is directed.
tween adjacent film and substrate atoms. • Surface diffusion Mobility of admolecules at
• Layer plus Island In the Stranski–Krastanov surfaces and interfaces such as grain boundaries;
mode, one or two monolayers form first, followed by dominant at medium substrate temperatures TS.
individual islands. • Bulk diffusion Mobility of admolecules in the
volume of grains; dominant at high TS.
Growth modes can be systematically classified in • Recrystallization Phase transition as a com-
terms of surface energies with Young’s equation plete change of crystal orientation; dominant at per-
taken into account 共Fig. 5兲. colation thickness, large film thickness, and high TS.
Island growth 共␸ ⬎ 0兲 requires that ␥B ⬍ ␥A ⫹ ␥*,
whereas layer growth 共␸ ⫽ 0兲 requires that ␥B ⬎ ␥A ⫹ For most metals and dielectrics, activation energies
␥*. Layer-plus-island growth occurs because the in- for diffusion are related to the melting temperature of
terface energy increases with film thickness; typically the material, Tm. Thus different basic processes can
the layer on top of the substrate is strained to fit the be expected to dominate different ranges of Ts兾Tm
substrate. The growth mode is controlled not only and to determine the real structure. This is the con-
by interface energies but also by supersaturation.10 cept of so-called structure zone models.11 In the
Generally, growth tends to shift from island to layer simplest case, real structure exists in three zones:
as supersaturation increases.
• Zone I Ts兾Tm ⬍ 0.3 共low mobility; admolecules
B. Coalescence stick where they land; the result is a fine-grained
The next stage of three-dimensional film formation is porous real structure兲.
the growth of islands until they touch one another to • Zone II 0.3 ⬍ Ts兾Tm ⬍ 0.5 共surface diffusion
form a continuous network. This so-called coales- occurs with activation energies of 0.1– 0.3 eV; a co-
cence process is extremely important for the design of lumnar real structure is obtained兲.
films with special properties. After solidlike coales- • Zone III Ts兾Tm ⬎ 0.5 共bulk diffusion occurs
cence of two islands there may remain a grain bound- with activation energies above 0.3 eV, resulting in a
ary between them, or they may fuse together in a rough equiaxed grained real structure兲.
liquidlike fashion to form a new, larger, and
boundary-free island. Surface energies and super- Such a generalization of homologous structure
saturation are the factors that control these processes zone models in terms of physical processes is impor-
through material transport by surface and bulk dif- tant for engineering film properties. Structure zone
fusion. The transition from isolated islands to a con- models have been deduced by Thornton for sputtered
tinuous macroscopic network can be characterized by films12–15 and by Messier et al.16 and Messier17 for
a percolation threshold thickness. To percolate ion-assisted deposition. Additionally, Grovenor et
means to pass or to cause to pass through a porous al.18 take the influence of substrate morphology into
material. This definition can be understood, for ex- consideration. For comparison, all models men-
ample, from measurements of electrical conductivity tioned are shown in Fig. 6.
between two macroscopically separated contacts Until now it has only briefly been mentioned that
upon an insulating substrate during the growth of a the growth of thin films for optics by physical-vapor
metallic layer between them. At percolation thick- deposition is a comparatively dirty process. Indeed,
ness, coalescence creates a continuous path for elec- under high-vacuum conditions in a normal produc-

1 June 2002 兾 Vol. 41, No. 16 兾 APPLIED OPTICS 3055

 Fig. 6. Structure zone models 共after Movchan,11 Thornton,12 Messier et al.,16 and Grovenor et al.18兲.

tion environment the rate of residual gas molecules lattice are segregated into the grain boundaries and
共water, hydrocarbons, etc.兲 striking the substrate sur- onto the growing film surface. At a critical impurity
face is of the same order of magnitude as the deposi- concentration, a fixed passivation layer forms, upon
tion rate of the film material. At a total pressure of which secondary nucleation may occur. Therefore,
10⫺4 Pa it takes only ⬃1 s to form one monolayer of nondiluted impurities are concentrated at interfaces.
residual gas molecules upon the substrate. Conse- In real structures, large impurity concentrations
quently, extrinsic impurity defects, whether present act in the same way as low substrate temperatures.
on the substrate surface or resulting from the evap- Structure zones are shifted along the Ts兾Tm axis to-
oration source or from the residual gas, have a great ward a fine crystalline, porous structure. Barnal
influence on film growth. The effect is comparable and Adamik19 introduced the basic structure zone
with that of the substrate temperature. Impurities model, which starts from the basic case of impurity-
markedly change the surface energies at all stages of free films 共Fig. 7兲 and then takes the increasing in-
film growth. Impurities that are not soluble in the fluence of impurities into consideration.

3056 APPLIED OPTICS 兾 Vol. 41, No. 16 兾 1 June 2002

 Table 1. Rate of Absorption Values to Defect Concentration in
Dielectric Thin Films

Type of Film ND 共cm⫺3兲 ␤ 共cm⫺1兲 1兾␤ k250 nm

Single crystal 1013 10⫺3 10 m 2 ⫻ 10⫺9

Thin film 1018 102 100 ␮m 2 ⫻ 10⫺4
Basic absorption 1022 106 10 nm 2

Absorption cross section ␴ for one photon is approx-

imated by the area of one atom 共10⫺16 cm2兲.23 Table
1 lists typical defect concentrations 共ND兲, absorption
coefficients 共␤兲, optical penetration depths 共1兾␤兲, and
extinction coefficients 共k250nm兲 at 250-nm wave-
length. The photon absorption cross section was es-
timated to be 10⫺16 cm2. Basic absorption means
absorption for wavelengths below the shortwave ab-
sorption edge.
Furthermore, real structure causes scatter losses.
All types of real-structure phenomena such as grains,
pores, defects, and rough interfaces are directly con-
nected to scattering.24
5. Metal Films
Growth of metal films starts with islands 共the
Volmer–Weber mechanism兲. Island films are trans-
parent to visible and infrared radiation. At percola-
Fig. 7. Basic and real-structure zone models for low, medium, and
tion thickness the film becomes continuous and is
high impurity concentrations 共after Barna19兲.
transparent in the visible spectral region while it
reflects the infrared. Finally, at larger thicknesses
all radiation is reflected. This process is one of the
4. Dielectric Films
most exciting phenomena in optics: Properties
change with film real structure only by addition of
Classic optical interference film systems are now ap- some nanometers of metal material, as is shown sche-
plied down to the vacuum-ultraviolet excimer-laser matically in Fig. 8.
wavelength range. Here the individual quarter-
wave fluoride films can be as thin as ⬃10 nm. Struc- A. Metal Island Films
ture zone models 共Figs. 6 and 7兲 show the real As has been known for many years, metal island films
structure of dielectric thin films. The connection be- 共Ag, Au, Cu, . . . 兲 do not behave optically similarly to
tween optical properties and real structure is possible the corresponding bulk material.25 Fifty years ago
by effective medium theories on the basis of the clas- this effect was called Anomalien der optischen Kon-
sic Lorenz–Lorentz model, e.g., for TiO2.20 Optical stanten 共anomalies of optical constants兲. Today
effects are inhomogeneities and anisotropies, i.e., these properties are of outstanding importance in op-
complex refractive-index changes with variable film tics.26 Metal islands may interact with light over
thickness and angle of incidence of light. Optical surface plasmons, namely, by agency of plasmon–
anisotropies caused by columnar film growth can be polaritons. Plasmons are strong collective oscilla-
used for special applications, such as polarizers for tions of electrons in the island in phase with the
normal incidence.21,22 This application is the most incoming light. The Mie resonance frequency of the
prominent example of how to make a virtue of neces- oscillation depends on three factors: the electronic
sity and how a microstructure can be tailored by
means of growth phenomena.
Optical absorption is caused by defects hosted in
the porous film structure. In most cases these de-
fects are water, oxygen, and hydrocarbons. As men-
tioned above, thin films contain higher numbers of
defects, by ⬃5 orders of magnitude, than do bulk
materials. To estimate how a concentration ND of
absorbing defects per volume unit influences absorp-
tion coefficient ␤, one can use the simple relation

Fig. 8. Growth of a metal film, starting from islands to continuous

␤ ⫽ ␴N D. (3) transparent to nontransparent films.

1 June 2002 兾 Vol. 41, No. 16 兾 APPLIED OPTICS 3057

properties of the metal, the size and shape of the
islands, and the properties of host material in which
the islands are embedded or upon whose surface they
are fixed.
Because metals are highly absorbing, only small
changes in cluster size and distribution can be used to
engineer the optical properties of the ensemble. Op-
tical constants can be calculated on the basis of
Maxwell–Garnett models and of the Drude theory of
free electrons.27,28 Practical applications of island
films require a macroscopic matrix in which the sen-
sitive nanometer-sized metal clusters are embedded.
In an optical film design, metal islands can be em- Fig. 9. Cross-sectional transmission electron microscopy picture
bedded in barrier layers such as SiOx, Al2O3, and of Cr–Sc multilayer mirrors with period spacing d ⫽ 1.57 nm 共left兲
NiCr to prevent oxidation or in other matrices such as and d ⫽ 3.17 nm 共right兲.34
transparent conductive oxides. Metal island films
have become important elements of present-day op-
tics and optoelectronics. Intensive research is being number of islands per unit area. At the same mean
conducted into active optoelectronic elements that film thickness, many small islands cover a larger
consist of island films, including optically active in- substrate area than do fewer but large islands. Tai-
dividual molecules. As an example of optically ac- loring percolation thickness to minimum values by
tive molecules, the Stranski–Krastanov layer-plus- increasing the deposition rate and reducing the sub-
island growth of Ge islands upon Si substrates for the
strate temperature is not possible, owing to the se-
production of self-assembled quantum dots may be
vere technological restrictions that are typical for
mentioned.29 Such deposition can be performed
large-area architectural coatings. However, the
only under ultrahigh vacuum conditions and upon
concept of changing surface energies 共Fig. 5兲 can be
clean single crystalline surfaces. In optics, deposi-
applied successfully. This can be done by plasma
tion conditions are far from being so well defined.
pretreatment of the substrate or by use of ultrathin
However, there are many industrial applications that
bonding layers such as Cr, Pd, and NiCr. Also, ion
make use of the optical, electronic, and mechanical
assistance can be used.32 At larger thicknesses,
properties of metal island films. Classic examples of however, abnormal grain growth occurs,33 as pre-
nano-optics are the red and yellow colors of Middle dicted by Grovenor’s structure zone model18 共Fig. 6兲.
Ages church windows, photographic systems, and so- Wetting can also be improved by the use of such
lar absorbers. Recent applications in the field of semiconductive transparent oxides as In2O3, SnO2,
photonic bandgap materials are based on ultrafast ZnO2, and In2O3 doped with 2–10% Sn. These ox-
light-switching phenomena, which can by used as ides are frequently used instead of, or mixtured with,
novel components in integrated optics for biosen- metals. Finding the best engineering technology is
sors or optical tweezers. We are just beginning to currently a field of keen competition among large-
use them in the engineering of novel optical films area coaters. State-of-the-art basic knowledge of
with extraordinary properties. film growth is of hardly any help today for finding
B. Continuous Transparent Metal Films solutions to improve wetting.
Another application of continuous metal films is as
At thicknesses greater than the percolation thick- multilayer mirror coatings for soft x radiation 共espe-
ness, metal films behave optically similarly to the cially in the water window: 2.3– 4.4 nm兲 and for
corresponding bulk materials and are transparent to extreme-ultraviolet radiation 共10 –100 nm兲. Impor-
visible radiation and reflective for infrared radiation tant applications in this context are microlithogra-
as long as the thickness is less than ⬃20 nm. In this phy, x-ray astronomy, plasma spectroscopy, medical
thickness interval, transparent metal films can be engineering, x-ray microscopy on live tissue, and la-
used as neutral beam splitters, induced transmission ser research and synchrotron radiation research.34
filters, solar control coatings, thermal insulating What has been achieved is near-picometer precision
coatings, transparent electrodes, and heating layers. for the production of nanometer multilayer mirrors
For example, silver is used for neutral-color highly for x rays 共Fig. 9兲. With ultraprecise biased magne-
transparent and thermal insulation coatings 共low tron sputtering it takes only approximately an hour
emissivity兲, variably colored solar control coatings, to deposit 600 layers for that wavelength range.35
and low-emissivity Sun coatings.30,31 For reduction
of absorption, the percolation thickness should be as
low as possible. Maximum wetting of the substrate C. Continuous Nontransparent Metal Films
can be achieved in the two-dimensional Frank–van Continuous nontransparent metal films have long
der Merwe growth mode. Unfortunately, as was al- been used as mirrors. It has been shown that, at
ready mentioned, optical film growth starts with high deposition rates and low substrate tempera-
three-dimensional islands. In that case one can de- tures, nucleation density is high and that conse-
crease the percolation thickness by increasing the quently thin films have a fine polycrystalline

3058 APPLIED OPTICS 兾 Vol. 41, No. 16 兾 1 June 2002

microstructure and maximum reflectivity. This has References
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