Formation and evolution of the phase composition and associated properties during
the growth of thin films
S. A. Kukushkin and A. V. Osipov
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences,
199178 St. Petersburg, Russia
Submitted April 29, 1996
Zh. Tekh. Fiz. 67, 112–120 October 1997
A complete system of equations describing the evolution of the phase composition of islands in
the Ostwald ripening stage during the growth of thin films is derived and a solution is
found. The distribution function of islands of solid solutions is obtained for different growth
mechanisms. A general approach to controlling the phase composition and associated properties
electrical, optical, strength, and so on in the multicomponent systems formed is developed.
The investigation is conducted for the example of thin multicomponent films. It is shown that the
greatest possibilities for controlling these properties are at the Ostwald ripening stage and in
the presence of nonlinear phenomena such as self-oscillation or self-organization. A relation is
found between the size and composition of the new-phase nuclei which form during the
condensation of films of solid solutions. A system of equations describing the evolution of the
distribution function of properties in island films of solid solutions as a function of the
external parameters of the system is derived and solved. It is shown that a strong dependence of
the composition on the external parameters appears for islands with radius R 10
-8
m,
irrespective of the type of material. A diagram of the coexistence of the corresponding properties
in concentration–temperature coordinates is constructed for island films of stoichiometric
compounds; this makes it possible to determine the necessary conditions for obtaining such films.
It is predicted that various properties in multicomponent systems which undergo a first-order
phase transition can vary periodically in time and space. © 1997 American Institute of Physics.
S1063-78429702010-2
INTRODUCTION
Thin films and coatings are widely used in optics, micro-
electronics, laser technology, and many other fields.
1
De-
pending on their sphere of application, they must have a set
of definite properties, for example, mechanical or electro-
physical. As a rule, these properties are largely associated
with the composition of the growing films
1
and with the size
of the crystal grains forming the films.
2
We note that the
problem of controlling the composition and size of clusters
or islands as well as the composition of continuous films was
incorporated in a series works.
1,3–10
. These investigations
showed that irrespective of the methods used to obtain them,
during growth the films pass through a series of stages which
are characteristic for any first-order phase transition:
nucleation
11–14
and growth
11
of clusters or islands of a new
phase, Ostwald ripening,
1
coagulation,
12
and formation of a
continuous film. If the nucleation process occurs in the pres-
ence of a large supersaturation, then the density of the is-
lands of the new phase and the degree of filling of the sub-
strate will be high and the stages following nucleation may
not occur.
1
Both the composition and structure will be deter-
mined by nucleation processes, which, as is well known,
have a complicated nonlinear nature.
14,15
For this reason,
control at this stage is virtually impossible. As shown in
Refs. 3–10, these parameters can be controlled only at the
Ostwald ripening stage, when nucleation of new islands no
longer occurs and a continuous film has still not formed. The
possibility of control is based on the fact that at this stage the
ensemble of islands of a new phase enters into a unique
interaction with general diffusion–heat fields, which form on
the substrate surface, and fluxes of atoms incident on the
surface.
A theory describing this phenomenon in detail is pre-
sented in Refs. 3–10, but there attention was focused mainly
on the analysis of the evolution of the island-size distribution
function and finding the time dependence of the island radii.
Our objective in the present paper is to find the dependence
of the island-composition distribution function and, corre-
spondingly, the distribution functions for one or another
composition-dependent property conductivity, mobility, and
so on. It has been shown previously that there is a large
difference between the evolution of islands growing from
substances forming a continuous series of solid solutions and
stoichiometric substances forming as a result of chemical
reactions. As a result, there is a large difference between film
growth at both the nucleation and Ostwald ripening
stages.
3–10
For this reason, these cases are studied separately.
EVOLUTION OF THE PHASE COMPOSITION IN ISLANDS OF
A NEW PHASE AT THE OSTWALD RIPENING STAGE
1) Evolution of the phase composition in islands of solid
solutions. Suppose that the equilibrium phase diagram of the
system
2
from which the films are grown is cigar-shaped
Fig. 1. This means that the growing films will be solid
solutions. We note that both nucleation and Ostwald ripening
are possible only if the supercooling temperature of the sys-
1212 1212 Tech. Phys. 42 (10), October 1997 1063-7842/97/101212-08$10.00 © 1997 American Institute of Physics