A Mechanism for Brightening
Linear Stability Analysis of the Curvature-Enhanced Coverage Model
G. B. McFadden,
z
S. R. Coriell, T. P. Moffat,* D. Josell, D. Wheeler,
W. Schwarzacher,* and J. Mallett
National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8910, USA
This work presents experiments and theory describing a mechanism for how brighteners in electrolytes function. The mechanism
involves change of local coverage of a deposition rate-enhancing catalyst adsorbed on the surface through change of local surface
area during growth as well as accumulation and consumption. A first-order perturbation analysis shows the surface is stable against
growth of perturbations for all wavelengths below a critical value that is deposition-condition dependent. The model predictions
are shown to be consistent with the experimental results.
© 2003 The Electrochemical Society. DOI: 10.1149/1.1593042 All rights reserved.
Manuscript submitted September 18, 2002; revised manuscript received March 3, 2003. Available electronically July 24, 2003.
Roughness evolution during electrodeposition is a subject of
wide-ranging scientific and technical interest. Experience has shown
that metal ion depletion at the interface is usually associated with
destabilization of planar growth fronts. This has been explained by
Mullins-Sekerka morphological stability theory which examines
system response to small perturbations from steady-state growth
conditions. Typically, a sinusoidal variation of surface height is im-
posed on the flat surface, and the resulting time evolution, to first
order in the amplitude of the perturbation, is analyzed.
1,2
A positive
growth rate reflects instability while a negative value results in at-
tenuation of the perturbation; the former yields a rough surface
while the latter case gives a smooth interface. This type of analysis
has been widely applied to study phase transformations ranging
from solidification,
1,2
to additive-free electroplating,
3-11
and chemi-
cal vapor deposition.
12,13
In contrast to the destabilizing influence of
the reactant gradient, it is known that capillarity, adatom diffusion,
and reaction kinetics dampen, and even stabilize the system, particu-
larly at shorter wavelengths.
An important aspect of electroplating practice involves the use of
electrolyte additives to generate smooth, optically bright films. In
certain instances, additives even allow the leveling of undesired sur-
face imperfections by inducing preferential deposition at the bottom
of features such as scratches. The traditional leveling mechanism
behind this process is the existence of a concentration gradient of
the inhibiting additive that results in lower deposition of the inhibi-
tor, with associated decreasing inhibition of the metal deposition, the
farther down one goes in the defect.
14-17
It is generally known that
electrolytes that otherwise deposit at equal rates on all surfaces can
be induced to deposit preferentially at the bottoms of polishing
scratches and other surface imperfections through the addition of
deposition-rate inhibiting additives.
It is generally recognized that the traditional leveling mechanism
will not affect deposition substantially when the dimensions of the
defect are orders of magnitude smaller than the thickness of the
boundary layer responsible for the concentration gradient. For opti-
cally relevant dimensions that are only a fraction of 1 m and a
typical boundary layer thickness of 100 m, the appropriateness of
such a model becomes questionable. For this reason, electrolytes
commonly used for industrial plating applications that require opti-
cally bright deposits typically contain a variety of additives that
have been empirically determined to yield bright deposits. There is
no fundamental basis for determining which additives to add or why.
Recent publications have detailed a mechanism for the supercon-
formal deposition process now used to achieve bottom-to-top filling
of submicrometer dimension features. The mechanism involves i
the adsorption of a deposition-rate enhancing catalyst on the deposit
surface and ii changes in the local catalyst coverage induced by the
changing surface area on regions with nonzero curvature.
18,19
Mod-
els based on this curvature enhanced accelerator coverage CEAC
mechanism yield predictions of superconformal filling of fine fea-
tures due to the increase of catalyst coverage during deposition on
the concave bottom surfaces of filling features.
18-22
The implications
for brightening of a mechanism that increases deposition rates at the
bottoms of valleys concave surfaces while slowing deposition on
the tops of hills convex surfaces have been noted. This mechanism
has also been shown to describe superconformal feature filling by
surfactant catalyzed chemical vapor deposition CVD of copper.
23
This work presents a linear stability analysis to establish just how
such a mechanism would stabilize a surface against roughening as
well as determining the parameters and conditions for which such a
mechanism will function optimally. An infinitesimal sinusoidal per-
turbation of the surface height and catalyst coverage is imposed on
the flat surface, and the resulting time evolution to the first order in
the amplitude of the perturbation is analyzed. In the tradition of
morphological stability analyses, the real part of the complex expo-
nent that describes the time dependence of the perturbation ampli-
tude determines the stability of the surface. A positive value indi-
cates growth of the instability while a negative value results in
attenuation.
Governing Equations
We consider electrodeposition of copper from an aqueous solu-
tion containing copper ions of concentration C
c
and a catalyst ac-
celerator of concentration C
a
in the presence of an overvoltage .
We assume that growth of solid copper occurs at constant velocity V
in the z direction. Diffusion equations in the solution for C
c
and the
catalyst C
a
are written in a reference frame moving with this con-
stant velocity
C
c
t
- V
C
c
z
= D
c
2
C
c
1
C
a
t
- V
C
a
z
= D
a
2
C
a
2
where t is time, and the constants D
c
and D
a
are the diffusion coef-
ficients for C
c
and C
a
, respectively. The mean position of the liquid-
solid interface is assumed to be z = 0. Far-field boundary condi-
tions in the solution are applied at the edge of a boundary layer at
z =
C
c
= C
c
C
a
= C
a
3
The catalyst is adsorbed on the solid-liquid interface and has a satu-
ration coverage
0
. The fractional catalyst coverage is described by
* Electrochemical Society Active Member.
z
E-mail: mcfadden@nist.gov
Journal of The Electrochemical Society, 150 9 C591-C599 2003
0013-4651/2003/1509/C591/9/$7.00 © The Electrochemical Society, Inc.
C591