Electrochemical Deposition (ECD)
EVOLVE has the ability to simulate electrochemical deposition using its
ECD module. The ECD module includes two finite element based solvers: the
pseudo-steady state solver and the transient solver. Between these two solvers, a
large fraction of possible electroplating situations can be addressed.
The pseudo-steady state solver
The pseudo-steady state (PSS) solver allows EVOLVE's ECD
module to solve problems for which Poisson's equation applies to a
stagnant film inside and around a feature or set of features. It is
referred to as pseudo-steady because the species concentration fields and
the electric field in the liquid phase come to equilibrium on a time scale
much shorter than the time scale for surface evolution. We take advantage
of this to speed up calculations.
Figure 1, below, shows the equations and boundary conditions that the PSS
solver must deal with to calculate the deposition rate at the surface.
Figure 1: The computational domain in which the pseudo-steady
state solver operates, and the equations and boundary conditions it solves
to find the deposition rate.
Figure 2: An example of an unstructured mesh the pseudo-steady
state solver uses for its finite element calculation of the species
concentration fields and the electric field.
The transient solver
The transient solver can be used whenever the
pseudo-steady assumption does not hold. This is true for a variety of
electroplating processes, including pulsed potential and depositions from
baths in which additives accumumlate on the surface throught the
deposition, such as for curvature enhance deposition [1,2]. The transient solver solver Laplace's equation in
the fluid phase, with appropriately varying boundary conditions, as shown
in Figure 3 below.
Figure 3: The computational domain in which the pseudo-steady
state solver operates, and the equations and boundary conditions it solves
to find the deposition rate.
Figures 4 and 5 below show simulations results for 2 sets of 5 identical
trenches with an aspect ratio of 2 for a modern 3-component bath with
additives to promote bottom up filling. The only difference in the intial
structures is the inter-trench spacing, but this clearly makes an
difference on the final deposited structure. These pattern density effects
can make in impact on post-ECD processing.
Figure 4: A set of five aspect ratio 2 idealized trenches
after simulated electrochemical deposition using a bath containing both an
accelerator and a suppressor species. The inter-trench spacing is 4 times
the trench width.
Figure 5: A set of five aspect ratio 2 idealized trenches
after simulated electrochemical deposition using a bath containing both an
accelerator and a suppressor species. The inter-trench spacing is equal to
the trench width.
Please look at a presentation of how the
transient solver can be used for a variety of purposes.
References
1.
A.C. West and S. Mayer and J. Reid, A superfilling model that
predicts bump formation, Electrochem. and Solid-State Letters,
4 (7), C50-C53, (2001).
2. T.P. Moffat and D. Wheeler and W.H. Huber and
D. Josell,
Superconformal deposition of copper, Electrochem. and Solid-State
Letters, 4 (4), C26-C29, (2001).