How to predict diffusion behaviours in a metallic platings-substrate system?

Hello
I want to qualify electroplatings (Ag or Sn for instance) on a Cu
substrate. (Ni underplated barrier present or not). Furthermore I want
to have an in-depth look at the ways of characterizing platings
regarding solid-solid diffusion properties. In a first approach, I
distinguish two problems at least.
DETERMINING THE CONSTANTS EXPERIMENTALLY
For the case of two semi-infinite media in a planar configuration, the
following formula well applies
thickness of the "diffusion affected
area"=squareroot(diffusionconstant*time)
Temperature enters through the diffusion constant which obeys an
Arrhenius law. This provides the basis for a time-temperature
correlation. Possibility for this prediction relies on the knowledge
of the two constants involved in the Arrhenius law: the
pre-exponential factor and the activation energy. Either one trusts
values in the tables, if available, or one performs measurements. If
one does the latter, one can let the samples in the furnace (inert
atmosphere), with different temperatures and/or different times of
exposure and then determine the concentration profiles by using a
profilometric technique: SIMS or GDS, for what I know. Then, two
situations have to be distinguished.
1- The elements are not miscible in every proportion
According (more or less!) to the phase diagram, some new layers are
grown. The thickness predicted by the above fundamental formula is the
overall thickness of these new layers.
In the connector industry, it is this way the growth of intermetallic
compounds is mitigated to reasonable low thickness by choosing the
mating surfaces according to their diffusion constants and the
required "mean" operating temperature during the timelife.
2- The elements are miscible in every proportion (e.g. Cu-Ni)
The concentrations of the elements are continuous functions of the
distances from the interfaces. Here it is much more tricky. Indeed,
experimental curves are noisy or do not look like a "beautiful"
theoretical one obtained with simple assumptions. Then fitting them is
not straightforward. This is a first problem.
TAKING INTO ACCOUNT THE NON TRIVIAL BOUNDARY CONDITIONS
A second problem, and the most critical in my opinion, is the
following: with the case of layers a few microns thick or less on a
substrate, the physics is more intrigate than with two semi-infinite
bodies. However predicting the behaviour during the lifetime of the
system requires formulas as well as an experimental measurement of the
diffusion constants! (Even likely less simple than the fundamental one
quoted above!). One faces the first problem also!...
Does someone know guidelines to use diffusion-accelerating assesments
and to exploit them for predicting the behaviour during the lifetime
of a system of a plated metallic substrate? Or may be a simple-minded
approach, that is a rough criterion, putting aside any theoretical
considerations?
NB: I am aware that diffusion is not the only phenomenom involved in
the aging of platings. It is on purpose I put aside corrosion problems
on the surface. Diffusion considerations are intended to ensure that
the material chosen from corrosion considerations to be on the surface
will not be replaced by an other one.
Pierre.
********************************************
Dr Pierre LAURAT
Project Manager - Materials Sciences
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Pierre LAURAT
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