3RD INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS 2010, 18-21 MAY 2010, CLUJ-NAPOCA, ROMANIA
Optimal Design of the Deposited Layer
Thickness during the Electroplating Process
M. Purcar, F. Muntean, N. Maxim, C. Pacurar, O. Garvasuc, L. Grindei, V. Topa and C. Munteanu
Abstract--This paper investigates a practical method proposed
by the authors in order to optimize the layer deposition thickness
during an electroplating process. The study case consists in a
hydraulic component protected by a thin Chromium layer. An
optimized current robbers system that is short circuited to the
work piece is used. The numerical simulations are done using a
3D FEM code. The obtained results with this approach are
compared with the numerical results for an electrodepositing
process without any addition “thief current systems”. An
excellent improvement of the layer deposition thickness on the
hydraulic component is obtained.
Index Terms--Electroplating Tool, 3D FEM, Electrochemical
Reactors, Current Robbers, Optimal Design
I. INTRODUCTION
LECTROPLATING process energy and material costs are
very important considerations in the product
manufacturing. The most important plating criteria,
however, are quality and plated uniformity of the deposited
metals. An accurate analysis is required to determine the
distribution of deposited thickness, current densities and
electrode potentials.
The design of an electroplating rack requires many
preliminary steps such as: the choice of the electrolyte, and the
location, shape and number of electrodes, masks and current
thieves. These parameters affect deposit thickness and plating
distribution. Preliminary steps taken to optimize a plating
process might be very time consuming if they are performed
in a trial-and-error fashion, i.e. plating parts, measuring
thickness, plating again etc. If those trial-and-error steps can
be simulated accurately, large gains can be made in overall
plating cost reduction and the time-to-market of new part
designs. The primary difficulty is in obtaining uniform
deposits on each part, in order to satisfy the thickness
tolerances assigned by the plating performance specifications.
We must often deposit more metal on a given area to achieve
the necessary minimum plating thickness in another area.
This not only increases overall cost but may also require
additional remedies in areas where there is an excess of plated
E
This work was supported by CNCSIS - UEFISCSU under research IDEI
program, grant number ID_2538/2008 with the title “Development of a
Mathematical Analysis Technique for Modeling Electrode Shape Changes in
Electrochemical Process, a New Virtual Design Tool”.
M. Purcar, F. Muntean, N. Maxim, C. Pacurar, O. Garvasuc, L. Grindei,
V. Topa and C. Munteanu, are with the Faculty of Electrical Engineering,
G. Baritiu 26-28, 400027, Romania. (e-mail: [email protected])
metal. Therefore, effective electrolytic plating thickness
simulation helps plating industries to design the most
appropriate rack and tools to produce the best deposit
uniformity on each part.
II. ELECTROCHEMICAL MODELS
The nature of the involved electrochemical processes is generally
very complex. However, several assumptions and simplifications of
limited validity can be made in order to tackle the main aspects of the
problem. For example if the electrode reactions take place at low
rates, such that the concentration gradients are neglected, the potential
distribution may be found using Laplace’s equation. As a
consequence, the resulting model describes the ohmic effects in the
electrolyte [1]. This model is referred to as the Potential Model (PM).
An early interest for modeling this kind of topics has been
shown in a number of works. Several authors applied the PM
to compute the current density distribution for electroplating
applications. Bergh and Alkire [2] applied the Finite Element
Method (FEM) to solve the resulting Laplace equation, with
nonlinear boundary conditions to account for the electrode
charge transfer reactions.
Deconinck et. al. [3] discretized the equations of the PM
using the Boundary Element Method (BEM) in order to
compute the changes of the electrode profile for nonlinear
boundary conditions. They also presented a complete study of
the electrode shape change as a function of electrode reactor
dimension for different angles between the electrode and an
adjacent insulator.
Using the Finite Difference Method (FDM), Bozzini and
Cavallotti [3] presented numerical simulations for the
Chromium plating process on corner-shaped cathodes. They
incorporated effects of mass-transport in the boundary
conditions of the potential model. Georgiadou et. al. [4]
studied copper deposition in a particular trench geometry. The
simulation of the shape evolution is coupled with a FDM for
solving diffusion governed transport in the trench.
Qiu and Power [5] developed a boundary element scheme
in order to solve the problem of electrode shape change in an
electrochemical process involving convection, diffusion and
migration. They paid particular attention to the role of each
mechanism in determining the pattern of deposition by
implying a B-spline function that represents the electrode at
each time step.
Most of the above mentioned papers deal with the
mathematical
and
numerical
formulation
of
the
electrochemical models but do not treat the aspects of
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3RD INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS 2010, 18-21 MAY 2010, CLUJ-NAPOCA, ROMANIA
optimization of the layer thickness and current density
distribution in the electrochemical reactors.
As these parameters are affected by the side effects, caused
by the complicated 3D shapes of the cathodes, the main
objective of this paper is to numerically investigate the effects
of the current robbers to find the optimal configuration of
such devices for a given system.
III. THE POTENTIAL MODEL
The electrolyte is modeled as an electric field problem without charge
distributions inside the domain and nonlinear boundary conditions at
the electrodes [4]. This problem is governed by Laplace’s equation:
∇ ⋅ (−σ ⋅ ∇U ) = 0 ,
IV. NUMERICAL SOLUTION
A. Model definition and assumptions
The numerical study case was applied for a hydraulic
component, as in Figure 1. Being part of a complex
mechanical system, this hydraulic part is usually under stress
due to friction and/or other forces. For these reasons some
parts of the surface must be protected and strengthened by a
thin Chromium layer, of around 10-30 μ m . The dimensions of
the studied part are of 20 cm height, with a diameter of 6 cm
for the interest zone (Figure 1). The area which must be
protected (the active zone) is composed from two zones and
has a surface of 278,75 cm2 .
(1)
where: U represents the electric potential in [V] and σ the electric
conductivity of the solution in [Ω-1 · m-1] . The current density J
according Ohm’s law is given by:
J = −σ ⋅ ∇U .
(2)
Note that the conductivity σ does not need to be constant. Indeed,
it is possible to couple domains with a different conductivity, or
systems with a local varying conductivity (e.g. function of the
temperature T). The boundaries conditions of equation (1) can be
essentially divided into insulating walls (insulators) and electrodes.
The reactor’s walls, as well as the gaseous medium in contact with
the electrolyte, can be seen as insulators. No current flows through
them and therefore the normal current density at each point is zero:
J n = J ⋅ l n = −σ ⋅ ∇U ⋅ l n = −σ ⋅
The active zone
∂U
=0,
∂n
Fig. 1 CAD model of the studied hydraulic component
In realistic conditions, the electrochemical process takes
place in large tanks with a lot of pieces (electrochemical
reactors). Due to the fact that the purpose of our study was to
optimize the Chromium distribution of a single component
with a current thief, a small square tank is considered, as in
the Fig. 2.
(3)
where: the subscript n refers the normal direction. The same
boundary conditions can be applied to symmetry planes.
Depending on the working conditions the current density
distribution can be presented using different expressions. One
option is to use a linear relation [4]:
J n = A ⋅ (V − U − E0 ) + B,
(4)
with: A and B the polarization constants.
This is often expected when large current densities are
applied at oxygen evolving electrodes, due to the thin
passivation layer.
For single metal deposition processes the current density
distribution is often quite accurately described by a ButlerVolmer type relation [4]:
⎛ α a ⋅F ⋅(η − E0 ) αRc⋅⋅TF ⋅(η − E0 ) ⎞
J n = J 0 ⋅ ⎜ e R⋅T
−e
⎟,
⎝
⎠
(5)
where: J0 is the exchange current density, αa and αc the anodic
and cathodic charge transfer coefficients for the deposition
reaction, R the gas constant in [J ·mol-1·K-1] and T the
temperature of the electrolyte in [K].
Fig. 2 Geometry of the electrochemical reactor
In order to obtain a uniform layer, very small currents are
used. The main disadvantage in this case is a very long
process time. For this reason, in the real life, higher currents
are used in order to increase the efficiency of the process, by
decreasing the total process time. But this change came with
some risk. If higher currents are used, side effects like
hydrogen evolution, Chromium over burn and porous deposit
may appear. In order to overcome these types of problems,
additional technical solutions must be applied. In our case, a
current robber system for the optimal design of the deposit
layer thickness is used.
The following phenomena are taken into account during the
optimization process:
• ohmic drop in the electrolyte solution;
• anodic polarization;
• cathode shape changes over different time steps;
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3RD INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS 2010, 18-21 MAY 2010, CLUJ-NAPOCA, ROMANIA
•
reactor configuration including anode positioning, screens
and current thieves;
• work piece shape and dimensions;
• selective insulation of work piece surfaces;
• total current injected and anode work piece contacting
method.
This model (Figure 2) takes into account the complex
geometry of the hydraulic component inside the
electrochemical reactor. After numerical analysis and
electroplating simulations the obtained results are compared
with the optimized one using current robbers system.
B. Dry run simulation
The first simulation is the so called “dry” run simulation.
The following parameters are used for simulations:
major categories: current robbers, shields and auxiliary
anodes.
A current rubber can be a simple lead tape or a complex
metal shape. There are two ways to connect these current
thieves, on short circuit with cathode or to an auxiliary power
source. The second method is more effective but also
expensive. As the name say, the job of this structure is to steel
current from the high current zones. These screens vary from
very simple forms to very complicated ones. Auxiliary anodes
are used for recessed areas of very complex shape parts in
order to bust up the deposit that other wise shouldn’t be
possible. For the “dry run simulation” in the Figure 5 is given
the deposition thickness for the whole studied hydraulic
component. The edge effects are obviously.
200
180
TABLE 1
160
30
4000
deposit [um]
140
Plating time Average current
[min]
density [A/m2]
Main current Main voltage Weight gain
[A]
source [V]
[g]
110
4.50
3.33
dry run step
120
100
80
60
40
Using the parameters given in the Table no. 1, the following
results are obtained, using the PM mathematical model and a
3D FEM solver. The thickness of the Cr deposition on the
active zone is between 35 μ m and 9 μ m (Figure 3). For these
values of the Cr deposition the current density is between
6.000 A/m2 and 2.300 A/m2 (Figure 4).
20
0
0
20
40
60
80
100
120
140
160
developed length [mm]
Fig. 5 Deposit over the plating surface on “first” run
C. Current robbers approach
In order to optimize the layer thickness deposition, current
robbers are used. Using such a tool, a uniform Cr deposit over
the active surface of the work piece is possible. The rubbing
system consists in (see the Figure 6):
• one ring robber near the top of the work piece;
• lead tape for the recessed area;
• lead tape for the hole's edges of the part, mounted on a
plastic support.
.
ring current robber
Fig. 3 Chromium depositing thickness on the hydraulic component
recessed area lead
Fig. 6 The current robbers system
Fig. 4
Current density distribution on the hydraulic component
The figures above indicate the risk for the occurrence of
chrome burn or other high current densities related defects. It
may easily be seen that some zones are exposed to risks and a
big grinding effort has to be made in order to obtain a smooth
surface. Machining of this part involves spending time and
money, aspect that can be avoided by means of electrodeposits
process optimization.
This process can be optimized by the aid of a conformal
tooling structure, witch mounted on the active part assure a
uniform deposit layer. These structures can be divided in three
The current robbers system is short circuited to the mass,
through the work pieces. The lead tape system is perfectly
joined with the plating area providing a cylindrical flat
surface. Optimization process consists in 3 steps in order to
obtain the desired specification:
1. The distance between the ring current robber and the part
of 20 mm width of the lead tape, 2 mm near each edge;
2. The distance between the ring current robber and the part
of 15 mm width of the lead tape, 4 mm near each edge;
3. The distance between the ring current robber and the part
of 8 mm width of the lead tape, 5 mm near each edge (in
this case the tape is joining to the edges of the recessed
area 10 mm width).
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3RD INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS 2010, 18-21 MAY 2010, CLUJ-NAPOCA, ROMANIA
Since the current robbers are part of the electrode system,
during the optimization process the main power source must
to be changed in order to keep the current density on the work
piece on constant 4.000 A/m2 value. In the figures below,
there are given the test hydraulic equipment component and
the obtained results after the optimization process, applying
the currents robber approach. It’s easy to observe that there
are no more “red zones” to indicate problems for the
Chromium deposit.
J avg[A/m2]
Current Density [A/m2]
45000
40000
35000
J min[A/m2]
30000
25000
J max[A/m2]
20000
15000
10000
5000
0
0
1
2
3
4
5
Simulation number
Fig. 9 Current density evolution during the optimization steps
350.00
Deposit [um]
300.00
Fig. 7 Chromium depositing thickness on the hydraulic component with the
current robbers
d avg[um]
250.00
d min[um]
200.00
d max[um]
150.00
100.00
50.00
0.00
0
1
2
3
4
5
Simulation number
Fig. 10 Chromium deposit evolution during the optimization steps
Fig. 8 Current density distribution on the hydraulic component with the
current robbers
In the Figure 9 it is given the evolution of the Chromium
deposition on the surface of the studied hydraulic component
during the optimization process. The edge effects are
significantly reduced and the thickness of the layer deposit is
kept constant (15 μ m ) on the active zone.
150
130
deposit [um]
110
optimisation step 1
optimisation step 2
optimisation final step
initial case
90
70
50
30
V. CONCLUSIONS
A component from a hydraulic system was studied for the
purpose of this paper. The chosen current robbers system
guarantee an uniform Cr layer deposition over the active
plating zone with 1,32% in term of standard deviation. The
advantage of the proposed technical approach is the higher
uniformity of the Cr thickness deposit, but with a higher
average value of the used current and a higher consumption of
the material from the electrolyte. The research will be
extended with new optimization tools, but also with an
extended finite element method, as numerical analysis tool.
10
-10 0
20
40
60
80
100
120
140
REFERENCES
160
developed length [mm]
Fig. 9 The Cr deposit over the plating surface for each optimization step
In the Table 2 are given the values of the current sources
(min, max, average values) and the obtained thickness of the
Cr depositions and current densities respectively, for each
optimization step. The evolution of both parameters during
the optimization process is given in the Figures 9 and 10.
TABLE 2
Case
Current
Source
Initial
110 A
case
Optimization
Step 1
127 A
Step 2
133 A
Final step
138 A
d[um]
J[A/m2]
Min
Value
10
2822
Max
Value
307.3
4236
Average
Value
16.63
3948
d[um]
J[A/m2]
d[um]
J[A/m2]
d[um]
J[A/m2]
6.65
2182
7.1
2287
7.33
2336
41.63
8159
28.85
6243
23.65
5429
15.55
4017
15.22
3971
15.07
3948
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