Pulse Reverse Plating

This tutorial explores how pulse reverse plating can be used as an additive-free alternative to attenuate small protrusions during copper metal deposition. By adjusting the process parameters, including the length of the forward and reverse pulses (duty cycles), a bright mirror-like metal surface can be created. Pulse reverse plating may also be used for improved dimensional control of printed circuit board (PCB) plating (Ref. 1), for co-deposition of metal alloys.

The model assumes that a quasi-stationary current distribution establishes quickly during each pulse, so that an average of the forward and reverse deposition rates can be used in the time-dependent deforming geometry simulation.

Model Definition

Figure 1 shows the model geometry. The single domain consists of an electrolyte with a conductivity of 5 S/m. The electrode surface is located at y = 0 mm, with a small protrusion with a height of 40 mm, centered around x = 0. The local current density iloc on electrode surface is modeled using Butler-Volmer kinetics.

Figure 1: Model geometry.

On the electrode surface, copper is assumed to be deposited according to

(1)

When modeling constant direct current (DC) plating, the average electrolyte current density of iavg, fwd = 5 A/dm2 is applied on the top boundary, and the resulting growth velocity along the electrode surface is used as a boundary condition for the deformed geometry (ALE) time-dependent simulation.

For the pulse reverse simulations, the average current density for the reverse pulse on the top boundary is set to iavg, rev = −50 A/dm2. Denoting the forward duty cycle (the relative time spent in forward mode) as tfwd (dimensionless), the forward pulse average current density can be calculated as

(2)

The simulated plating time is 1 h, whereas the forward-to-reverse pulse switching is assumed to occur on a time scale significantly shorter (a few seconds), since concentration gradients due to the mass-transport limitations at the higher current densities during the reverse pulse must not be allowed to form.

The current distributions for the pulse reverse plating are assumed to be quasi-stationary within each pulse period, and the current distributions during the forward and the reverse pulse are solved simultaneously on the same time-dependent geometry, using different potential dependent variables. The local growth velocity on the electrode surface is then based on the time-averaged sum of the local current densities during the forward and reverse pulses:

(3)

where ρ and M are the density and molar mass or copper, respectively, and iloc, fwd and iloc, rev are the local current density on the electrode surface during the forward and reverse pulses.

Solving the quasi-stationary current distributions separately for the forward and reverse pulses, using constant average current densities for each pulse period, saves computational time. The reason is that the time-dependent solver then does not need to resolve the explicit switching of the current density.

In order to mitigate potential issues with inverted mesh elements, the upper boundary is moved using a velocity proportional to the average current density according to

(4)

Results and Discussion

Figure 2 shows the electrode profile evolution during pure DC plating. The initial protrusion grows in size and will result in a non-even surface.

Figure 2: Profile evolution during DC plating.

Figure 3 shows the profile evolution for tfwd = 0.85. The initial protrusion is now attenuated, approaching a flat surface as the plating proceeds.

Figure 3: Profile evolution for tfwd = 0.85.

Finally, Figure 4 shows a comparison of the final profiles at t=1 h.

Figure 4: Comparison of final electrode surface profiles for different values of tfwd.

Reference

1. P. Leisner, P. Møller, M. Fredenberg, and I. Belov, “Recent progress in pulse reversal plating of copper for electronics applications,” Transactions of the IMF, vol. 85, no. 1, pp. 40–45, 2007.

Electrodeposition_Module/Tutorials/pulse_reverse_plating

Modeling Instructions

This tutorial consists of two parts. In the first part you will set up a direct current (DC) plating model to simulate how a small protrusion grows during the plating process.

In the second part you will add a current distribution model also for a reverse plating pulse, and examine how the protrusion is attenuated depending on the length of the reverse pulse.

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

Load the model parameters from a text file.

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file pulse_reverse_plating_parameters.txt.

Geometry 1

Polygon 1 (pol1)

In the toolbar, click

Load the coordinates of corners of the geometry from a text file.

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file pulse_reverse_plating_coordinates.txt.

Click

Fillet 1 (fil1)

Round the corners by adding fillets.

In the toolbar, click

On the object , select Point 4 only.

In the window for , locate the section.

In the text field, type H_prot/10.

Click

Fillet 2 (fil2)

In the toolbar, click

On the object , select Points 3 and 6 only.

In the window for , locate the section.

In the text field, type W_prot/2.

Click

Secondary Current Distribution (cd)

Now start setting up the DC plating current distribution model.

Electrolyte 1

In the window, under click .

In the window for , locate the section.

From the σl list, choose . In the associated text field, type sigma.

Electrolyte Current 1

In the toolbar, click

and choose .

Select Boundary 3 only.

In the window for , locate the section.

From the list, choose .

In the il,average text field, type i_avg.

Electrode Surface 1

In the toolbar, click

and choose .

Use a box selection to select all the (lower) boundaries pertaining to the electrode surface, including the protrusion.

Select Boundaries 2, 4–6, and 8–10 only.

In the window for , locate the section.

Click

By creating a selection in this way you can conveniently select the same set of boundaries again later on.

In the dialog box, type Electrode Surface in the text field.

Click .

In the window for , click to expand the section.

Use a Species to define the growth velocity of the electrode surface.

Click

In the table, enter the following settings:


Species	Density (kg/m^3)	Molar mass (kg/mol)
Cu	rho	M

Clear the check box.

Electrode Reaction 1

In the window, expand the node, then click .

In the window for , locate the section.

In the n text field, type 2.

In the table, enter the following settings:


Species	Stoichiometric coefficient (1)
Cu	1

Locate the section. From the list, choose .

In the i0 text field, type i0.

In the αa text field, type alpha_a.

In the αc text field, type alpha_c.

Multiphysics

Nondeforming Boundary 1 (ndb1)

Modify the default selection of the node to only include the vertical boundaries.

In the window, under click .

Select Boundaries 1 and 7 only.

In the window for , locate the section.

From the list, choose .

Definitions

We will now set up the boundary velocity of the upper boundary to a user-defined expression. First, load some variable expressions from a text file.

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file pulse_reverse_plating_variables.txt.

The vn_avg variable is marked in orange indicating a missing definition. This is expected. We will properly define and make use of this variable in the second part of the tutorial.

The vn_bnd variable will next be used now to set up the upper boundary velocity.

Deformed Geometry (dg)

In the window, under click .

Prescribed Normal Mesh Velocity 1

In the toolbar, click