Copper Electroless Deposition

In the electroless deposition, partial oxidation and reduction reactions occur simultaneously at the same position at the electrode surface. The difference between the equilibrium potentials for the two reactions is hence the driving force for the deposition process. The potential at the electrode surface is estimated from the mixed potential theory so that the total anode current density is equal and opposite to the total cathode current density (Ref. 1 and Ref. 2). Since the sum of all reaction current densities sum up to zero locally on the surface, the electroless deposition can be used for plating on objects with low electric conductivity, for instance plastics.

This model simulates copper electroless deposition wherein copper reduction is a cathodic reaction and formaldehyde oxidation is an anodic reaction. The model accounts for mass transport by diffusion and electrochemical reactions at the electrode surface. The equilibrium potentials of partial electrochemical reactions are considered to be concentration dependent. The model estimates the change in current density, deposition thickness and concentration of ionic species during the electroless deposition.

Model Definition

The model is solved over a 1D computational domain that consists of a diffusion layer with an electrode surface at one end and a bulk electrolyte at the other end, as shown in Figure 1. The diffusion layer thickness is set to 2 mm.

Figure 1: Description of the boundary layer adjacent to the steel surface.

Mass transport by diffusion for five ionic species is solved using the physics interface:

(1)

where ci (mol/m3) is the concentration, Ni (mol/(m2·s)) is the flux vector, Di (m2/s) is the diffusion coefficient, and subscript i indicates ith species. All species are assumed to be diluted in water. The species along with their diffusion coefficients and initial concentrations are tabulated in Table 1.

Table 1: Modeled species with their respective diffusion coefficients (Ref. 1).
Species	D (m2/s)·109	cref (mol/m3)·10-3
Cu(OH)2L2-4	0.7	0.06
HCHO	1.2	0.22
HCOO-	1.454	0
OH-	5.273	0.016
L-2	0.794	0.39

Concentration at the bulk electrolyte boundary is set to the reference concentration as tabulated in Table 1.

(2)

At the electrode surface boundary, an boundary condition is used wherein the total current is set to 0. This boundary condition yields a constant potential,

, at the electrode surface boundary, which satisfies the condition:

(3)

where

(4)

The initial value for boundary electric potentials is set to -0.85 V.

Electrochemical reactions

The following electrochemical reactions occur at the electrode surface:

Copper reduction

(5)

Formaldehyde oxidation

(6)

is used to model copper reduction and formaldehyde oxidation reactions, which will set the local current density according to

(7)

where i0,m is the exchange current density, CR,m is the reduced species expression, CO,m is the oxidized species expression and η,m is the overpotential for species m (Cu and HCHO, respectively).

The overpotential η,m (V) is calculated from

(8)

The equilibrium potentials for the copper reduction and formaldehyde oxidation reactions are calculated using the Nernst Equation,

(9)

(10)

At the electrode surface boundary, fluxes of ionic species are defined in terms of the electrochemical reactions as

(11)

where

is the stoichiometric coefficient, ij is the local current density, nj is the number of electrons and F is Faraday’s constant (96485 C/mol). The subscript j signifies the

electrochemical reaction. This will set the flux to be proportional to the electrode current density according to Faraday’s law. The electrode kinetics parameters: i0,Cu=1 A/m2 and i0,HCHO=1 A/m2 are taken from the current-potential curves reported in Ref. 2.

Results and Discussion

Figure 2 shows the change in the mixed potential at the electrode surface during electroless deposition. It can be seen that the change is significant during the initial stages of deposition, which is attributed to the equilibrium potentials of copper reduction and formaldehyde oxidation reactions, and the constraint of equal and opposite anode and cathode current densities. At about 400 s the potential reaches a maximum.

Figure 2: The change in the mixed potential at the electrode surface against time during electroless deposition.

Figure 3 shows the change in the local current density at the electrode surface during electroless deposition. It can be seen that the current density is considerably increased in the initial stages of electroless deposition, corresponding to the trend observed for the mixed potential in Figure 2.

Figure 3: The change in the local current density at the electrode surface against time during electroless deposition.

Figure 4 shows the change in the deposition thickness at the electrode surface during electroless deposition. It can be seen that after approximately 400 s, the increase in electroless plating thickness is almost linear with time.

Figure 4: The change in the deposition thickness at the electrode surface against time during electroless deposition.

Figure 5 shows the change in the normalized concentration of various ionic species at the electrode surface during electroless deposition. It can be seen that the concentrations of the copper complex and formaldehyde species decrease with time, since they are consumed during the deposition. The free tartrate ligand (L22) concentration increases with time since it is produced in the deposition process.

Figure 5: The change in the normalized concentration at the electrode surface against time during electroless deposition.

References

1. M. Ramasubramanian, B.N. Popov, R.E. White, and K.S. Chen, “A Mathematical Model for Electroless Copper Deposition on Planar Substrates”, Journal of The Electrochemical Society, vol. 146, no. 1, pp. 111–116, 1999.

2. M. Paunovich and M. Schlesinger, Fundamentals of electrochemical deposition, 2nd edition, Chapter 8, Wiley-Interscience, a John Wiley & Sons, Inc. Publication, 2006.

Electrodeposition_Module/Tutorials/cu_electroless_deposition

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