COMSOL 6.4 - Copper Deposition in a Through-Hole Via

Copper electrodeposition in a Through-Hole (TH) via is prevalent in electronic industry, particularly for the Printed Circuit Boards (PCBs). This model demonstrates the “butterfly” filling mechanism of the TH via during copper electrodeposition. Due to the presence of halide-suppressor additives in the electrolyte, electrodeposition occurs selectively at the center of the via, thus avoiding the formation of electrolyte enclosures. The example is based on a scientific paper (Ref. 1).

The purpose of the model is to demonstrate the use of deforming geometries for plating processes and the use of the Adsorbing-Desorbing Species functionality to model the influence of a suppressor on the plating result.

Model Definition

The model is defined by the material balances for the involved species (copper, Cu2+; chloride, Cl-; and suppressor additive polyether, P) in the electrolyte solution and the adsorbed species (chloride, Cl, and suppressor additive polyether, P) on the electrode surface as well as an electrolyte charge balance assuming the presence of a supporting electrolyte.

The model geometry is shown in Figure 1. A 2D axisymmetric space dimension is considered in the model. The upper horizontal boundary represents the anode and the cathode is placed at the bottom. The rightmost and leftmost vertical walls correspond to insulation (axial symmetry). The bottommost horizontal boundary corresponds to symmetry.

Figure 1: Model domain with boundaries corresponding to the anode, cathode, and symmetry walls.

The flux for each of the species in the electrolyte is given by the Nernst–Planck equation

where Ni denotes the transport vector (mol/(m2·s)), ci the concentration in the electrolyte (mol/m3), zi the charge for the ionic species, ui the mobility of the charged species (m2/(s·J·mole)), F Faraday’s constant (As/mole), and ϕl the potential in the electrolyte (V). The material balances are expressed through

one for each species, that is i = 1, 2, and 3.

The electrolyte charge transport is solved assuming a supporting electrolyte charge conservation model according to

At the cathode surface, copper electrodeposition reaction occurs according to

The boundary condition for the cathode is given by the Butler–Volmer equation for copper deposition. This gives the following relation for the local current density as a function of potential and copper concentration

where η denotes the overpotential defined as

where ϕs,0 denotes the electronic potential of the respective electrode. The equilibrium potentials for the copper reduction reaction is calculated using the Nernst equation

The exchange current density, i0, is defined in terms of surface coverage of the suppressor additive polyether, P, and the cupric ion concentration according to

(1)

wherei0,unsuppr is the unsuppressed reference exchange current density, i0,suppr is the suppressed reference exchange current density and θP is the surface coverage of the suppressor additive polyether, P.

The flux condition for the copper ions at the cathode boundary is defined as

where n denotes the normal vector to the boundary.

For the chloride ions, flux condition is defined as

For the suppressor additive polyether, P, flux condition is defined as

Using the Electrode Surface boundary node, with an added Dissolving-Depositing species, the ion fluxes and the boundary mesh velocity are based on the reaction currents, the number of electrons, and the specified stoichiometric coefficients of the electrode reactions. The sign of the stoichiometric coefficient for a species depends on whether the species is getting oxidized (positive) or reduced (negative) in the reaction. The stoichiometric coefficient is νCu = −1 for the copper ions in the electrolyte, whereas that for the copper atoms in the electrode is νd,Cu = 1.

Using the Electrode Surface boundary node, with an added Adsorbing-Desorbing species, surface coverage is evaluated according to

where

and

are adsorption kinetics,

and

are deactivation kinetics for chloride and suppressor, respectively, and deposition velocity, v (m/s), is calculated according to

where M is the mean molar mass (63.55 g/mol) and ρ is the density (8960 kg/m3) of the nickel atoms and n is number of participating electrons.

At the anode surface, the electrolyte potential is set to 0 and concentration of all involved species is set to their initial concentrations.

All other boundaries are insulating.

The initial conditions set the composition of the electrolyte according to

You set up the above equations using the Tertiary Current Distribution, Nernst–Planck Equations interface. The Deformed Geometry node keeps track of the deformation of the mesh.

Results and Discussion

Figure 2 shows the surface plot for concentration distribution of chloride ions along with contour plot and the displacement of the cathode surface after 14.5 minutes of operation. The figure clearly shows that copper electrodeposition occurs selectively at the center of the TH and grows radially inward, leading to sidewall impingement at the TH via center and resulting in “butterfly” filling of copper in the TH via. The selective copper electrodeposition, avoiding the formation of undesirable electrolyte entrapment, is attributed to chloride-polyether additives adsorption-desorption at the cathode surface. The chloride ion concentration depletion can also be seen in Figure 2 toward the center of the TH via.

Figure 2: Chloride ion concentration (mol/m3) along with contour plot and electrode displacement in the cell after 14.5 minutes of operation.

Figure 3 shows the thickness of the deposition from the center along the vertical cathodic surface of the TH via. The lines reveal the development of the nonuniform deposition which is found to be more toward the center of via when compared to the mouth of the via.

Figure 3: Thickness of the deposition from the center along the vertical cathode boundary of TH via.

Figure 4 shows the surface coverage of chloride ions along the vertical cathodic surface of the TH via. The lines reveal that adsorption of additive (chloride) begins at the mouth of the TH via and then gradually covers the entire surface of the TH via. The surface coverage of additives is found to be the lowest at the center of the TH via leading the highest copper electrodeposition in that region.