In the above discussion, we have implicitly characterized deposition by a single overpotential and rate for the surface of interest. In practice, however, the rate varies over the surface of the piece being plated, as illustrated schematically in Figure 13.12. To avoid the problems associated with deposition under mass-transport control, practical systems typically operate at a fraction of the limiting current. Because we are operating well below the limiting current, local deposition rates are governed by the potential field and described by the secondary current distribution.
Figure 13.12 Schematic illustration of the impact of the current distribution on plating uniformity.
Current Distribution and Wagner Number
For the Tafel region most relevant to industrial electrodeposition, the uniformity of the current distribution is characterized by the Wagner number (Wa) defined in Chapter 4 as
(4.65)
This dimensionless group represents the kinetic resistance divided by the ohmic resistance. Higher values of Wa correspond to a more uniform current distribution. The factors that influence the uniformity of the current distribution are those reflected on the right side.
The conductivity of the solution is one of the primary factors that influence the uniformity of the current distribution. The conductivity, in turn, is influenced by the concentration of ions in solution, the temperature of the electrolyte, and the degree of complexation of the electrolyte. Concentrations of metal ion are often limited by solubility, and salts are added to enhance solution conductivity. The cost of precious metals leads to the use of reduced concentrations of these ions and lower solution volumes than what otherwise might be used. Effluent considerations (e.g., disposal or treatment) may also influence metal ion concentrations, as well as the types of ions used in solution. Complexation reduces the charge and increases the size of the ions being transferred, and thus has a substantial influence on conductivity. Although temperature influences the conductivity, the impact of temperature on the rate of the desired reaction and side reaction(s) is probably more important.
As discussed in Chapter 4, the length over which the current must travel in solution to different locations on the work piece is critical as even a small difference in the overpotential can cause a substantial difference in the local reaction rate (see Figure 13.12). Strategies such as the use of multiple anodes can be used to make the current density more uniform.
Deposit uniformity decreases as the average current density is increased. This happens because the ohmic resistance becomes a larger portion of the total resistance at higher current densities. Both the conductivity and exchange current density increase with increasing temperature, leading to a current density that increases with temperature at a given cell potential. Since the iavg is a stronger function of temperature than the conductivity, an increase in temperature at a constant cell potential tends to decrease the Wa and make the current distribution less uniform. In contrast, increasing the temperature while maintaining a constant current density will decrease the cell potential and increase uniformity since the current is constant, but the conductivity is higher at the higher temperature. Finally, we note that the rate of side reactions also increases with increasing temperature and, depending on the activation energy, may lead to increased relative importance of a given side reaction and, therefore, to greater loss of efficiency. The side reaction may, however, improve the uniformity of the plating as discussed below.
The final parameter in the Wa is the transfer coefficient or, equivalently, the Tafel slope. Small values of αc correspond physically to reactions that are less sensitive to potential. Consequently, the current distribution that corresponds to a given potential distribution will be more uniform for a reaction with a small transfer coefficient. In practice, additives that complex with the metal ions can be used to increase the Tafel slope (decrease αc), by changing the reaction mechanism.
Experimental Devices for Examining Current Distribution
Two different types of experimental cells are used routinely in industry for plating diagnosis and optimization. The first is the Hull Cell shown in Figure 13.13a. This type of cell comes in a standard size and is designed to explore a range of current densities in a single test, a task made possible by the slanted cathode. It is an excellent tool for comparing bath compositions and for determining the approximate current density at which the desired plating characteristics can be achieved.
Figure 13.13 Cells for experimental examination of current distribution. (a) Hull cell. (b) Haring–Blum cell.
The second type of experimental cell is the Haring–Blum cell shown in Figure 13.13b. It is used to quantify the throwing power of a bath. A bath with a high throwing power yields more uniform deposition. The cell consists of an anode with two cathodes, one on either side of the anode. The backsides of the cathodes are insulated so that only the surface facing the anode is active. The two cathodes are placed at different distances from the anode, x1 and x2. Usually, x1/x2 ≈ 5. The different distances correspond to different values of the electrolyte resistance, which is larger for the cathode furthest away from the anode. For Wa ≫ 1, the electrolyte resistance is not significant and the weight of the deposits on the two cathodes will be the same. For Wa ≪ 1, the weight of the deposit on the electrode closest to the anode will be greater, consistent with a nonuniform current distribution. The results from the Haring–Blum cell are most frequently expressed in terms of the throwing power, which is defined as follows:
(13.32)
where K = x1/x2 and B = w2/w1 (weight ratio of the deposits on the two cathodes). The equation is designed to give throwing powers between −100 (very poor) and +100 (very good). The best possible uniformity would correspond to equal weights of the deposits at the two electrodes (B = 1), which corresponds to a throwing power of 100%. A throwing power of 0% corresponds to the situation where K and B are equal and deposition is inversely proportional to the solution resistance. To illustrate, if K = 5 and the throwing power = 0%, the mass of the deposit at x1, the electrode farthest away from the anode, would be 1/5 of that on the closest electrode, x2. Negative values are possible because of side reactions that may yield B values greater than K in situations where the current at the closest electrode is dominated by the side reaction (see next section).
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