Uniformity of Current Distribution

Nonuniformity of the current density at the edge of the substrate being plated was discussed in Section 3.2. The current distribution was discussed there for three simple geometries. In the real world, the geometry is rarely simple, and the current distribution cannot be calculated using the analytical solution of an equation. It can, however, be determined by numerical calculations. Commercial software is available to simulate different positions and shapes of the coimter electrode with respect to the 

The expected uniformity of current distribution of a given plating bath can be estimated from its conductivity and kinetics, as discussed in the next section 

The Wagner number is a dimensionless parameter that helps us determine the probable level of uniformity of current distribution in electroplating. There are two limiting cases to be discussed (i) Primary current distribution, where the uniformity of plating is determined exclusively by the conductivity of the solution and the geometry of the cell, (ii) Secondary current distribution, where the current distribution is determined by the kinetic parameters of the deposition process. As usual, reality is somewhere in between, it is neither purely primary nor purely secondary. The transition from one regime to another is characterized by the dimensionless Wagner number, defined as  

The partial derivative, taken at constant concentration (and, of course, constant temperature and pressure), is the differential Faradaic resistance, in units of Q cm. The solution resistance, expressed in the same units, can be written as  

In the absence of mass transport limitations, the local current density at a given potential is determined by the sum of two resistances in series the Faradaic resistance and the solution resistance. For values of Wj 1 the solution resistance is dominant and the current distributions depends primarily on geometry. This is the realm of primary current distribution. For Wa1 the Faradaic resistance is predominant and secondary current distribution is observed. 

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Cell geometry, such as tab/terminal positioning and battery configuration, strongly influence primary current distribution. The monopolar constmction is most common. Several electrodes of the same polarity may be connected in parallel to increase capacity. The current production concentrates near the tab connections unless special care is exercised in designing the current collector. Bipolar constmction, wherein the terminal or collector of one cell serves as the anode and cathode of the next cell in pile formation, leads to gready improved uniformity of current distribution. Several representations are available to calculate the current distribution across the geometric electrode surface (46—50). 

H. Use of the Wagner Polarization Parameter to Estimate Qualitatively the Uniformity of Current Distribution... 

Fig. 7C The angle (p between metal and insulator determines the uniformity of current distribution near the edge of an electrode.

Figure 9.3.11 Diagnostic plot for the uniformity of current distribution at an RDE. Conductivities of some typical background electrolytes at 25°C in aqueous solution are marked on log (/Coo) scale in the figure. Note dildr) is in units of Koo is bulk electrolyte conductivity in [From W. J. Albery and M. L. Hitchman, Ring-Disc Electrodes, Clarendon, Oxford, 1971, Chap. 4, by permission of Oxford University Press.]...

Fig. 3.2 Electrode design with various geometries to minimize non-uniformity of current distribution...

Influence of grid and plate design on the uniformity of current distribution over the grid surface. (a,b) flat surface covered with a uniform PAM layer — uniform current density (c) non-uniform... 

Optimization of the electrochemical cell s geometry is the primary factor that determines the uniformity of current distribution. The two major geometrical arrangements are parallel-plate electrodes and concentric cylinders. PaiaUel-plate geometry is common in large-scale production of base metals when the metal concentration in the electrolyte is high. Cylindrical cells are used in the treatment of less concentrated solutions, in the recovery of noble metals, and also in the production of base metals. The current distribution between two parallel electrodes is only uniform when a nonconducting containment of the same cross section surrounds the interelectrode space. 

The effect of scaling up electrode size is to improve the uniformity of current distribution, as shown in a short worked example. 

Thus for reactors with small interelectrode gaps uniformity of current distribution is maintained. Keeping current distribution uniform becomes difficult, however, when reactor dimensions are eomparable or when no one dimension eontrols reactor behavior. 

Electrode polarization was considered by Tobias in terms of adopting a linear approximation to the Tafel equation. The influence of polarization, which is in essence a bubble-independent resistance, acts in series with the ohmic resistance, improving the uniformity of current distribution. 

As we have seen in Section 5.1.2, bipolar connections lead to greater uniformity of current distribution on the electrodes in a cell stack. Analysis of current distribution on bipolar connected electrodes assumes that the electrochemical characteristics of the cell in the stack of electrodes can be represented by pure resistance. Results are conveniently expressed by an effectiveness factor Ef, denoting the ratio of the total current fed to the electrode to the maximum possible if the electrode is at a uniform (maximum) potential. Figure 5.29 shows the typical variation of Ef with... 

The uniformity of current distribution can be conveniently expressed in terms of the concept of effectiveness fy given by" ... 

Standard anode electrode potential Standard cathode electrode potential Defined in Eq. (5.3) = nLI2d Effectiveness factor for the uniformity of current distribution in parallel plate cells... 

A complete evaluation of the uniformity of current distribution should take into account the finite rate of the charge-transfer reaction that is taking place at the interface. When this is done, the current density becomes more uniform, and it neither declines to zero, nor does it increase to infinity at the edge, as implied above. 

In studies of electrode kinetics it should be borne in mind that the fundamental equations used are derived with the tacit assumption of uniformity of current distribution. Hence, the analysis of the current-potential relationship is valid only when this assumption applies to a very good approximation. 

It is well to remember that using the impressed current cathodic protection does not alleviate the need to calculate the current distribution and locate the anodes in a way that ensures the best uniformity of current distribution on the protected structure. 

Uniformity of current distribution can always be a problem in electroplating, but in alloy plating there could be an added complication In addition to leading to nonuniform thickness, it could also lead to nonuniform composition, since the rate of deposition of the alloying elements may depend differently on the local current density. 

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