A mathematical model of copper plating of a through-hole is developed which relates uniformity of deposition to bulk electrolyte composition, applied potential difference, aspect ratio, through-hole diameter, and deposition kinetics. The electrochemical transport equations governing plating in a through-hole are solved assuming that the fluid within the through-hole is stagnant. Conditions for uniform plating are determined both for Butler-Volmer kinetics considering the effects of dissociation of bisulfate ions in the electrolytic solution and for kinetics limited by complexation of cupric ions with an adsorbed neutral additive species.

A general mathematical model of electroplating of high aspect ratio through-holes of multilayer printed circuit boards is developed. This two-dimensional model includes transport by electrical migration, diffusion, and convection in the through-hole. The solution of the model is used to examine the effects of plating variables on uniformity in an acid copper plating bath with and without additives in the bath. Different regimes of plating conditions are examined with particular emphasis on ohmic control. The general model is used to determine the necessary conditions to achieve ohmic-limited plating. These criteria and the solution of the ohmic-limited model used determine the type of flow enhancement required to achieve ohmic-limited plating. General guidance for selection of a model for through-hole plating is developed.

Two process configurations of periodic flow reversal with two equistant counterelectrodes and of unidirectional flow using only a downstream counterelectrode are analyzed using a general model of through-hole electroplating. Although plating rates greater than attained with an ohmic-limited process cannot be achieved with a flow reversal process, the flow required in the through-holes can be significantly reduced. The use of only a downstream counterelectrode can improve the uniformity of deposition and increase the plating rate over ohmic-limited plating under certain conditions. Our previous modeling efforts (1-3), as well as others (4-9), have indicated that higher plating rates than those currently achieved of 20-40 mA/cm 2 for through-hole aspect ratios of 6:1 (10) are attainable from plating under ohmic-limited conditions with the use of bath additives. The likely impediments to reaching these higher rates of deposition in industrial processes are insufficient flow in the through-holes or an uneven current distribution across the surface of the circuit board. If two counterelectrodes equidistant from the circuit board are used, the criterion to insure electroplating of the through-hole in the ohmiclimited regime was previously determined to be Pe/(~v~a ~ >-12 (1). If flow in the through-hole is provided that at least meets this requirement, the plating rate and the deposition uniformity for a through-hole of fixed dimensions only can be improved by increasing the conductivity of the plating solution or by using bath additives to decrease the dependence of the rate on the potential difference. As the ohmic-limited rate profile is symmetrical around the center of the through-hole, the plating uniformity is independent of the flow direction or periodic flow reversal.However, the rate under conditions of ohmic-mass transport limited plating is strongly dependent on the direction of flow. Accordingly, plating uniformities in this regime of control can be improved by different plating schemes. Plating in the ohmic-mass transport limited regime using periodic reversed flow or unidirectional flow with only a downstream counterelectrode may allow plating at higher rates than plating in the ohmic-limited regime. These types of plating processes are examined in this paper.In a previous paper (1) we developed a general twodimensional mathematical model of electroplating of high aspect ratio through-holes of multilayer printed circuit boards. This model included transport by electrical migration, diffusion, and convection in the through-hole. The solution of the model was used to examine the effects of plating variables, as applied to an acid copper plating bath with and without additives in the bath, on uniformity. Different regimes of plating conditions, particularly ohmiclimited control, were examined to determine criteria for selection of a model for through-hole plating.The flow reversal and downstream counterelectrode processes will be investigated using our general model of through-hole plating (1). The major ass...

ance are shown in Fig. 3. The platinum loading for all cases is 1 mg/cm 2. The optimum platinum/Nation ratio is 1:1. Polymer fractions that are much higher than 0.5 are kinetically limited, and polymer fractions that are much lower than 0.5 are diffusion limited.The effect of platinum loading on MEA performance during discharge is shown in Fig. 4. MEAs with platinum loadings of 4.0, 2.0, 1.0, and 0.5 mg/cm 2 were simulated for e = 0.5 and a 50 mV applied potential across the catalyst zone. The best performance was achieved with a 1.0/cm 2 loading. The current densities are highest at the gas-membrane interface (x = 0). The local current density decreases rapidly in the catalyst zone for the case where the platinum loading was 4 mg/cm 2. Improved performance was achieved for the 1 mg/cm 2 loading, because the local current density was more uniformly distributed in the catalyst zone. ConclusionsThe model reported here is a useful tool which can be used to determine conditions where MEA performance is optimized. The structure of the catalyst zone has been shown to affect the performance of the MEA. When the particles are densely packed, the performance is gas diffusion limited, and when the particles are loosely packed, the performance becomes kinetically limited.