A model has been developed to predict current distribution in electrodeposition onto substrates that contain lithographic patterns. The aim of the work was to understand the strong effects that substrate patterning can exert on the thickness distribution of plated films. Based on the familiar potential-theory model for secondary current distribution in electrochemical cells, the model is applicable at length scales that are large compared to the individual features of a pattern. The pattern is described entirely as a continuous distribution of"active-area density," a property that reflects any relative change in the electroactive area of the substrate due to the pattern. The active-area density enters the expression that relates the surface overpotential to the current density. An implementation of the model, using the boundary-element method, has been applied to several problems that illustrate the effects of substrate patterning on current distribution. For each example, the dimensionless groups that characterize the current distribution have been identified, general solutions have been obtained over wide parameter ranges, and behavioral trends have been interpreted.
The effect of lithographic patterning on electrodeposit thickness uniformity was investigated in a series of experiments. Copper was electrodeposited from an acid‐sulfate solution onto a specially patterned cathode under controlled agitation provided by a reciprocating paddle. The thickness nonuniformity resulting from a difference in “active‐area‐density” between adjacent zones was measured by profilometry. At current densities far below the mass‐transfer limit, the thickness distributions agreed well with predictions from a recently developed secondary‐current‐distribution model, in which each zone is treated as a continuum. Since this “secondary” model was found to be insufficient to describe behavior at higher current densities, it was extended to include a simple treatment of mass transfer. The resulting “tertiary” model better described the observed behavior. It was discovered that the influence of mass transfer can either decrease or increase the nonuniformity, depending on the importance of radially enhanced diffusion at individual features.
A numerical model is used to examine how the uniformity of current distribution at a flat electrode can be improved using a coplanar auxiliary electrode. A boundary-element code, based on potentialtheory and Tafel kinetics, determines the current that must be passed at a surrounding auxiliary electrode to minimize nonuniformity on a round cathode. Nonuniformity is quantified by the root-mean-square deviation from the mean current density over the cathode surface. The importance of geometric factors such as the size and position of the auxiliary electrode is examined. Applications to plating in the electronics industry and to rotating-disk electrodes are discussed.) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 134.129.120.3 Downloaded on 2015-06-20 to IP
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