Time‐Averaged Current Distribution for a Rotating‐Disk Electrode under Periodic Current Reversal Conditions

Abstract

The time-averaged current distribution over the surface of a rotating-disk electrode is calculated under conditions of periodic current reversal by simultaneously solving the transient-convective-diffusion equation and Laplace's equation. The calculated results compare well with experiments performed using the copper/copper sulfate system. The grid search technique is used to determine the optimum plating conditions in terms of uniform thickness of electrodeposits by varying the duty factor and the ratio of anodic to cathodic current density.Pulsed current (PC) technology has long been used in electroplating industries due to the improvements in the quality of electrodeposits, and its characteristics are well described in the monograph by Puippe and Leaman (1). But the current distribution over the electrode surface in pulse plating is generally less uniform than that in dc plating. Recently, Wan and Cheh (2) developed a mathematical model of the pulse plating of copper for the case below the limiting current density condition and calculated the tertiary current distribution on a rotating-disk electrode. Also Chin et al. (3), computed the secondary current distribution on a planar electrode neglecting the mass-transfer effect. They showed that the nonuniform ohmic potential drop in the solution outside the diffusion layer contributed to the nonuniform current distribution.In order to minimize the nonuniformity of thickness distribution, organic additives as well as periodic current reversal (PCR) technique has been practiced in plating industries largely based on empiricism. The organic additives which act as levelers or brighteners generally tend to increase the polarization resistance, leading to an increase in throwing power (4). Popov et al. (5) showed that the macrothrowing power was considerably better with a PCR than with a PC. Also Granato and Sobral (6) found that dendritic growth of gold was not observed even at high current density in electrorefining with PCR technique.Fedkiw and Brouns (7) developed a mathematical model of PCR plating on a planar electrode with an assumption of steady state. Recently, Pesco and Cheh (8,9) presented a simulation of plated through-holes, and compared the current distribution between dc, PC, and PCR. They indicated that plating with PCR appeared to be a promising technique to obtain more uniibrm metal-thickness distribution at low current densities. In addition, it was demonstrated that the PCR technique can decrease the energy consumption due to the low anodic overpotential at the lead electrode in the electrowinning of zinc in acidic media (11) and increase the current efficiency of zinc electrodeposition in the presence of 5 mg/1 of lead (12). Mass6 and Piron (13) also showed that the beneficial effect of PCR in zinc electrowinning remained even in the presence of nickel.In this study, a mathematical model to describe the current distribution on the rotating-disk electrode under periodic reversal conditions is presented with experimental confirmations followed by obt...

A Tertiary Current Distribution Model for the Pulse Plating of Copper into High Aspect Ratio Sub-0.25 μm Trenches

“…Although literature on the pulse plating of copper [4][5][6][7][8] is abundant, articles are scarce on pulse plating of copper into submicrometer features of large aspect ratio and no model seems to have been reported for dual damascene structures. Hume et al 9 studied dc plating through polymeric masks for features with small aspect ratios.…”

Fabrication & characterization of high aspect ratio fine pitch deep reactive ion etched through-wafer electroplated copper interconnects

“…Variation in the current density causes the non-uniformity on the scales of substrate, pattern and individual feature. Three main types of variations in the current density are: primary [138][139][140]142], secondary [143], and tertiary [144] and are detailed later. When an electric potential is applied between two electrodes, each point in the electrolyte assumes some intermediate potential between that of the two electrodes.…”

“…This distribution is determined completely by the geometry of the plating cell and the interelectrode gap, and is independent of the electrolyte properties. The primary current density at a given point is reciprocal to the distance from the anode [138][139][140]142].…”

“…There are several numerical models that predict the current density distribution during the copper electroplating process[137][138][139][140][141][142][143][144]. A simple model showing the current density distribution in rotating disk electrode is illustrated in Figure 5.1.…”

“…The limiting current depends upon the diffusion thickness (δ). If δ is larger the tertiary current density will be smaller[137][138][139][140].…”