Analysis of convective mass transfer during electrochemical metal plating and etching using a linear overpotential relaxation technique
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Description
A linear overpotential relaxation technique has been used successfully to determine liquid-phase mass transfer boundary-layer thicknesses and salt film thicknesses during electrochemical metal plating and etching. This method was tested and verified for iron and copper dissolution from a rotating disk, copper deposition at a rotating disk in the presence of additives, and mixed natural and forced convection copper deposition at a segmented vertical flat plate. For both anodic dissolution and cathodic deposition processes experimentally measured concentration overpotentials were found to decay linearly with respect to the square-root of time immediately after current interruption. A mathematical model, which was derived by combining the solution to Fick's Second Law of diffusion with the Nernst equation, predicted this linear overpotential decay behavior. Liquid-phase mass transfer boundary-layer thicknesses and salt film thicknesses were computed by matching short-time overpotential decay data to the mathematical model Liquid-phase mass transfer boundary-layer thicknesses during active and transpassive iron etching were in good agreement with those predicted by the Levich equation. The thickness of prepassive FeSO$\sb4$ salt films were found to be dependent on the disk rotation speed and anode potential. Liquid-phase effective mass transfer boundary-layer thicknesses during active copper dissolution were found to be $\sim$56% smaller than those during cathodic deposition. Steady-state prepassive CuSO$\sb4$ film thicknesses were dependent on 1/3 power of the anode potential and $-$1/3 power on the disk rotation speed Liquid-phase effective mass transfer boundary-layer thicknesses during copper deposition with Selrex Cubath and Cl$\sp-$ addition agents were found to be equal to those for an additive free case. Mass transfer boundary-layer thicknesses for an electrolyte containing Copper Gleam-PC and Cl$\sp-$ addition agents were found to be smaller than those predicted by the Levich equation at low disk rotation speeds and applied currents A Sherwood number correlation for currents below and near the limiting current was derived for mixed assisting natural and forced convection copper plating. During opposing natural and forced convection flows the flow pattern at the top and the bottom edges of the plate were found to be laminar at all forced convection velocities. The fluid velocity over the remaining portion of the electrode was found to be turbulent