Anisotropic Chemical Pattern Etching of Copper Foil: III. Mathematical Model

A mathematical model for wet chemical etching of copper in acid chloride solutions was developed for exploring the phenomenon of anisotropic etching reported in Parts I and II of this study. The model considered a two-dimensional rectangular cavity and accounted for laminar convection, diffusion, migration, homogeneous equilibria, and heterogeneous electrochemical reactions involving eight ionic species. Two compositions (3.5M CuCl₂ + 0.5M HCl + 0.5M KCl and 0.5M CuCl₂ + 0.5M HCl + 0.5M KCl) and two cavity aspect ratios (width:depth = 5:1 and 1:1) were considered. Calculation of the flow field demonstrated the existence of recirculating eddies which play a significant role on local transport, particularly in the interior corners. Calculation of the concentration contours of the reaction product, CuCl₃^-2, indicated that the solution was supersaturated for 1:1 cavities as well as for 5:1 cavities in the case of the 3.5M CuCl₂ + 0.5M HCl + 0.5M KCl solution. For 5:1 cavities in 0.5M CuCl₂ + 0.5M HCl + 0.5M KCl solution, supersaturation occurred only in the corner regions for 54 < Pe ≤ 5400. The predicted local etch rate was nonuniform owing to the presence of recirculating flow eddies. The predicted average etch rate for the two aspect ratios was compared with experimental data over the range 54 < Pe < 3000 and was found to agree to within 10 to 15% for the 0.5M CuCl₂ solution, and to within 15 to 30% for the 3.5M CuCl₂ solution.