Optimizing thickness uniformity in double-pulse nickel electroforming via a physics-guided COMSOL®–ANN–WOA framework

Abstract

The thickness uniformity of electroformed layers critically determines the dimensional accuracy, surface quality, and reliability of micro-electroformed devices. This work investigates nickel deposition under double-pulse current with a focus on quantifying the effects of positive-pulse current $I_{\mathrm{avg},\mathrm{a}}$ , negative-pulse current $I_{\mathrm{avg},\mathrm{c}}$ , and duty-cycle fractions D_a:D_c on thickness inhomogeneity and morphology, training and validating an artificial neural network (ANN) surrogate for rapid prediction, and ultimately identifying an optimal pulse window under practical bounds. With a fixed negative pulse, increasing the positive-pulse current (0.032 to 0.035 A) steadily reduces macroscopic thickness uniformity; the best uniformity occurs at 0.032 A, while the microstructure evolves from compact equiaxed grains to oriented/needle-like and eventually coarse faceted textures. Duty-cycle modulation strongly improves uniformity: raising D_a:D_c from 0.50:0.15 to 0.575:0.075 reduces thickness inhomogeneity from 352% to 125%. A crested porcupine optimizer (CPO)-initialized back-propagation artificial neural network (BP-ANN) surrogate trained on 1610 COMSOL^®-generated samples (70/30 split) maps power-supply parameters to thickness inhomogeneity α and serves as a rapid proxy for simulations. Coupled with the Whale Optimization Algorithm (WOA) for single-objective minimization of α, the framework identifies optimal pulse parameters (a₁–a₄) = (0.0412 A, 0.066 A, 0.549, 0.081), yielding α ≈ 96.5% in simulation and verified experimentally by bright, fine-grained deposits with improved uniformity. A physics-guided hybrid framework is proposed—integrating COMSOL^® secondary-distribution data into a CPO-initialized BP-ANN surrogate, followed by optimization using the WOA—which delivers experimentally validated improvements in thickness uniformity without auxiliary cathodes or shields, relying on pulse shaping alone.