Optimal pulse shapes for periodic reverse electroplating



In this report, time-dependent carrier concentration in electrolytic cells, due to some basic periodic shapes of excitation signal, has been studied. Exact analytical solutions for step, sinusoidal and periodic pulse reverse inputs are derived. The effect of frequency, forward and reverse amplitudes and duty cycle are investigated. An analytical solution of the model is obtained as Fourier series using Laplace transformations applied to a one-dimensional model with linearized Butler-Volmer electrode kinetics. The results are applied to an acid-copper bath. It is shown that optimal operation points exist. Optimal current waveforms for obtaining an efficient and enhanced deposition process, and faster deposition rate compared to simple DC electroplating is discussed.