Optimization of waveform shape and frequency in periodic reverse electroplating

In this report, the time-dependent carrier concentration in electrolytic cells, due to some basic periodic shapes, 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 pulse modulation width are investigated. Analytical solution of the model is obtained as a 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 and discussed. It is shown that there exist optimal operation points or optimal current waveforms to obtain efficient and enhanced deposition processes