Electrochemical printing: mass transfer effects

Abstract

Electrochemical printing (EcP) is a maskless solid freeform microfabrication process capable of depositing metal and alloy patterns on macroscopically large conductive substrates. The maximum plating rate achievable with EcP is dictated by the mass transfer limiting current density (ilim). The dependence of ilim on the dimensionless fly-height (h/d), the nozzle Reynolds number (Re) and the Schmidt number (Sc) is well known for classical impinging jet systems that employ a well-supported electrolyte and electrodes of similar size to the impinging jet nozzle. Significant ion migration and a large cathode (relative to the nozzle) make EcP mass transfer unique when compared to a classical impinging jet electrode. In this paper, we report experimentally measured limiting currents between 2 and 25 A cm−2. The corresponding simulated limiting currents fall between 1 and 20 A cm−2, for 14 < Re < 290, 0.28 < h/d < 0.7 and Sc = 5507. Best fits of experiments and simulations show the limiting current depends on Re0.31±0.03 for experiments and on Re0.48±0.01 for simulations; both fall in the expected range of Re1/3 and Re1/2 for Sc ≫ 1. The fly-height dependence, however, is significantly stronger than a classical impinging jet electrode due to the role of ionic migration and the unique geometry. This work provides useful engineering tools to help implement EcP.