A theory for impurity segregation in electrochemical processes is formulated based on the Nernst equation, which forms the theoretical foundation for electrorefining. It is found that the current two-electrode configuration, while being widely used to purify metals, is incapable of producing ultrahigh purity. A three-electrode configuration is required, in which the potential applied to the anode or the cathode with respect to the reference electrode is the key to produce ultrapure materials. The theory is applied to electrorefining of metallurgical-grade silicon to produce solar-grade silicon. It is suggested that two-step electrorefining is required to remove all the impurities, in which the anode and cathode potentials are controlled in separate steps. The precise anode and cathode potentials for each step are determined from the impurity concentrations in metallurgical-grade silicon and the target impurity concentrations for solar-grade silicon. It is also found that low process temperatures promote effective electrorefining. (C) 2012 Elsevier Ltd. All rights reserved.