We present a tertiary current-distribution model for copper electrodeposition under galvanostatic conditions, with detailed surface chemistry kinetics for the model system of copper electrodeposition. The values of the kinetic parameters are extracted from results of statistical chronoamperometry and linear sweep voltammetry experiments using a potential-dependent, diffusion-adsorption-desorption model of the experimental system. The resulting surface chemistry description is combined with fundamental conservation laws, including mass transport, potential distribution, and competitive adsorption, to form the tertiary current distribution model. Two-dimensional finite element simulations of this model provide information about the causes of the thickness of the copper electrodeposition layer, including potential variations of the cathodic surface, fluctuations in the cupric ion concentration and coverage of the accelerator. The model is used to predict the filling process with different current densities and SPS concentrations and is verified by copper electrodeposition experiments. The "optimal zone" was determined for the SPS concentration and the inward current density to achieve good TSV filling. Sample points in the outer zone were selected and the failure mechanism was studied to help to infer the right direction toward the "optimal zone" in copper electrodeposition. The models are potentially useful tools for measuring the properties of electrolyte solutions and for the optimization of copper electrodeposition processes. (C) 2016 The Electrochemical Society. All rights reserved.