We present a two-dimensional, transient, tertiary current-distribution model for copper electrochemical deposition, with detailed surface chemistry kinetics for the model system of copper deposition with three representative additives; polyethylene glycol, bis-͑sodium sulfopropyl͒ disulfide, and hydrogen chloride. Values of kinetic parameters are extracted from statistically designed rotating-disk-electrode experiments using a transport-reaction model of the experimental system. The resulting surface chemistry description is combined with fundamental conservation laws, including transient mass transport, momentum transport, and potential distribution, to form the tertiary current distribution model. Two-dimensional finite element simulations of this model provide new insight into causes of film thickness variations across the wafer, including large potential variations originating from the initial seed-layer thickness ͑terminal effect͒, a nonuniform mass-transport boundary-layer thickness resulting from cell geometry, and fluctuations in the additive concentrations. An application of pulse plating is also explored. The surface chemistry and the tertiary current distribution models could potentially form useful tools for design and optimization of copper electrochemical deposition processes.