Copper is one of the most concerned contaminants for silicon process, due to its detrimental effects on device performance if present in active regions. Gettering of Cu by changing the surface conditions at the wafer surface is commonly used. Acceleration of Cu out-diffusion and surface precipitation was observed with changes of the surface potential, which could be altered by both existing Cu precipitates and organics at the surface. In this work, physically based models are developed to describe the Cu evolution at the wafer surface including the dependence of surface potential. These models are verified by comparison to the experiment measurements from Ohkubo et al. [Jpn. J. Appl. Phys. 1 44, 3793 (2005)].