A surface creep model is presented for analyzing Cu-to-Cu direct bonding under thermal compression. The driving force is a pressure gradient, which squeezes layers of atoms to fill voids at the bonding interface. The link among the key parameters of surface roughness, experimental bonding time, temperature, and pressure is presented in a kinetic equation. The theoretical bonding time can be calculated through these key parameters. The benchmark of the theoretical bonding time is the time required for the bonding area to reach 95%, which is measured from TEM images of the bonding interface. The experimental bonding time might be longer, and the bonding area might larger than 95%. Because the bonding mechanism includes surface diffusion and grain boundary diffusion, it is difficult to distinguish their individual influence. Therefore, the effective diffusivity (Deff) is calculated from the bonding conditions of other research and the equation of bonding model. If the bonding surface is highly (111)-oriented, the Deff is close to the (111) surface diffusivity. From the surface creep bonding model, the theoretical bonding time of grain boundary diffusion is very sensitive to the bonding temperature, while that of (111) surface diffusion is not. Additionally, at low temperature bonding (<250°C), the theoretical bonding time of (111) surface diffusion is much lower than grain boundary diffusion. However, the experimental bonding time of (111) surfaces need to take grain boundary formation into consideration. Hence, the control of (111) oriented Cu microstructure is the most promising way to achieve low temperature bonding.