Copper (Cu) is used in integrated circuits and microdevices and has the potential to replace aluminum alloys due to its low resistivity, strong electromigration properties, and affordability. However, a significant factor that influences the performance of devices at the micro and nano scales is the surface roughness of the deposits. LAMMPS software is employed to simulate the deposition Cu on an ideal state for a stainless-steel substrate. The deposition process and deformation behavior of Cu on the surface and the roughness of the deposition surface are analyzed. Taking the deposition process of Cu atoms as an object, the effects of different atomic numbers, different temperatures, different velocities, and different heights on the surface roughness of the deposits were investigated. The atomic structure composition of the deposition velocity is analyzed, and the radial distribution function is analyzed to reveal the microscopic mechanism of action. The results of the theoretical deposition and analysis show that the surface roughness increases with the number of atoms deposited and decreases with increasing substrate temperature. The surface roughness first decreases and then, after some fluctuation, stays constant at a particular level with increasing velocity. Additionally, as the deposition height increases, the surface roughness reduces. There is a nonlinear relationship between the various components and the deposited surface roughness. The surface quality of deposits can be improved during the deposition process by optimizing the deposition parameters of deposition atoms, substrate temperature, deposition velocity, and deposition height.