A three-dimensional model based on molecular dynamics has been developed to describe the formation of a single cathode spot in vacuum arcs. The formation of the cathode spot is assumed to be controlled by the plasma ions, the effect of which is simulated in LAMMPS through the process of ion bombardment. The cathode is represented by structured copper atoms, while the ions are continuously injected into the domain with a certain velocity towards the cathode surface. Ion bombardment leads to the appearance of a crater, which is caused by the accumulation of pressure effect against the relaxation of substrate temperature. The size of the crater is found to be determined by the spatial distribution of the injected ions. The formation of the cathode spot is also scrutinised by electron emission from the cathode surface with variable surface temperature during the cathode spot development process. In addition, the evaporated atoms forming the metal vapour are observed. This study provides a description of the formation of the cathode spot at microscale, which shall be helpful to further studies of the arc rooting and arc contact (electrode) erosion in vacuum environment.