Non-adiabatic dynamic study of S vacancy formation in MoS<sub>2</sub>

<sec>Defect is one of the central issues in semiconductors. MoS₂ is sensitive to irradiation and can be damaged by electron beams, accompanied with the generation of sulfur vacancies. However, the dynamics for the defect generation process is still unclear. In this work, we employ the time-dependent density functional theory to simulate the process of a sulfur atom sputtering from the MoS₂, producing a sulfur vacancy defect in the lattice. We find that there exists a strong non-adiabatic effect in the process.</sec><sec>During the formation of the sulfur vacancy, there exist electron transitions which can be described by the Landau-Zener model. As the sulfur atom leaves away from the lattice, two energy levels from the valence bands rise up and one energy level from the conduction band falls down. When the spin-orbit coupling (SOC) is not considered, those levels do not couple with each other. However, when the SOC is taken into account, electrons can transit between those levels. The transition probability is related to the kinetic energy of the sputtered sulfur atom. As the kinetic energy of the sulfur atom increases, the non-adiabatic electron transitions are enhanced. The evolution of the energy levels is also strongly dependent on the kinetic energy of the sputtered sulfur atom, which is induced by the non-adiabatic electron transition. It is worth noting that the SOC plays a key role in sputtering sulfur atoms, although the system produces no magnetic moments in the whole process.</sec><sec>The non-adiabatic effect enhances the energy barrier of the sulfur sputtering. As the initial kinetic energy of the sputtered sulfur atom increases, the energy barrier increases, and exhibits a jump around the initial kinetic energy of ~22 eV, which can be explained by the non-adiabatic electron occupation and the Coulomb repulsion. Beside the energy barrier, the non-adiabatic effect also modifies the charge distribution. When the kinetic energy of the sputtered sulfur atom is relatively low, more electrons occupy the <i>p</i>_<i>z</i> level; when the kinetic energy is relatively high, more electrons occupy the <i>p</i>_<i>xy</i> level instead. The sputtered sulfur atom always carries a bit more electrons, leaving holes around the vacancy defect.</sec><sec>Our work reveals the dynamics of the sulfur sputtering and vacancy formation in MoS₂, particularly the non-adiabatic effect in the process. It builds the theoretical foundation for defect engineering.</sec>