Multi-scale simulations of single particle displacement damage in silicon

Silicon devices are extensively used in space and other radiation-rich environments. They must withstand radiation damage processes that occur over wide range of time and length. Ion implantation technique, one of the most important process in the fabrication of integrated circuits, can also create the displacement damage in silicon lattice. Exposure of silicon wafer or silicon device to radiation causes the creations of variety of defects and has adverse effects on the electrical properties of devices. Although phenomenological studies on the radiation effects in silicon have been carried out in the past decades, the features of multi-scale of displacement damage make it difficult to characterize the defect production and evolution experimentally or theoretically. Recently, the silicon device with ultra-low leakage current was shown to be very sensitive to the permanent displacement damage induced by single particles, called single particle displacement damage (SPDD) event. To the best of our knowledge, the investigation of single particle displacement damage (SPDD) event in silicon device by the coupling molecular dynamics (MD) and kinetic Monte Carlo (KMC) techniques has not yet been reported so far. In this paper, MD simulations are combined with KMC simulations to investigate the formation and evolution of SPDD event in silicon. In MD simulations, Tersoff potential is used to describe the Si-Si atomic interactions. The potential smoothly joins to Ziegler-Biersack-Littmark potential that describes the energetic short range interactions well. All atoms in the MD cell are allowed to evolve 0.205 ns to track the damage production and short-term evolution. A multi-phase simulations are performed to improve the simulation efficiency. Then the nearest neighbor criterion is employed to identify the configurations and spatial distributions of interstitials and vacancies, which are used as input in KMC simulations to study the thermal diffusion and interactions of those defects in the time interval from 0.205 ns to 1000 s. The results show that no defects are missing when transferring from MD to KMC simulation and the whole damage obtained in MD simulations is reproduced in KMC simulations. Since the production and evolution of defects are simulated, the SPDD current could be calculated based on Shockley-Read-Hall theory. We derive the formula to calculate the SPDD current and its annealing factor related to interstitials and vacancies in the depletion region. The calculated annealing factors of defects are compared with the annealing factors of SPDD currents and also with the experimental results. The results show that an annealing factor of defects has the same value as the annealing factor of an SPDD current when only one type of defect is considered in the calculations, while there are some differences between these two annealing factors when two and more types of defects are considered. The annealing factors of defects can be used to represent the annealing behaviors of SPDD currents since the divergences between these two annealing factors are not significant. Finally, SPDD current annealing factor based MD simulation results obtained with Tersoff potential are compared with the results in our previous study in which the Stillinger-Weber potential is used, and also compared with experimental results. The comparisons show that the simulation results with considering both Stillinger- Weber potential and Tersoff potential are in good agreement with experimental results. Compared with the calculated results with considering the Tersoff potential, the results with considering the Stillinger-Weber potential are closer to experimental results.