Modelling of point defect complex formation and its application to H+ ion implanted silicon

The diffusion and interaction of impurity atoms in semiconductors play an important role in modelling of the technological processes for device fabrication. Being mobile, impurity atoms, vacancies and interstitials can recombine and/or precipitate in the form of stable complexes which leads to the modification of target material properties. Here, we present an analytic model that predicts the concentrations of such complexes as a function of point defect concentrations using the probabilities for point defects to encounter and the probabilities for the formation of specific complexes dependent on their formation energies. This approach is general and can be used in different systems. We applied this model to the formation of different complexes after H+ implantation in silicon at room temperature. The formation energies of the complexes were calculated using the density functional theory. We linked the macroscopic strain measured in the implanted crystal to the individual deformation fields generated by the different complexes and to their concentrations. Such model calibration allowed determining the diffusion coefficients of silicon vacancies and interstitials at room temperature, the time required for the formation of all the complexes, the concentrations of complexes as a function of H concentration and the specific role of some complexes in generating strain. The model can be extended to the case of the systems co-implanted with different ions and can be applied for developing the SmartCut® technology used for creating innovative substrates.