Modeling of phosphorus diffusion in silicon oxide and incorporation in silicon nanocrystals

We approached the rate equation modeling of P dopant incorporation in Si nanocrystals (NCs) embedded in the SiO2 matrix by diffusion from a spatially separated solid source. The experimental approach allows the study of the microscopic parameters regulating the interaction between P and the already formed and stable NCs; at the same time, we investigated the diffusion of P in SiO2 matrices shedding light on the atomistic mechanism of P diffusion in SiO2. The model parameters were assessed by fitting of P diffusion profiles, measured by time of flight secondary ion mass spectrometry and calibrated by channeling Rutherford backscattering spectrometry. Transmission electron microscopy data provided the NC geometrical parameters. Simulations allowed quantitative description of the emission process of P by the source, the evolution of P diffusivity in the oxide, and P trapping/de-trapping at the SiO2/Si NCs interface, extracting the associated thermal energy barriers, providing a decisive description of the system very close to the equilibrium. This fundamental approach on a well-assessed template system provided valuable insights into the nanoscale doping processes, applicable in principle to investigate nanostructures other than Si.