Boron diffusion mechanism and effect of interface Ge atoms in Si/SiO$_{2}$ and SiGe/SiO$_{2}$ interfaces

In metal-oxide-semiconductor field effect transistors (MOSFETs) it is known that implanted B dopants easily segregate to the oxide during thermal annealing after ion implantation, causing threshold voltage shift and sheet resistance increase. On the other hand, SiGe alloys have been considered as a promising material for $p$-type MOSFETs due to reduced B diffusion and high hole mobility. However, there is a lack of studies for B diffusion in Si/SiO$_{2}$ and SiGe/SiO$_{2}$ interfaces. In this work, we perform first-principles density functional calculations to study the mechanism for the B diffusion in Si/SiO$_{2}$ and SiGe/SiO$_{2}$ interfaces. We investigate the diffusion pathways and migration barriers by using the climbing nudged elastic band and dimer methods. For Si/SiO$_{2}$ interface, B in Si turns into an interstitial B and tends to intervene between the Si and bridge O atoms at the interface. The overall migration barrier is calculated to be about 2 eV, comparable to that in bulk SiO$_{2}$. In SiGe/SiO$_{2}$, interface Ge atoms enhance the stability of B-related defects in the interface region, resulting in the higher migration barrier of about 3.7 eV. Our results indicate that Si/SiO$_{2}$ interface does not hinder the B diffusion, however, the B diffusion is suppressed in the presence of interface Ge atoms.