Dopant levels in large nanocrystals using stochastic optimally tuned range-separated hybrid density functional theory

We apply a stochastic version of an optimally tuned range-separated hybrid functional to provide insight on the electronic properties of P- and B-doped Si nanocrystals of experimentally relevant sizes. We show that we can use the range-separation parameter for undoped systems to calculate accurate results for dopant activation energies. We apply this strategy for tuning functionals to study doped nanocrystals up to 2.5 nm in diameter at the hybrid functional level. In this confinement regime, the P and B dopants have large activation energies and have strongly localized states that lie deep within the energy gaps. Structural relaxation plays a greater role for B-substituted dopants and contributes to the increase in activation energy when the B dopant is near the nanocrystal surface.