Trap-limited hydrogen diffusion in boron-doped silicon

The hydrogen diffusion process in boron-doped silicon for temperatures T in the range from 60 °C to 140 °C is entirely trap limited and shows no dependence on the diffusivity of the free hydrogen. The effective hydrogen diffusion coefficient ${\mathit{D}}_{\mathrm{eff}}$ is determined at two values of the boron concentration ${\mathit{N}}_{\mathit{A}}$=1.4×${10}^{15}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and ${\mathit{N}}_{\mathit{A}}$=3.8×${10}^{16}$ ${\mathrm{cm}}^{\mathrm{-}3}$. The values of ${\mathit{D}}_{\mathrm{eff}}$ satisfy the Arrhenius equation ${\mathit{N}}_{\mathit{A}}$ ${\mathit{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}=\mathit{P}0}$exp(-${\mathit{E}}_{\mathit{p}}$/kT) with ${\mathit{E}}_{\mathit{P}}$=1.28 eV and ${\mathit{P}}_0$=1×${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}1}$ ${\mathrm{s}}^{\mathrm{-}1}$. We present a model which predicts that ${\mathit{N}}_{\mathit{A}}$ ${\mathit{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}=}$ν/(4πR), where ν is the dissociation frequency of the BH complex and R≃3.5 nm the collision radius which describes the trapping of H at the boron atom.