Positron annihilation and the charge states of the phosphorus-vacancy pair in silicon

After electron irradiation two positron lifetimes 250+or-1 and 268+or-3 ps, are observed in phosphorus-doped Si ((P)=3*10¹⁶ cm ^-3) depending on the temperature and the electron fluence. The lifetimes are assigned to the negative and neutral charge states of the phosphorus-vacancy pair (P-V). The longer lifetime at the neutral charge state indicates a larger open volume of the vacancy and implies an outward relaxation of the phosphorus-vacancy pair in the charge-state transition (P-V)^- to (P-V)⁰. A comparison with the theoretical lifetimes yields a breathing-mode relaxation of the nearest-neighbour atoms Delta r/r₀ approximately 5.1% (r₀ is the Si-Si bond length), or Delta r approximately 0.12 AA. The positron trapping coefficients 2*10 ¹⁶ s^-1 at 20 K and 2*10¹⁵ s^-1 at room temperature at the negatively charged state (P-V)^- are estimated. A weakly bound Rydberg-like precursor state is invoked to explain the temperature dependence of positron trapping at the negatively charge centres (P-V)^- and V^- in Si. The binding energy at the precursor state is 15-30 meV.