  We study the structure, the formation and binding energies and the transfer
levels of the zinc-phosphorus vacancy complex [Zn_In - V_P] in Zn doped p-type
InP, as a function of the charge, using plane wave ab initio DFT-LDA
calculations in a 64 atom supercell. We find a binding energy of 0.39 eV for
the complex, which is neutral in p-type material, the 0/-1 transfer level lying
0.50 eV above the valence band edge, all in agreement with recent positron
annihilation experiments. This indicates that, whilst the formation of
phosphorus vacancies (V_P) may be involved in carrier compensation in heavily
Zn doped material, the formation of Zn-vacancy complexes is not.
  Regarding the structure: for charge states Q=+6 to -4 the Zn atom is in an
sp^2 bonded DX position and electrons added/removed go to/come from the
remaining dangling bonds on the triangle of In atoms. This reduces the
effective vacancy volume monatonically as electrons are added to the complex,
also in agreement with experiment. The reduction occurs through a combination
of increased In-In bonding and increased Zn-In electrostatic attraction. In
addition, for certain charge states we find complex Jahn-Teller behaviour in
which up to three different structures, (with the In triangle dimerised,
antidimerised or symmetric) are stable and are close to degenerate. We are able
to predict and successfully explain the structural behaviour of this complex
using a simple tight binding model.
