Identification of charge states of indium vacancies in InP using the positron-electron auto-correlation function

The positron-electron auto-correlation function (ACF) is calculated for neutral and negatively charged indium vacancies in InP as well as a perfect InP material. Ab initio calculations are performed for the electron wave functions in the density functional theory (DET) with the local density approximation (LDA) for the exchange-correlation potential of electrons. The positron wave function is calculated by directly diagonalizing the single-particle Hamiltonian of the positron in the LDA with a density-gradient correction. It is found that the ACF is suitable for identifying the charge states of the indium vacancies. Neutral indium vacancies greatly diminish the nearest peaks and dips (P1 and D1) of the ACF which are located after the nearest-neighbouring lattice points in the case of a perfect material. Negatively charged indium vacancies nearly eliminate these peaks and dips, together with the next-nearest peaks (P2) located at the next-nearest-neighbouring lattice points. Therefore, the diminution of the P1 and D1 can be taken as an indication of the formation of neutral indium vacancies, and that of the P2 can be taken as an indication of the formation of negatively charged indium vacancies. However, the three negative charge states of the indium vacancies (V-In(1-), V-In(2-) and V-In(3-)) are still difficult to distinguish from each other by means of the ACF method.