We show that the Doppler broadening measurement of positron annihilation radiation can be used to identify vacancies in semiconductors. Annihilation of the trapped positron with surrounding core electrons reveals chemical information that becomes visible when the experimental background is reduced by the coincidence technique. The utility of the method is demonstrated by several examples, especially in InP based compounds. In electron irradiated InP we show that the sublattice of the vacancy can be identified by the magnitude of the core annihilation spectrum. The atomic structure of the DX center is studied in Al x Ga 0 . 5 1 - x In 0 . 4 9 P (x = 0.36) overlayers. Due to the low magnitude of the measured core annihilation spectrum, we infer that the DX center consists of a vacancy in the group-III sublattice. As an example of a vacancy-impurity pair, we demonstrate that the native vacancy defects in heavily Zn-doped InP can be identified as P vacancies decorated by Zn atoms.