Positron states in Si and GaAs

Positron states in perfect Si and GaAs lattices and at small vacancy-cluster-type defects in these semiconductors are calculated. The method is based on the superposition of free atoms and the solution of the resulting Schr\"odinger equation by a fully-three-dimensional numerical relaxational method. Positron lifetimes are calculated and compared with available experimental data. The main emphasis is put on the dependence of the positron lifetime on the size of the vacancy cluster and on the role of the lattice relaxation around vacancies.