Screening of positrons in semiconductors and insulators

Theoretical models are presented for the enhancement of the electron density at a positron in a semiconductor or insulator host. The model better suited for typical semiconductors is based on the many-body theory for the screening of a positron in electron gas. The starting point of the model for insulators is the atomic polarizability. The common parameter in both models is the high-frequency dielectric constant. Moreover, the enhancement depends on the ambient electron density in the semiconductor model and on the unit-cell volume in the insulator model. With use of the models developed, positron lifetimes in perfect semiconductor and insulator crystals have been calculated. In the calculations, three-dimensional electron densities and electrostatic potentials are obtained by atomic superposition and the fully three-dimensional positron wave functions are solved by a relaxation method. The calculated positron lifetimes agree with the experimental ones within a few picoseconds. Moreover, we have used the model to predict lifetimes of positrons trapped by lattice defects such as vacancies and vacancy clusters.