Fraction of positronium formation at semiconductor surface

The fraction of positronium formation (f(ps)) has been calculated in Ge(110), Ge(111), Si(110) and Si(111) surfaces by solving the diffusion equation for positrons in semiconductors and by setting up the rate equation to describe the processes that are supposed to occur when a thermalised positron encounters the surface including the trapping of positrons in neutral and negative vacancies. Certain parameters used in the evaluation of f(ps), e.g., the bulk annihilation rate (lambda(s)), the positron diffusion length (L+), the diffusion coefficient (D+) and the implantation profile parameter (A), have Lees taken from the experiments. The calculated values of f(ps) as a function of incident positron energy and temperature in Ge(110) and Si(111) have been compared with the experimental results. it has been found that in general the calculated results are in good agreement with the experimental ones. The calculation also confirms that the trapping rate of positrons into negative vacancy has a T-1/2 dependence with respect to the temperature.