A method for quantifying annihilation rates of bulk point defects at surfaces

Point defects such as vacancies and interstitial atoms serve as primary mediators of solid-state diffusion in many materials. In some cases, the defects encounter surfaces where annihilation can occur. Quantification of annihilation rates presents formidable challenges, since point defect concentrations are typically low and therefore difficult to monitor directly. The present work develops a method for such quantification based upon measurements of diffusional profile spreading of a foreign species, using as an example isotopically labeled silicon implanted into a silicon matrix. Optimal experimental design techniques together with maximum-likelihood estimation indicate that the loss probability for Si interstitials on nitrogen-covered Si(100) lies at 7.1× 10-4.