Ostwald ripening of end-of-range defects in silicon

Abstract

End-of-range (EOR) defects are interstitial type dislocation loops which nucleate just beneath the crystalline/amorphous (c/a) interface formed by ion implantation in Si, after the preamorphization of the substrate, and during the ramping-up of the anneal. They originate from the presence of a high supersaturation of “excess” Si self-interstitial atoms located just beneath the c/a interface. Upon annealing, the mean radius of the defects increases while their density decreases through the exchange of Si self-interstitial atoms between the loops. The number of interstitials stored in the loops stays constant. For sufficiently high thermal budgets, when the nucleation is finished, and when the local equilibrium between extended and point defects is established, the coarsening of the EOR defects can be modeled through the Ostwald ripening theory applied to the dislocation loops geometry. Indeed, and as expected from the theory, the square of the mean radius of the loop population increases with time while the loop density decreases proportional to 1/t. Furthermore, the theoretical function describing the size distributions perfectly matches the time evolution of the experimental stack histograms, for different annealing temperatures. During the asymptotic steady-state coarsening regime, the activation energy for the loop coarsening is 4.4 eV, which is in the range of values given in the literature for self-diffusion in Si. Nevertheless, an activation energy of about 1–2 eV is found during the transient period preceding the local equilibrium, i.e., in the range of the migration energy of self-interstitials. The limiting phenomenon for the loop growth appears to be diffusion, since it is the hypothesis that leads to the best fit between theory and experiment. An estimate of DiCi* has been derived from the growth laws of the EOR defects. A value of about 1.8×107 cm−1 s−1 at 1000 °C is obtained and compares well with the values given in the literature.