Strain-induced transformation of amorphous spherical precipitates into platelets: Application to oxide particles in silicon

Abstract

The spherical shape of an amorphous precipitate becomes unstable if the combination P2R of precipitate radius R and pressure P exceeds some critical value. This critical value was found to be about 4.44 Gσ, where G is the matrix shear modulus and σ is the specific energy of the precipitate/matrix interface. Once this instability criterion is fulfilled, the initially spherical particle will reduce the total free energy (the sum of strain energy and the surface energy) by becoming a thin oblate spheroid (effectively, a platelet). The actual pressure P in the course of oxygen precipitation in silicon is controlled by a high self-interstitial supersaturation caused by emission of self-interstitials by growing precipitates. The duration of annealing necessary to reach the stage of collapse of spheres into platelets is calculated as a function of temperature and the precipitate density. Calculated results are compatible with the experimentally observed annealing conditions for platelet formation. Another important example of sphere to platelet transformation is microdefect formation in vacancy-type silicon. In this case a large negative value of P is sufficient to induce collapse.