Development of periodical spatial distribution of donor states in heat-treated silicon

It is considered kinetics of oxygen thermo-donor states formation in silicon when atomically dissolved oxygen reacts to form a sequence of kinetically linked aggregates (complexes). One takes into account oxygen diffusion and elastic interaction between oxygen atoms. We obtain analytic homogeneous solution of the corresponding non-linear kinetic equations and examine its stability. It is shown that due to the interaction of oxygen atoms the homogeneous state becomes unstable at some crystal temperature domain if oxygen concentration larger than certain threshold value. Spatial periodical distribution of oxygen atoms and their complexes develops. Due to anisotropy of interaction the zones enriched by oxygen form the periodical situated planes which are perpendicular some determined direction in crystal. Period of the spatial periodical distribution unmonotonously changes in range from 10 to 1000 Angstrom with the parameter variation.