The Ohio State
University 
Department of
Physics



Extended silicon interstitial defects and their order of stabilityClustering of point defects in silicon leads to the formation of extended defects during annealing process following ionimplantation or highenergy electron irradiation. Transmission electron microscopy (TEM) reveals three distinct stable extended defects whose nucleation, evolution, and stability still challenge us: {311} and {111} rodlike defects, and Frank dislocation loops. The core atomic configurations of extended interstitial defects in the (011) bilayer plane, crosssectional views of defects. The in/out of page is parallel to the elongation direction for both rodlike defects and Frank loops in Fig. 1. The dark atoms represent interstitialchains running in/out of page: 4 interstitialchains are depicted in (a) and (b), 8 chains in (c). Endunits E form boundaries between defects and bulk Si; the separation between E's determines the width of the defect. In each figure, structures are oriented so that the habit plane horizontally closes two endunits and interstitialchains, and extends in/out of page. (a) The {311} rodlike defect is a combination of interstitialchains and eightmember rings O. (b) The {111} rodlike defect is a regular sequence of double five and single eightmember rings. (c) The Frank loop connects interstitialchains to form a stacking fault bounded by a dislocation line, i.e., endunits E's.

Relative stability of extended defects with respect to the number of infinitely long interstitialchains enclosed. Each data point was obtained by the full firstpriciple relaxation of 3000atom supercells. {311} rodlike defects are the most stable structures for a small number of interstitial clusters. As the number of interstitial increases the order of stability changes. The ever decreasing trend eventually makes Frank loops become the most stable ones, with the asymptotic value 0.03 eV. The formation energies with an infinite number of interstitialchains are from the calculations with infinite planar models, i.e., periodically repeating structures in both width and length directions.


Largescale firstprinciple relaxationsDefect calculations must use large supercells, so the images generated by periodic boundary conditions do not invalidate results for real defects. We use supercells with more than 3000 atoms. These unprecedented large supercells used in our firstpriciple calculations reduce the finitesize error due to the longrange strain field. This graph demonstrates that even defects with a small number of interstitialchains (one or two) produce quite a longrage field, and the converged formation energy per interstitial to 0.01 eV can only be obtained when supercells with more than 1000 atoms.


Thermal transformation of rodlike defects to Frank dislocation loopsIn an irradiated sample, interstitials aggregate to form small compact clusters first, and during subsequent annealing they grow into larger extended defects. Our calculations show that for extended defects, rodlike {311} defects are intitially favored. If the temperature is high enough to thermally activate the transformation, rodlike defects can evolve into Frank loos that are more stable and compact for large number of interstitials.


Silicon interstitials : from point to extended defects
