Figure 1

Plan view, weak-beam, dark-field TEM images of different extrinsic extended defects in silicon: (a) {311} rodlike defects (Ref. 1) and (b) Frank loops (Ref. 2). {311} are habit planes for interstitials in most rodlike defects, but rodlike defects with {111} habit planes have also been observed. Rodlike defects extend in $⟨011⟩$. The Frank loop has a piece of faulted interstitial plane in {111} habit plane. The extra plane is bounded by a dislocation line, which appears as a bright elliptical line with the large axis parallel to $⟨011⟩$ in (b).Reuse & Permissions

Figure 2

The core atomic configurations of extended interstitial defects in the $\left(01\overline{1}\right)$ bilayer plane—cross-sectional views of defects. The in/out of paper is parallel to the elongation direction for both rodlike defects and Frank loops in Fig. 1. The dark atoms represent interstitial chains running in/out of paper: four interstitial chains are depicted in (a) and (b), eight chains in (c). End units $E$ 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 end units and interstitial chains, and extends in $\left[01\overline{1}\right]$ direction, in/out of paper. (a) The {311} rodlike defect is a combination of interstitial chains and eight-member rings $O$. (b) The {111} rodlike defect is a regular sequence of double five- and single eight-member rings. (c) The Frank loop connects interstitial chains to form a stacking fault bounded by a dislocation line, i.e., end units $E$’s.Reuse & Permissions

Figure 3

Relative stability of extended defects with respect to the number of infinitely long interstitial chains enclosed. {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 interstitial chains are from the calculations with infinite-planar models, i.e., periodically repeating structures in both width and length directions.Reuse & Permissions

Figure 4

Formation energy per interstitial (GGA-PW91) convergence with respect to the supercell size for infinitely long defects with a single interstitial chain and $EIIE$ {311}. Even for defects with a small number of chains, the converged $E_{\text{int}}^f$ to 0.01 eV can only be obtained when supercells with more than 1000 atoms are used due to the long-range strain field.Reuse & Permissions