The Ohio State University  |   Department of Physics

Extended silicon interstitial defects and their order of stability

Clustering of point defects in silicon leads to the formation of extended defects during annealing process following ion-implantation or high-energy electron irradiation.  Transmission electron microscopy (TEM) reveals three distinct stable extended defects whose nucleation, evolution, and stability still challenge us: {311} and {111} rod-like defects, and Frank dislocation loops.

The core atomic configurations of extended interstitial defects in the (011) bi-layer plane, cross-sectional views of defects. The in/out of page is parallel to the elongation direction for both rod-like defects and Frank loops in Fig. 1.  The dark atoms represent interstitial-chains running in/out of page: 4 interstitial-chains are depicted in (a) and (b), 8 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/out of page. (a) The {311} rod-like defect is a combination of interstitial-chains and eight-member rings O. (b) The {111} rod-like 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.

 

 

Relative stability of extended defects with respect to the number of infinitely long interstitial-chains enclosed.  Each data point was obtained by the full first-priciple relaxation of 3000-atom supercells.  {311} rod-like 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.

 

 

Large-scale first-principle relaxations

Defect 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 first-priciple calculations reduce the finite-size error due to the long-range strain field.  This graph demonstrates that even defects with a small number of interstitial-chains (one or two) produce quite a long-rage 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 rod-like defects to Frank dislocation loops

In 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, rod-like {311} defects are intitially favored.  If the temperature is high enough to thermally activate the transformation, rod-like defects can evolve into Frank loos that are more stable and compact for large number of interstitials.

 

  • The dimer-rotation on (011) planes is the key mechanism of the transformation from {311} to the Frank loop.
  • The number of dimer-rotations needed for the full transformation is the same as the number of the interstitial atoms.
  • The average reaction barrier of the rotation is about 1.7 eV (GGA-PW91), but expected to be lower for inner defected layers.
  • The transformation is not rigid, bur more-or-less layer-by-layer.
  • The inter-layer correlation exists, but not so strong (need further study: correlation length, temperature dependence, etc.).

 

Silicon interstitials : from point to extended defects

  • Molecular dynamic simulations : OHMMS + RTMRA with silicon MEAM potential.
  • RTMRA technique enables us to study detailed dynamics (diffusion, transition, growth, etc) of silicon-intersitial clusters even at temperatures (700 - 1200 K) without costly relaxations.
  • From point to extended defects, multiple path ways have been identified.