Self-Interstitial clusters in silicon
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Self-Interstitial clusters in silicon. M. M. De Souza, M. P. Chichkine and E. M. Sankara Narayanan. Emerging Technologies Research Centre, De Montfort University, Leicester, United Kingdom LE1 9BH.
ABSTRACT In this paper we propose structural models of self-interstitial clusters in silicon using the empirical potential method. Novel, fully co-ordinated compact clusters based on the hexagonal interstitial up to size four have been proposed. The energetics of their formation indicates that energy minimisation occurs due to elimination of dangling bonds. While the conventional dangling bond model yields an exponential decrease in the formation energy with size, we observe stable defects for sizes in multiples of four. The energy barrier required for a transition from compact model to the dangling bond chain model can possibly explain the experimentally observed energy barrier for sizes greater than eight. Introduction: There exists a considerable interest in the understanding of {113} defects generated by ion implanted / irradiated samples in silicon. This is because the accuracy of modelling tools necessary for the development of future ULSI circuits demands atomic level details of the kinetics of formation and annealing of these defects. Over the years a considerable amount of knowledge from experimental and theoretical modelling has become available [1-3]. However, the link between the precursors and the mechanism of their conversion into the conventional III, IO and IIO type rings present in {311} defects is yet to be clearly understood [4]. In this paper, we investigate structures for clusters of point defects in silicon using the Ackland potential [5]. This potential has the unique property of maintaining 4-fold co-ordinated structures and therefore is ideally suited for the study of clusters in silicon. This fact also causes an inability of the potential to reproduce a low formation energy for the split interstitial [6,7]. However, the main advantage of an “empirical” description is to provide a rapid and less computationally intensive method to investigate various structures, which can further be confirmed by more accurate techniques. Calculational details: The total energy in the Ackland potential can be expressed as
(
)
3 4 1 1 N N 1 N 4 −αrij − βrik E = ∑∑ Ae − ∑∑ Brik e + ∑∑ ∑ C cos ωRkmkn + 3 2 i =1 j =1 2 i =1 k =1 i n =1 m =n +1
2
The first term represents the repulsive pairwise interaction, which each ion has with every other ion. The second term represents the sum over all valence electrons of the bond energy, with each ion bonded to 4 neighbours. The last term is essential to stabilise reconstructed defect formation energies. The form of this term is set such that the minimum of the energy should occur for the tetrahedral bond angle for the diamond structure in silicon. The C value can be changed to yield different quantitative values of formation energy. Furthermore, the C value also controls the energy cost of introducing dangling bonds
B11.3.1
within structures i.e. dangling bonds
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