Abstract
A method is described to estimate the temperature dependent interaction between two uncharged point defects in Si based on DFT calculations. As an illustration, the formation of the uncharged di-vacancy V2 is discussed, based on the temperature dependent attractive field between both vacancies. For that purpose, all irreducible configurations of two uncharged vacancies are determined, each with their weight given by the number of equivalent configurations. Using a standard 216-atoms supercell, nineteen irreducible configurations of two vacancies are obtained. The binding energies of all these configurations are calculated. Each vacancy is surrounded by several attractive sites for another vacancy. The obtained temperature dependent of total volume of these attractive sites has a radius that is closely related with the capture radius for the formation of a di-vacancy that is used in continuum theory. The presented methodology can in principle also be applied to estimate the capture radius for pair formation of any type of point defects.
Highlights
Silicon crystals grown by the Czochralski technique can contain voids leading to so-called crystal originated pits (COP’s) on polished wafer surfaces
The obtained temperature dependent of total volume of these attractive sites has a radius that is closely related with the capture radius for the formation of a di-vacancy that is used in continuum theory
Point defect pair formation kinetics are described by rate equations, assuming a temperature independent capture radius.[6]
Summary
Silicon crystals grown by the Czochralski technique can contain voids leading to so-called crystal originated pits (COP’s) on polished wafer surfaces These voids that are observed in Czochralski-grown germanium crystals, are large vacancy clusters that are formed during cooling immediately after solidification.[1] COP’s have a detrimental impact on gate oxide integrity and can cause problems with epitaxial layer quality.[2,3,4] Besides intrinsic point defect pairs and clusters, a wide variety of impurity-intrinsic point defect pairs and clusters are known.[5] In continuum theory, point defect pair formation kinetics are described by rate equations, assuming a temperature independent capture radius.[6] The capture radius that is used in these rate equations, is mostly chosen arbitrarily in order to have a good agreement with experimental results. Isotropic diffusion is mostly assumed in the theory of diffusion-limited reactions of reacting point defects in a solid,[6] while in real crystals the point defect diffusivity depends on the crystallographic directions
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