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Density functional theory study on the impact of heavy doping on Si intrinsic point defect properties and implications for single crystal growth from a melt
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Density functional theory (DFT) calculations are performed to obtain the formation energies of the vacancy V and the self-interstitial I at all sites within a sphere around the dopant atom with 6 Å radius for V and 5 Å radius for I in Si crystals. Substitutional p-type (B and Ga), neutral (C, Ge, and Sn), and n-type (P, As, Sb, and Bi) dopants were considered. The results show that the formation energies of V and I around dopant atoms change depending on the types and sizes of the dopants, i.e., depending on the electrical state and the local strain around the dopants. The dependence of the total thermal equilibrium concentrations of point defects (sum of free V or I and V or I around the dopants) at melting temperature on the type and concentration of each dopant is obtained. Further DFT calculations reveal that most of the total incorporated point defects from the melt contribute to pair recombination. An appropriate model of point defect behavior in heavily doped single crystal Si growing from a melt is proposed on the basis of DFT calculations. (1) The incorporated total V and I concentrations at melting point depend on the types and concentrations of dopants. (2) Most of the total V and I concentrations during Si crystal growth contribute to the pair recombination at temperatures much higher than those to form grown-in defects. The Voronkov model successfully explains all reported experimental results on intrinsic point defect behavior dependence on dopant type and concentration for heavily doped Si while taking the present model into consideration.
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