General Model of Diffusion of Interstitial Oxygen in Silicon and Germanium Crystals
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General Model of Diffusion of Interstitial Oxygen in Silicon and Germanium Crystals Vasilii Gusakov Institute of Solid State and Semiconductor Physics, P. Brovka str. 17, Minsk, 220072, Belarus. ABSTRACT A theoretical modeling of the oxygen diffusivity in silicon and germanium crystals both at normal and high hydrostatic pressure has been carried out using molecular mechanics, semiempirical and ab-initio methods. It was established that the diffusion process of an interstitial oxygen atom (Oi) is controlled by the optimum configuration of three silicon (germanium) atoms nearest to Oi. The calculated values of the activation energy ∆Ea (Si) = 2.59 eV, ∆Ea (Ge) = 2.05 eV and pre-exponential factor D0 (Si) = 0.28 cm2 s-1, D0 (Ge) = 0.39 cm2 s-1 are in a good agreement with experimental ones and for the first time describe perfectly an experimental temperature dependence of the Oi diffusion constant in Si crystals (T=350 1200°C). Hydrostatic pressure ( P ≤ 80 kbar ) results in a linear decrease of the diffusion barrier ( ∂ P ∆Ea ( P ) = -4.38 10-3 eV kbar-1 for Si crystals). The calculated pressure dependence of Oi diffusivity in silicon crystals agrees well with the pressure-enhanced initial growth of oxygenrelated thermal donors. INTRODUCTION It is common knowledge that the diffusion of interstitial oxygen atoms in silicon crystals is of crucial importance in the processes of oxygen agglomeration (formation of thermal donors) and in the gettering of metallic impurities in industrial processing of silicon and, as a result, the experimental measurements of the diffusivity of oxygen in silicon have received much attention. As pointed out by Mikkelsen [1] most experimental data can be consistently fit over a wide temperature range (350 – 1200 oC) by a single expression of the form D=0.13exp (-2.53 eV/kBT) cm2 s-1. The expression has been obtained by fitting to data from six independent experiments. This expression is generally believed to be the intrinsic diffusion constant involving oxygen jumping from a bond-center to one of the six nearest bond-center cites. Several theoretical efforts have attempted to calculate the diffusion parameters, but different results were obtained. Thus the calculated values of the barrier is ranging from 1.2 eV [2], 2.0 eV [3] up to 2.3 eV [4, 5], 2.5 eV [6]. All these calculations (except [7]) assume the saddle point configuration for diffusion in a (110) plane and the midway between the two bond-center sites. The remaining degrees of freedom and the position of the other Si atoms were determined by total-energy minimization. The resulting total energy, measured from the energy of the equilibrium configuration, results the adiabatic activation energy for diffusion. Using empirical interatomic potentials Jiang and Brown [7] have concluded that the saddle point of Oi migration is past the midpoint, but their conclusion is open to question [8]. Moreover Ramamoorthy and Pantelides [8] have offered that a seemingly simple oxygen jump is actually a complex process which can be properly d
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