Formation energy of intrinsic point defects in nanometer-thick Si and Ge foils and implications for Ge crystal growth from a melt



Formation energies of vacancies and self-interstitials in nanometer-thick Si and Ge foils are calculated by means of Density Functional Theory applying thin film models. Plate models consisting of six to sixteen atomic layers with c(4×2) dimer structures on both surfaces with a vacuum slab are used. The formation energies Ef of the intrinsic point defects of Si and Ge in the middle of the foil and obtained from the twelve layer models, are in good agreement with reported values for bulk material. In all cases, Ef in the middle of the foil decreases with decreasing foil thickness. Using the same twelve or more layers thin plate models for Si and Ge thus also allows comparing the formation energies of intrinsic point defects in the bulk. The thermal equilibrium concentration of Ge self-interstitials near melt temperature is more than one order of magnitude lower than that of Si self-interstitials while the vacancy concentrations are of same order of magnitude. Contrary to Si, the diffusivity of Ge self-interstitials can therefore not recover the unbalance of the thermal equilibrium concentrations during crystal growth, even if the growth rate is reduced to very low values. This is the reason why Ge crystals grown from a melt are always vacancy-rich which results in void formation in-dependent of the crystal growth conditions. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)