(Invited) Application of DFT Calculation for the Development of High Quality Si and Ge Substrates: From Ultra Large Diameter Crystal Pulling to Metal Gettering

Abstract

During the last decade, considerable progress has been made in understanding the properties and behavior of the vacancy V and self-interstitial I in silicon (Si) and germanium (Ge) crystals. This is to a large extent due to the maturing of density functional theory (DFT) calculation techniques and the increase of computing power enabling to calculate not only the formation and migration energies of V and I, but also the interaction with impurities and with crystal surfaces. Furthermore, the impact of internal and external stress on formation and migration enthalpies of both intrinsic point defects has been clarified recently. In this paper an overview will be given of recent results obtained by the author’s group calculating the interaction of V and I with the melt-solid interface, and the impacts of stress and doping on V and I properties. The useful application of DFT calculations for research and process development on the control and engineering of intrinsic point defects in Si and Ge single crystal growth from a melt are presented in focusing on (i) the difference of the dominant point defect in Si and Ge, (ii) the impact of thermal stress on intrinsic point defects in large-diameter Si crystal and (iii) the dopant impact on intrinsic point defects in Si. The results indicate that DFT calculation will be a necessary tool for the cost-effective development of the advanced crystal growth processes that will be needed for the new family of 450 mm diameter Si crystals or for V-poor, large diameter Ge crystals [1]. Besides the crystal growth, DFT calculations are also useful to for the development of “impurity gettering” technology in large-diameter Si wafers. Very recently, a C3H5 cluster ion implantation technique for proximity gettering has been reported with the low energy of around 1015/cm2 dose without recovery heat treatments. The main feature of this technique is that the gettering efficiency is higher than that by C monomer implantation, even though irradiation defects are too small to clarify by TEM observation. In the present work, we evaluate the binding energies of metal atoms with candidate gettering sites of C, H, intrinsic point defects and related complexes in Si wafers induced by C3H5 cluster ion implantation or different methods, for example, H implantation etc. by using DFT calculations. In addition to C and H atoms, we consider donor P and O atoms contained in an n- CZ-Si wafer for use in a CMOS image sensor. The simplest complexes of substitutional/interstitial C (Cs/Ci), Hi, Ps, Oi, and incorporated intrinsic point defects (vacancy (V) and self-interstitial Si (I)) by C3H5 implantation were also considered. We found that Cs-I (= Ci), Ci-Ci, Hi-I, VHn (n =1 to 3), and VO complexes are the best candidates for gettering sites. Gettering by C3H5 cluster ion implantation is more effective than that by C monomer implantation due to the formation of VHn (n = 1–3) and Hi-I complexes, which provides more effective gettering sites [2]. An approach based on statistical thermodynamics and DFT calculations to predict properties of materials composed of different types of atoms is presented. The key point of the “Hakoniwa” method is to take into account all possible structural supercells constructed by the fixed number of atoms of each species according to the composition of the target material [3]. The conservation of the total number of atoms enables calculating the average value of a material property for a given temperature by applying statistical thermodynamics to the material property values obtained for each of the possible supercells. The applications of the Hakoniwa method to the crystal growth and metal gettering are mentioned.