Density Functional Theory Study on Frenkel Pair Formation from Oxygen Clusters in Si Crystal
Authors: Fukuda Hiroaki , Sueoka Koji 
Published: February 2020

Silicon (Si) wafers, which are the most widely used semiconductors for integrated circuit fabrication, are produced by polishing after slicing Czochralski (CZ) grown Si ingots. Oxygen (O) atoms with a concentration of 1×1018 atom/cm3 are incorporated from the melt of Si charged in the SiO2 crucible during crystal growth. Most of the O atoms in Si crystals exist as interstitials (Oi) at the center of Si - Si bonds, which are detected with the Fourier transform infrared (FTIR) method. As the solubility of O atoms in Si crystals is about 4.4×1016 atom/cm3 at 800°C, the typical temperature at which integrated circuits are fabricated, the oxygen in as-grown CZ Si crystals is usually supersaturated. Therefore, the Oi atoms precipitate in the subsequent heat treatments and grow into oxide precipitates (SiO2). It is well known that self-interstitial (I) atoms are emitted from growing oxide clusters to relieve the compressive lattice strain. Since these emitted atoms interact with dopant atoms, impurities, lattice defects, etc., and affect the performance of Si wafers, the mechanism of emission from Oi clusters should be clarified and taken into consideration in the computer simulation of oxygen precipitation. In this study, we analyzed the Frenkel (self-interstitial I and vacancy V) pair formation from oxygen clusters in Si crystal by density functional theory (DFT) study.
The program package used in this study was CASTEP code. The ground state of the system in this method was found by solving the Kohn-Sham equation, which is a rule equation of electronic systems for given atom placement. The wave function was expanded as plane waves, and the ultrasoft pseudopotential was used to reduce the plane wave number. A Si 64-atom cubic cell, a 2 × 2 × 2 supercell constructed with a conventional cell, was used in this study. The cell was surrounded by (100), (010), and (001) planes, and each edge of the cell was along the [100], [010], and [001] directions. Three-dimensional periodic boundary conditions were set for each calculation. The cutoff energy for the plane-wave expansion was 340 eV. Generalized gradient approximation (GGA) was used for the exchange-correlation term, and the functional form was of the Perdew-Burke-Ernzerhof (PBE) type. The density mixing method was used to minimize the energy of the electronic system, and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimizing structure method was run to optimize atom placement. The 2 × 2 × 2 points were used for k sampling. The binding energies of up to five Oi atoms in Si crystal were calculated. In addition, the formation energy of the Frenkel (I and V) pair was calculated in a perfect cells and Oi cluster involving cells.
For the cluster including two Oi atoms, the O2 dimer of Si-Oi-Si-Oi-Si has the lowest binding energy of about 0.45 eV. The binding energy depends not only on the distance between two Oi atoms but also their atomic configuration. From n = 2 to 6, the binding energies of an Oi and On-1 cluster increase with increasing Oi number n. The calculated formation energies of the Frenkel pair from Oi clusters are about 2.30 eV (O2), 1.83 eV (O3), 1.17 eV (O4), 1.48 eV (O5), and 1.56 eV (O6). The formation energy of the Frenkel pair in perfect Si is about 4.87 eV. This result indicates that the formation of I becomes easier by the accumulation of Oi atoms in Si. The formation of Frenkel pairs around dopant atoms is ongoing.