Development of a ReaxFF Reactive Force Field for Interstitial Oxygen in Germanium and Its Application to GeO ₂ /Ge Interfaces

We developed the ReaxFF force field parameters for Ge/O/H interactions, specifically targeted for the applications of Ge/GeO ₂ interfaces and O-diffusion in bulk Ge. The original training set, taken from the Zheng et al. work, includes quantum mechanics (QM) data for equations of state and heats of formation of GeO and GeO ₂ condensed phases as well as dissociation energies for single and double bonds of Ge and angle distortion of O-Ge-O. We expanded this training set with the additional crystal data containing the formation energies of different O-interstitial centers and the minimum energy migration pathway of O atoms in diamond Ge. After refitting the force field parameters based upon the extended training set, the ReaxFF results show that the equations of state and heats of formation of the GeO and GeO ₂ condensed phases retain a good fit with the QM calculations. In addition, the ReaxFF correctly predicts the relative stability of the O-interstitial centers in the diamond Ge to be bond-center â†' split â†' tetrahedral â†' hexagonal from most stable to least stable with the energies showing a quantitative agreement with density functional theory (DFT). Furthermore, O atoms diffuse along a pathway between neighboring bond-centered (BC) interstitial sites and go through the asymmetric transition state at the split site as in DFT. We also examined the temperature dependence of O diffusion in bulk Ge and subjected the GeO ₂ /Ge interface to heat treatment based on the ReaxFF and Tersoff potential. Based on the results of molecular dynamics simulations, the ReaxFF accurately predicts the diffusion barrier value as 50.02 kcal/mol within the temperature range of 800-2000 K. At the temperatures over 1400 K, ReaxFF allows the O atom to diffuse along the theoretically reported pathway between the adjacent BC centers, whereas Tersoff potential contradicts the DFT reports by resulting in diffusion between the BC and H interstitial sites. For the Ge/GeO ₂ interface, the ReaxFF results show that the thickness of GeO ₂ increases and the Ge substrate is consumed depending on the temperature and the oxidation time, supported by the experiments, while no change was observed in the thicknesses of the Ge substrate and GeO ₂ slab in the Tersoff-based simulations.