Development of a ReaxFF Reactive Force Field for Interstitial Oxygen in Germanium and Its Application to GeO2/Ge Interfaces
Evidence and attribution¶
Authority of statements
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Summary¶
A Ge/O/H ReaxFF is extended from prior work with additional QM training on O interstitial energies and migration in diamond Ge and on bulk GeO/GeO2 condensed-phase data. The refined FF reproduces equations of state and heats of formation and ranks O-interstitial sites (bond-centered, split, tetrahedral, hexagonal) consistently with DFT. Oxygen diffusion between bond-centered sites and through the split-like transition state matches the intended DFT picture; ReaxFF predicts an effective barrier near 50 kcal/mol over 800–2000 K. GeO2/Ge interface oxidation simulations show oxide thickening and Ge consumption with temperature and time, unlike Tersoff-based runs that miss this behavior.
Methods¶
2 — Force-field training. A Ge/O/H ReaxFF (“ReaxFF\(_\text{present}\)” in the article) is refit against the Zheng et al. GeO/GeO₂ condensed-phase training set plus interstitial O in diamond Ge, including formation energies and the DFT BC→BC migration pathway through the split-type saddle (PBE-class DFT as cited in J. Phys. Chem. C). After reoptimization, the model reproduces condensed GeO/GeO₂ energetics and the O-interstitial stability sequence BC → split → tetrahedral → hexagonal with near-DFT energy splittings (Table 1 in the paper).
1 — MD application. Engine / code: ReaxFF-based trajectories are run with ADF/ReaxFF; the parallel Tersoff study uses LAMMPS (the article states both explicitly). 3D PBC are used, with an unwrapped-coordinate post-processing path for diffusion. System / composition: O-interstitial diffusion in diamond-structure Ge uses periodic supercells with hundreds to thousands of host Ge atoms (exact supercell multiplicity and O placement in J. Phys. Chem. C Methods / Figs.). O diffusion in bulk Ge (800–2000 K, both force fields compared): two-stage NVT with Berendsen thermostat; stage 1 — coupling 100 fs, 0.01 K/step heating to the target T, 1 ns equilibration; stage 2 — 3.5 ns at fixed T with weaker coupling 1000 fs and unwrapped-trajectory sampling (every 100 MD frames) for the diffusion analysis. a-GeO₂ glass preparation (as used in the Ge/GeO₂ stack work) includes NPT at 300 K for 0.5 ns in the Methods. Time integration step in fs (integrator, not thermostat damping): not captured in the text pass used for this curation; N/A — use the J. Phys. Chem. C PDF for the exact femtosecond timestep (the text quotes 100 fs / 1000 fs damping constants for the thermostat). Barostat in the NVT diffusion stages: N/A (constant-volume NVT). For the quoted NPT glass-formation block, isotropic servocontrol is NPT at the conditions given in the paper. Mean external electric field on the cell: N/A. Umbrella / metadynamics: N/A — conventional sampling.
3 — Static DFT in Methods: DFT supports the ReaxFF training; N/A as a standalone “DFT-only paper” — the MD + Tersoff comparisons are central.
Findings¶
1 — Outcomes and mechanisms. ReaxFF\(_\text{present}\) recovers the O-interstitial ordering and a DFT-consistent hopping topology (BC–BC via a split-like saddle). MD between 800 K and 2000 K yields a reported effective O-diffusion barrier of ~50.02 kcal mol⁻¹ in the abstract/Results text. 2 — Comparisons. For T ≳ 1400 K along the O-hopping path, ReaxFF follows the intended route, while Tersoff-based trajectories visit H-site-flavored jumps that disagree with the cited DFT picture. For Ge/GeO₂ interface heating, ReaxFF (but not the Tersoff comparison the authors highlight) shows time- and temperature-dependent GeO₂ thickening and Ge consumption, qualitatively consistent with the cited experiments, whereas the Tersoff parallel shows nearly static film thicknesses in the same side-by-side comparison. 3 — Sensitivity and levers. Temperature and oxidation time are the main knobs; 4 — Outlook / authored limits — see ## Limitations and the J. Phys. Chem. C discussion for transferability caveats (empirical potentials, prepared interface geometry).
Limitations¶
Still an empirical reactive model—quantitative barriers and rates need continued benchmarking across defect configurations. Interface studies are specific to the prepared initial geometries and thermal protocol.
Relevance to group¶
Core group contribution on semiconductor oxidation and defect diffusion with ReaxFF, relevant to Ge CMOS dielectric stacks.
Citations and evidence anchors¶
- Local PDF:
papers/Nayir_JPC_C_GeOx_2019.pdf - DOI: https://doi.org/10.1021/acs.jpcc.8b08862