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Development of a ReaxFF reactive force field for interstitial oxygen in germanium and its application to GeO2/Ge interfaces

Corpus note

Maintainer catalog (SI/galley/proof PDF roles): https://github.com/asepehri93/vanDuinWiki/blob/main/docs/corpus/NON_PRIMARY_ARTICLE_PAPER_SLUGS.md PDF filename includes 2019; frontmatter year follows the corpus record. Confirm bibliographic year and DOI from the publisher PDF.

Summary

The authors extend a prior Ge/O/H ReaxFF training set (Zheng et al.) with DFT data for oxygen interstitial configurations, formation energies, and minimum-energy migration paths for O in diamond Ge, then refit ReaxFF. Applications include O diffusion in bulk Ge (temperature-dependent MD), comparison to Tersoff for GeO\(_2\)/Ge interface oxidation/thickness evolution, and validation of amorphous GeO\(_2\) structural properties.

The introduction motivates germanium as a CMOS candidate once high-κ gate stacks mitigate historical GeO\(_x\) quality limits; high-mobility Ge devices require reliable Ge/oxide interfaces, so atomistic control of oxygen interstitial sites and diffusion pathways is tied to process modeling. The article contrasts ReaxFF against Tersoff for Ge/GeO\(_2\) heat treatment to highlight where empirical two-body oxidation models miss DFT-consistent interstitial transport. Consult the peer-reviewed PDF and any Supporting Information for authoritative tables, figures, and numerical diagnostics behind the summaries above.

Methods

Force-field training (ReaxFF, Ge/O/H)

Parent parameters follow Zheng et al. for Ge/O/H, augmented with DFT training data for O-interstitial formation energies and minimum-energy migration pathways in diamond Ge. QM reference: VASP DFT with PAW potentials, GGA-PBE functional, 520 eV plane-wave cutoff, and k-point sampling as in Section 2 of the article (per indexed abstract). Optimization reoptimizes bonded and vdW terms until ReaxFF reproduces the added QM benchmark energies and barriers; reference data include GeO/GeO\(_2\) equations of state and heats of formation from the original training set plus the new interstitial set.

Static QM / NEB (training)

NEB/DFT pathways define the asymmetric split transition state between bond-centered O sites used to judge ReaxFF migration behavior against DFT.

MD application (bulk O diffusion and GeO\(_2\)/Ge interfaces)

  • Engine / code: LAMMPS molecular dynamics with ReaxFF and, for comparison, Tersoff as reported in J. Phys. Chem. C.
  • System size & composition: Bulk Ge supercells for O diffusion; quartz GeO\(_2\)/Ge(100) interface stacks and amorphous GeO\(_2\) validation cells—atom counts and dimensions in Methods/figures.
  • Boundaries / periodicity: PBC throughout the published setups.
  • Ensemble: NVT for the 800–2000 K diffusion and interface heat-treatment trajectories described in the abstract—confirm any NVE/NPT substeps in the full PDF.
  • Timestep: Femtosecond timestep per Section 2 (not re-listed here from the proof ingest alone).
  • Duration / stages: Production lengths sufficient to extract diffusion statistics and oxide thickening trends over the reported temperature window; see article for ps/ns totals.
  • Thermostat: Thermostat choice and coupling constants in Methods (e.g. Nose–Hoover-class if so stated).
  • Barostat: N/A — hydrostatic barostat not indicated for the cited constant-volume oxidation MD unless the PDF documents NPT—verify locally.
  • Temperature: 800–2000 K temperature range for bulk O diffusion and Ge/GeO\(_2\) comparisons (abstract).
  • Pressure: N/A — external pressure targets not emphasized in the abstract-level summary for these cells; confirm in PDF.
  • Electric field: N/A — electric field not applied.
  • Enhanced sampling: N/A — umbrella, metadynamics, bond boost not indicated.

Findings

Outcomes and mechanisms

ReaxFF retains good agreement with QM for GeO/GeO\(_2\) condensed-phase data after refitting and reproduces the DFT ordering of O-interstitial sites. O diffusion proceeds by BC–BC hops through an asymmetric split transition state; the abstract quotes a ReaxFF diffusion barrier of 50.02 kcal/mol across 800–2000 K. Above ~1400 K, ReaxFF allows BC–BC transport consistent with DFT, whereas Tersoff favors BC–hex hops that contradict the DFT reports in the same comparison.

Comparisons

Side-by-side ReaxFF vs Tersoff Ge/GeO\(_2\) heat treatment shows GeO\(_2\) thickening and Ge consumption with temperature and oxidation time in ReaxFF, while Tersoff leaves slab thicknesses essentially static in the authors’ simulations—experiments cited in the article support the ReaxFF picture for oxidation kinetics.

Sensitivity

Oxidation extent and diffusivity depend strongly on temperature (the 800–2000 K window) and simulation duration as parameterized in Results.

Limitations and outlook

Proof PDF ingest: confirm pagination and any publisher corrections against the version of record; force-field transferability beyond the trained Ge/O/H chemistry should follow the article’s caveats.

Corpus honesty

Indexed text here is p1–2-depth plus abstract; numerical protocol details must be verified in pdf_path or the VOR sibling if added later.

Limitations

Proof PDF; confirm DOI/volume pages from the published article.

Relevance to group

van Duin coauthored Ge/GeO\(_x\) ReaxFF refinement for semiconductor oxidation pathways.

Citations and evidence anchors

  • Obtain DOI from the publisher PDF if not yet in normalized/papers/*.json.