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Development of the ReaxFF Reactive Force Field for Cu/Si Systems with Application to Copper Cluster Formation during Cu Diffusion Inside Silicon

Cu/Si ReaxFF trained on DFT data (including Cu diffusion barriers in Si), applied to reactive MD of Cu in bulk Si (up to 762 atoms in the abstract’s framing), clustering versus temperature, and uniaxial stress–strain with elastic modulus trends.

Summary

A ReaxFF description for copper in crystalline silicon is developed by training against density functional theory data, explicitly including the energy barrier for an isolated Cu hop in the Si lattice. Molecular dynamics with this potential explores temperature-dependent diffusion, the onset of Cu clustering (reported above 500 K in the abstract), and mechanical loading: stress–strain under uniaxial tension for Cu/Si compositions, showing reduced elastic modulus with higher Cu content and microcracking in Si tied to Cu cluster formation near surfaces.

Methods

1 — MD application. Reactive MD of diamond Si supercells with interstitial/aggregated Cu up to 762 atoms in the abstract’s scaling claim; additional runs apply uniaxial tensile strain and report stress–strain and elastic modulus trends. Engine—LAMMPS-class ReaxFF MD is standard in this JPCC line; N/A on this page for the exact input script (see article/SI). PBC bulk cells with 3D periodicity. NVT/NVE segments for thermal ramp/hold and deformation stages as described in the main text. Timestep (fs), equilibration and production duration (ps–ns), and Nose–Hoover (or equivalent) thermostat parameters—take from the JPCC file. Barostat/NPT—N/A for the uniaxial load path unless the authors mixed NPT relaxation steps; check VOR Section on mechanics. Target temperatures follow the K-scale schedules for diffusion/clustering. Electric field and replica/metadynamics—N/A in the abstracted scope.

2 — Force-field training. A ReaxFF for Cu/Si is fit to DFT energies and barriers, explicitly including the hopping barrier for an isolated Cu in Si. The force field extends prior ReaxFF lineages in the same element space with parrex/least-squares-style ReaxFF optimization as described in the article.

3 — Static QM / DFT. DFT data underpin formation and defect energetics used in the ReaxFF training; N/A as a free-standing B3LYP/hybrid study in the abstracted summary.

4 — Galley. Local PDF is a galley; confirm values in the version of record.

Findings

Kinetics and clustering. Cu diffusion is temperature-dependent; Cu atoms form crystalline-like clusters in bulk Si above about 500 K (as stated in the abstract). Mechanical response. The Young’s-related modulus decreases with rising Cu concentration in the modeled Cu/Si blends (abstract). Failure morphology. Uniaxial tensile tests show spontaneous microcracking of Si when a small Cu cluster sits next to a free Si surface (abstract claim). Comparisons in the main text may include DFT-based barriers vs ReaxFF for selected paths; see JPCC for scope. Sensitivity to temperature and impurity concentration is central. Caveat: the local file is a galley; any revised numbers belong to the VOR PDF (Limitations below).

Limitations

Ingested PDF is a galley; consult the version of record for final wording and any corrected numerical tables. Full DFT and ReaxFF training sets and all MD protocol details are in the main text/SI.

Relevance to group

Metal impurity diffusion and clustering in Si is a core microelectronics reliability topic; this paper delivers a validated ReaxFF and large-cell MD demonstration. Cross-link to other Cu/Si and semiconductor defect application notes in the KB when building process-induced defect narratives.

Citations and evidence anchors

Reader notes (navigation)

  • paper_keywords includes keyword:galley-or-proof-pdf.