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Epitaxial formation of ultrathin HfO2 on multilayer graphene by sequential oxidation

Summary

The study combines scanning transmission electron microscopy and related techniques with ReaxFF-based reactive molecular dynamics (and hybrid force-biased Monte Carlo / MD in Amsterdam Modeling Suite) to follow oxidation of epitaxial Hf on few-layer graphene. Experimentally, sequential oxidation yields amorphous suboxide, then an epitaxial hexagonal suboxide (h-HfO\(_x\)), and ultimately monoclinic HfO\(_2\) (m-HfO\(_2\)), all retaining epitaxial relationships to the graphene template. Simulations are used to interrogate phase coexistence, oxidation depth, and the role of graphene in templating crystalline metal and suboxide.

Methods

  • Experiments: Ultrathin Hf is deposited on few-layer graphene in UHV, then exposed to native and/or thermal oxidation protocols; STEM, SAED, EELS, and s-SNOM probe structure and conductivity trends (see article Methods).
  • Reactive MD setup (ReaxFF in AMS): An hcp-Hf slab is built from a Materials Project unit cell expanded to a 16×16×6 supercell (3072 Hf atoms), orthorhombically represented with thickness ~2.775 nm, placed on a four-layer AB-stacked graphene support (4800 C atoms, 3.4 Å interlayer spacing initially). O\(_2\) molecules (2–3072 per cell) occupy vacuum above the slab in a periodic cell (~24 Å lateral gap across the Hf slab in the layout described). Eighteen parameter combinations with/without graphene and varying O\(_2\) content are summarized in Table S1.
  • Equilibration and heating: After conjugate-gradient minimization, systems are held at 300 K in NVT for 100 ps with Berendsen thermostats (100 fs damping). Hf/O ReaxFF interactions are disabled during equilibration/heating so oxygen does not react prematurely; the slab is then heated 300 → 900 K at 10 K/ps with separate Berendsen thermostats on Hf, graphene, and O\(_2\) (100 fs damping each). Hf/O interactions are enabled for the annealing segment: 900 K NVT, 2 ns, still with split thermostats (10,000 fs on Hf and O\(_2\), 100 fs on graphene) and 0.1 fs timestep.
  • Hybrid fbMC/MD: Uniform-acceptance fbMC/MD alternates 10\(^7\) MD and 10\(^7\) fbMC iterations (parameters dr\(_\mathrm{max}\)=0.1, imcfrq=10,000, imcstp=10,000, imcroo=4 in the “control” file cited), with 36,000,000 MD iterations each side, 0.1 fs timestep, totaling ~3.6 ns equivalent MD segment at 900 K as described. The authors note Hf/C covalency is outside the training scope of the Hf/C/H/O field used.

Slot summary (reactive MD): Hf/O ReaxFF in AMS; 3072 Hf atoms + 4800 C (graphene) + O\(_2\) loadings; 3D PBC periodic cell as given; NVE/NVT ensemble in minimization, heating, and fbMC/MD; timestep 0.1 fs; ps–ns duration; split Berendsen thermostat (damping in article); annealing at 900 K; N/A — barostat / 1 atm NPT not used in the annealing segment summarized (constant-volume NVT for that block); N/A — pressure-targeted NPT not quoted here. N/A — external electric field; N/A — standard umbrella (uses fbMC/MD instead).

Findings

  • Oxidation proceeds through a-HfO\(_x\) → epitaxial h-HfO\(_x\) → m-HfO\(_2\), with STEM supporting epitaxial relationships between hcp-Hf, h-HfO\(_x\), m-HfO\(_2\), and graphene.
  • Simulations reproduce coexistence of crystalline (hcp-Hf, h-HfO\(_x\), m-HfO\(_2\)) and amorphous suboxide regions and show graphene correlates with more layered, hcp-rich metal before full oxidation and promotes more contiguous crystalline oxide growth versus vacuum–oxide clusters without graphene.
  • At the highest O\(_2\) loadings, bond-length and angle distributions align with predominantly m-HfO\(_2\), with slab-averaged O:Hf approaching ~1.82 in the largest O\(_2\)-loading case, interpreted as m-HfO\(_2\) coexisting with suboxide—a sensitivity trend with O\(_2\) concentration in the simulation supercell as reported. Outcomes are compared to STEM experiments (same article); this note is evidence-tied to the galley PDF and should be checked against the version-of-record for final numbers.

Limitations

  • The corpus PDF is a galley/proof-style ACS Nano file; pagination and some production metadata may differ from the version of record.
  • Reactive FF accuracy for Hf–O phase transitions and epitaxy is limited by the parameterization; graphene–Hf covalent interactions are not targeted by the field.

Relevance to group

Adri C. T. van Duin is a co-author; the project applies AMS ReaxFF MD and accelerated hybrid sampling to oxide epitaxy on graphene, relevant to 2D electronics dielectric integration.

Citations and evidence anchors

Reader notes (navigation)

  • The ingested file papers/Liu_Mao_ACSNano_Hf_graphene_2025_galley.pdf is a galley PDF; replace with the published VOR PDF when available and refresh hashes via the manifest sync workflow.