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First-principles investigation of hydrogen-related reactions on (100)–(2 × 1) - H diamond surfaces

MetadataDetails
Publication Date2024-02-20
JournalCarbon
AuthorsEmerick Yves Guillaume, Danny E. P. Vanpoucke, Rozita Rouzbahani, Luna Pratali Maffei, Matteo Pelucchi
InstitutionsPolitecnico di Milano, IMEC
Citations7
AnalysisFull AI Review Included

This study provides a comprehensive first-principles investigation of hydrogen radical kinetics on the diamond (100)-(2x1):H surface, crucial for optimizing Chemical Vapor Deposition (CVD) growth.

  • Core Achievement: Accurate calculation of effective reaction rate coefficients (rn) for key gas-surface and surface-surface reactions using Density Functional Theory (DFT) combined with Variational Transition State Theory (VTST).
  • Surface Activation: The second hydrogen desorption (H-radical attack on a half-passivated dimer, RH + H° -> R + H2) is the fastest activation mechanism (rn = 3.364 x 106 s-1 at 1200 K), creating the necessary clean (R) sites for carbon incorporation.
  • Steady-State Coverage: Under typical CVD conditions (T=1200 K, 1% H radical), the surface remains highly passivated: 93.94% fully passivated (RH2), 3.82% half-passivated (RH), and 2.24% clean (R) sites.
  • Migration Anisotropy: H-vacancy migration is highly anisotropic, favoring movement across dimer rows (rg ~ 6.0 x 103 s-1) over movement along dimer rows (rs ~ 1.0 x 102 s-1), suggesting preferential defect movement.
  • Kinetic Dominance: Gas-surface interactions (radical attack/recombination) dominate surface-surface migration reactions under standard CVD growth conditions.
  • Methodological Rigor: Inclusion of van der Waals (vdW) dispersion corrections (DFT-D3) was essential, yielding significantly lower and more accurate energy barriers compared to non-corrected calculations.

Data extracted for typical CVD conditions (T = 1200 K, P = 25 kPa, V = 0.33 m3, assuming 1% H radical and 99% H2).

ParameterValueUnitContext
Simulation Temperature (T)1200KStandard CVD growth condition used for rate calculation.
Simulation Pressure (P)25kPaAssumed gas phase pressure.
H Radical Concentration ([H])1% molarAssumed representative concentration in gas phase.
H2 Concentration ([H2])99% molarAssumed representative concentration in gas phase.
Slab Model Size4x4x11LayersPeriodic slab containing 176 C and 32 H atoms.
Plane-Wave Cut-off Energy650eVDFT calculation setting.
Force Convergence Criterion0.02eV/AGeometric optimization threshold.
Effective Rate (rn) - H-Desorption 16.143 x 105s-1RH2 + H° -> RH + H2 (Activation of first H).
Effective Rate (rn) - H-Desorption 23.364 x 106s-1RH + H° -> R + H2 (Activation of second H/Clean site creation).
Effective Rate (rn) - H2 Recombination 11.468 x 107s-1RH + H2 -> RH2 + H° (Reverse of Dissociation 1).
Effective Rate (rn) - Vacancy Migration (Across Rows)5.999 x 103s-1Fastest single H-vacancy migration path (rg).
Effective Rate (rn) - Vacancy Migration (Along Rows)1.023 x 102s-1Slowest single H-vacancy migration path (rs).
Steady-State Coverage (RH2)93.94%Fully passivated dimers at 1200 K.
Steady-State Coverage (R)2.24%Clean (vacant) dimers at 1200 K (active sites).
Energy Barrier (ETS) - H-Desorption 10.091eVTight Transition State (tTS) using DFT-D3 (1x1x1 sampling).

The study employed a rigorous, multi-step computational methodology to determine the kinetics of hydrogen-related reactions on the diamond (100) surface.

  1. System Modeling:

    • A periodic 4x4x11 slab model was used to represent the (100)-(2x1):H reconstructed diamond surface.
    • The bottom 16 C atoms and their passivating H atoms were kept frozen to simulate bulk-like behavior.
  2. Electronic Structure Calculation (DFT):

    • Calculations were performed using the Vienna Ab initio Simulation Package (VASP).
    • The Perdew-Burke-Ernzerhof (PBE) functional was used, incorporating spin-polarization to handle radical species.
    • Critical Correction: Van der Waals (vdW) dispersion corrections (primarily DFT-D3) were applied, as these long-range interactions are significant for gas-surface reactions (distances 1 to 5 A).
  3. Minimum Energy Path (MEP) Determination:

    • The (climbing image) Nudged Elastic Band (cNEB) method was used to locate the MEP and identify the geometry and energy of the Transition States (TS).
  4. Reaction Rate Calculation (TST/VTST):

    • Tight Transition States (tTS): Standard Transition State Theory (TST) was applied for reactions exhibiting a clear energy barrier (e.g., first H-desorption).
    • Loose Transition States (lTS): Variational Transition State Theory (VTST) was applied for barrierless reactions (e.g., second H-desorption, unimolecular dissociation), where the TS position varies with temperature.
    • Kinetic Parameters: Calculations included the exponential prefactor (An) and the transmission coefficient (κ) to account for quantum tunneling effects.
  5. Effective Rate Calculation (rn):

    • The calculated reaction rate coefficients (kn) were multiplied by the density of the associated gas-phase reactant (H or H2) to yield the effective reaction rate (rn), allowing direct comparison between gas-surface and surface-surface mechanisms under specific CVD conditions (1200 K, 25 kPa).

The fundamental kinetic data derived from this study is essential for optimizing the CVD process, which is the primary method for manufacturing high-quality synthetic diamond materials.

Industry/ApplicationRelevance of Findings
Diamond CVD ManufacturingProvides accurate, ab-initio derived kinetic parameters (rn) necessary for detailed and semi-detailed chemistry models of the gas phase and surface reactions.
High-Power ElectronicsGrowth of high-purity, single-crystal diamond required for heat sinks and high-frequency/high-power devices (e.g., RF transistors). Understanding surface activation controls defect incorporation.
Quantum Sensing and ComputingControl over H-vacancy migration and surface activation is crucial for creating specific nitrogen-vacancy (NV) centers and other color centers used in quantum applications.
Tooling and AbrasivesCVD diamond coatings are used for cutting tools and wear-resistant components. Optimized growth kinetics ensure high deposition rates and material quality.
Optical Windows and OpticsProduction of large-area, high-purity diamond windows for high-power laser systems, where low defect density (controlled by surface kinetics) is critical for transparency.
Process Modeling and SimulationThe calculated reaction rates (Table II) serve as input parameters for macro-scale kinetic models (e.g., computational fluid dynamics models of CVD reactors), enabling predictive control of growth rate and uniformity.