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

At a Glance

Metadata	Details
Publication Date	2024-02-20
Journal	Carbon
Authors	Emerick Yves Guillaume, Danny E. P. Vanpoucke, Rozita Rouzbahani, Luna Pratali Maffei, Matteo Pelucchi
Institutions	University of Namur, IMEC
Citations	7
Analysis	Full AI Review Included

Technical Documentation & Analysis: Hydrogen Kinetics on Diamond (100) Surfaces

Executive Summary

This analysis summarizes a first-principles investigation into the atomic-scale mechanisms governing hydrogen radical interactions on H-passivated diamond (100) surfaces, a critical process for MPCVD diamond growth.

Core Mechanism Quantified: Comprehensive calculation of reaction rate coefficients (k_n) and effective rates (r_n) for hydrogen adsorption, desorption, and vacancy migration using Density Functional Theory (DFT), Climbing Image Nudged Elastic Band (cNEB), and Variational Transition State Theory (VTST).
Surface Coverage Prediction: At typical CVD conditions (T=1200 K, H₂/H radical ratio f~100), the steady-state surface is highly passivated: 93.94% fully passivated (RH₂), 3.82% half-passivated (RH), and 2.24% clean dimers (R).
Reactive Site Importance: The small fraction of half-passivated and clean dimers (totaling ~6%) represents the crucial reactive sites necessary for subsequent carbon insertion and diamond layer deposition.
vdW Correction Necessity: Inclusion of van der Waals (vdW) dispersion corrections (e.g., DFT-D3) is essential, leading to significantly lower and more accurate energy barriers (E^TS) compared to non-vdW calculations.
Anisotropic Migration: H-vacancy migration is shown to be anisotropic, occurring preferentially across dimer rows (r_g = 5.999 x 10³ s^-1) rather than along dimer rows (r_s = 1.023 x 10² s^-1).
Dominant Reactions: Bimolecular recombination (RH + H’ → RH₂) is highly favored (r_n ~ 10⁷ s^-1), confirming the rapid passivation of reactive sites in an H-rich atmosphere.

Technical Specifications

Data extracted from the first-principles calculations, primarily focusing on conditions at T = 1200 K.

Parameter	Value	Unit	Context
Modeled Surface Orientation	(100)-(2x1):H	N/A	H-passivated diamond slab
Simulation Temperature (T)	1200	K	Typical experimental CVD setting
Simulation Pressure (P)	25	kPa	Typical experimental CVD setting
H₂ / H Radical Ratio (f)	100	N/A	Assumed molar concentration ratio
Steady-State Coverage (RH₂)	93.94	%	Fully passivated dimers
Steady-State Coverage (RH)	3.82	%	Half-passivated dimers (Reactive)
Steady-State Coverage (R)	2.24	%	Clean dimers (Reactive)
First H-Desorption Barrier (E^TS)	0.095	eV	Tight TS, DFT-D3 corrected
H-Vacancy Migration Rate (Across Rows, r_g)	5.999 x 10³	s^-1	Reaction 9, preferential movement
H-Vacancy Migration Rate (Along Rows, r_s)	1.023 x 10²	s^-1	Reaction 8, slower movement
Bimolecular Recombination Rate (r_n)	1.468 x 10⁷	cm³.mol^-1.s^-1	RH + H’ → RH₂ (Highly favored)
Unimolecular Dissociation Rate (k_n)	4.992 x 10^-3	s^-1	RH₂ → RH + H’ (Very slow)

Key Methodologies

The study employed advanced quantum mechanical techniques to model gas-surface interactions and reaction kinetics:

System Modeling: A periodic 4x4x11 slab model of the (100)-oriented H-passivated diamond surface was constructed, featuring 176 C atoms and 32 H atoms, consistent with the 2x1 reconstruction along dimer rows.
Computational Framework: Density Functional Theory (DFT) was performed using the PBE functional, incorporating spin-polarization to accommodate the radical nature of the species involved.
Dispersion Correction: Van der Waals (vdW) dispersion corrections (specifically DFT-D3) were applied to accurately model long-range interactions between gas-phase species and the diamond surface, which is critical for calculating accurate energy barriers (E^TS).
Transition State Identification: The Climbing Image Nudged Elastic Band (cNEB) method was used to determine the Minimum Energy Path (MEP) and locate the saddle points (Transition States, TS) for reactions exhibiting an energy barrier (Tight TS, tTS).
Reaction Rate Calculation: Variational Transition State Theory (VTST) was applied to compute accurate reaction rate coefficients (k_n) for both tTS and barrierless reactions (Loose Transition States, ITS), incorporating the exponential prefactor (A_n) and tunneling effects.
Vibrational Analysis: Vibrational spectra were calculated using the finite difference method to derive the necessary partition functions for the initial, final, and transition states, enabling the calculation of the Arrhenius prefactor.
Boundary Conditions: The bottom 16 C atoms and their passivating H atoms were kept frozen during cNEB calculations to simulate a bulk-like structure and prevent slab movement.

6CCVD Solutions & Capabilities

The research provides fundamental kinetic data essential for optimizing MPCVD diamond growth, particularly concerning the creation and stability of reactive surface sites. 6CCVD is uniquely positioned to supply the high-quality materials and engineering support required to experimentally validate and extend this computational work.

Applicable Materials

The accuracy of this research relies on a perfectly defined, reconstructed (100) surface. To replicate or extend these findings experimentally, researchers require:

Electronic Grade Single Crystal Diamond (SCD) Wafers: 6CCVD supplies high-purity SCD substrates with precise (100) orientation and minimal defects, ensuring the surface reconstruction modeled in the DFT calculations (2x1:H) is accurately realized in the reactor.
High-Quality Polycrystalline Diamond (PCD) Plates: For large-area applications or scaling up growth models, 6CCVD offers PCD plates up to 125 mm in diameter, polished to Ra < 5 nm, suitable for large-scale CVD kinetic studies.

Customization Potential

6CCVD’s advanced fabrication capabilities directly address the needs of fundamental surface science and CVD engineering:

Precision Surface Preparation: The study emphasizes the importance of a pristine H-passivated surface. 6CCVD guarantees ultra-low roughness polishing (Ra < 1 nm for SCD) to minimize non-(100) facets and maximize the uniformity of the modeled dimer rows.
Custom Crystallographic Orientations: The authors suggest generalizing this approach to other orientations. 6CCVD can supply custom-oriented SCD substrates (e.g., (110) or (111)) to investigate the orientation dependence of H-radical kinetics.
Advanced Metalization Services: While this study is theoretical, future experimental work involving electrical characterization of reactive sites (e.g., using BDD) will require contacts. 6CCVD offers in-house custom metalization (Ti/Pt/Au, W, Cu) for creating precise electrode patterns on the diamond surface.
Custom Dimensions and Thickness: 6CCVD provides SCD and PCD materials in thicknesses ranging from 0.1 µm to 500 µm, and substrates up to 10 mm thick, allowing for flexibility in experimental reactor design and integration.

Engineering Support

Understanding the complex interplay between gas-phase radicals and surface kinetics is crucial for achieving high-quality diamond growth.

6CCVD’s in-house PhD team, specializing in MPCVD processes and material science, offers direct consultation on material selection and surface preparation protocols necessary to validate the calculated reaction rate coefficients for Fundamental CVD Growth Kinetics projects.
We provide technical assistance in selecting the optimal diamond grade and surface termination (H-terminated vs. O-terminated) required for specific experimental conditions, ensuring the material matches the theoretical model.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

Tech Support

Original Source

DOI: https://doi.org/10.1016/j.carbon.2024.118949