Ab-initio calculation of point defect equilibria during heat treatment - Nitrogen, hydrogen, and silicon doped diamond

At a Glance

Metadata	Details
Publication Date	2022-04-30
Journal	Diamond and Related Materials
Authors	Mubashir Mansoor, Mehya Mansoor, Maryam Mansoor, Ammar Aksoy, Sinem N. Seyhan
Institutions	University of Warsaw, Istanbul Technical University
Citations	17
Analysis	Full AI Review Included

Technical Analysis and Material Sourcing Documentation: Point Defect Equilibria in MPCVD Diamond

This document analyzes the research preprint “Ab-initio calculation of point defect equilibria during heat treatment: Nitrogen, hydrogen and silicon doped diamond” to derive critical material specifications and process recommendations, directly correlating the findings with 6CCVD’s advanced Monocrystalline and Polycrystalline CVD diamond capabilities.

Executive Summary

The research utilizes Density Functional Theory (DFT) and monolithic Kröger-Vink diagrams to model defect transformations in N, H, and Si co-doped diamond under extreme simulated conditions, providing a crucial framework for accelerated defect engineering in optoelectronic and quantum materials.

Accelerated Defect Engineering: A robust, cost-effective computational pathway (DFT + Kröger-Vink modeling) is demonstrated, allowing engineers to predict stable defect concentrations (e.g., NV, SiV, N₄V) as a function of temperature (500 K - 3000 K) and trace chemistry.
NV Center Dependence: The study confirms that the desired NV center concentration, and critically, its annealing temperature, is highly sensitive to the initial total nitrogen content (1 ppb to 1000 ppm) and the partial pressure of hydrogen (pH₂).
Thermodynamic Stability of Key Defects: N₄V (B center) is confirmed as the most thermodynamically favored nitrogen aggregate defect at lower temperatures (< 2000 K), highlighting the necessity of precise thermal post-processing to achieve active centers like NV.
SiV Center Confirmation: Silicon-based complexes, particularly the SiV (neutral and -1 charge states), are predicted to dominate at temperatures above 2000 K in Si-N co-doped systems, supporting their thermal stability for high-performance quantum applications.
Process Independence: Defect equilibria during typical bulk heat treatments (HPHT/LPHT) are shown to be largely independent of external pressure (0 GPa to 55 GPa), simplifying the material processing parameters required for converting defects post-growth.
Future Material Design: The methodology supports the rapid development of large defect databases, enabling high-throughput design of novel co-doped semiconducting and dielectric materials.

Technical Specifications

The following key data points were extracted from the ab-initio calculations and material modeling context.

Parameter	Value Range	Unit	Context
Simulated Temperature Range	500 - 3000	K	Range for plotting defect concentration equilibria.
Simulated Pressure Range	0 - 55	GPa	Range used for calculating pressure dependence of formation energies.
Nitrogen Doping Content Modeled	1 ppb, 1 ppm, 1000 ppm	Concentration	Representative trace chemistry for CVD and natural diamond.
Hydrogen Partial Pressure (pH₂)	10^-6 and 1	atm	Modeling hydrogen-poor and hydrogen-rich environments.
DFT Supercell Size	3x3x3 (216 atoms)	Volume	Used for formation energy calculations.
Pristine SCD Lattice Constant (0 GPa)	3.574	Å	Reference calculation using GGA-PBE.
Lattice Constant (55 GPa)	3.451	Å	Calculated constant at maximum pressure.
Critical Defect Annealing Temperature	> 2000	K (approx. 1727 °C)	Temperature required to anneal out N_aV defects (NV, N₂V, N₃V, N₄V).
NV Annealing Temperature Shift	Up to 500	°C	Increase in annealing temperature when N content rises (1 ppb to 1000 ppm).
DFT Correction Factor (ΔØ)	0.478	eV	Used to correct differences between GGA-PBE and HSE06 functionals.

Key Methodologies

The researchers employed a rigorous computational pathway leveraging high-performance computing resources to model defect thermodynamics in diamond.

Density Functional Theory (DFT) Setup: Used spin-polarized DFT (SP-DFT) with the generalized gradient approximation (GGA-PBE) functional, implemented via VASP 6.1, to model materials under periodic boundary conditions.
Defect Formation Energy Calculation: Calculated formation energies (ΔH) for a comprehensive library of 300 distinct defect combinations involving N, H, Si, and vacancies (V) across five different charge states.
Supercell and Convergence: Modeled defects using a 3x3x3 cubic supercell (216 atoms) with a 500 eV cut-off energy. Structures were relaxed until Hellmann-Feynman forces were below 1 meV/Å.
Charge Neutrality Correction: Applied the fully ab-initio FNV (Freysoldt, Neugebauer, Van de Walle) correction scheme, supplemented by the West, Sun, Zhang method, to accurately account for finite supercell size and charged defects.
Defect Equilibria Modeling (Kröger-Vink): Plotted monolithic Kröger-Vink diagrams by solving a non-linear system of 300 term equations numerically using the Newton-Rhapson algorithm.
Chemical Potential Treatment:
- Non-adiabatic Approach: Assumed equilibration with external gas reservoirs (H₂, C) for fast-diffusing dopants (H, V), relevant for thin film growth.
- Adiabatic Approach: Assumed constant total dopant concentration (N, Si), modeling defect-defect reactions dominating during bulk heat treatment (HPHT), validating the pressure-independent findings.

6CCVD Solutions & Capabilities: Defect Engineering for Quantum Materials

This research provides direct computational evidence necessary for engineering stable, high-concentration point defects crucial for quantum computing (NV, SiV) and advanced optoelectronic devices. 6CCVD is uniquely positioned to supply the highly controlled MPCVD diamond required to realize these results experimentally.

Applicable Materials

To replicate and extend the computational findings on NV, SiV, and N-H complexes, researchers require diamond materials with precise control over initial defect incorporation and extreme thermal stability.

Target Defect / Application	Recommended 6CCVD Material	Critical 6CCVD Specification Match
Nitrogen-Vacancy (NV^-) Centers	Optical Grade Single Crystal Diamond (SCD)	Extremely low non-N intrinsic impurities. Low N concentration (to model ppb/ppm levels) achieved via highly controlled growth recipes.
Silicon-Vacancy (SiV^-) Centers	Silicon-Doped SCD or PCD	Precise, intentional co-doping (Si: 1 ppm modeling) during MPCVD growth to form stable SiV precursors.
High-Performance Sensors / Qubits	High Purity SCD Plates	Thickness control from 0.1µm up to 500µm required for specific device architectures and waveguiding.
High-Throughput Device Substrates	Polycrystalline Diamond (PCD)	Custom dimensions up to 125mm for scalability in sensor and large-area optoelectronics.
Conductive Diamond Extension	Heavy Boron-Doped Diamond (BDD)	Required if extending research to p-type doping, which significantly impacts the equilibrium Fermi energy (E_f).

Customization Potential for Defect Control

The research confirms that successful defect engineering relies on both precise trace chemistry control during growth and optimized post-processing (heat treatment/metalization). 6CCVD’s advanced processing capabilities ensure experimental validation of the modeled equilibria:

Custom Doping Control: 6CCVD guarantees the ability to control N and Si trace chemistries in the ppb and ppm range, matching the critical input parameters used in the Kröger-Vink simulations (N: 1 ppb, 1 ppm, 1000 ppm; Si: 1 ppm).
Precision Polishing: To enable optical readout and integration of defects like NV and SiV, ultra-smooth surfaces are mandatory. 6CCVD achieves superior polishing quality with Ra < 1nm for SCD and Ra < 5nm for inch-size PCD.
Integrated Metalization: Device integration often requires complex ohmic contacts or waveguides. 6CCVD offers internal metalization services (Au, Pt, Pd, Ti, W, Cu), providing reliable thin films essential for studying charged defects and device performance.
Custom Geometry and Dimensions: We offer custom laser cutting and shaping services to deliver wafers and plates up to 125mm, required for advanced lithography and large-scale R&D experiments utilizing the predicted defect stability regions.

Engineering Support

The complexity of defect thermodynamics requires strong collaboration between computational modeling and physical material realization. 6CCVD’s in-house PhD team specializes in MPCVD process optimization and defect characterization. We are equipped to assist clients with:

Material Recipe Selection: Utilizing data similar to the Kröger-Vink diagrams presented in this paper to optimize CVD growth parameters (T, H₂ partial pressure, N/Si precursors) for maximized yield of target defects (e.g., NV^- or SiV^-).
Post-Growth Treatment Consultation: Advising on optimal HPHT or LPHT annealing protocols to convert N_s to NV, or to ensure desired SiV thermal stability above 2000 K, matching the calculated thermodynamic driving forces.
Quantum Applications Support: Providing expertise in material selection for quantum computer and optical sensor projects, focusing on achieving the required coherence times and optical properties derived from targeted defect concentrations.

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.diamond.2022.109072

References

2000 - Effects of point defects on the electrical properties of doped diamond [Crossref]
2018 - Optoelectronic diamond: growth, properties, and photodetection applications [Crossref]
2004 - Observation of coherent oscillations in a single electron spin [Crossref]
2006 - Processing quantum information in diamond [Crossref]
2011 - Ultra-nanocrystalline diamond electrodes: optimization towards neural stimulation applications
2015 - Hermetic diamond capsules for biomedical implants enabled by gold active braze alloys [Crossref]
2021 - Progress of structural and electronic properties of diamond: a mini review [Crossref]
2013 - Optical defects in diamond: a quick reference chart [Crossref]
2001 - Coloration of diamond