Influence of extended defects on the formation energy, hyperfine structure, and zero-field splitting of NV centers in diamond

At a Glance

Metadata	Details
Publication Date	2021-02-15
Journal	Physical review. B./Physical review. B
Authors	Wolfgang Körner, Daniel F. Urban, Christian Elsässer
Institutions	University of Freiburg, Fraunhofer Institute for Mechanics of Materials
Citations	14
Analysis	Full AI Review Included

Technical Documentation & Analysis: Influence of Extended Defects on NV Centers in Diamond

This document analyzes the research paper “Influence of extended defects on the formation energy, the hyperfine structure, and the zero-field splitting of NV centers in diamond” using the perspective of an expert material scientist and technical sales engineer for 6CCVD.

Executive Summary

This Density Functional Theory (DFT) analysis provides critical insights into the behavior of negatively charged Nitrogen-Vacancy (NV^-) centers when located near extended planar defects (Intrinsic Stacking Faults (ISF), Extrinsic Stacking Faults (ESF), and Coherent Twin Boundaries (CTB)) in diamond.

Energetic Preference: NV centers are energetically preferred near extended defects, showing a maximum formation energy reduction of approximately -0.25 eV relative to the bulk crystal. This suggests defects can act as natural segregation sites for NV centers.
ZFS Deviation: The Zero-Field Splitting (ZFS) longitudinal component (D) is significantly altered, reduced by up to 9% from the bulk value (3.049 GHz) due to local hexagonal stacking sequences (Lonsdaleite-like environment).
Symmetry Breaking: The presence of extended defects breaks the C_3v symmetry for basal-oriented NV centers, resulting in a non-zero ZFS transversal component (E) of up to 250 ± 30 MHz.
HFS Alteration: Hyperfine Structure (HFS) constants for ¹⁴N and ¹³C are strongly influenced, with variations up to ±10% (for ¹⁴N) and 20 MHz (for ¹³C), depending on the local charge accumulation/reduction at the probe atom site.
Short-Range Influence: The influence of these extended defects on NV electronic properties is strictly short-range, decaying to bulk-like behavior within approximately 6 Å (three double layers).
Application Relevance: These results are essential for interpreting Optically Detected Magnetic Resonance (ODMR) and Electron Paramagnetic Resonance (EPR) spectra in NV-doped diamond, particularly for engineering high-density, localized NV ensembles for quantum sensing and computing applications.

Technical Specifications

The following hard data points were extracted from the DFT analysis:

Parameter	Value	Unit	Context
Bulk Diamond Lattice Constant (a)	3.567	Å	Primitive cubic cell
Plane-Wave Cutoff Energy	420	eV	VASP calculations for valence electrons
Force Relaxation Threshold	< 0.01	eV/Å	Required for structural relaxation
Max NV Formation Energy Reduction	-0.25	eV	Axial NV center at ISF (double layer n=1)
Theoretical Bulk ZFS (D₀)	3.049	GHz	PBE calculation for ³A₂ ground state
Experimental Bulk ZFS (D)	2.872(2)	GHz	Measured value
Max ZFS D Reduction near Defect	~9	%	Consistent with hexagonal Lonsdaleite stacking
Max ZFS Transversal Component (E)	250 ± 30	MHz	Basal NV orientation near extended defects
Defect Influence Range	~6	Å	Approximately three atomic double layers
Max ¹⁴N HFS A_ii Variation	±10	%	Near ISF/ESF/CTB defects
Max ¹³C HFS A_ii Variation	20	MHz	Near ISF/ESF/CTB defects

Key Methodologies

The computational study relied on precise supercell modeling and advanced DFT calculations:

Computational Framework: Density Functional Theory (DFT) was performed using the Vienna Ab Initio Simulation Package (VASP) version 5.4.4.
Exchange-Correlation Functional: The Generalized Gradient Approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) was used to describe exchange-correlation interactions.
Supercell Construction: Hexagonal supercell models were built to simulate extended planar defects (ISF, ESF, CTB) oriented along the {111} planes, with the largest model (CTB) containing 1152 atoms.
Energy Cutoff: A plane-wave cutoff energy of 420 eV was applied for valence electrons.
Structural Relaxation: Atom positions were relaxed under constant volume conditions until residual forces were below 0.01 eV/Å, ensuring highly accurate structural prerequisites for HFS calculations.
Parameter Calculation: Hyperfine Structure (HFS) tensor components (A_ij) and Zero-Field Splitting (ZFS) tensor components (D_ij) were calculated to quantify the influence of local structural changes on the NV electronic spin state.

6CCVD Solutions & Capabilities

This research highlights the critical interplay between crystal defects and the quantum properties of NV centers. To replicate, control, and extend this fundamental research into practical quantum devices, engineers require diamond materials with exceptional purity, precise orientation, and controlled defect density.

6CCVD, as an expert supplier of MPCVD diamond, offers tailored solutions that directly address the material requirements implied by this study.

Applicable Materials

To achieve the high level of structural control necessary for NV center research, the following 6CCVD materials are recommended:

Optical Grade Single Crystal Diamond (SCD): Essential for minimizing background strain and unwanted defects that could mask the effects of the targeted extended defects (ISF, ESF, CTB). Our SCD offers the highest purity required for long NV coherence times (T₂).
Custom {111} Substrates: Since the extended defects studied (ISF, ESF, CTB) are oriented along {111} planes, 6CCVD can supply SCD substrates specifically grown and polished to the {111} orientation, facilitating targeted defect engineering or analysis.

Customization Potential

The paper’s findings underscore the need for precise material engineering, especially when creating localized NV ensembles (few nanometer thin layers).

Research Requirement/Challenge	6CCVD Solution & Capability
Precise Defect Control & Localization	Custom Thickness Control: We offer SCD layers with thickness control from 0.1 µm up to 500 µm, enabling researchers to create the ultra-thin, localized NV layers necessary for high-density arrays, as discussed in the paper’s introduction.
Large-Scale Quantum Device Fabrication	Large Area Wafers: 6CCVD supplies SCD and PCD plates/wafers up to 125 mm in diameter, supporting the transition from fundamental supercell modeling to scalable device prototypes.
Integration of Measurement Structures	In-House Metalization Services: We provide custom deposition of metals (Au, Pt, Pd, Ti, W, Cu) for creating microwave antennas or electrodes directly on the diamond surface, crucial for performing high-precision ODMR/EPR measurements referenced in the study.
Surface Quality for Lithography	Ultra-Low Roughness Polishing: Our SCD polishing achieves surface roughness Ra < 1 nm, ensuring optimal surface quality for subsequent lithography and fabrication steps required to integrate NV centers into microstructures.

Engineering Support

The complex analysis of ZFS and HFS parameters requires deep material science expertise. 6CCVD’s in-house PhD team specializes in the growth and characterization of diamond for quantum applications. We can assist researchers working on similar solid-state qubit and high-resolution magnetometry projects by:

Consulting on optimal growth parameters to minimize or intentionally introduce specific extended defects.
Providing material characterization data (e.g., strain mapping, defect density) to correlate with measured ODMR/EPR spectra, helping to interpret variations traced back to extended defects.

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

View Original Abstract

We present a density-functional theory analysis of nitrogen-vacancy (NV) centers in diamond, which are located in the vicinity of extended defects, namely, intrinsic stacking faults, extrinsic stacking faults, and coherent twin boundaries on {111} planes in diamond crystals. Several sites for NV centers close to the extended defects are energetically preferred with respect to the bulk crystal. This indicates that NV centers may be enriched at extended defects. We report the hyperfine structure and zero-field splitting parameters of the NV centers at the extended defects, which typically deviate by about 10% but in some cases up to 90% from their bulk values. Furthermore, we find that the influence of the extended defects on the NV centers is of short range: NV centers that are about three double layers (corresponding to ≈6Å) away from defect planes already show bulklike behavior.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.103.085305