Accurate defect excitation energies from DFT-1/2 band structures - the NV$^-$ center in diamond

At a Glance

Metadata	Details
Publication Date	2017-05-30
Journal	arXiv (Cornell University)
Authors	Bruno Lucatto, L. V. C. Assali, Ronaldo Rodrigues Pelá, Marcelo Marques, L. K. Teles
Analysis	Full AI Review Included

Technical Documentation & Analysis: NV¯ Center Excitation Energies in Diamond

Executive Summary

This research validates an extended DFT-1/2 methodology for calculating accurate optical transition energies in deep defects, specifically benchmarking against the negatively charged Nitrogen-Vacancy (NV^-) center in diamond. This work is highly relevant to the development of solid-state quantum computing and advanced sensing applications.

Core Achievement: Developed a low-cost computational method (DFT-1/2 extension) to accurately predict optical transition energies (E_Ab, E_Em) for localized deep defects.
Benchmark System: The negatively charged Nitrogen-Vacancy (NV^-) center in diamond, a leading candidate for solid-state qubits due to its long coherence time.
Accuracy Validation: Calculated transition energies show remarkable agreement with experimental data, achieving an accuracy of 0.1 eV.
Computational Efficiency: The method calculates transition energies directly from Kohn-Sham eigenvalues, significantly reducing the computational cost compared to traditional total energy difference methods (e.g., HSE, GW).
Material Requirement: The success of NV^- centers relies fundamentally on the high purity and structural integrity of the diamond host crystal.
6CCVD Value Proposition: 6CCVD provides the necessary high-purity, low-nitrogen Single Crystal Diamond (SCD) substrates required for the precise creation and study of NV centers for quantum applications.

Technical Specifications

The following data points summarize the key calculated and experimental parameters related to the NV^- center in diamond, validating the DFT-1/2 methodology.

Parameter	Value	Unit	Context
Diamond Band Gap (Experimental)	5.47	eV	Reference value for bulk diamond
Diamond Band Gap (Calculated, GGA-1/2)	5.01	eV	Maximized using C_Bulk CUT=2.5 bohr
Vertical Absorption Energy (E_Ab, Calculated)	2.18	eV	GGA-1/2 eigenvalues (Matches Exp.)
Vertical Absorption Wavelength	569	nm	Corresponds to green light pumping
Vertical Emission Energy (E_Em, Calculated)	1.68	eV	GGA-1/2 eigenvalues
Vertical Emission Wavelength	704	nm	Corresponds to red light emission
Zero Phonon Line (ZPL, Experimental)	1.95	eV	Energy difference between relaxed states
Calculation Accuracy (E_Ab/E_Em)	± 0.1	eV	Agreement with experimental data
Supercell Size for Defect Simulation	216	atoms	3x3x3 supercell
Plane Wave Basis Set Cutoff	530	eV	VASP computational parameter

Key Methodologies

The theoretical approach relies on extending the DFT-1/2 method to accurately model localized defect levels within the diamond band gap.

Computational Framework: Calculations were performed using Density Functional Theory (DFT) combined with the Generalized Gradient Approximation (GGA-PBE) exchange-correlation potential, utilizing the VASP package and the Projected Augmented Wave (PAW) method.
Defect Modeling: The NV^- center was simulated within a 3x3x3 supercell (216 atoms), created by substituting a carbon atom adjacent to a vacancy with a nitrogen atom, and adding one electron for the negative charge state.
Structural Relaxation: Spin-polarized structural relaxation was performed for both the electronic ground state ($^{3}$A₂) and the first excited state ($^{3}$E) geometries, fixing the cell volume and shape.
DFT-1/2 Local Correction: The standard DFT-1/2 method was extended to apply local corrections to the defect levels. This involved calculating the orbital character of the defect levels (2a₁ and e) on the nitrogen and neighboring carbon atoms (C_Defect).
Parameter Optimization (CUT): The variational parameter (CUT) for the trimming function was optimized by maximizing the bulk diamond band gap (CUT = 2.50 bohr for C_Bulk) and maximizing the energy difference between the defect levels (CUT = 3.00 bohr for N, 2.50 bohr for C_Defect).
Transition Energy Determination: Optical transition energies (E_Ab, E_Em) were derived directly from the difference between the corrected Kohn-Sham eigenvalues of the defect levels, avoiding the need for computationally intensive total energy calculations.

6CCVD Solutions & Capabilities

This research underscores the critical need for high-quality diamond substrates to realize solid-state quantum devices based on NV centers. 6CCVD is uniquely positioned to supply the necessary materials and engineering support to replicate and advance this research.

Applicable Materials for NV Center Research

The creation of stable, high-coherence NV centers requires diamond with extremely low intrinsic nitrogen content to allow for controlled, targeted doping or implantation.

6CCVD Material	Specification	Application Relevance
Optical Grade SCD	SCD, High Purity, Low Nitrogen (Type IIa)	Ideal host material for creating NV centers via implantation or controlled doping. Essential for minimizing background defects and maximizing coherence time.
Custom Doped SCD	Controlled Nitrogen Doping (N-doped)	Required for studies focusing on specific NV concentration control and integration into quantum architectures.
Polished SCD Wafers	Ra < 1 nm surface finish	Minimizes surface scattering and decoherence, critical for optical excitation and emission studies (E_Ab, E_Em, ZPL).

Customization Potential for Quantum Device Integration

The theoretical work provides the foundation for physical device fabrication. 6CCVD offers specialized services necessary to translate these calculations into functional quantum hardware:

Custom Dimensions: We supply SCD plates and PCD wafers up to 125 mm in diameter, accommodating large-scale fabrication needs for quantum integrated circuits.
Thickness Control: SCD layers are available from 0.1 µm (for thin film integration) up to 500 µm (for bulk studies), allowing researchers to optimize the depth and environment of the NV centers.
Advanced Metalization: For integrating NV centers into microwave control structures or electrical contacts (e.g., for BDD conductivity studies), 6CCVD offers in-house metalization services, including:
- Au, Pt, Pd, Ti, W, and Cu deposition.
- Custom patterning and lithography support.
Boron-Doped Diamond (BDD): For experiments requiring conductive diamond layers (e.g., gate electrodes or charge state control), we offer heavy Boron-Doped Diamond (BDD) materials.

Engineering Support

The complexity of defect physics, as demonstrated by the extended DFT-1/2 methodology, requires deep material expertise. 6CCVD’s in-house PhD team specializes in MPCVD growth and defect engineering.

Material Selection Consultation: We provide expert guidance on selecting the optimal diamond type (SCD vs. PCD, doping level, purity) to maximize NV center yield and performance for specific quantum projects.
Process Optimization: Assistance with material preparation, polishing, and post-processing steps necessary for high-fidelity defect creation (e.g., ion implantation, annealing).
Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) of sensitive, high-value diamond materials directly to your research facility.

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

Tech Support

Original Source

DOI: None