Photoionization of negatively charged NV centers in diamond - Theory and ab initio calculations

At a Glance

Metadata	Details
Publication Date	2021-12-06
Journal	Physical review. B./Physical review. B
Authors	Lukas Razinkovas, M. Maciaszek, Friedemann Reinhard, Marcus W. Doherty, Audrius Alkauskas
Institutions	Kaunas University of Technology, University of Rostock
Citations	46
Analysis	Full AI Review Included

Technical Documentation & Analysis: Photoionization of NV Centers in Diamond

This document analyzes the theoretical and ab initio calculations presented in the research paper on NV center photoionization, translating key findings into actionable technical specifications and material recommendations for engineers and scientists utilizing 6CCVD’s MPCVD diamond products.

Executive Summary

Core Achievement: The paper provides the first ab initio calculation of absolute photoionization cross sections ($\sigma_{ph}$) and thresholds for the negatively charged Nitrogen-Vacancy (NV⁻) center in diamond, crucial for quantum technology development.
Key Thresholds Confirmed: Theoretical photoionization thresholds were calculated for the ground state (IP(³A₂) = 2.67 eV) and the excited triplet state (IP(³E) = 1.15 eV).
Spin-to-Charge Conversion Mechanism: The study validates the mechanism of spin-to-charge conversion under dual-beam excitation, explaining why sub-ZPL photon energies (1.17 eV and 1.93 eV) are most efficient for high-fidelity spin readout.
New Methodology: A novel computational methodology is introduced, combining dense k-point mesh integration with band unfolding and interpolation, yielding smooth and accurate cross sections for point defects.
Charge State Dynamics: The work confirms that photoionization from the NV⁻ excited state (³E) transitions directly into the metastable neutral NV⁰ state (⁴A₂), explaining observed spin polarization in Electron Spin Resonance (ESR) experiments.
Material Relevance: These findings are essential for designing and optimizing experiments involving charge-state dynamics, Photocurrent Detection of Magnetic Resonance (PDMR), and stimulated emission in high-quality Single Crystal Diamond (SCD).

Technical Specifications

The following hard data points were extracted from the ab initio calculations and experimental comparisons presented in the paper.

Parameter	Value	Unit	Context
Diamond Band Gap (E_g)	5.34	eV	Calculated using HSE Functional
Lattice Constant (a)	3.548	Å	Calculated using HSE Functional
Refractive Index (n_D)	2.4	-	Bulk Diamond Constant
Dielectric Constant (ε_∞)	5.7	-	Bulk Diamond Constant
IP(³A₂) Photoionization Threshold	2.67 (Theory) / 2.6 (Exp)	eV	NV⁻ Ground State (³A₂)
IP(³E) Photoionization Threshold	1.15	eV	NV⁻ Excited Triplet State (³E)
IP(¹E) Photoionization Threshold	2.2 ± 0.1	eV	NV⁻ Excited Singlet State (Estimated)
NV⁻ ZPL Energy (E_ZPL)	1.945	eV	Triplet Transition (³A₂ → ³E)
NV⁰ ZPL Energy (E_ZPL)	2.156	eV	Neutral Defect
Calculated Radiative Lifetime (τ_rad)	12.2	ns	³E → ³A₂ Transition (PBE functional)
Zero-Field Splitting D(⁴A₂)	1.69	GHz	NV⁰ Metastable State

Key Methodologies

The theoretical analysis relied on advanced computational materials science techniques to accurately model the NV center in the diamond lattice.

Electronic Structure and Geometry: Calculations were performed within the Density Functional Theory (DFT) framework, utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional. Geometry relaxation used 4 × 4 × 4 supercells (512 atomic sites).
Excitation Energies: The delta-self-consistent-field (ASCF) method was employed to calculate the energies of the excited states (³E and ⁴A₂).
Cross Section Calculation: Optical matrix elements were calculated using the PBE functional. The photoionization cross section ($\sigma_{ph}$) was determined by integrating over the Brillouin zone.
Brillouin Zone Integration Correction: To achieve smooth and accurate cross sections, a novel procedure was used:
- Integration performed on highly dense k-point meshes (up to 300 × 300 × 300).
- Band unfolding and interpolation techniques were applied to correct distortions caused by the artificial periodicity of the supercell approach.
Vibrational Coupling: The effects of electron-phonon coupling were included by calculating the spectral function A(ε), which introduces vibrational broadening and shifts the cross section weight to higher energies.
Charge State Approximation: Calculations utilized the neutral (q=0) charge state approximation, validated by high overlap integrals (>99.6%) between the neutral and negatively charged defect wavefunctions.

6CCVD Solutions & Capabilities

The research confirms that high-fidelity quantum experiments, such as PDMR and spin-to-charge conversion, rely fundamentally on ultra-high purity, low-strain diamond material. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond substrates and customization services to replicate and advance this research.

Applicable Materials

To replicate the high-coherence physics studied in this paper, researchers require material optimized for minimal background noise and stable defect formation.

Primary Recommendation: Optical Grade Single Crystal Diamond (SCD). This material offers the lowest native defect density and strain, ensuring stable NV⁻ centers and minimizing competing photoionization or recombination pathways.
Alternative for Large Area Devices: High-Purity Polycrystalline Diamond (PCD). For applications requiring large-area PDMR arrays or sensors, 6CCVD offers PCD wafers up to 125mm in diameter with excellent purity.

Customization Potential for NV Experiments

The paper highlights the importance of integrating NV centers into complex electrical and optical setups (e.g., PDMR). 6CCVD provides end-to-end material engineering solutions:

Research Requirement	6CCVD Capability	Technical Specification Match
Substrate Dimensions	Custom Plates and Wafers	We supply SCD plates and PCD wafers up to 125mm, with thicknesses ranging from 0.1µm to 500µm (SCD/PCD) and substrates up to 10mm thick.
Surface Preparation	Precision Polishing	SCD surfaces polished to Ra < 1 nm and inch-size PCD polished to Ra < 5 nm, critical for minimizing scattering losses during optical readout and dual-beam excitation.
Electrical Integration (PDMR)	In-House Metalization	We offer custom deposition of contact metals (Au, Pt, Pd, Ti, W, Cu) to facilitate electrical readout and PDMR device fabrication, directly supporting the spin-to-charge conversion protocols discussed.
Defect Engineering	Controlled Doping	6CCVD’s MPCVD process allows for precise control of nitrogen incorporation during growth, optimizing the precursor concentration necessary for subsequent NV center creation via implantation and annealing.

Engineering Support

6CCVD’s in-house PhD team specializes in the material science of quantum defects. We can assist researchers in:

Material Selection: Choosing the optimal SCD grade and thickness based on specific experimental parameters (e.g., laser wavelength, power density, and required coherence time).
Process Optimization: Consulting on post-processing steps, including surface termination and annealing protocols, to maximize NV⁻ yield and stability for similar spin-to-charge conversion and PDMR projects.
Global Logistics: Ensuring reliable, global shipping (DDU default, DDP available) of sensitive diamond materials.

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

View Original Abstract

We present ab-initio calculations of photoionization thresholds and cross\nsections of the negatively charged nitrogen-vacancy (NV) center in diamond from\nthe ground $^{3}\!A_2$ and the excited $^{3}\!E$ states. We show that after the\nionization from the $^{3}\!E$ level the NV center transitions into the\nmetastable $^{4}\!A_2$ electronic state of the neutral defect. We reveal how\nspin polarization of $\mathrm{NV}^{-}$ gives rise to spin polarization of the\n$^{4}\!A_2$ state, providing an explanation of electron spin resonance\nexperiments. We obtain smooth photoionization cross sections by employing dense\n$k$-point meshes for the Brillouin zone integration together with the band\nunfolding technique to rectify the distortions of the band structure induced by\nartificial periodicity of the supercell approach. Our calculations provide a\ncomprehensive picture of photoionization mechanisms of $\mathrm{NV}^{-}$. They\nwill be useful in interpreting and designing experiments on charge-state\ndynamics at NV centers. In particular, we offer a consistent explanation of\nrecent results of spin-to-charge conversion of NV centers.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.104.235301