Determining the Dependence of Single Nitrogen−Vacancy Center Light Extraction in Diamond Nanostructures on Emitter Positions with Finite−Difference Time−Domain Simulations

At a Glance

Metadata	Details
Publication Date	2023-12-31
Journal	Nanomaterials
Authors	Tianfei Zhu, Jia Zeng, Feng Wen, Hongxing Wang
Institutions	Xi’an Jiaotong University
Analysis	Full AI Review Included

Executive Summary

This study utilizes Finite-Difference Time-Domain (FDTD) simulations to determine the optimal geometry and emitter orientation for maximizing light extraction efficiency (LEE) from Nitrogen-Vacancy (NV) centers embedded in diamond nanostructures.

Core Achievement: Demonstrated that nanocone and nanopillar geometries exhibit distinct optimal performance based on the NV center dipole polarization.
Nanocone Superiority (s-polarization): Nanocones achieved the highest LEE of 57.96% for s-polarized emitters (parallel to the x-y plane), significantly surpassing the nanopillar’s 47.20% for the same polarization.
Nanopillar Superiority (p-polarization): Nanopillars achieved a higher LEE of 38.40% for p-polarized emitters (perpendicular to the x-y plane), compared to the nanocone’s 32.89%.
Sensitivity Difference: The nanocone structure’s LEE is highly sensitive to changes in emitter depth and polarization angle, attributed to faster mode conversion from guided to radiative modes due to the sidewall angle.
Fabrication Method: The nanocone prototype was based on a structure fabricated using a scalable thermal annealing method combined with Inductively Coupled Plasma (ICP) etching on IIa-type CVD diamond.
Mechanism Explained: Differences in LEE are attributed to the evolution of photon propagation modes (guided vs. radiative) and internal reflection effects influenced by the nanostructure geometry (sloped sidewalls in nanocones vs. vertical sidewalls in nanopillars).

Technical Specifications

Parameter	Value	Unit	Context
Best LEE (Nanocone)	57.96	%	s-polarization, 25 nm depth
Best LEE (Nanopillar)	38.40	%	p-polarization, 25 nm depth
NV Center Coherence Time (T₂)	1.8	ms	Room temperature
Diamond-Air Critical Angle	24.4	°	Total Internal Reflection (TIR) limit in bulk diamond
Emitter Wavelength	637	nm	FDTD simulation
Diamond Refractive Index	2.42	N/A	FDTD simulation parameter
Objective Numerical Aperture (NA)	0.95	N/A	Equivalent collection efficiency
Fabricated Nanocone Height	415	nm	Actual height (trigonometrically calculated)
Fabricated Nanocone Base Diameter	290	nm	Measured from SEM
Nanocone Cone Angle	33.01	°	Calculated from geometry
Emitter Depth Range (Simulated)	25, 50, 75, 100	nm	Measured from the top surface

Key Methodologies

The study involved two main phases: fabrication of the nanocone prototype using thermal annealing and subsequent FDTD simulation modeling.

1. Nanocone Fabrication (Thermal Annealing Method)

Substrate Preparation (IIa-type CVD Diamond):
- HPHT diamond substrate was cleaned in a mixed acid (H₂SO₄:HNO₃:HClO₄, 31.2:36:11.4 volume ratio) at 250 °C for 1 h.
- Alkali cleaning followed (NH₄OH:H₂O₂:H₂O, 4:3:9 volume ratio) at 80 °C for 10 min.
Epitaxial Growth (CVD):
- Pressure: 100 Torr.
- Gas Flows: H₂ (500 sccm), O₂ (2.9 sccm), CH₄ (40 sccm).
- Growth Time: 30 h (resulting thickness approx. 300 µm).
Mask Formation:
- SPR-220 photoresist (PR) was spun (3 µm thickness).
- Photolithography created round hole patterns (1 µm diameter).
- Gold film (10 nm thickness) was deposited via electron beam evaporation and lift-off.
Thermal Annealing (Gold Dewetting):
- Samples were annealed at 1100 °C for 5 min.
- Micro-sized gold disks dewetted into nanoscale gold spheres, which served as the etching mask.
ICP Etching (Nanostructure Formation):
- Etching Gas: O₂ (50 sccm flow rate).
- Chamber Pressure: 10 mTorr.
- Coil Power: 450 W.
- Platen Power: 25 W (to obtain nanocone morphology).
- Etching Time: 3 min.

2. FDTD Simulation Setup

Model Geometry: Nanocone and nanopillar models were built with comparable dimensions (Height 415 nm, Diameter 290 nm).
Material Parameters: Diamond refractive index set to 2.42; air to 1.
Source Placement: Electric dipoles (representing NV centers) were placed along the central axis at depths of 25, 50, 75, and 100 nm from the top.
Polarization States:
- s-polarization (0°): Parallel to the x-y plane.
- p-polarization (90°): Perpendicular to the x-y plane (along the axis).
- Intermediate Angles: 30°, 45°, and 60° relative to the s-orientation were also modeled.
Boundary Conditions: Perfectly Matched Layers (PML) were used.
Efficiency Calculation: Collection efficiency (η) was calculated by integrating the far-field electric field intensity (I_NA) within the NA 0.95 collection angle, normalized by the total source power (I_total) emitted by a bulk diamond.

Commercial Applications

The development of high-efficiency, directionally controlled single-photon sources based on NV centers in diamond nanostructures is critical for several emerging quantum and sensing technologies.

Industry/Field	Application	Relevance to Technology
Quantum Computing & Communication	Single-photon sources (SPS), Quantum key distribution (QKD)	High LEE (57.96%) and directional emission are essential for scalable, high-fidelity quantum networks.
High-Precision Quantum Sensing	Magnetometry, Thermometry, Stress/Pressure sensors	NV centers are used as quantum sensors; increased photon extraction improves the signal-to-noise ratio and detection accuracy of the external environment.
Biological Detection & Imaging	Intracellular temperature sensing, Magnetic field imaging of bacteria	High photon output enables sensitive detection and imaging in complex biological environments at room temperature.
Nano-Optics & Photonics	Integrated micro- and nano-optics, Solid-state light sources	Provides design guidance for optimizing nanostructure geometry (nanocones vs. nanopillars) to match specific dipole orientations (s-pol vs. p-pol) for maximum coupling.
Materials Science & Fabrication	Scalable Nanostructure Production	The use of the thermal annealing method offers a large-scale, cost-effective alternative to conventional electron beam lithography for fabricating high-performance SPS arrays.

View Original Abstract

In this study, we obtained a diamond nanocone structure using the thermal annealing method, which was proposed in our previous work. Using finite-difference time-domain (FDTD) simulations, we demonstrate that the extraction efficiencies of nitrogen-vacancy (NV) center emitters in nanostructures are dependent on the geometries of the nanocone/nanopillar, emitter polarizations and axis depths. Our results show that nanocones and nanopillars have advantages in extraction from emitter dipoles with s− and p−polarizations, respectively. In our simulations, the best results of collection efficiency were achieved from the emitter in a nanocone with s−polarization (57.96%) and the emitter in a nanopillar with p−polarization (38.40%). Compared with the nanopillar, the photon extraction efficiency of the emitters in the nanocone is more sensitive to the depth and polarization angle. The coupling differences between emitters and the nanocone/nanopillar are explained by the evolution of photon propagation modes and the internal reflection effects in diamond nanostructures. Our results could have positive impacts on the design and fabrication of NV center−based micro− and nano−optics in the future.

Tech Support

Original Source

DOI: https://doi.org/10.3390/nano14010099

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