An ab initio effective solid-state photoluminescence by frequency constraint of cluster calculation

At a Glance

Metadata	Details
Publication Date	2020-12-16
Journal	Journal of Applied Physics
Authors	Akib Karim, Igor Lyskov, Salvy P. Russo, Alberto Peruzzo, Akib Karim
Institutions	Centre for Quantum Computation and Communication Technology, RMIT University
Citations	11
Analysis	Full AI Review Included

Technical Documentation & Analysis: Ab-Initio Photoluminescence of NV Centers in Diamond

This document analyzes the research paper “An ab-initio effective solid state photoluminescence by frequency constraint of cluster calculation,” focusing on the methodology for simulating the photoluminescence (PL) spectrum of Nitrogen-Vacancy (NV^-) centers in diamond. The findings are leveraged to highlight 6CCVD’s capabilities in supplying high-purity, custom-engineered MPCVD diamond materials essential for advancing solid-state quantum technology.

Executive Summary

The research successfully demonstrates a novel ab-initio method for accurately simulating the room-temperature photoluminescence (PL) spectra of solid-state defects, specifically the NV^- center in diamond, overcoming computational limitations inherent in cluster calculations.

Core Challenge Addressed: Finite-size effects in nanodiamond cluster simulations introduce spurious low-frequency vibrational modes that distort the PL spectrum compared to bulk solid-state material.
Methodology: The study utilizes Time-Dependent Density Functional Theory (TD-DFT) combined with the Displaced Harmonic Oscillator (DHO) model and applies a low-frequency cutoff to the vibrational modes.
Key Innovation: A constrained optimization technique is used to identify the cutoff frequency (e.g., 357 cm^-1 or 469 cm^-1) that effectively removes surface-related vibrational coupling.
Validation: The predicted PL spectrum for the C₁₉₇N H₁₄₀ nanodiamond cluster, when the cutoff is applied, successfully matches the experimental PL peaks and lineshape of the solid-state NV^- center.
Material Relevance: This technique provides a valuable tool for predicting and understanding the properties of solid-state single photon emitters, which rely on high-quality Single Crystal Diamond (SCD) substrates.
Quantum Application: The work directly supports the development of next-generation quantum technologies, including deterministic single photon sources and quantum computing architectures based on diamond defects.

Technical Specifications

The following data points were extracted from the simulation results, primarily focusing on the C₁₉₇N H₁₄₀ nanodiamond cluster, which yielded the most accurate Zero-Phonon Line (ZPL) match.

Parameter	Value	Unit	Context
Defect Center Simulated	NV^-	N/A	Nitrogen-Vacancy in Diamond
Nanodiamond Composition	C₁₉₇N H₁₄₀	N/A	Cluster size (1.31 nm diameter)
Adiabatic Energy (E_adiab)	1.95	eV	Difference between relaxed ground and excited states
Experimental ZPL Value	1.945	eV	Target value for E_adiab match
Vertical Absorption (E_abs)	2.10	eV	Calculated via TD-DFT
Vertical Emission (E_emit)	1.56	eV	Calculated via TD-DFT
Total Huang-Rhys Constant (S)	4.32	dim-less	Calculated for C₁₉₇N H₁₄₀ with cutoff
Optimal Low Frequency Cutoff 1	357	cm^-1	Used to recover solid-state PL spectrum
Optimal Low Frequency Cutoff 2	469	cm^-1	Used to recover solid-state PL spectrum
Simulation Temperature	300	K	Room temperature PL simulation
Line Broadening Convolution	200	cm^-1	Gaussian width applied to replicate experimental FWHM
DFT Functional Used	PBE0	N/A	Optimal exchange-correlation function for NV^- TD-DFT
Basis Set Used	def2-SV(P)	N/A	Used for geometry optimization

Key Methodologies

The simulation of the NV^- photoluminescence spectrum relied on a multi-step ab-initio approach combining Density Functional Theory (DFT) for ground state properties and Time-Dependent DFT (TD-DFT) for excited state properties.

Cluster Construction: Nanodiamond clusters (e.g., C₁₉₇N H₁₄₀) containing the NV^- defect were constructed, terminated by hydrogen atoms (CH and CH₂ groups).
Ground State Optimization: DFT calculations were performed using the PBE0 functional and def2-SV(P) basis set to obtain the optimized ground state geometry under C_3v symmetry constraints.
Vibrational Mode Calculation: Normal mode calculations were performed under the harmonic approximation in DFT to yield the eigenfrequencies (E_vib) and normal coordinates.
Excited State Optimization (Unconstrained): TD-DFT was used to optimize the excited state geometry under C_s symmetry, yielding the adiabatic energy (E_adiab), displacement vector (D), and unconstrained Partial Huang-Rhys (PHR) factors.
Excited State Optimization (Constrained): A second TD-DFT optimization was performed with the outermost CH and CH₂ groups constrained (fixed) to mimic the solid-state environment, yielding constrained PHR factors.
Cutoff Determination: The difference between the constrained and unconstrained PHR spectra was analyzed to identify the low-frequency region where vibrational modes are suppressed in the solid state. The cutoff frequency (e.g., 357 cm^-1) was determined as the arithmetic mean of the boundary frequencies.
PL Spectrum Calculation: The PHR spectrum, modified by applying the low-frequency cutoff, was input into the Displaced Harmonic Oscillator (DHO) model under the Franck-Condon approximation. The resulting correlation function was Fourier transformed to yield the final PL spectrum, subsequently convoluted with a 200 cm^-1 Gaussian to match experimental line broadening.

6CCVD Solutions & Capabilities

This research validates advanced theoretical methods for predicting the performance of solid-state quantum emitters. Successful experimental realization of high-coherence NV^- centers requires ultra-high purity, low-strain diamond substrates—precisely the materials 6CCVD specializes in.

Applicable Materials for Quantum Emitter Research

To replicate or extend this research into functional quantum devices, researchers require diamond with minimal background defects and superior surface quality.

6CCVD Material	Specification	Application Relevance
Optical Grade SCD	Nitrogen concentration < 1 ppb. Low strain.	Essential for creating high-coherence NV^- centers via implantation or in-situ growth. Minimizes decoherence.
Electronic Grade SCD	High purity, low compensation.	Ideal for high-power applications or when precise electrical control (e.g., Stark tuning) of the NV^- center is required.
Custom PCD Substrates	Plates up to 125 mm diameter.	Provides large-area platforms for high-throughput processing, integration of photonic circuits, or use as high-quality heat spreaders in related systems.
Boron-Doped Diamond (BDD)	Custom doping levels (p-type).	Useful for creating integrated electrical contacts or for research into other defect centers requiring charge control.

Customization Potential for Integrated Quantum Systems

The integration of NV^- centers into scalable quantum architectures demands precise material engineering that goes beyond standard wafer supply. 6CCVD offers full customization to meet the stringent requirements of photonic integration.

Custom Dimensions and Thickness: We supply SCD plates and wafers in custom dimensions, with thicknesses precisely controlled from 0.1 µm (thin films for integration) up to 500 µm. Substrates up to 10 mm thick are available for high-power or high-pressure applications.
Ultra-Low Roughness Polishing: For optical integration and minimizing surface-related decoherence (a critical factor in nanodiamond research), 6CCVD guarantees Ra < 1 nm for Single Crystal Diamond (SCD) surfaces.
Precision Metalization: For creating electrical contacts, waveguides, or bonding layers necessary for device fabrication, 6CCVD provides in-house deposition of standard and custom metal stacks, including Ti/Pt/Au, W, Cu, Pd, and Pt.
Advanced Fabrication: We offer precision laser cutting and etching services to create custom shapes, micro-structures, or alignment features required for coupling NV^- emitters to photonic resonators or waveguides.

Engineering Support

6CCVD’s in-house team of PhD-level material scientists and engineers specializes in the growth and characterization of MPCVD diamond for quantum applications. We provide expert consultation on:

Material Selection: Guiding researchers in choosing the optimal diamond grade (e.g., nitrogen content, isotopic purity) for specific quantum emitter projects (NV^-, SiV^-, GeV^-, etc.).
Defect Engineering: Advising on post-processing techniques (e.g., high-temperature annealing, ion implantation) to maximize the yield and coherence of desired defect centers.
Surface Preparation: Ensuring the material meets the required surface quality for subsequent lithography, metalization, and integration steps.

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

View Original Abstract

Measuring the photoluminescence of defects in crystals is a common experimental technique for analysis and identification. However, current theoretical simulations typically require the simulation of a large number of atoms to eliminate finite-size effects, which discourages computationally expensive excited state methods. We show how to extract the room-temperature photoluminescence spectra of defect centers in bulk from an ab initio simulation of a defect in small clusters. The finite-size effect of small clusters manifests as strong coupling to low frequency vibrational modes. We find that removing vibrations below a cutoff frequency determined by constrained optimization returns the main features of the solid-state photoluminescence spectrum. This strategy is illustrated for the negatively charged nitrogen vacancy defect in diamond (NV−) presenting a connection between defects in solid state and clusters; the first vibrationally resolved ab initio photoluminescence spectrum of an NV− defect in a nanodiamond; and an alternative technique for simulating photoluminescence for solid-state defects utilizing more accurate excited state methods.

Tech Support

Original Source

DOI: https://doi.org/10.1063/5.0033417