Microscopic processes during ultra-fast laser generation of Frenkel defects in diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-01-01 |
| Journal | arXiv (Cornell University) |
| Authors | Benjamin Griffiths, Andrew Kirkpatrick, Shannon S. Nicley, R. L. Patel, Joanna M. Zajac |
| Institutions | University of Oxford, Michigan State University |
| Citations | 21 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study presents a combined theoretical and experimental investigation into the ultra-fast laser generation of Frenkel defects (vacancy-interstitial pairs) in diamond, a critical step for engineering solid-state quantum devices.
- Defect Mechanism Identified: Frenkel defect generation is attributed to the thermally activated non-radiative recombination of self-trapped biexcitons (STbX), rather than solely being proportional to the initial photoionization event.
- High Non-Linearity Quantified: Experimental data and the coupled rate equation model (PDE) show an effective non-linearity of approximately 40 at the onset of defect generation, followed by rapid saturation above 20 nJ.
- Critical Energy Barrier: The model successfully fits experimental data, yielding a precise activation energy barrier (Eb) of 0.47 ± 0.01 eV for the non-radiative STbX recombination pathway.
- Efficiency Dependence: Longer laser pulses (e.g., 500 fs to 1 ps) generate defects more efficiently than shorter pulses (120 fs) due to increased impact ionization and greater carrier heating, which accelerates the thermally activated defect formation process.
- Spatial Control: Simulated defect distributions show a tight focus (Full-Width Half-Maximum of ~50 nm radius and ~250 nm depth), consistent with the positional accuracy required for NV center engineering.
- Modeling Tool: The developed coupled PDE model provides a general, quantitative framework for optimizing fabrication parameters (pulse energy, duration, NA) for defect engineering in wide-bandgap materials.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Defect Generation Non-Linearity | ~40 | N/A | Effective non-linearity relative to laser pulse energy (16-18 nJ range). |
| Activation Energy Barrier (Eb) | 0.47 ± 0.01 | eV | Energy barrier for non-radiative STbX recombination. |
| Diamond Type | 1b single-crystal | N/A | Nitrogen concentration: 2 ppb. |
| Laser Wavelength | 790 | nm | Ti:Sapphire laser source. |
| Pulse Energy Range (Tested) | 10 to 24 | nJ | Single pulse writing energy range. |
| Pulse Duration Range (Tested) | 120 fs to 1 | ps | Varied via CPA tuning. |
| Focusing Objective | 1.4 | NA | Oil immersion (Olympus PlanApo). |
| GR1 Fluorescence Peak | 740 | nm | Wavelength used to detect neutral vacancies (V0). |
| Exciton Binding Energy (Ex) | 80 | meV | Diamond material property. |
| Biexciton Binding Energy (Ebx) | 12 | meV | Diamond material property. |
| Simulated Defect FWHM (Radius) | ~50 | nm | For 5.5 nJ pulse at 20 ”m depth. |
| Graphitization Threshold | 9% | Natomic | Carrier density threshold for lattice damage/melting. |
| Quasi-Equilibrium Temperature | > 500 | K | Temperature required for efficient Frenkel defect formation (competing with radiative decay). |
Key Methodologies
Section titled âKey MethodologiesâThe study utilized a combination of ultra-fast laser processing and a comprehensive time-domain simulation model.
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Laser Writing Setup:
- Single ultra-fast pulses (790 nm, 10-20 nJ) were focused 20 ”m deep into the diamond sample using a high-NA (1.4) oil immersion objective.
- A Spatial Light Modulator (SLM) was employed to correct spherical aberrations at the oil-diamond interface, ensuring a diffraction-limited focal spot, and to control the effective NA (0.95 to 1.4).
- Pulse duration was precisely controlled (120 fs to 1 ps) via tuning the Chirped Pulse Amplifier (CPA) compression.
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Defect Quantification:
- The number of generated Frenkel defects (vacancies) was measured indirectly via Photoluminescence (PL) spectroscopy, focusing on the GR1 fluorescence peak (740 nm) characteristic of neutral vacancies (V0).
- Fluorescence intensity was measured as a function of pulse energy, NA, and pulse duration to generate the experimental data sets.
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Rate Equation Modeling (PDE):
- A set of eight coupled, non-linear partial differential equations (PDEs) was solved numerically using finite difference methods, tracking the system dynamics from the pulse onset to 100 ps after the pulse.
- The model tracked: optical intensity, electron/hole concentrations, exciton/biexciton concentrations, self-trapped biexciton (STbX) concentration, lattice temperature, and Frenkel defect concentration.
- Carrier Generation: Included multi-photon absorption, Zener breakdown, and avalanche processes, calculated using diamondâs Density Functional Theory (DFT) band structure.
- Defect Formation Hypothesis: Frenkel defect generation was modeled as a thermally activated process from the STbX population, with the rate dependent on the lattice temperature (TL) and the derived energy barrier (Eb = 0.47 eV).
Commercial Applications
Section titled âCommercial ApplicationsâThe ability to precisely generate isolated vacancies in wide-bandgap materials using ultra-fast lasers is foundational for next-generation quantum and advanced materials technologies.
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Quantum Computing and Sensing:
- NV Center Fabrication: Direct, high-yield laser writing of isolated vacancies, which are precursors to Nitrogen-Vacancy (NV) centers, essential for solid-state quantum bits (qubits) and quantum sensors.
- 3D Qubit Arrays: Enabling the creation of deep, three-dimensional arrays of quantum defects with high positional accuracy (~50 nm radius), crucial for scalable quantum architectures.
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Advanced Materials Micro-machining:
- Precision Dielectric Modification: Optimizing laser parameters for controlled modification and micro-machining of transparent materials like diamond, silicon carbide (SiC), and fused silica (SiO2).
- Integrated Photonics: Creating integrated waveguides and optical components within diamond by controlling localized refractive index changes induced by the laser-generated defects.
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High-Power Optics:
- Damage Threshold Prediction: The quantitative model for carrier dynamics and lattice heating provides a tool for predicting laser-induced damage and breakdown thresholds in high-power optical components made from wide-bandgap materials.
View Original Abstract
Engineering single atomic defects into wide bandgap materials has become an attractive field\nin recent years due to emerging applications such as solid-state quantum bits and sensors. The\nsimplest atomic-scale defect is the lattice vacancy which is often a constituent part of more complex\ndefects such as the nitrogen-vacancy (NV) centre in diamond, therefore an understanding of the\nformation mechanisms and precision engineering of vacancies is desirable. We present a theoretical\nand experimental study into the ultra-fast laser generation of vacancy-interstitial pairs (Frenkel\ndefects) in diamond. In a range of other materials, Frenkel defect formation has previously been\nlinked to the recombination of laser generated excitonic states, however the mechanism in diamond\nis currently unknown and to date no quantitative agreement has been found between experiment\nand theory. Here, we find that a model for Frenkel defect generation via the recombination of\na bound biexciton as the electron plasma cools provides good agreement with experimental data.\nThe process is described by a set of coupled rate equations of the pulsed laser interaction with the\nmaterial and of the non-equilibrium dynamics of charge carriers during and in the wake of the pulse.