Lattice thermal conductivity in isotope diamond asymmetric superlattices
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-12-14 |
| Journal | Japanese Journal of Applied Physics |
| Authors | Hsu Kai Weng, Akira Nagakubo, Hideyuki Watanabe, Hirotsugu Ogi |
| Institutions | The University of Osaka, National Institute of Advanced Industrial Science and Technology |
| Citations | 1 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research investigates the lattice thermal conductivity (Îș) of 12C/13C isotope diamond superlattices (SLs) using theoretical modeling to achieve precise thermal control while preserving diamondâs mechanical integrity.
- Thermal Reduction Mechanism: The thermal conductivity of the SLs is significantly reduced compared to pure diamond, primarily due to the decrease in phonon group velocity caused by the folded Brillouin zone structure.
- Asymmetry Advantage: Asymmetric superlattices (where the number of 12C layers differs from the number of 13C layers) exhibit higher Îș than symmetric SLs of the same total period.
- Optimal Control Point: The minimum thermal conductivity for a fixed superlattice period is achieved when the 13C concentration is approximately 75% (a 12C:13C layer ratio of ~1:3). This minimum results from a trade-off between increasing phonon specific heat (due to heavier 13C) and decreasing phonon group velocity.
- Impurity Sensitivity: The presence of isotopic impurities (modeled as thin 13C layers) drastically reduces Îș, achieving a calculated reduction of up to ~33% relative to pure 12C diamond, validating prior experimental findings.
- Structural Integrity: The use of isotopic layering ensures minimal lattice mismatch (~0.01%) at the interface, suggesting that the inherent high stiffness and strength of diamond are maintained.
- Controllability: The findings confirm that thermal conductivity can be controlled over a wide range by tuning the superlattice period, layer asymmetry, and isotopic purity.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Purified Diamond Îș (Reference) | ~3000 | W/mK | Thermal conductivity of isotopically purified 12C diamond. |
| Natural 13C Content | 1.1 | % | Natural isotopic ratio of carbon. |
| Isotopic Lattice Mismatch (12C/13C) | ~0.01 | % | Minimal mismatch, preserving mechanical properties. |
| Interatomic Bond Strength Difference | ~0.2 | % | Difference in bond strength between 12C and 13C. |
| Maximum Calculated Îș Reduction | ~33 | % | Reduction in Îș observed with 1% isotopic impurity content. |
| Minimum Îș Ratio (Calculated) | ~64 | % | Lowest normalized thermal conductivity (Îș/Îș12C) achieved in asymmetric SLs (at 13C content ~75%). |
| Stacking Direction | [100] | Direction | Direction of superlattice layer growth. |
| Temperature Range (Modeling) | 0 to 2000 | K | Range used for calculating temperature dependence of Îș. |
Key Methodologies
Section titled âKey MethodologiesâThe study utilized a computational approach based on phonon transport theory to model the thermal properties of the superlattices:
- Lattice Thermal Conductivity Calculation: The core calculation followed phonon kinetic theory, determining the total thermal conductivity (Îș) by summing the contributions of individual phonon modes (λ).
- Specific Heat Modeling: The specific heat C(Ï) for each phonon mode was calculated using the quantum harmonic oscillator model combined with the Planck distribution.
- Lattice Dynamics Simulation: The out-of-plane phonon group velocity (vλ,z) was derived from a lattice dynamics model. This model treated each atom bonded to four first-nearest neighbors and twelve second-nearest neighbors, incorporating bond-stretching and bond-bending stiffness parameters.
- Parameter Calibration: The stiffness parameters used in the lattice dynamics model were calibrated against existing experimental data on phonon dispersion relationships and measured elasticity (via picosecond ultrasound spectroscopy).
- Mean Free Time Normalization: To simplify the comparison of different superlattice structures, the thermal conductivity was normalized by the phonon mean-free time (Îș/Ïλ), assuming Ïλ is the same for all modes.
- Scattering Mechanism Analysis: The relaxation time (Ï-1) for the dominant mini-Umklapp scattering process was modeled to explain the observed minimum Îș in asymmetric structures, relating it to temperature, frequency, and the mass difference fraction (ÎM/M).
Commercial Applications
Section titled âCommercial ApplicationsâThe ability to precisely tailor the thermal conductivity of diamond while maintaining its superior mechanical properties is critical for several high-performance engineering fields:
- Thermoelectric Energy Conversion: Creating highly efficient thermoelectric materials by maximizing the figure of merit (ZT). Diamond superlattices offer a path to drastically reduce Îș (improving ZT) without sacrificing the materialâs inherent stability or electrical properties.
- Advanced Thermal Management: Developing customized heat spreaders and thermal barriers for high-power density electronics (e.g., RF amplifiers, power converters) where directional heat flow control is essential to prevent localized overheating.
- Acoustic and Phononic Devices: Utilizing the engineered phonon band gaps and dispersion curves to create high-frequency acoustic filters, resonators, and phononic crystals for sensing and signal processing.
- Quantum Computing and Sensing: Isotopic purification and layering are fundamental for controlling defect centers (like NV centers) in diamond. Precise thermal control is necessary to maintain the long coherence times required for quantum information processing and sensing applications.
- High-Performance Substrates: Manufacturing substrates for wide-bandgap semiconductors (like GaN or SiC) that require extreme mechanical robustness combined with tailored thermal dissipation characteristics.
View Original Abstract
Abstract We study the lattice thermal conductivity of isotope diamond superlattices consisting of 12 C and 13 C diamond layers at various superlattice periods. It is found that the thermal conductivity of a superlattice is significantly deduced from that of pure diamond because of the reduction of the phonon group velocity near the folded Brillouin zone. The results show that asymmetric superlattices with a different number of layers of 12 C and 13 C diamonds exhibit higher thermal conductivity than symmetric superlattices even with the same superlattice period, and we find that this can be explained by the trade-off between the effects of phonon specific heat and phonon group velocity. Furthermore, impurities and imperfect superlattice structures are also found to significantly reduce the thermal conductivity, suggesting that these effects can be exploited to control the thermal conductivity over a wide range.