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Lattice thermal conductivity in isotope diamond asymmetric superlattices

MetadataDetails
Publication Date2021-12-14
JournalJapanese Journal of Applied Physics
AuthorsHsu Kai Weng, Akira Nagakubo, Hideyuki Watanabe, Hirotsugu Ogi
InstitutionsThe University of Osaka, National Institute of Advanced Industrial Science and Technology
Citations1
AnalysisFull AI Review Included

Technical Documentation & Analysis: Isotope Diamond Superlattices for Thermal Management

Section titled “Technical Documentation & Analysis: Isotope Diamond Superlattices for Thermal Management”

This research demonstrates the precise control of lattice thermal conductivity ($\kappa$) in diamond using isotopically engineered $^{12}$C/$^{13}$C superlattices. This capability is critical for developing advanced thermal management and thermoelectric devices.

  • Core Achievement: Systematic control of diamond’s ultra-high thermal conductivity over a wide range by manipulating the superlattice period and the ratio of $^{12}$C to $^{13}$C layers.
  • Mechanism: Thermal conductivity reduction is primarily driven by the decrease in phonon group velocity near the folded Brillouin zone, a direct result of the periodic mass difference.
  • Asymmetric Control: Asymmetric superlattices (e.g., 1:3 ratio of $^{12}$C:$^{13}$C) achieve the lowest thermal conductivity for a given period, offering superior tunability compared to symmetric structures.
  • Impurity Sensitivity: The model confirms that even minor isotopic impurities (1%) significantly reduce thermal conductivity by approximately 33%, highlighting the necessity of precise material purity control in SCD growth.
  • Material Implication: The study validates the use of high-quality, epitaxially grown SCD thin films (achieved via MPCVD) as the foundational material for advanced phonon engineering.
  • 6CCVD Value Proposition: 6CCVD specializes in providing the high-purity, ultra-thin SCD layers and custom metalization required to replicate and extend this research into functional thermal devices.

The following hard data points were extracted from the theoretical calculations and referenced experimental observations:

ParameterValueUnitContext
Thermal Conductivity (Purified $^{12}$C)$\approx 3000$W/mKReference 16, High-purity SCD baseline
Natural $^{13}$C Isotope Content1.1%Standard carbon source
Target Purified $^{13}$C Content0.1%Used for high-$\kappa$ reference material
Interfacial Lattice Mismatch ($^{12}$C/$^{13}$C)$\approx 0.01$%Extremely low, enabling high-quality epitaxy
Optimal Asymmetric Ratio ($^{12}$C:$^{13}$C)$\approx 1:3$ (or 0.75 $^{13}$C content)N/ARatio yielding minimum thermal conductivity
Minimum Normalized $\kappa$ (297 K)$\approx 64$%Relative to pure $^{12}$C diamond (for 100-layer period)
Impurity Effect (1% Impurity)$\approx 33$% ReductionConfirmed reduction in thermal conductivity
Superlattice Stacking Direction[100]N/AGrowth orientation for superlattice structure
Calculation Temperature Range0 to 2000KRange of theoretical thermal conductivity analysis

The study employed theoretical calculations based on phonon kinetic theory and lattice dynamics to model heat conduction in the superlattices.

  1. Lattice Thermal Conductivity Calculation: The investigation utilized the method established by Tamura et al. (Reference 20), starting from the phonon kinetic theory ($\kappa = \sum \kappa_{\lambda}$).
  2. Specific Heat Calculation: Specific heat $C(\omega)$ was calculated using the quantum harmonic oscillator and the Planck distribution.
  3. Lattice Dynamics Model: The out-of-plane group velocity ($v_{\lambda,z}$) was determined using a lattice dynamics model incorporating bond-stretching and bond-bending stiffnesses, calibrated against experimental phonon dispersion data.
  4. Thermal Conductivity Normalization: Thermal conductivity ($\kappa$) was evaluated normalized by the phonon mean-free time ($\tau_{\lambda}$), assuming $\tau_{\lambda}$ is identical for each mode, simplifying the analysis to focus on structural effects.
  5. Asymmetric Structure Analysis: Systematic investigation of superlattices denoted $(n_{12C}, n_{13C})$, where $n$ represents the number of atomic layers, with stacking along the [100] direction.
  6. Impurity and Imperfection Modeling: The model was extended to simulate the effects of isotopic impurities and structural imperfections (thicker layers) on phonon group velocity and thermal conductivity.

The research highlights the need for ultra-high purity, precisely controlled epitaxial diamond layers—a core competency of 6CCVD. Our MPCVD capabilities are perfectly suited to supply the foundational materials necessary for replicating and advancing this phonon engineering research.

Research Requirement6CCVD Solution & CapabilityValue Proposition
High-Purity Isotope ControlOptical Grade SCD: 6CCVD provides high-purity Single Crystal Diamond (SCD) with extremely low nitrogen and non-carbon impurity incorporation, essential for achieving the high baseline thermal conductivity ($\approx 3000$ W/mK) required for controlled reduction.Precise Purity: Enables researchers to isolate the effects of engineered superlattice structure from unintentional impurity scattering.
Ultra-Thin Layer GrowthSCD Thickness Control: We offer SCD layers from 0.1 ”m up to 500 ”m. This precision is vital for fabricating the specific $n_{12C}/n_{13C}$ superlattice periods (e.g., 8, 40, 100 layers) required for phonon bandgap engineering.Structural Fidelity: Guarantees the precise layer thickness needed to achieve the calculated asymmetric thermal conductivity minimum (e.g., 1:3 ratio).
Interface QualityUltra-Low Roughness Polishing: Achieving the minimal $\approx 0.01%$ lattice mismatch requires an atomically flat starting surface. 6CCVD guarantees Ra < 1nm polishing on SCD, critical for high-quality epitaxial growth.Epitaxial Success: Minimizes interfacial defects that would otherwise dominate phonon scattering and mask the superlattice effect.
Custom Device IntegrationCustom Metalization Services: For integrating these engineered thermal materials into functional thermoelectric or thermal spreading devices, 6CCVD offers in-house metalization (Au, Pt, Pd, Ti, W, Cu) and laser cutting services.Turnkey Fabrication: Provides ready-to-use substrates with contacts, accelerating the transition from theoretical study to prototype device testing.
Scale and DimensionsLarge Area PCD/SCD: We offer custom dimensions for plates/wafers up to 125mm (PCD) and substrates up to 10mm thick, facilitating the scale-up of successful superlattice designs.Scalability: Supports manufacturing processes beyond the lab bench, enabling commercial viability for new thermal devices.

6CCVD’s in-house PhD engineering team possesses deep expertise in MPCVD growth parameters and material characterization, offering critical support for projects focused on advanced phonon transport and thermal management.

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

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.