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Ab initiostudies on the lattice thermal conductivity of silicon clathrate frameworks II and VIII

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2016-01-28
JournalPhysical review. B./Physical review. B
AuthorsVille J. HÀrkönen, Antti J. Karttunen
InstitutionsUniversity of JyvÀskylÀ
Citations18
AnalysisFull AI Review Included

Technical Documentation & Analysis: Lattice Thermal Conductivity in Silicon Clathrates

Section titled “Technical Documentation & Analysis: Lattice Thermal Conductivity in Silicon Clathrates”

Executive Summary

Section titled “Executive Summary”

This documentation analyzes the ab initio study of lattice thermal conductivity ($\kappa$) in silicon clathrate frameworks II and VIII, focusing on the implications for advanced material engineering and connecting the research requirements to 6CCVD’s specialized MPCVD diamond capabilities.

  • Research Focus: Computational analysis (DFT + Iterative BTE) of Si-II and Si-VIII clathrates to quantify their intrinsically low lattice thermal conductivity for thermoelectric applications.
  • Key Achievement: Si-II and Si-VIII exhibit significantly lower $\kappa$ than diamond-structure Silicon (d-Si), confirming their potential as efficient thermoelectric materials.
  • Quantified Reduction: In the 100-350 K range, Si-II and Si-VIII $\kappa$ values are reduced to 42-38% and 36-31% of d-Si values, respectively.
  • Room Temperature Data: Calculated $\kappa$ at 300 K is approximately 52 W/(m K) for Si-II and 43 W/(m K) for Si-VIII.
  • Mechanism Identified: The lower $\kappa$ is primarily driven by differences in the harmonic phonon spectra and shorter phonon relaxation times (RTs), particularly in the Si-VIII structure.
  • 6CCVD Relevance: While the study focuses on low-$\kappa$ silicon, 6CCVD provides the industry standard for extreme thermal management (high-$\kappa$ SCD) and functional materials (BDD) required for high-power electronic and electrochemical systems where precise thermal control is paramount.

Technical Specifications

Section titled “Technical Specifications”

The following hard data points were extracted from the computational results, focusing on thermal transport properties and structural parameters.

ParameterValueUnitContext
Temperature Range Studied100 - 350KPrimary range for lattice thermal conductivity ($\kappa$) comparison.
Calculated $\kappa$ (Si-II)$\approx 52$W/(m K)Lattice thermal conductivity at 300 K.
Calculated $\kappa$ (Si-VIII)$\approx 43$W/(m K)Lattice thermal conductivity at 300 K.
$\kappa$ Reduction (Si-II vs. d-Si)42 - 38%Si-II $\kappa$ relative to d-Si $\kappa$ (100-350 K range).
$\kappa$ Reduction (Si-VIII vs. d-Si)36 - 31%Si-VIII $\kappa$ relative to d-Si $\kappa$ (100-350 K range).
Si-II Acoustic Mode RT ($\tau$)1.44 - 0.80s x 10-10Relaxation time $\tau(j)$ at 300 K (Modes 1-3).
Si-VIII Acoustic Mode RT ($\tau$)0.90 - 0.48s x 10-10Relaxation time $\tau(j)$ at 300 K (Modes 1-3).
SCD Acoustic Mode RT ($\tau$)0.37 - 0.08s x 10-10Relaxation time $\tau(j)$ at 300 K (Modes 1-3).
Si-II Unit Cell Atoms34Atoms/cellPrimitive cell size (Fd3m structure).
Si-VIII Unit Cell Atoms23Atoms/cellPrimitive cell size (I43m structure).

Key Methodologies

Section titled “Key Methodologies”

The study utilized advanced computational physics techniques to model phonon transport, requiring high-precision calculation of interatomic forces and scattering rates.

  1. Computational Foundation: Ab initio Density Functional Theory (DFT) was used for structural optimization and calculation of harmonic phonon eigenvalues.
  2. Transport Model: The lattice thermal conductivity ($\kappa$) was calculated using the iterative solution of the linearized Boltzmann Transport Equation (BTE).
  3. Software Implementation: Calculations relied on the Quantum Espresso (QE) package for DFT and the ShengBTE program (v1.0.2) for BTE solution and $\kappa$ calculation.
  4. Force Constant Calculation: Third-order atomic force constants (required for anharmonic scattering) were calculated up to 6th-nearest neighbors.
  5. Supercell Geometry: Different supercell sizes were employed to calculate force constants: d-Si (4,4,4), Si-VIII (3,3,3), and Si-II (2,2,2).
  6. Scattering Inclusion: Both three-phonon scattering (anharmonic effects) and isotopic scattering were included in the BTE model.
  7. Convergence Thresholds: High convergence thresholds were maintained, including 10-12 a.u. for total energy self-consistency in supercell calculations.

6CCVD Solutions & Capabilities

Section titled “6CCVD Solutions & Capabilities”

This research highlights the critical role of phonon engineering and thermal transport modeling in developing advanced materials, particularly for thermoelectric and high-power applications. 6CCVD provides the highest quality MPCVD diamond materials essential for thermal management and functional device integration.

Applicable Materials for Thermal Management and Device Integration

Section titled “Applicable Materials for Thermal Management and Device Integration”

While the paper focuses on low-$\kappa$ silicon clathrates, many advanced electronic and optical systems require materials with extreme thermal conductivity for heat spreading and dissipation. 6CCVD specializes in these high-performance materials.

Application Requirement6CCVD Material SolutionKey Capability Match
Extreme Heat SpreadingOptical Grade Single Crystal Diamond (SCD)SCD offers the highest known thermal conductivity (up to 2200 W/(m K) at 300 K), vastly exceeding d-Si. Ideal for high-power laser diodes and RF electronics.
Functional ElectrodesHeavy Boron-Doped Polycrystalline Diamond (BDD)Provides low electrical resistivity combined with robust thermal and chemical stability, crucial for electrochemical sensing and high-temperature semiconductor applications.
Mechanical/Wear ResistancePolycrystalline Diamond (PCD)Available in large formats (up to 125mm wafers) with high mechanical strength and excellent thermal properties (up to 1800 W/(m K)).

Customization Potential for Advanced Research

Section titled “Customization Potential for Advanced Research”

Future experimental replication or extension of this research, especially involving thin films or integrated devices, requires precise material specifications and processing capabilities. 6CCVD offers full customization to meet these demands:

  • Custom Dimensions: We supply plates and wafers up to 125mm (PCD) and custom-cut SCD substrates, allowing researchers to move from computational models to large-scale device fabrication.
  • Thickness Control: Precise control over material thickness is available: SCD and PCD layers from 0.1 ”m up to 500 ”m, and substrates up to 10 mm.
  • Surface Finish: Ultra-smooth surfaces are critical for minimizing boundary scattering effects in thin films. We provide polishing to achieve roughness values of Ra < 1 nm (SCD) and Ra < 5 nm (Inch-size PCD).
  • Integrated Metalization: For creating contacts or interconnects necessary for thermal or electrical measurements, 6CCVD offers in-house deposition of standard and custom metal stacks, including Au, Pt, Pd, Ti, W, and Cu.

Engineering Support

Section titled “Engineering Support”

The complexity of the BTE and phonon relaxation time analysis used in this paper demonstrates the necessity of deep material science expertise. 6CCVD’s in-house PhD engineering team is proficient in analyzing phonon transport, scattering mechanisms, and thermal modeling.

  • Consultation: Our experts can assist researchers in selecting the optimal diamond material (SCD, PCD, or BDD) based on specific thermal, electrical, or optical requirements for projects related to thermal management, high-frequency electronics, or quantum sensing.
  • Modeling Assistance: We provide technical guidance on how material properties (e.g., isotopic purity, boron doping concentration, surface roughness) impact phonon scattering and overall device performance, ensuring successful integration of diamond into complex systems.

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

View Original Abstract

The lattice thermal conductivities of silicon clathrate frameworks II and VIII are investigated by using ab initio lattice dynamics and iterative solution of the linearized Boltzmann transport equation(BTE) for phonons. Within the temperature range 100-350 K, the clathrate structures II and VIII were found to have lower lattice thermal conductivity values than silicon diamond structure (d-Si) by factors of 1/2 and 1/5, respectively. The main reason for the lower lattice thermal conductivity of the clathrate structure II in comparison to d-Si was found to be the harmonic phonon spectra, while in the case of the clathrate structure VIII, the difference is mainly due to the harmonic phonon spectra and partly due to shorter relaxation times of phonons. In the studied clathrate frameworks, the anharmonic effects have larger impact on the lattice thermal conductivity than the size of the unit cell. For the structure II, the predicted lattice thermal conductivity differs approximately by factor of 20 from the previous experimental results obtained for a polycrystalline sample at room temperature.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 1957 - Semiconductor Thermoelements and Thermoelectric Cooling
  2. 1995 - CRC Handbook of Thermoelectrics

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