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6CCVD Research

Thermal Transport Properties of Diamond Phonons by Electric Field

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2022-09-28
JournalNanomaterials
AuthorsYongsheng Zhao, Fengyun Yan, Xue Liu, Hongfeng Ma, Zhenyu Zhang
InstitutionsLanzhou University of Technology
Citations3
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This study utilized first-principles calculations to investigate the thermal transport properties of diamond under external electric fields (E-fields), focusing on optimizing diamond for high-performance heat sinks.

  • Anisotropic Response: The thermal conductivity (TC) of diamond exhibits strong anisotropy, with responses varying significantly across the [001], [110], and [111] crystallographic directions.
  • TC Modulation: Applying a positive E-field increases the lattice TC, while a negative E-field decreases it. This regulation mechanism is viable for controlling thermal dissipation.
  • Maximum Modulation: The [111] orientation showed the largest TC change at 300 K and an E-field strength of ±0.004 a.u.
    • Positive E-field (+0.004 a.u.): TC increased to 2654 W·m-1K-1 (a 36.1% increase).
    • Negative E-field (-0.004 a.u.): TC decreased to 1283 W·m-1K-1 (a 34% decrease).
  • Underlying Mechanism: The E-field breaks the symmetry of the diamond lattice, causing electron density segregation and altering interatomic force constants. This, in turn, modifies phonon mean free path and lifetime.
  • Phonon Sensitivity: The thermal transport response is primarily concentrated in the low-frequency phonon part (frequencies less than 30 THz).
  • Stability Limit: The diamond structure becomes unstable and exhibits imaginary frequencies when the E-field strength reaches 0.00736 a.u.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Reference Thermal Conductivity (TC)1960.80W·m-1K-1Calculated TC at 0 a.u. E-field (300 K)
Maximum TC ([111] direction)2654W·m-1K-1Applied E-field: +0.004 a.u. (300 K)
Minimum TC ([111] direction)1283W·m-1K-1Applied E-field: -0.004 a.u. (300 K)
TC Increase Percentage ([111])36.1%Relative to 0 a.u. TC
TC Decrease Percentage ([111])-34%Relative to 0 a.u. TC
E-field Stability Limit0.00736a.u.E-field strength causing lattice instability
C-C Bond Length1.547AUnchanged with or without E-field
Critical Phonon Frequency30THzFrequency below which phonon properties are most sensitive to E-field
Maximum Phonon Group Velocity1 x 104m/sVelocity of low-frequency phonon group
Temperature Range Studied240 to 500KRange for TC variation curves
Constant Volume Specific Heat ([111], +0.000736 a.u.)1.45 x 10-4eV/cellIncreased value
Constant Volume Specific Heat ([111], -0.000736 a.u.)1.22 x 10-4eV/cellDecreased value

Key Methodologies

Section titled “Key Methodologies”

The thermal transport properties were determined using first-principles calculations based on Density-Functional Perturbation Theory (DFPT) and the single-mode Relaxation Time Approximation (RTA).

  1. Computational Software: ABINIT was used for DFPT calculations (interatomic force constants, total energy, phonon dispersion), and Phono3py was used for lattice thermal conductivity calculation.
  2. E-Field Modeling: A uniform, absolute electric field was applied directly to the diamond primitive cell. The lattice structure and atomic positions were fixed during the calculation to isolate the effects of electron density distribution changes.
  3. Force Constant Calculation: Second-order and third-order force constants were calculated using the finite displacement method with supercells (3x3x3 and 2x2x2, respectively). Atomic displacements were set to 0.06 A.
  4. Pseudopotentials and Exchange: Norm-conserving pseudopotentials (ONCVPSP) and Projector-Augmented-Wave (PAW) methods were employed. The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) was used for electron exchange phase control.
  5. Convergence Parameters:
    • Cutoff energy for ONCVPSP pseudopotential: 41 Ha.
    • Cutoff energy for PAW fine meshes: 50 Ha.
    • Brillouin zone sampling grid: 12 x 12 x 12.
    • q-grid sampling: 56 x 56 x 56.
  6. Thermal Conductivity Calculation: Lattice TC was calculated by directly solving the Boltzmann phonon transport equations using the RTA method, incorporating second- and third-order force constants.

Commercial Applications

Section titled “Commercial Applications”

The ability to regulate diamond’s thermal conductivity via external electric fields has significant implications for high-performance thermal management and advanced electronic devices.

  • High-Performance Thermal Management:
    • Integrated Circuit (IC) Heat Sinks: Tailoring the TC of Chemical Vapor Deposition (CVD) diamond substrates to optimize heat dissipation in high-density electronic packages.
    • Power Electronics: Improving thermal performance in high-power Insulated Gate Bipolar Transistor (IGBT) equipment and power energy systems where diamond is used for its excellent thermal properties (>2000 W·m-1K-1).
  • Advanced Semiconductor Technology:
    • Wide-Band Gap Devices: Utilizing diamond (band-gap ~4.5 eV) as a substrate material where controlled thermal properties are necessary for device stability and efficiency.
    • Electro-Acoustic Devices: Exploiting the strong electro-acoustic coupling observed, where the E-field transfers energy to phonons, potentially enabling new electro-thermal switching or modulation devices.
  • Quantum Technology:
    • Quantum Sensors: Applying E-fields during or after diamond synthesis to fine-tune thermal pathways, critical for maintaining stable operating conditions in diamond-based quantum sensors.
View Original Abstract

For the preparation of diamond heat sinks with ultra-high thermal conductivity by Chemical Vapor Deposition (CVD) technology, the influence of diamond growth direction and electric field on thermal conductivity is worth exploring. In this work, the phonon and thermal transport properties of diamond in three crystal orientation groups (<100>, <110>, and <111>) were investigated using first-principles calculations by electric field. The results show that the response of the diamond in the three-crystal orientation groups presented an obvious anisotropy under positive and negative electric fields. The electric field can break the symmetry of the diamond lattice, causing the electron density around the C atoms to be segregated with the direction of the electric field. Then the phonon spectrum and the thermodynamic properties of diamond were changed. At the same time, due to the coupling relationship between electrons and phonons, the electric field can affect the phonon group velocity, phonon mean free path, phonon-phonon interaction strength and phonon lifetime of the diamond. In the crystal orientation [111], when the electric field strength is ±0.004 a.u., the thermal conductivity is 2654 and 1283 W·m−1K−1, respectively. The main reason for the change in the thermal conductivity of the diamond lattice caused by the electric field is that the electric field has an acceleration effect on the extranuclear electrons of the C atoms in the diamond. Due to the coupling relationship between the electrons and the phonons, the thermodynamic and phonon properties of the diamond change.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2013 - First Principle Study of Valence-Band Offsets at AlN/Diamond Heterojunctions [Crossref]
  2. 2020 - Investigation on the Interface Characteristic between TiN and Diamond by First-Principles Calculation [Crossref]
  3. 1993 - Thermal Conductivity of Isotopically Modified Single Crystal Diamond [Crossref]
  4. 2001 - Thermal Conductivity Measurements on CVD Diamond [Crossref]
  5. 1997 - Measuring Local Thermal Conductivity in Polycrystalline Diamond with a High Resolution Photothermal Microscope [Crossref]
  6. 2018 - Lattice Thermal Transport in Superhard Hexagonal Diamond and Wurtzite Boron Nitride: A Comparative Study with Cubic Diamond and Cubic Boron Nitride [Crossref]
  7. 2017 - Design of Interfacial Cr3C2 Carbide Layer via Optimization of Sintering Parameters Used to Fabricate Copper/Diamond Composites for Thermal Management Applications [Crossref]
  8. 2019 - Tunable Coef Fi Cient of Thermal Expansion of Cu-B/Diamond Composites Prepared by Gas Pressure in Fi Ltration [Crossref]
  9. 2020 - Fabrication of High Thermal Conductivity Copper/Diamond Composites by Electrodeposition under Potentiostatic Conditions [Crossref]

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