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First principles kinetic-collective thermal conductivity of semiconductors

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2017-04-07
JournalPhysical review. B./Physical review. B
AuthorsPol Torres, Àlvar Torelló, J. Bafaluy, J. Camacho, Xavier Cartoixà
InstitutionsUniversitat AutĂČnoma de Barcelona
Citations61
AnalysisFull AI Review Included

6CCVD Technical Analysis: Kinetic-Collective Thermal Transport in Diamond and Semiconductors

Section titled “6CCVD Technical Analysis: Kinetic-Collective Thermal Transport in Diamond and Semiconductors”

This document summarizes the findings of the research paper “First principles Kinetic-Collective thermal conductivity of semiconductors” (arXiv:1606.01149v2) and outlines how 6CCVD’s advanced MPCVD Diamond products (SCD/PCD/BDD) are uniquely positioned to meet the material requirements necessary to replicate, validate, and extend this critical thermal transport research.

Executive Summary

Section titled “Executive Summary”

A predictive theoretical framework for understanding heat transport in semiconductors, particularly diamond, has been validated using first-principles calculations, offering critical insights for ultra-fast thermal management applications.

  • Model Validation: A fully predictive Kinetic-Collective Model (KCM) was validated for thermal conductivity ($\kappa$) estimation in Si, Ge, GaAs, and C (Diamond) using first-principles calculations, requiring zero fitting parameters.
  • Performance Confirmation: The model confirms Diamond’s status as the paramount thermal conductor, predicting bulk thermal conductivity ($\kappa$) near 104 W/mK across the 100K-300K range.
  • Non-Fourier Analysis: The KCM successfully addresses non-Fourier thermal behavior by separating total thermal transport ($\kappa$) into distinct kinetic ($\kappa_{K}$) and collective ($\kappa_{C}$) contributions.
  • Size and Time Scale Relevance: The separation of contributions is crucial for interpreting ultra-fast heating experiments (pump-probe) and size-dependent phenomena in thin films and nanowires.
  • Methodology: Predictions rely exclusively on first-principles calculations (DFT, LDA) of phonon spectra, relaxation times ($\tau$), and density of states (DOS), ensuring high theoretical fidelity.
  • Key Parameter: The dimensionless switching factor ($\Sigma$) determines the relative importance of collective transport, showing a strong temperature dependence and a transition from a pure kinetic regime at low temperatures.

Technical Specifications

Section titled “Technical Specifications”

The following table extracts key material and computational parameters from the research:

ParameterValueUnitContext
Target MaterialsSi, Ge, C (Diamond), GaAsN/AGroup IV and III-V Semiconductors
Predicted Thermal Conductivity ($\kappa$)~104W/mKHighest predicted value for Bulk Diamond (C) at 100K - 300K.
Simulation Temperature Range10 to 300KRange tested for bulk and nanoscale thermal properties.
Phonon Frequency Range ($\omega$)0 to 14THzRange for Thermal Conductivity Spectral Distribution (TCSD) analysis.
DFT Plane Wave Cutoff60HartreeEnergy cutoff for Quantum ESPRESSO first-principles calculation.
Q-Point Grid Density20x20x20N/ASampling density for phonon Brillouin zone calculation.
Minimum SCD Phonon MFP ($l_{C}$)~102nmCollective mean free path at T=300K, highest frequencies.
Kinetic Boundary Scattering ($\tau_{B}$)$\tau_{B}(\omega) = L_{eff}/v(\omega)$N/ACasimir expression used for size effects in the kinetic term.
Impurity Scattering Dependence ($\tau_{I}$)$\tau_{I}^{-1}$ $\propto$ $\omega^{4}$N/ATamura’s expression used for intrinsic impurity collision rates.

Key Methodologies

Section titled “Key Methodologies”

The KCM methodology utilized a rigorous sequence of first-principles Density Functional Theory (DFT) calculations combined with the BTE solution to determine thermal transport properties without empirical fitting.

  1. Model Basis: The Kinetic-Collective Model (KCM) was derived from the solution of the Boltzmann Transport Equation (BTE), expanded using eigenstates of the normal collision operator.
  2. Software and Framework: All microscopic magnitudes (phonon spectra, relaxation times) were calculated using the QUANTUM ESPRESSO package, implementing Density Functional Theory (DFT) under the Local Density Approximation (LDA).
  3. Simulation Setup: Norm-conserving pseudo-potentials (Von Barth-Car type) were used, and the plane wave cutoff energy was set at 60 Hartree.
  4. Force Constant Determination: Second and third-order force constants were computed by introducing small atomic Cartesian displacements within a 3x3x3 super-cell (216 atoms).
  5. Sampling Resolution: A dense 20x20x20 q-point grid was employed for phonon Brillouin Zone sampling; Density of States (DOS) calculations utilized a highly refined 160x160x160 mesh.
  6. Relaxation Time Calculation: Normal ($\tau_{N}$) and Umklapp ($\tau_{U}$) phonon relaxation times were calculated from anharmonic force constants using the ALAMODE open code package.
  7. Boundary and Impurity Scattering: Boundary collision rates ($\tau_{B}$) for the kinetic regime were determined using the Casimir expression dependent on the effective length ($L_{eff}$). Impurity collision rates ($\tau_{I}$) were calculated using Tamura’s expression, proportional to the mass variance of the sample.

6CCVD Solutions & Capabilities

Section titled “6CCVD Solutions & Capabilities”

6CCVD is the leading supplier of high-purity MPCVD diamond materials required to validate and advance research into phonon transport and non-Fourier heat conduction, particularly in the extreme thermal limits demonstrated by diamond.

Research Requirement / Opportunity6CCVD Solution & CapabilityValue Proposition
Ultra-High Thermal Conductivity Materials: The KCM confirms Diamond (C) reaches $\kappa$ $\sim$ 104 W/mK.High-Purity Single Crystal Diamond (SCD): We supply optical-grade and electronic-grade SCD wafers, ensuring the extremely low impurity levels necessary to achieve the theoretical maximum intrinsic thermal conductivity.Access to the most thermally conductive material on Earth, verified by first-principles modeling, enabling high-gradient thermal experiments.
Thin Film and Nanoscale Transport Study: The KCM framework is applied to thin films and nanowires, requiring precise thickness control for $L_{eff}$ analysis.Precise Thickness Control (0.1 ”m - 500 ”m): 6CCVD offers SCD and PCD thin films and substrates with thickness control down to 0.1 ”m, crucial for manipulating boundary scattering and studying the transition from kinetic to collective transport regimes.Direct control over the effective length ($L_{eff}$) parameter central to the KCM’s boundary scattering calculations.
Ultra-Fast Measurement Device Fabrication: Experiments like pump-probe thermoreflectance require specialized contact layers and localized heaters.In-House Custom Metalization: 6CCVD provides integrated metalization services (Au, Pt, Pd, Ti, W, Cu) on diamond surfaces, streamlining the fabrication of heating elements and contact pads necessary for ultra-fast transient thermal experiments.Reduces complexity and risk by delivering ready-to-use, fully metalized substrates optimized for advanced thermal characterization.
Non-Ideal Materials Investigation: Need to understand phonon scattering in materials with controlled doping or defects (e.g., BDD).Boron-Doped Diamond (BDD) Synthesis: We specialize in the growth of BDD films, allowing researchers to precisely tune impurity levels and study the effect of mass variance ($\Gamma$) on the intrinsic impurity collision rate ($\tau_{I}^{-1}$ $\propto$ $\omega^{4}$).Enables controlled experimental verification of the impurity scattering term defined by Tamura’s expression (Eq. 5) in the KCM framework.
Minimal Surface Scattering: Accurate measurements require ultra-smooth surfaces to minimize experimental error in boundary scattering models.Superior Polishing (Ra < 1 nm): Our state-of-the-art polishing achieves Single Crystal Diamond (SCD) surface roughness (Ra) less than 1 nm, minimizing phonon scattering at the sample boundary.Guarantees that experimental results reflect intrinsic material properties and KCM predictions, not roughness artifacts.

6CCVD’s in-house PhD engineering team possesses expertise in CVD growth mechanics and material physics, and can assist researchers with material selection, doping profiles, and customized geometry specifications for projects involving non-Fourier heat transport and ultra-fast thermal dynamics.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).

View Original Abstract

A fully predictive Kinetic Collective Model using first principles phonon\nspectra and relaxation times is presented. Thermal conductivity values obtained\nfor Si, Ge, C (diamond) and GaAs in a wide range of sizes and temperatures have\ngood agreement with experimental data without the use of any fitting parameter.\nThis validation of the model open the door to discuss how the precise\ncombination of kinetic and collective contributions to heat transport could\nprovide a useful framework to interpret recent complex experiments displaying\nnon-Fourier behavior.\n

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2007 - Quantum Theory of Solids

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