Thermal Management Materials for Electronic Packaging E-Book
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Thermal Management Materials for Electronic Packaging
Practical resource exploring the theoretical and experimental basis as well as solutions for the development of new thermal management materials for electronic packaging
Thermal Management Materials for Electronic Packaging: Preparation, Characterization, and Devices provides in-depth and systematic summaries on cutting-edge thermal management materials for high-power density electronic devices, introducing the preparation methods and application scenarios of thermal management materials for electronic packing, covering refinements of thermal conductivity theory and performance prediction models for multiphase composites, and overall focusing on key scientific issues related to the subject, such as the internal interface of new high thermal conductive substrate materials and the mechanism of spatial topology on performance.
The text also discusses key issues on the design and preparation of thermal conductive substrate materials with high thermal conductive properties, including their characterization, properties, and manipulation, as well as the latest methods, techniques, and applications in this rapidly developing area.
Sample topics covered in Thermal Management Materials for Electronic Packaging include:
- Basic concepts and laws of thermal conduction, heat conduction differential equation and finite solution, and thermal conductivity of solids
- Definition and classification of electronic packaging, thermal management in electronic equipment, and requirements of electronic packaging materials
- Synthesis and surface modification of high thermal conductive filler and the synthesis of substrates and preparation of thermal conductive composites with inorganic ceramic skeleton structure
- Assembly of thermal conductive materials in different dimensions and preparation of composite materials, and reliability analysis and environmental performance evaluation
Thermal Management Materials for Electronic Packaging serves as an ideal reference for researchers and workers in related fields to significantly improve the mechanical and thermal management properties of materials, expand the material selection and design margin of substrates, and develop substrates that meet the application needs of different gradients.
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Veröffentlichungsjahr: 2023
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Overview of Works
The Key Technology
Description
Key Features
Next Work Assumption
Acknowledgments
1 Physical Basis of Thermal Conduction
1.1 Basic Concepts and Laws of Thermal Conduction
1.2 Heat Conduction Differential Equation and Finite Solution
1.3 Heat Conduction Mechanism and Theoretical Calculation
1.4 Factors Affecting Thermal Conductivity of Inorganic Nonmetals
References
2 Electronic Packaging Materials for Thermal Management
2.1 Definition and Classification of Electronic Packaging
2.2 Thermal Management in Electronic Equipment
2.3 Requirements of Electronic Packaging Materials
2.4 Electronic Packaging Materials
References
3 Characterization Methods for Thermal Management Materials
3.1 Overview of the Development of Thermal Conductivity Test Methods
3.2 Test Method Classification and Standard Samples
3.3 Steady‐State Method
3.4 Non‐Steady‐State Method
3.5 Electrical Properties and Measurement Techniques
3.6 Material Characterization Analysis Technology
3.7 Reliability Analysis and Environmental Performance Evaluation
3.8 Conclusion
References
4 Construction of Thermal Conductivity Network and Performance Optimization of Polymer Substrate
4.1 Synthesis and Surface Modification of High Thermal Conductive Filler and the Synthesis of Substrates
4.2 Study on Polymer Thermal Conductive Composites with Oriented Structure
4.3 Preparation of Thermal Conductive Composites with Inorganic Ceramic Skeleton Structure
4.4 Improved Thermal Conductivity of Fluids and Composites Using Boron Nitride Nanoparticles Through Hydrogen Bonding
4.5 Improved Thermal Conductivity of PEG‐Based Fluids Using Hydrogen Bonding and Long Chain of Nanoparticle
4.6 Conclusion
References
5 Optimal Design of High Thermal Conductive Metal Substrate System for High‐Power Devices
5.1 Power Devices and Thermal Conduction
5.2 Optimization and Adaptability Design, Preparation and Modification of High Thermal Conductive Matrix and Components
5.3 Formation and Evolution Rules of High Thermal Conductive Interface and Its Control Method
5.4 Formation and Evolution Rules of High Thermal Conductive Composite Microstructure and Its Control Method
References
6 Preparation and Performance Study of Silicon Nitride Ceramic Substrate with High Thermal Conductivity
6.1 Rapid Nitridation of Silicon Compact
6.2 Optimization of Sintering Aids for High Thermal Conductivity Si
3
N
4
Ceramics
6.3 Investigation of Cu‐Metalized Si
3
N
4
Substrates Via Active Metal Brazing (AMB) Method
References
7 Preparation and Properties of Thermal Interface Materials
7.1 Conception of Thermal Interface Materials
7.2 Polymer‐Based Thermal Interface Materials
7.3 Metal‐Based Thermal Interface Materials
7.4 Carbon‐Based Thermal Interface Materials
7.5 Molecular Simulation Study of Interfacial Thermal Transfer
7.6 Conclusion
References
8 Study on Simulation of Thermal Conductive Composite Filling Theory
8.1 Molecular Simulation Algorithms for Thermal Conductivity Calculating
8.2 Molecular Simulation Study on Polymers
8.3 Molecular Simulation Study on TC of Si
3
N
4
Ceramic
8.4 Molecular Simulation Study on TC of Diamond/ Copper Composites
8.5 Simulation Study on Polymer‐Based Composites
References
9 Market and Future Prospects of High Thermal Conductivity Composite Materials
9.1 Basic Concept of Composite Materials
9.2 Thermal Conductivity Mechanism and Thermal Conductivity Model
9.3 Composite Materials in Electronic Devices
9.4 Thermal Functional Composites
9.5 The Modification of Composite Materials
9.6 The New Packaging Material
9.7 Thermal Management of Electronic Devices
9.8 Methods for Improving Thermal Conductivity of Composite Materials
9.9 The Application of Composite Materials
9.10 Conclusion
References
Index
End User License Agreement
List of Tables
Chapter 2
Table. 2.1 Properties of common metal packaging materials.
Table. 2.2 Performance of common reinforcements.
Table. 2.3 The development of metal matrix packaging materials.
Table. 2.4 Performance of ceramic packaging materials.
Table. 2.5 Thermal conductivity of common polymers at room temperature.
Table. 2.6 Thermal conductivity of filler.Source: Adapted from Ref. [27]....
Chapter 3
Table. 3.1 Main failure modes of electronic packaging.
Chapter 4
Table. 4.1 Thermal conductivity of BN particle‐contained fluids.
Table. 4.2 Thermal conductivity of BN particle‐contained polyurethane compo...
Table. 4.3 Thermal conductivity of BN particle‐contained fluids with the ad...
Table. 4.4 Thermal conductivity of BN particle containing polyurethane comp...
Table. 4.5 Thermal conductivity of hex‐BN nanoparticle‐contained PEG 400 fl...
Table. 4.6 Thermal conductivity of MWNT‐OH contained PEG 400 fluids.
Table. 4.7 Thermal conductivity of PEG400 with the addition of the combinat...
Table. 4.8 Thermal conductivity of PEG400 fluids with the addition of the c...
Table. 4.9 Thermal conductivity of PEG400 with the addition of the combinat...
Chapter 5
Table. 5.1 Physical parameters of common carbide‐forming elements.
Table. 5.2 Secondary diamond addition design table.
Table. 5.3 Diamond particle size ratio design table.
Table. 5.4 Parameters used to predict thermal expansion coefficient.
Table. 5.5 Parameters of graded diamond/copper composites.
Chapter 6
Table. 6.1 The different compositions and theoretical densities of samples ...
Table. 6.2 Properties of samples with different Y
2
O
3
:Eu(4 mol%)/MgO ratios ...
Table. 6.3 Content of β‐Si
3
N
4
after nitridation of four samples of Y, YEu, ...
Table. 6.4 Nitridation rate, expansion rate, and relative density of sample...
Table. 6.5 Relative density, weight loss, and thermal properties of the pre...
Table. 6.6 Oxygen contents of the Si
3
N
4
samples before and after pre‐sinter...
Table. 6.7 Grain sizes, secondary phases' volume fractions, and thermal con...
Table. 6.8 The thermal conductivity of Si
3
N
4
doped with different REH
2
.
Chapter 9
Table 9.1 Thermophysical properties of the common electronic packaging mater...
Table 9.2 Main properties of metal matrix composites for electronic packagin...
List of Illustrations
Chapter 1
Figure. 1.1 Temperature field and temperature gradient.
Figure. 1.2 Isotherms and heat flux.
Figure. 1.3 Cube element.
Figure. 1.4 Relationship between metal thermal conductivity and temperature....
Figure. 1.5 Relationship between thermal conductivity and temperature of die...
Figure. 1.6 Relationship between thermal conductivity and temperature of ino...
Chapter 2
Figure. 2.1 Graph of failure factor against device temperature.
Figure. 2.2 Schematic diagram of electronic packaging structure.
Figure. 2.3 Thermal interface material.
Figure. 2.4 Classification of thermal interface material.
Figure. 2.5 Metal substrate structure.
Figure. 2.6 Structure of epoxy molding compound after molding.
Chapter 3
Figure. 3.1 Schematic diagram for steady‐state method.
Figure. 3.2 Schematic diagram for longitudinal heat flow method.
Figure. 3.3 Schematic diagram for mechanism of the guarded heat flow meter m...
Figure. 3.4 Schematic diagram for mechanism of the guarded heat plate method...
Figure. 3.5 Schematic diagram for the laser flash method.
Figure. 3.6 Schematic diagram for hot‐wire method.
Figure. 3.7 Schematic diagram of hot disk while test solid‐state sample.
Figure. 3.8 The system for testing the resistivity of a bulk material.
Figure. 3.9 The configuration diagram of four‐point collinear probe used for...
Figure. 3.10 The configuration diagram of the Van der Pauw method used for r...
Figure. 3.11 The configuration diagram of optical microscopy.
Figure. 3.12 The configuration diagram of SEM.
Figure. 3.13 The configuration diagram of TEM.
Figure. 3.14 The configuration diagram of C‐mode scan furnishes a two‐dimens...
Figure. 3.15 The configuration diagram of AFM.
Figure. 3.16 The configuration diagram of TMA.
Figure. 3.17 Stress–strain relationship obtained by DMA. tan
δ
=
E
″/
E
′....
Figure. 3.18 The configuration diagram of DMA.
Chapter 4
Figure. 4.1 Schematic diagram of halide‐assisted hydrothermal synthesis of h...
Figure. 4.2 Characterization of MG SiC
nw
: (a) SEM image, (b) SEM magnificati...
Figure. 4.3 Schematic diagram of the growth process of MG SiC
nw
.
Figure. 4.4 (a) FTIR spectra of h‐BN, DDM, and DDM @ h‐BN; (b) Raman spectra...
Figure. 4.5 Thermal conductivity of TMBPDGE. (a) TMBPDGE‐DDM@h‐BN relationsh...
Figure. 4.6 (a) Preparation of CER/h‐BN@CNT‐NH
2
composites. SEM: (b) h‐BN; t...
Figure. 4.7 Cross‐sectional SEM of (a–c) CER/h‐BN@CNT‐NH
2
; (d–f) CER/CNT‐NH
2
Figure. 4.8 CER/CNT‐NH
2
/h‐BN, CER/h‐BN@CNT‐NH
2
, and CER/h‐BN filled composit...
Figure. 4.9 Preparation of CER/NfG@h‐BN composite.
Figure. 4.10 Cross‐section of (a) and (d) CER/NfG@h‐BN‐10 wt%, (b) and (e) C...
Figure. 4.11 CER/CNT‐NH
2
/Fe@hBN preparation process.
Figure. 4.12 CER/Fe@hBN and CER/CNT‐NH2/Fe@hBN filled composites of (a) stre...
Figure. 4.13 (a) Preparation of hollow h‐BN and its epoxy resin composite; (...
Figure. 4.14 Cross‐sectional SEM of EP/BNMB composites. (a–e) Are the micros...
Figure. 4.15 (a, b) Plots of dielectric constant and dielectric loss of EP/B...
Figure. 4.16 Preparation of f‐BNNS, porous SiCw/f‐BNNS skeleton, and its epo...
Figure. 4.17 Microscopic morphological analysis of BN and BNNS. (a) SEM imag...
Figure. 4.18 Microscopic morphology of porous skeleton and its epoxy resin c...
Figure. 4.19 Analysis of anisotropic thermal conductivity of EP/SiC
w
‐f‐BNNS ...
Figure. 4.20 Thermal expansion performance characterization of EP/SiC
w
‐f‐BNN...
Figure. 4.21 Illustration of experimental procedure.
Figure. 4.22 Diagram of hydrogen bonding.
Figure. 4.23 (a, b) Structure and SEM image of carbon nanofibers; (c, d) Str...
Figure. 4.24 Chemical structure of (a) glycerol, (b) Polyalphaolefin (PAO), ...
Figure. 4.25 Thermal conductivity value of various base fluids with 14 wt% b...
Figure. 4.26 Thermal conductivity increases per weight percentage loading of...
Figure. 4.27 Thermal conductivity value of polyurethane composites containin...
Figure. 4.28 Thermal conductivity increases per weight percentage with the a...
Figure. 4.29 Thermal conductivity of BN particle containing polyurethane com...
Figure. 4.30 Illustration of experimental procedure.
Figure. 4.31 Diagram of hydrogen bonding between two water molecules.
Figure. 4.32 (a, b) Structure and SEM image of carbon nanofibers; (c, d) Str...
Figure. 4.33 Thermal conductivity as a function of weight percentage of nano...
Chapter 5
Figure. 5.1 Typical package diagram of flip chip ball grid array.
Figure. 5.2 Thermal conductivity–thermal expansion coefficient distribution ...
Figure. 5.3 Schematic diagram of preparation process of Gr/Cu composite.
Figure. 5.4 (a–c) SEM images of 0.75 vol% Gr/Cu composited powders. (d) Rama...
Figure. 5.5 Microstructures of the bulk 0.75 vol%‐Gr/Cu‐laminated composites...
Figure. 5.6 (a) Thermal conductivity and (b) thermal diffusivity in the in‐p...
Figure. 5.7 (a) Coefficient of thermal expansion (CTE) of 0.75 vol% Gr/Cu co...
Figure. 5.8 Thermal strain at the Si–heat sink interface. (a) Schematic of t...
Figure. 5.9 (a, b) Morphology of flake graphite. (c) XRD of flake graphite. ...
Figure. 5.10 (a, b) TEM and HRTEM images of graphite flakes. (c–f) microscop...
Figure. 5.11 (a) Structural model of graphite/Cu composites. SEM images of g...
Figure. 5.12 Original morphology of spherical Cu powder as matrix and graphi...
Figure. 5.13 Original morphology of ball‐milled flake Cu powder and graphite...
Figure. 5.14 (a) Schematic diagram of the measurement of polarization Raman ...
Figure. 5.15 Anisotropic thermal conductivity of Gf/Cu composites. (a) Therm...
Figure. 5.16 (a) SEM images of the microscopic morphology of the Gf/Cu compo...
Figure. 5.17 (a, b) SEM images of the in situ grown Gr/Cu (flake Cu, 1–2 μm)...
Figure. 5.18 (a, b) Thermal conductivity and thermal diffusion coefficient o...
Figure. 5.19 Curves of the coefficient of thermal expansion (CTE) correspond...
Figure. 5.20 Thermal conductivity of diamond–Cu composites in different inte...
Figure. 5.21 Composition analysis of diamond/Cu‐Cr composites interface area...
Figure. 5.22 Interfacial structures of diamond/copper composites with differ...
Figure. 5.23 Fracture microstructure of diamond/copper composites with diffe...
Figure. 5.24 Thermal conductivity and bending strength of diamond/copper com...
Figure. 5.25 XRD analysis of diamond/Cu‐B composites.
Figure. 5.26 Surface morphology of diamond particles extracted from diamond/...
Figure. 5.27 Fracture microstructure of diamond/Cu composites with different...
Figure. 5.28 Thermal conductivity and bending strength of diamond/Cu‐B compo...
Figure. 5.29 Flowchart for the preparation of in situ grown Gr‐modified diam...
Figure. 5.30 (a) SEM image of the ion beam polished surface of Dia/Gr/Cu and...
Figure. 5.31 (a) Thermal conductivity and thermal diffusion coefficient of D...
Figure. 5.32 Schematic diagram of the preparation process of Dia/Gr/Cu model...
Figure. 5.33 (a) Differences in acoustic impedance between diamond and Cu. (...
Figure. 5.34 Thermal conductivity and bending strength of diamond/copper wit...
Figure. 5.35 Thermal conductivity and bending strength of diamond/copper wit...
Figure. 5.36 The CTE of diamond/copper composites with different diamond con...
Chapter 6
Figure. 6.1 XRD of nitrided samples with different Y
2
O
3
:Eu(4 mol%)/MgO ratio...
Figure. 6.2 SEM of samples with different (YEu)
2
O
3
/ MgO ratios after nitrid...
Figure. 6.3 XRD pattern of post‐sintered samples with different (YEu)
2
O
3
/MgO...
Figure. 6.4 SEM of sintered samples with different (YEu)
2
O
3
/MgO ratios.
Figure. 6.5 Density, relative density, and weight loss of SRBSN samples with...
Figure. 6.6 Bending strength and hardness of SRBSN samples with different ra...
Figure. 6.7 Thermal diffusion and thermal conductivity of SRBSN samples with...
Figure. 6.8 Thermogravimetric curves of the green body.
Figure. 6.9 XRD of four samples of Y, YEu, Y + Eu, and Eu after nitridation....
Figure. 6.10 Microstructures of samples after nitridation at 1400 °C for 4 h...
Figure. 6.11 XRD of the sample after holding at 1900 °C for 4 h.
Figure. 6.12 Density and relative density of samples at different sintering ...
Figure. 6.13 The shrinkage curves of four samples of Y, YEu, Y + Eu, and Eu....
Figure. 6.14 SEM of the nitrided sample after sintering at 1900 °C for 4 h. ...
Figure. 6.15 Mechanical properties of samples after sintering at 1900 °C for...
Figure. 6.16 SEM of the fracture surface of (a) Y, (b) YEu, (c) Y + Eu, (d) ...
Figure. 6.17 (a) Thermal diffusion and (b) thermal conductivity of four samp...
Figure. 6.18 The XRD patterns of samples before and after being heated in va...
Figure. 6.19 The
in situ
sintering shrinkage behavior of 3Z4M.
Figure. 6.20 (a) HAADF‐STEM image of sample 3Z4M; (b) EDS spectrum and compo...
Figure. 6.21 The microstructure of ZrSi
2
and SiO
2
mixture powder after being...
Figure. 6.22 Schematic drawing of the densification mechanism of Si
3
N
4
ceram...
Figure. 6.23 The XRD patterns of the Si
3
N
4
ceramics samples after sintering ...
Figure. 6.24 The low‐magnification images of polished and plasma‐etched surf...
Figure. 6.25 The high‐magnification images of polished and plasma‐etched sur...
Figure. 6.26 SEM view of a crack path in 3Z4M.
Figure. 6.27 The phase composition of mixtures doped with REH
2
after ball mi...
Figure. 6.28 The XRD patterns of the Si
3
N
4
ceramics: (a) after ball milling,...
Figure. 6.29 The EDS mapping of the Si
3
N
4
ceramics: (a) after ball milling, ...
Figure. 6.30 The XRD patterns of powder mixture of YH
2
and SiO
2
before and a...
Figure. 6.31 The shrinkage curves of the Si
3
N
4
ceramics.
Figure. 6.32 The relative density of Si
3
N
4
samples after gas pressure sinter...
Figure. 6.33 The weight loss of Si
3
N
4
samples after gas pressure sintering....
Figure. 6.34 (a) The SEM micrograph of the polished surface of sample 3YM af...
Figure. 6.35 The XRD patterns of Si
3
N
4
samples after sintered at 1900 °C for...
Figure. 6.36 Schematic illustration of the Si
3
N
4
–Y
2
O
3
–SiO
2
phase diagram at ...
Figure. 6.37 The low‐magnification SEM micrographs of the polished surfaces ...
Figure. 6.38 The high‐magnification SEM micrographs of the polished surfaces...
Figure. 6.39 HAADF images and EDS analyses of samples (a) YOM, (b) YHM.
Figure. 6.40 The thermal conductivity of Si
3
N
4
samples after gas pressure si...
Figure. 6.41 The mechanical properties of Si
3
N
4
ceramics: (a) flexural stren...
Figure. 6.42 Schematic diagram of the action mechanism of YH
2
as a sintering...
Figure. 6.43 Peeling curves of Cu‐metalized ceramic substrates prepared at d...
Figure. 6.44 Peeling curves of Cu‐metalized ceramic substrates prepared at d...
Figure. 6.45 Peeling curves of Cu‐metalized ceramic substrates prepared at d...
Chapter 7
Figure. 7.1 Schematic representation of working principle of a TIM. An inter...
Figure. 7.2 Schematic illustration of a typical ball grid array (BGA) electr...
Figure. 7.3 Schematic of (a) a PVA/h‐BN composite film stretched in the tran...
Figure. 7.4 Schematic diagram of (a) 3D BN‐reduced graphene oxide (rGO)/epox...
Figure. 7.5 Schematic diagram of (a) preparation of graphene oxide/graphene ...
Figure. 7.6 (a) Thermal conductive models of epoxy/Ag NW (left) and epoxy/Ag...
Figure. 7.7 (a) Schematic of the hydrogen bond between PVA and hydroxyl func...
Figure. 7.8 (a) Schematic of idealized LPS solder microstructure showing HMP...
Figure. 7.9 Vertically aligned copper–tin nanowire arrays as supersolder. (a...
Figure. 7.10 Schematic process procedure of preparing Cu–Cu
x
–O nanoparticles...
Figure. 7.11 The thermal resistance of liquid metals is close to a factor of...
Figure. 7.12 Carbon‐based TIMs and their applications.
Figure. 7.13 (a) Schematic illustration of the structural change of the grap...
Figure. 7.14 (a) Heat dissipation capability of GHP‐TIM. (b) The calculated ...
Figure. 7.15 Experimental setup and typical morphology of VG arrays. (a) Sch...
Chapter 8
Figure. 8.1 Thermal conductivity of drawn PE chains. (a) Representative morp...
Figure. 8.2 NEMD simulation study on thermal conductivity of polycrystalline...
Figure. 8.3 Effect of inter‐zone chain on thermal conductivity of crystallin...
Figure. 8.4 e‐DPD study on thermal conductivity of polymer composites with v...
Figure. 8.5 e‐DPD study on “pseudo” heat transporting pathways formed at low...
Figure. 8.6 Silicon nitride model with defect.
Figure. 8.7 Effect of defect ratio on thermal conductivity of silicon nitrid...
Figure. 8.8 NEMD simulation on β‐Si
3
N
4
with defects of oxygen replacement or...
Figure. 8.9 Schematic diagram of models: (a) the diamond/Cu system and (b) t...
Figure. 8.10 Diamond/TiC/Cu composites with varied TiC layer thickness. (a) ...
Figure. 8.11 Schematic diagram of the model of the Diamond/TiC/Cu systems wi...
Figure. 8.12 The interfacial thermal conductance (ITC) of diamond/TiC/Cu sys...
Figure. 8.13 (a) The finite element simulation is used to simulate the heat ...
Figure. 8.14 Heat transfer process simulated by finite element simulation. T...
Figure. 8.15 Simulated (a) temperature distribution and (b) heat flux distri...
Figure. 8.16 (a) Finite element models, (b) simulated temperature distributi...
Figure. 8.17 Finite element analysis of heat transfer in Gw‐CNT/PI composite...
Figure. 8.18 Finite element analyses. Temperature profile of the (a) ABG/PDM...
Figure. 8.19 Finite element analysis and simulated results of heat transfer ...
Figure. 8.20 The graphene and BNNT interface bonded by VdW interaction (a) a...
Figure. 8.21 (a) Schematic illustrating the structure of the BNNS connected ...
Figure. 8.22 (a) The model diagram of calculation of rGO@CN thermal conducti...
Figure. 8.23 (a) Schematic diagrams of smooth heat flow, reduced phonon scat...
Figure. 8.24 The calculated thermal conductance at the graphene−SiC nanorod ...
Figure. 8.25 (a) Simulation modeling for comparing the effects of AgNW and A...
Figure. 8.26 (a) Simulation modeling for exhibiting thermal conductivity of ...
Chapter 9
Figure. 9.1 Preparation procedure for EG/PEI composites.
Figure. 9.2 Schematic illustration of interface hear transfer in interfacial...
Figure. 9.3 Toughening mechanism of particle interleaving: (a) Particle brid...
Figure. 9.4 SEM of polyvinyl alcohol (PVA)/BNNS/PDMS composites with section...
Figure. 9.5 Microstructure of SiC GFs/Al composites: (a) 60Vol%Al; (b) 20Vol...
Figure. 9.6 SEM images of liquid crystal epoxy resin (a–a”) and SiCNWs‐LCE/l...
Figure. 9.7 Quality change curves under different aging environments.
Figure. 9.8 Infrared spectra of T800 carbon fiber/epoxy composites under dif...
Figure. 9.9 Schematic diagram of thermal vibration enhancement of thermally ...
Figure. 9.10 TG curves of composite at different heating rates.
Figure. 9.11 Microscopic morphology of graphene, pure PP, and graphene/PP co...
Figure. 9.12 Relationship between thermal conductivity and content of compos...
Figure. 9.13 Bending strength of the E51/Al
2
O
3
composites.
Figure. 9.14 SEM images of composite powders with different contents of grap...
Figure. 9.15 Glass transition temperature (a), DSC curves (b), Tg retention ...
Figure. 9.16 SEM images of TGO under different temperatures: (a) 600 °C, (b)...
Figure. 9.17 Schematics of hot‐pressing preparations and heat conduction alo...
Figure. 9.18 SEM images of TAGA with different GO concentrations.
Guide
Cover
Table of Contents
Title Page
Copyright
Overview of Works
Acknowledgments
Begin Reading
Index
End User License Agreement
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Thermal Management Materials for Electronic Packaging
Preparation, Characterization, and Devices
Edited by Xingyou Tian
Editor
Prof. Xingyou TianChinese Academy of SciencesInstitute of Solid State PhysicsHefei Institutes of Physical Science350 Shushanhu Road230031 HefeiChina
Cover Image: © Xuanyu Han/Getty Images
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Overview of Works
Abstract: With high thermal conductive components → interface → structural design as the main line, the frontier exploration and research of high power density thermal management materials are carried out by combining experimental characterization, theoretical analysis, modeling simulation, and application verification. It will reveal the thermophysical response characteristics under the conditions of multiple, multi‐dimensional, multi‐level, and multi‐field coupling and establish a full‐chain common theory and technology platform through design and preparation, device integration, and service evaluation. Through the micro–nano interface layer, local dense stack distribution, spatial network distribution, orientation distribution, and other composite configurations, the substrate thermal management efficiency is significantly improved. This book prepares high thermal conductive substrate materials through theoretical guidance, structural control, and process screening.
Keywords: Devices; Electronic packaging; Preparation; Spatial nerwork structure; Thermal management Materials
The Key Technology
1. The design control and surface modification technology of substrates and high thermal conductive components can improve their physical and chemical compatibility.
2. Micro‐ and nanoscale interface layer design and fine control technology can realize the balanced matching of interface bonding strength and interface thermal conductivity.
3. The multi‐scale design and control technology of composite configuration can improve the design margin of macro‐mechanical and thermophysical properties.
4. The densification and near‐net molding technology of substrate materials can improve the density and optimize the thermal flow conduction path.
This book has good guiding significance for the preparation, production, and device application of thermal management materials.
Description
Thermal management materials first introduce the basic principles and basic concepts of thermal conductivity of materials. Then the key issues of the design and preparation of thermal management materials with high thermal conductivity are discussed, including their characterization, performance, operation, and related research.
The latest methods, techniques, and applications are explained in detail regarding this rapidly developing area. The book will support the work of academic researchers and graduate students, as well as engineers and materials scientists working in industrial research and development.
In addition, it will be of great value to those directly involved in the industrial industry related to thermal management materials, as well as to researchers in the fields of materials science, polymer science, materials chemistry, nanomaterials, and others working on thermally conductive materials.
Key Features
This paper focuses on how to design and prepare thermal management materials with high thermal conductivity.
Includes new techniques for adjusting the thermal conductivity of thermal management materials.
Recent advances in the fields related to thermal management materials are reviewed, providing valuable insights into potential development pathways.
Next Work Assumption
Electronic packaging materials: Focus on the bottleneck problem of the electronic industry and the demands of national strategic for improving the anti‐risk ability, promote the large‐scale and stable mass production and application of achievements as soon as possible, and break the foreign technological monopoly. Strengthen cooperation and exchange with domestic downstream enterprises in the production and application of packaging materials, make full use of the existing pilot production line and first‐class testing platform, timely control the changes in market demand, and develop world‐class electronic packaging materials.
Packaging process and platform: The future work will be closely focused on the “14th Five‐Year Plan” national strategic development needs. Focus on high‐reliability ASIC design technology, third‐generation semiconductor device driving and packaging technology related research work. Strive to make breakthroughs in the fields of new energy vehicle chip and application technology, aerospace intelligent sensing and interconnection technology, design, driving, packaging and testing technology of wide band gap semiconductor power devices, special motor drive and control technology, intelligent sensing and intelligent control technology, and high reliability packaging technology.
Acknowledgments
The author sincerely thanks Shuguang Bian and Bin Yang (High Technology Research and Development Center, Ministry of Science and Technology of China), Qing Yan and Guangyi Fu (Chinese Academy of Sciences), Tao Deng (Shanghai Jiao Tong University), Hongda Chen (Institute of Semiconductors, Chinese Academy of Sciences), and Daojun Song (Hefei High‐Tech Zone) for fruitful discussions. The National Key R&D Program of China (No. 2017YFB0406200) and the Science and Technology Service Network Initiative of the Chinese Academy of Sciences (guide project for innovative and entrepreneurial) (No. KFJ‐STS‐SCYD‐112) are acknowledged for financial support of our work in this area.
1Physical Basis of Thermal Conduction
Xian Zhang1, Ping Zhang2, Chao Xiao1, Yanyan Wang1, Xin Ding1, Xianglan Liu1, and Xingyou Tian1
1Chinese Academy of Sciences, Institute of Solid State Physics, Hefei Institutes of Physical Science, 350 Shushanhu Road, Hefei, 230031, Anhui, P. R. China
2School of Materials Science & Engineering, Anhui University, 111 Jiulong Road, Hefei, 230601, Anhui, P. R. China
1.1 Basic Concepts and Laws of Thermal Conduction
1.1.1 Description of Temperature Field
The difference in temperature drives the heat transfer from the high‐temperature zone to the low‐temperature zone; it is therefore important to understand the temperature distribution of the object for studying the heat transfer. The temperature distribution can be expressed in mathematical equations and image forms using a scalar temperature field, which is a function of time (t) and space coordinates (x, y, z):
According to the temperature variation with time, the temperature field can be divided into steady temperature field and unsteady temperature field. In the steady‐state temperature field, the temperature of the object is only related to space but not to time change. It can be expressed by
According to the dimensional correlation with the spatial coordinates, the temperature field can be divided into one‐dimensional, two‐dimensional, and three‐dimensional temperature fields, that is, the object temperature is only related to one, two, or three coordinates of space. For example, one‐dimensional steady temperature field can be expressed by
When the temperature field is described by an image, the image formed by connecting the same points of temperature is called an isothermal surface. By analogy, a cluster of curves is formed in the two‐dimensional temperature field, which is called an isotherm. As shown in Figure 1.1, there is no temperature difference on an isotherm, so heat can only transfer between different isotherms.
Figure. 1.1 Temperature field and temperature gradient.
1.1.2 Temperature Gradient
As shown in Figure 1.1, the temperature difference between isotherms is the same. However, the ratio limit of the temperature difference to the distance of a point in different directions is different. The limit of the ratio of the temperature difference to the distance in the normal direction of the point is the maximum. The maximum limit value is defined as the temperature gradient, which is recorded as ∇T, it is a vector whose direction points to the direction of temperature rise along the isotherm normal and can be expressed by
1.1.3 Fourier's Law
In 1882, French scholar Fourier proposed the basic law of heat conduction process, namely Fourier's law. The expression is [1]
where q is the heat flow density in W/m2 and k is the thermal conductivity in W/m K. Formula (1.5) shows that q is a vector, and its direction lies on the same normal of the temperature gradient isotherm, pointing to the direction of temperature reduction.
1.1.4 Heat Flux Density Field
In the space coordinate system, the heat flux expression is
where , , are unit vectors in x‐, y‐, z‐directions, respectively. The heat flux distribution inside the object constitutes a heat flux field, which is a vector field. As shown in Figure 1.2, the solid line represents the isotherm, and the dotted line represents the isochore. Isothermal streamline is a set of curves perpendicular to the isotherm everywhere. The heat flux density on the isothermic streamline is equal everywhere, the direction of the heat flux density at any point is always tangent to the isothermic streamline, and the heat flux transmitted between two adjacent dotted lines is equal everywhere.
Figure. 1.2 Isotherms and heat flux.
1.1.5 Thermal Conductivity
According to Formula (1.5),
where S is the area, Q is the heat transferred through the area S in t time, and d is the distance of heat transfer. Thermal conductivity is a proportional coefficient in Fourier's law, which reflects the thermal conductivity of an object, that is, the heat flow that can be transferred through a unit area under the action of a unit temperature gradient.
The thermal conductivity of object usually varies with temperature. When the temperature range of the objective is small, the thermal conductivity is linearly related to the temperature:
where k0 is the thermal conductivity under a certain reference state and b is the constant determined experimentally. Due to the difference of heat conduction mechanism, the thermal conductivity of object in different forms is quite different. The heat conduction of objects is the collision and transfer of microscopic particles, including the thermal movement of molecules, the phonon movement formed by lattice vibration, and the movement of free electrons. Generally, the thermal conductivity of solid is the highest, while that of gas is the lowest.
1.2 Heat Conduction Differential Equation and Finite Solution
1.2.1 Heat Conduction Differential Equation
Figure 1.3 shows a cube element with side lengths of dx, dy, dz. Here, the density ρ, specific heat Cp, and thermal conductivity k are constants.
According to the law of conservation of energy, the sum of the net heat flowing into the cube unit in a certain time ΔQi and the heat generated by the cube unit itself ΔQp is equal to the increase in the enthalpy ΔE of the infinitesimal cube.
Figure. 1.3 Cube element.
During dτ time, the total net inflow heat in the x‐, y‐, z‐directions is
The heat generated by the heat source in the cube unit in time dτ is
where q1is the calorific value of the heat source per unit time and volume, and the unit is W/m3.
The increase in enthalpy of the heat source of the cube unit in time dτ is
According to the conservation of energy,
It can also be written as
where ∇2 is Laplace operator, and α is the thermal diffusion coefficient with unit of m2/s. Formulas (1.12) and (1.13) are the differential equations of heat conduction, which describes the variation of temperature field in the heat conduction system with time and space.
Thermal diffusion coefficient (α = k/ρc) is a physical parameter related to the type of material, and the value depends on the thermal conductivity, density, and specific heat of the object. It reflects the ability of the object to transmit temperature changes.
For the steady‐state temperature field with constant thermal conductivity, the thermal conductivity differential equation becomes
For steady‐state temperature field with constant thermal conductivity and no internal heat source, the thermal conductivity differential equation is expressed as
The above equation is called Laplace equation, which is the most basic differential equation for studying the steady‐state temperature field.
1.2.2 Definite Conditions
The differential equation of heat conduction is a universal equation for heat conduction problems. For specific heat conduction problems, the eigenvalue conditions of the corresponding problem must be given. These conditions include initial conditions (initial state of heat conduction system) and boundary conditions (interface characteristics, relationship between system and environment), where the initial condition expression is
If the initial temperature is uniform and constant (T = Ti), the initial condition is not required for the steady‐state heat conduction problem. There are three common types of boundary problems.
The first boundary condition is that the boundary temperature distribution of the system is known:
The second boundary condition is that the heat flux distribution on the boundary is known:
The third boundary condition is that the convective heat transfer coefficient and fluid temperature between the object and the surrounding fluid are known:
1.3 Heat Conduction Mechanism and Theoretical Calculation
The heat transfer of gases relies on the thermal motion and collision of molecules and atoms. The heat transfer in liquids relies on irregular elastic vibrations (or similar gases). In solids, heat energy is transferred through electrons and lattice vibrations. In metal solids, heat conduction is mainly realized by the interaction and collision of electrons. On the contrary, in dielectric solids including semiconductors and insulators, heat is mainly transferred through quantized lattice vibration. Among these heat conduction mechanisms, the speed of heat transfer through electron collision is the highest, while the one by molecular or atomic collision is the lowest.
1.3.1 Gases
The heat conduction mechanism of gases involves the heat transfer caused by the thermal movement of molecules and the collision between molecules. According to the theory of ideal gas molecular motion, the mathematical expression of molecular heat conduction mechanism can be deduced as [1]
where k is the thermal conductivity, is the heat capacity per unit volume of gas, v is the average velocity of gas molecules, and is the average free path of gas molecules. Because the heat capacity of the gas and the average speed of molecular motion increase with the increase in temperature, the thermal conductivity of the gas also increases with the increase in temperature.
Chapman and Cowling [2] associate the thermal conductivity of simple gas with viscosity and specific heat at constant volume, and the expression is
where f is constant, 2.5 for smooth spherically symmetric molecules and 2.522 for rigid elastic spheres; η is the kinematic viscosity with a unit of kg/(m s); and cv is the specific heat of constant volume with a unit of W/(kg K).
Eucken [3] correlated the thermal conductivity of monatomic gas with viscosity and specific heat at atmospheric pressure and 0 °C:
Hirschfelder et al. [4] later modified the Euken equation:
where H and v are the complex interaction coefficients between molecular pairs, M is the molecular weight, and R is the ideal gas constant.
1.3.2 Solids
The lattice in solid is fixed and can only vibrate slightly near its equilibrium position. The heat conduction in solids is mainly realized by the lattice wave of lattice vibration and the movement of free electrons. According to quantum theory, the energy of lattice vibration is quantized, and the quantum of lattice vibration is usually called phonon [5]. Therefore, phonons can be regarded as free “gas” particles by analogy with gas heat conduction [6]. The contribution of phonons or electrons to heat conduction varies greatly depending on the type of solid.
1.3.2.1 Metals
There are a large number of unbound free electrons with light mass in metals. The electrons move like “electron gas.” The interaction or collision between electrons is the main mechanism of metal heat conduction, that is, electronic heat conduction. Metals are also crystals; hence, lattice vibration (phonon) also contributes to the heat transfer in metals. Therefore, the thermal conductivity k of metal can be expressed by the following formula:
where ke is the thermal conductivity representing the contribution of free electrons, and kp is the thermal conductivity representing the contribution of phonon.
Based on the results of the kinetic theory of gas molecules, the mathematical expression of ke is
where Cve is the heat capacity of electrons per unit volume, is the average velocity of electrons, and is the average free path of the electron.
Free electrons in metals serve as both the carrier of heat and the carrier of electricity, so metal heat conduction and conductivity are closely related. The relationship between thermal conductivity and conductivity of metals follows Wiedman–Franz law:
where σ is the electrical conductivity, e is the absolute value of electronic charge, and kB is the Boltzmann constant. The law shows that the thermal conductivity of metal is proportional to the electrical conductivity.
The law of electron heat conduction in metal changing with temperature is shown in Figure 1.4. At very low temperatures, the electron thermal conductivity increases linearly with temperature; at medium temperatures, the electron thermal conductivity is almost constant and does not change with temperature; and at very high temperatures, the electron thermal conductivity decreases slightly with the increase in temperature.
Figure. 1.4 Relationship between metal thermal conductivity and temperature.
1.3.2.2 Inorganic Nonmetals
Crystal In dielectric crystals, heat energy is transferred by lattice vibration. Therefore, the propagation of lattice waves is regarded as the movement of phonons. The scattering encountered by lattice waves in the crystal is regarded as the collision between phonons, phonons and grain boundaries, and lattice defects. The thermal resistance in an ideal crystal is attributed to the collision between phonons.
According to Debye's assumption, by analogy with gases, it is considered that the mathematical expression of thermal conductivity in dielectric crystals should be the similar to that in gases. Therefore, the expression of phonon thermal conductivity can be expressed by
where Cvpn,, and are the volume heat capacity, average velocity, and average free path of phonons, respectively.
According to the Klemens model, the lattice thermal conductivity of blocky solid is given by
where i is the index of phonons, v is the group velocity of phonons, τ is the relaxation time, and q is the wave vector.
The curve of thermal conductivity of dielectric crystal changing with temperature is shown in Figure 1.5[7]. At very low temperatures, the phonon‐specific heat capacity is proportional to T3. It means that heat conduction of crystal increases proportionally with the third power of temperature [8]. At higher temperatures, on the one hand, the phonon heat capacity does not change with temperature and is close to a constant 3R. On the other hand, the mean free path of phonons decreases gradually with the increase in temperature, and the mean free path of phonons is inversely proportional to the temperature (l ∝ 1/T). Therefore, the thermal conductivity of the dielectric crystal at a higher temperature decreases [9].
Figure. 1.5 Relationship between thermal conductivity and temperature of dielectric crystals.
The formulas for calculating the theoretical thermal conductivity of dielectric crystals are summarized below:
Debye formula
where ρ is the density, v is the propagation velocity of phonons, C is the heat capacity, x0 is the compression coefficient, v is the frequency, kB is the Boltzmann constant, T is the absolute temperature, and α is the correlation coefficient.
Compton formula
where b = 4m1m2/(m1 + m2), m is the mass of different atoms, n2 is the number of atoms per unit area perpendicular to the heat flow, d is the atomic spacing parallel to the heat flow, R is the gas constant of a single molecule, v is the atomic vibration frequency, C0 is the constant determined by thermal conductivity at a given temperature, T is the absolute temperature, and β is a constant.
Pell formula
where Θ is the Debye temperature, T is the absolute temperature, and A and B are constants.
Papapecchu formula
where V is the gram atomic volume; l = l0u0/u is the average free path; R is the gas constant; u = 3LE, E is the average energy of a wave and L is the Loschmidt constant; v is the average propagation speed; C is the specific heat of gram atom; and T is the absolute temperature.
Entuo formula
where kB is the Boltzmann constant, n is a factor determined by the type of spatial lattice, N is the number of atoms per unit area, d is the atomic spacing, R is the gas constant, h is Planck constant, v is the natural vibration frequency, and T is the absolute temperature.
Noncrystal Inorganic amorphous materials have a long‐range disorder and short‐range ordered structure. To analyze their heat conduction mechanism, they are generally treated as a “crystal” composed of very fine grains with only a few lattices spacing sizes. Allen and Feldman [10] studied the heat transfer mechanism in amorphous materials using lattice dynamics calculations and divided the vibration modes into three different categories: plane wave propagator, diffuser, and locator. The relative contribution of each mode determines the thermal conductivity of the material, including its value, dependence on sample size, and temperature [11]. In 1911, Einstein [12], first proposed the “amorphous limit” model to predict the minimum lattice thermal conductivity of amorphous solids. In 1979, Slack [13] further developed the “amorphous Limit” model, which equates the minimum mean free path of phonons with the wavelength of lattice waves and is called the “minimum thermal conductivity” model.
Cahill–Pohl model [14] simulates the thermal conductivity of amorphous solids by assuming that the average free path of each vibration mode is half of its wavelength. Agne et al. [15] simplified the Cahill–Pohl model results to
where kB is the Boltzmann constant, n is the atomic number density, vT is the lateral propagation velocity, and vL is the longitudinal speed. In 1992, Cahill et al. [15] further modified the “minimum thermal conductivity” model.
For the relationship between thermal conductivity and temperature of inorganic amorphous, the contribution of photonic heat conduction should be considered at higher temperatures, and it will be mainly determined by the relationship between heat capacity and temperature in other temperature ranges. The thermal conductivity of inorganic amorphous materials changes with temperature as shown in Figure 1.6[17]. At low temperatures, the thermal conductivity of inorganic amorphous increases monotonously with the increase in temperature. At this time, the change of phonon heat conduction with temperature is determined by the change rule of phonon heat capacity with temperature. As the temperature increases, the phonon heat capacity increases, so the thermal conductivity of the amorphous increases accordingly. From medium temperature to high temperature, although the temperature increases, the phonon heat capacity no longer increases but gradually becomes constant. Therefore, the phonon heat conduction no longer varies with temperature, and the thermal conductivity curve presents a straight line nearly parallel to the horizontal axis. Above the high temperature, the phonon heat conduction changes little with the further increase in temperature. As the average free path of photons increases significantly, the thermal conductivity of inorganic amorphous is proportional to the third power of temperature.
Figure. 1.6 Relationship between thermal conductivity and temperature of inorganic amorphous solids.
Source: Reproduced with permission from Ref. [16]; ©1993 American Physical Society.
1.3.3 Liquids
The heat conduction mechanism of liquids is still controversial. One view is that the heat conduction mechanism of liquids is similar to that of gases. However, the unreasonable thing is that the distance between liquid molecules is relatively close, and the intermolecular force has a greater impact on the collision process than in gases. Another point is that the heat conduction mechanism of liquid is similar to that of non‐metallic solids, mainly due to the effect of elastic waves.
The simplest equation applicable to all organic liquids is [18]
where Tc is the critical temperature, B, C, D are constants, A is the pseudo‐critical thermal conductivity.
Bridgman [19] provides a simple formula that can accurately calculate the thermal conductivity of some liquids:
where vs is the longitudinal speed of sound in a liquid, d is the mean distance between the centers of molecules and can be calculated from d = n−1/3, and n is the number density of molecules in the liquid.
Chapman–Enskog [20] gives the thermal conductivity of liquids as follows:
where D is the effective diameter of the molecule, m is the mass of a liquid molecule, ρ is the density of the liquid (kg/m3), and T is the absolute temperature.
van Elk vet al. [21] developed an equation for the correlation between the components of binary mixed liquids and thermal conductivity, and verified various types of mixed liquids:
The components are so selected that k2 ≥ k1; the constant 0.72 may be replaced by an adjustable parameter when k2 < k1.
In 1974, Saksena and Harminder [22, 23] also successively proposed and improved the calculation formula for thermal conductivity of binary mixed liquids; Jamieson suggested that the thermal conductivity of binary mixture can be calculated by the following formula:
The components are so selected that k2 ≥ k1; α is an adjustable parameter that is set equal to unity if mixture data are unavailable for regression purposes. Equation (1.39) enables one to estimate m within about 7% for all types of binary mixtures with or without water.
In 1982, Rowley Method [24] proposed the thermal conductivity equation for multi‐component mixed liquids using the two liquid theory modeling:
where km is the liquid mixture thermal conductivity, W/(m K); wi is the weight fraction of component; wji is the local weight fraction of component j relative to a central molecule of component i; and kji is the characteristic parameter for the thermal conductivity that expresses the interactions between j and i, W/(m K).
In 1976, Li [25] provided a new idea for the calculation of thermal conductivity of multi‐component mixed liquids:
where Xi is the mole fraction of component i and ϕi is the superficial volume fraction of i. Vi is the molar volume of the pure liquid.
1.4 Factors Affecting Thermal Conductivity of Inorganic Nonmetals
1.4.1 Temperature
After summarizing the measurement results of the thermal conductivity of a large number of dielectric crystals and amorphous solids, Eueken [26] concluded that (i) the thermal conductivity of single crystals increases with the decrease of temperature, while the thermal conductivity of amorphous solids shows inverse trend; (ii) the thermal conductivity is inversely proportional to the absolute temperature of the crystal; and (iii) the thermal conductivity of amorphous solids is roughly proportional to the specific heat.
Except for lead oxide, the thermal conductivity of inorganic non‐metallic crystals is almost proportional to the reciprocal of absolute temperature above room temperature [10]:
where T is the absolute temperature, and A and B are constants determined experimentally.
For inorganic amorphous, the thermal conductivity increases approximately in direct proportion to the temperature [27]:
where T is the absolute temperature, and C is the constant determined experimentally.
For the mixture of inorganic crystal and amorphous, the relationship between thermal conductivity and temperature can be expressed as
1.4.2 Pressure
Under pressure, the correlation between thermal conductivity and pressure can be divided into increasing, decreasing, independent, and abnormal trends.
For example, the thermal conductivity of an object can increase sharply under pressure. This is because the strain generated by pressure enhances the atomic interaction and compresses the bond, changing the phonon dispersion, thus greatly increasing the propagation speed of phonons. Such enhancement is nonlinear in some cases, which can be attributed to the combined effect of decreasing phonon relaxation time and increasing phonon group velocity [28].
In addition, the thermal conductivity of the object can also be reduced under pressure, because phonon anharmonicity and phonon softening induced by pressure increase [29]. The first‐principle calculation shows that the reduced thermal conductivity under pressure is mainly due to the stronger cubic anharmonic interaction, large mass ratio, and significant acousto‐optic frequency gap [30].
In some cases, the thermal conductivity is independent of the pressure, which may be caused by the strong electron correlation effect driven by the electronic topological transition [31].
Several mechanisms have been proposed to understand abnormal thermal conductivity changes under pressure. The abnormal decrease of thermal conductivity of some materials under pressure can be ascribed to the large phonon frequency gap of materials under high pressure. The contribution of the inherent three‐phonon scattering process is smaller than that of other cases, and the complex scattering process between more phonons dominates and increases the overall phonon scattering [32]. In the case of another non‐monotonic behavior, the thermal conductivity first increases and then decreases with the increase in pressure. The possible mechanism of this behavior is the competitive scattering process of three phonons interacting with four phonons under high pressure [33] or the interaction between group velocity and phonon relaxation time under pressure [34]. When some rare earths show different pressure dependences of thermal conductivity, the pressure dependence is determined by the competition between the enhancement of phonon group velocity and the reduction of phonon relaxation time [35].
1.4.3 Crystal Structure
The more complex the crystal structure, the lower the thermal conductivity. For example, the structure of magnesia alumina spinel (MgAl2O4) is similar to that of alumina (Al2O3) and magnesium oxide (MgO), and their thermal solubility, thermal expansion coefficient, and elastic modulus are similar. However, due to the complex structure of the former, its thermal conductivity is much lower than the latter two. In addition, the mean free path of phonons of materials with complex structures is easy to approach or reach its minimum limit value, that is, the lattice size value, at high temperatures to obtain lower thermal conductivity.
The structural integrity and regularity of polycrystals are worse than that of single crystals. In addition, the influence of impurities and distortion on the grain boundary increases the phonon scattering, which is more significant at higher temperatures. In different crystal axis directions, the thermal conductivity of single crystals is also different, with anisotropy, and the phonon scattering is different. The difference of thermal conductivity of single crystals in different crystal axis directions decreases with the increase in temperature, because anisotropic crystals tend to improve or enhance their symmetry with the increase in temperature.
1.4.4 Thermal Resistance
As we all know, the smaller the thermal resistance, the greater the thermal conductivity. The main factor affecting thermal resistance is Debye temperature. The Debye temperature is closely related to atomic weight, theoretical density, and compressibility. The total thermal resistance in the crystal is
where A is the atomic weight, Θ is the Debye temperature, ρ is the theoretical density, and X is the compression coefficient. Generally, the smaller the theoretical density is, the greater the Debye temperature is. The greater the Debye temperature, the smaller the thermal resistance. Therefore, lighter substances usually have higher thermal conductivity. The smaller the compression coefficient or the larger the Young's modulus, the higher the Debye temperature. The higher the Debye temperature, the smaller the thermal resistance. Therefore, materials with higher binding energy usually have higher thermal conductivity. The smaller the atomic weight, the higher the Debye temperature. Therefore, materials with large atomic weights have high thermal conductivity.
1.4.5 Others
Defects and impurities have a great influence on the thermal conductivity of materials, which is determined by the phonon heat conduction mechanism of dielectric crystals [10]. They are the center of phonon scattering, which will reduce the mean free path and thermal conductivity of materials [7]. Because the thermal conductivity of gas in the porosity is far lower than that of materials, porosity always reduces the thermal conductivity of the materials. Peierls‐Boltzmann [36] revealed the process of strain affecting thermal conductivity and found the power law scaling relationship between thermal conductivity and temperature and strain. Strain first affects the speed of phonon propagation and then affects the relaxation time, while temperature only affects the relaxation time.
The experimental work of Krupskii and Manzhelli on the unconstrained argon sample revealed that the thermal conductivity has a deviation in addition to the inverse temperature dependence predicted theoretically [37]. They attributed the bias to the higher‐order four‐phonon interaction, while Clayton and Batchelder attributed it to the thermal expansion effect [38]. Dugdale and MacDonald assumed that micro‐area lattice expansion would occur due to thermal expansion resulting from the temperature gradient [39]. For example, for a material with a positive thermal expansion coefficient, the relative expansion of the hotter region and the compression of the cooler region produces additional heat transfer sources, which further reduce the thermal conductivity.
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