NANO/MICROSCALE HEAT TRANSFER.

Preface
Contents
List of Symbols
	Dimensionless Parameters
	Greek Symbols
	Subscripts
1 Introduction
	1.1 Limitations of the Macroscopic Formulation
	1.2 The Length Scales
	1.3 From Ancient Philosophy to Contemporary Technologies
		1.3.1 Microelectronics and Information Technology
		1.3.2 Lasers, Optoelectronics, and Nanophotonics
		1.3.3 Microfabrication and Nanofabrication
		1.3.4 Probe and Manipulation of Small Structures
		1.3.5 Energy Conversion and Storage
		1.3.6 Biomolecule Imaging and Molecular Electronics
	1.4 Objectives and Organization of This Book
	References
2 Overview of Macroscopic Thermal Sciences
	2.1 Fundamentals of Thermodynamics
		2.1.1 The First Law of Thermodynamics
		2.1.2 Thermodynamic Equilibrium and the Second Law
		2.1.3 The Third Law of Thermodynamics
	2.2 Thermodynamic Functions and Properties
		2.2.1 Thermodynamic Relations
		2.2.2 The Gibbs Phase Rule
		2.2.3 Specific Heats
	2.3 Ideal Gas and Ideal Incompressible Models
		2.3.1 The Ideal Gas
		2.3.2 Incompressible Solids and Liquids
	2.4 Heat Transfer Basics
		2.4.1 Conduction
		2.4.2 Convection
		2.4.3 Radiation
	2.5 Summary
	Problems
	References
3 Elements of Statistical Thermodynamics and Quantum Theory
	3.1 Statistical Mechanics of Independent Particles
		3.1.1 Macrostates Versus Microstates
		3.1.2 Phase Space
		3.1.3 Quantum Mechanics Considerations
		3.1.4 Equilibrium Distributions for Different Statistics
	3.2 Thermodynamic Relations
		3.2.1 Heat and Work
		3.2.2 Entropy
		3.2.3 The Lagrangian Multipliers
		3.2.4 Entropy at Absolute Zero Temperature
		3.2.5 Macroscopic Properties in Terms of the Partition Function
	3.3 Ideal Molecular Gases
		3.3.1 Monatomic Ideal Gases
		3.3.2 Maxwell’s Velocity Distribution
		3.3.3 Diatomic and Polyatomic Ideal Gases
	3.4 Statistical Ensembles and Fluctuations
	3.5 Basic Quantum Mechanics
		3.5.1 The Schrödinger Equation
		3.5.2 A Particle in a Potential Well or a Box
		3.5.3 A Rigid Rotor
		3.5.4 Atomic Emission and the Bohr Radius
		3.5.5 A Harmonic Oscillator
	3.6 Emission and Absorption of Photons by Molecules or Atoms
	3.7 Energy, Mass, and Momentum in Terms of Relativity
	3.8 Summary
	Problems
	References
4 Kinetic Theory and Micro/Nanofluidics
	4.1 Kinetic Description of Dilute Gases
		4.1.1 Local Average and Flux
		4.1.2 The Mean Free Path
	4.2 Transport Equations and Properties of Ideal Gases
		4.2.1 Shear Force and Viscosity
		4.2.2 Heat Diffusion
		4.2.3 Mass Diffusion
	4.3 Intermolecular Forces
		4.3.1 Intermolecular Attractive Forces
		4.3.2 Total Intermolecular Pair Potentials
	4.4 The Boltzmann Transport Equation
		4.4.1 Hydrodynamic Equations
		4.4.2 Fourier’s Law and Thermal Conductivity
	4.5 Micro/Nanofluidics and Heat Transfer
		4.5.1 The Knudsen Number and Flow Regimes
		4.5.2 Velocity Slip and Temperature Jump
		4.5.3 Gas Conduction—From the Continuum to the Free Molecule Regime
	4.6 Summary
	Problems
	References
5 Thermal Properties of Solids and the Size Effect
	5.1 Specific Heat of Solids
		5.1.1 Lattice Vibration in Solids: The Phonon Gas
		5.1.2 The Debye Specific Heat Model
		5.1.3 Free-Electron Gas in Metals
	5.2 Quantum Size Effect on Specific Heat
		5.2.1 Periodic Boundary Conditions
		5.2.2 General Expressions of Lattice Specific Heat
		5.2.3 Dimensionality
		5.2.4 Thin Films and Nanowires
		5.2.5 Nanoparticles or Nanocrystals
		5.2.6 Graphite, Graphene, and Carbon Nanotubes
	5.3 Electrical and Thermal Conductivities of Solids
		5.3.1 Electrical Conductivity
		5.3.2 Thermal Conductivity of Metals
		5.3.3 Derivation of Conductivities from the BTE
		5.3.4 Thermal Conductivity of Insulators
	5.4 Thermoelectricity
		5.4.1 The Seebeck Effect and Thermoelectric Power
		5.4.2 The Peltier Effect and the Thomson Effect
		5.4.3 Thermoelectric Generation and Refrigeration
		5.4.4 Onsager’s Theorem and Irreversible Thermodynamics
	5.5 Classical Size Effect on Conductivities
		5.5.1 Simple Geometric Considerations
		5.5.2 Conductivity Along a Thin Film Based on the BTE
		5.5.3 Conductivity Along a Thin Wire Based on the BTE
		5.5.4 Size Effects on Crystalline Insulators
		5.5.5 Mean-Free-Path Distribution
	5.6 Quantum Conductance and the Landauer Formalism
	5.7 Summary
	Problems
	References
6 Electron and Phonon Transport
	6.1 The Hall Effect
	6.2 General Classifications of Solids
		6.2.1 Electrons in Atoms
		6.2.2 Insulators, Conductors, and Semiconductors
		6.2.3 Atomic Binding in Solids
	6.3 Crystal Structures
		6.3.1 The Bravais Lattices
		6.3.2 Primitive Vectors and the Primitive Unit Cell
		6.3.3 Basis Made of Two or More Atoms
	6.4 Electronic Band Structures
		6.4.1 Reciprocal Lattices and the First Brillouin Zone
		6.4.2 Bloch’s Theorem
		6.4.3 Band Structures of Metals and Semiconductors
		6.4.4 Electronic Properties of Graphene
	6.5 Phonon Dispersion and Scattering
		6.5.1 The 1D Diatomic Chain
		6.5.2 Dispersion Relations for Real Crystals
		6.5.3 Scattering Mechanisms
		6.5.4 Phononics and Coherent Phonons
	6.6 Atomistic Simulation of Lattice Thermal Properties
		6.6.1 Interatomic Force Constants (IFCs)
		6.6.2 Lattice Dynamics and Fermi’s Golden Rule
		6.6.3 Evaluation of Thermal Conductivity
	6.7 Electron Emission and Tunneling
		6.7.1 Photoelectric Effect
		6.7.2 Thermionic Emission
		6.7.3 Field Emission and Electron Tunneling
	6.8 Electrical Transport in Semiconductor Devices
		6.8.1 Number Density, Mobility, and the Hall Effect
		6.8.2 Generation and Recombination
		6.8.3 The p-n Junction
		6.8.4 Optoelectronic Applications
	6.9 Summary
	Problems
	References
7 Nonequilibrium Energy Transfer in Nanostructures
	7.1 Phenomenological Theories
		7.1.1 Hyperbolic Heat Equation
		7.1.2 Dual-Phase-Lag Model
		7.1.3 Two-Temperature Model
	7.2 Heat Conduction Across Layered Structures
		7.2.1 Equation of Phonon Radiative Transfer (EPRT)
		7.2.2 Solution of the EPRT
		7.2.3 Thermal Boundary Resistance (TBR)
		7.2.4 Atomistic Green’s Function (AGF)
	7.3 Heat Conduction Regimes
	7.4 Thermal Metrology
		7.4.1 Microbridge and Suspended Microdevices
		7.4.2 Scanning Probe Microscopic Techniques
		7.4.3 Noncontact Optical Techniques
	7.5 Summary
	Problems
	References
8 Fundamentals of Thermal Radiation
	8.1 Electromagnetic Waves
		8.1.1 Maxwell’s Equations
		8.1.2 The Wave Equation
		8.1.3 Polarization
		8.1.4 Energy Flux and Density
		8.1.5 Dielectric Function
		8.1.6 Propagating and Evanescent Waves
	8.2 Blackbody Radiation: The Photon Gas
		8.2.1 Planck’s Law
		8.2.2 Radiation Thermometry
		8.2.3 Radiation Pressure and Photon Entropy
		8.2.4 Limitations of Planck’s Law
	8.3 Radiative Properties of Semi-infinite Media
		8.3.1 Reflection and Refraction of a Plane Wave
		8.3.2 Total Internal Reflection and the Goos–Hänchen Shift
		8.3.3 Bidirectional Reflectance Distribution Function
		8.3.4 Emittance (Emissivity) and Kirchhoff’s Law
	8.4 Dielectric Function Models
		8.4.1 Kramers–Kronig Dispersion Relations
		8.4.2 The Drude Model for Free Carriers
		8.4.3 The Lorentz Oscillator Model for Phonon Absorption
		8.4.4 Semiconductors
		8.4.5 Superconductors
		8.4.6 Metamaterials with a Magnetic Response
	8.5 Experimental Techniques
		8.5.1 Sources
		8.5.2 Detectors
		8.5.3 Dispersive Instruments
		8.5.4 Fourier-Transform Infrared Spectrometer
		8.5.5 BRDF and BTDF Measurements
		8.5.6 Ellipsometry
	8.6 Summary
	Problems
	References
9 Radiative Properties of Nanomaterials
	9.1 Radiative Properties of a Single Layer
		9.1.1 The Ray-Tracing Method for a Thick Layer
		9.1.2 Thin Films
		9.1.3 Partial Coherence
		9.1.4 Effect of Surface Scattering
	9.2 Multilayer Structures
		9.2.1 Thin Films with Two or Three Layers
		9.2.2 The Matrix Formulation
		9.2.3 Thin Films on a Thick Substrate
		9.2.4 Waveguides and Optical Fibers
	9.3 Photonic Crystals and Periodic Gratings
		9.3.1 Photonic Crystals
		9.3.2 Periodic Gratings
		9.3.3 Rigorous Coupled-Wave Analysis (RCWA)
		9.3.4 Effective Medium Formulations
	9.4 Bidirectional Reflectance Distribution Function (BRDF)
		9.4.1 The Analytical Model
		9.4.2 The Monte Carlo Method
		9.4.3 Surface Characterization
		9.4.4 Comparison of Modeling with Measurements
	9.5 Plasmon, Polariton, and Electromagnetic Surface Wave
		9.5.1 Surface Plasmon (or Phonon) Polariton
		9.5.2 Localized Surface Plasmon Resonance
		9.5.3 Polaritons in Thin Films and Layered Structures
		9.5.4 Magnetic Polariton
		9.5.5 Graphene: Optical Properties and Graphene Plasmon
		9.5.6 Hyperbolic (Plasmon or Phonon) Polariton
		9.5.7 General Effective Medium Theory
	9.6 Spectral and Directional Control of Thermal Radiation
		9.6.1 Polariton-Enhanced Transmission
		9.6.2 Perfect Absorption
		9.6.3 Tailoring Thermal Emission with Nanostructures
	9.7 Summary
	Problems
	References
10 Near-Field Energy Transfer
	10.1 From Near-Field Optics to Nanoscale Thermal Radiation
	10.2 Photon Tunneling and Near-Field Radiative Heat Transfer
		10.2.1 Photon Tunneling by Coupled Evanescent Waves
		10.2.2 Thermal Energy Transfer Between Closely Spaced Dielectrics
		10.2.3 Resonance Tunneling Through Periodic Dielectric Layers
		10.2.4 Photon Tunneling with Negative Index Materials
	10.3 Energy Streamlines and Superlens
	10.4 Radiative Transfer Between Two Semi-Infinite Media
		10.4.1 Fluctuational Electrodynamics
		10.4.2 Near-Field Radiative Heat Transfer Between Two Parallel Plates
		10.4.3 Effect of Surface Plasmon Polaritons (SPPs)
		10.4.4 Effect of Surface Phonon Polaritons (SPhPs)
		10.4.5 The Landauer-Like Formulism
	10.5 Multilayers, Anisotropic Media, and 2D Materials
		10.5.1 Multilayers and Hyperbolic Modes
		10.5.2 Graphene and Hexagonal Boron Nitride
		10.5.3 Anisotropic Media
		10.5.4 Green’s Functions for Multilayer Structures
	10.6 Nanostructures and Numerical Methods
		10.6.1 The Scattering Theory for Periodic Structures
		10.6.2 Finite-Difference Time-Domain (FDTD) Method
		10.6.3 Boundary Element Method (BEM)
		10.6.4 Multiple Dipole Approaches
	10.7 Measurements and Applications
		10.7.1 Measurements of Near-Field Thermal Radiation
		10.7.2 Application Prospects of Nanoscale Thermal Radiation
	10.8 Summary
	Problems
	References
Appendix A Physical Constants
Appendix B Mathematical Background
B.1 Some Useful Formulae
B.1.1 Series and Integrals
B.1.2 The Error Function
B.1.3 Stirling’s Formula
B.2 The Method of Lagrange Multipliers
B.3 Permutation and Combination
B.4 Events and Probabilities
B.5 Distribution Functions
B.6 Complex Variables
B.7 The Plane Wave Solution
B.8 The Sommerfeld Expansion
Index