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Nano-to-Macroscale Transport Processes (Microscale Heat Transfer) A Quick Review Ronggui Yang Department of Mechanical Engineering ECME 136, 427 UCB University of Colorado Boulder, CO 80309-0427 Tel: (303) 735-1003, Fax: (303) 492-3498 Email: Ronggui.Yang@Colorado.Edu http://spot.colorado.edu/~yangr

Nano-to-Macroscale Transport Processes (Microscale Heat Transfer) This course concentrates on comprehension warm vitality transport over all scales and especially when gadget measurements approaches the principal lengths-sizes of the charge and vitality bearers in nanostructures. The course will address measure consequences for warm and liquid transport in nanostructures and how to potentially design novel powerful transport properties. Besides, the present cutting edge advancements in the microscale warm transport field will be looked into. Points incorporate the vitality levels, the factual conduct and inner vitality, vitality transport in the types of waves and particles, scrambling and vitality discussion forms, Boltzmann condition and deduction of established laws, deviation from traditional laws at nanoscale and their suitable portrayals, with applications in nanotechnology and microtechnology. Reading material Gang Chen, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons. New York: Oxford University Press, 2005. ISBN: 019515942X. Reviewing: Bi-week by week homework 30%, midterm 25%, last test of the year 45% Learning Goals Understand, Analyze, Innovate

Course Objectives Students in this course will: Gain a comprehension of the key components of strong state material science. Create aptitudes to get continuum physical properties from sub-continuum standards. Apply measurable and physical standards to portray vitality transport in present day little scale materials and gadgets.

No Pains, No Gains! Required Textbook Gang Chen, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons . New York: Oxford University Press, 2005. ISBN: 019515942X. Prescribed Books C. Kittel, Introduction to Solid State Physics, seventh Ed., Wiley, 1996. N.W. Ashroft and N.D. Mermin, Solid State Physics, Brooks Cole, 1976 C. Kittel and H. Kroemer, Thermal Physics, second Ed., Freeman and Company, 1980. M. Lundstrom, Fundamentals of Carrier Transport, second Ed, Cambridge University Press, 2000. Z.M. Zhang, Nano/Microscale Heat Transfer, Wiley, 2007. Address Notes References MIT Courses: 2.57 Nano-to-Macroscale Transport Processes 6.728 Quantum Mechanics and Statistical Mechanics 6.730 Solid State Physics 6.720 Physics of Semiconductor Devices 6.772 Physics of Semiconductor Compounds and Devices Lecture Notes by associates in different colleges

red platelet ~5 m (SEM) diatom 30 m DNA proteins nm Simple particles <1nm microorganisms 1 m nm m 10 - 10 - 9 10 - 8 10 - 7 10 - 6 10 - 5 10 - 4 10 - 3 10 - 2 SOI transistor width 0.12 m semiconductor nanocrystal (CdSe) 5nm Circuit plan Copper wiring width 0.2 m Nanometer memory component (Lieber) 10 12 bits/cm 2 (1Tbit/cm 2 ) IBM PowerPC750 TM Microprocessor 7.56mm×8.799mm 6.35×10 6 transistors Length Scales

Revolution and Evolution in Electronics

Biology Nano-Bio Interface Nanoelectronics Conventional Spintronics Molectronics Nanotubes NANO Nanosciences Nanostructures Nanomaterials Nanophotonics Photonic Crystals Plasmonic Photonics Energy Conversion, Storage, and Transportation Nanotechnology Landscape

bearers wavelength electrons phonons photons air atoms 10-100 nm 1 nm 0.1-10 0.01 nm Characteristic Lengths of Energy Carriers Room Temperature

Microscopic Picture of Thermal Transport T h T c Air atoms Phonon gas ε = nhν Free electron display T h T h T c T c Free electron Atom center Conduction - arbitrary movement of vitality transporters Gas Molecules Electrons Phonons

q x Hot Cold x v x t x Simple Kinetic Theory Taylor Expansion: , neighborhood thermodynamics balance: u = u ( T )

Heat Conduction in Solids Heat is directed by electrons and phonons. k is dictated by electron-electron, phonon-phonon, and electron-phonon impacts. Hot Cold p - Cold To comprehend transport and vitality transformation, we have to know: How much vitality/energy can a molecule have? What number of particles have the predefined vitality E? How quick do they move? How far would they be able to travel? How would they collaborate with each other?

Microstructure of solids Atomic bonds Crystalline, polycrystalline, nebulous materials Bravais cross section, corresponding grid, Miller lists

U: Potential Energy a+b x Energy Repulsion = ¥ U Harmonic Force Approximation Interatomic Distance Attraction Equilibrium Position Transmission wave Reflection wave Energy obstruction U 0 ENERGY AND Incoming wave WAVEFUNCTION n=3 n=2 n=1 x U =0 u r Quantum Mechanics 101 Problem 2.10 Next Lecture

Vibrations in solids Crystal vibrations, scattering relations Quantization and phonons Phonon branches and modes Lattice particular warmth Thermal extension Phonon dissipating Heat conduction

Lattice Constant, a x n+1 y n-1 x n y n 1-D Lattice with Diatomic Basis Consider a straight diatomic chain of iotas (1-D display for a precious stone like NaCl): In harmony: Applying Newton's second law and the closest neighbor estimate to this framework gives a scattering connection with two "branches":

1-D Lattice with Diatomic Basis: Results - (k) �� 0 as k �� 0 acoustic modes (M 1 and M 2 move in phase) + (k) �� max as k �� 0 optical modes (M 1 and M 2 move out of stage) These two branches might be outlined schematically as takes after: optical crevice in permitted frequencies acoustic

3-D Solids: Phonon Dispersion In a genuine 3-D strong the scattering connection will contrast along various headings in k-space. By and large, for a p iota premise, there are 3 acoustic modes and p-1 gatherings of 3 optical modes, despite the fact that for some engendering headings the two transverse modes (T) are worsen.

Density of States w D Phonon Frequency w E 3-D Solids: Heat Capacity Einstein Model Debye Model (an) Optical Phonons Acoustic Phonons Density of States Phonon Frequency w

Thermal Expansion If the bend is not symmetric, the normal position in which the particle sits shifts with temperature. Bond lengths thusly change (normally get greater for expanded T). Warm extension coefficient is nonzero.

k = C v l 1 3 Thermal Conductivity C ~ steady l Phonon mfp k l um ~ e Q/T Specific warmth Phonon gather speed C ~ T d l = v t Matthiessen Rule: l st ~ l um l limit ~ consistent l polluting influence ~ frail dependance on T Low T : High T : Umklapp phonon dispersing: l um ~ e Q/T If T > Q, C ~ steady If T << Q, C ~ T (d: measurement) Specific warmth :

Electrons in solids Free electron hypothesis of metals Fermi-Dirac insights Electron structure and quantization Band structures of metals, semiconductors, and covers Electron scrambling and transport

The Free Electron Gas Model Plot U(x) for a 1-D precious stone cross section : Simple and unrefined limited square-well model: U = 0 Can we legitimize this model? In what manner would one be able to supplant the whole cross section by a steady (zero) potential?

Properties of the FEG By utilizing occasional limit conditions for a cubic strong with edge L and volume V = L 3 , we characterize the arrangement of permitted wave vectors: This demonstrates the volume in k-space per arrangement is: And accordingly the thickness of states in k-space is: Since the FEG is isotropic, the surface of consistent E in k-space is a circle. In this manner for a metal with N electrons we can compute the most extreme k esteem (k F ) and the greatest vitality (E F ). k y k x k z Fermi circle

Density of States N(E) We frequently need to know the thickness of electron states , which is the quantity of states per unit vitality , so we can rapidly ascertain it: The differential number of electron states in a scope of vitality dE or wavevector dk is: This permits: Now utilizing the general connection: we get:

Heat Capacity of the Quantum-Mechanical FEG Quantum mechanics demonstrated that the control of electron states is represented by the Pauli rejection rule, and that the likelihood of control of a state with vitality E at temperature T is: the place = concoction potential E F for kT << E F

Heat Capacity of Metals: Theory versus Expt. at low T Very low temperature estimations uncover: Results for straightforward metals (in units mJ/mol K) demonstrate that the FEG qualities are in sensible concurrence with test, yet are dependably too high: The inconsistency is "represented" by characterizing a successful electron mass m* that is because of the disregarded electron-particle connections

Energy Bands and Energy Gaps in a Periodic Potential Recall the electrostatic potential vitality in a crystalline strong along a line going through a line of molecules: exposed particles strong Along a line parallel to this however running between iotas , the divergences of the intermittent potential vitality are mellowed: U x A basic 1–D scientific model that catches the periodicity of such a potential is:

Metals, Insulators, and Semiconductors • Metals are solids with not entirely filled vitality groups • Semiconductors and protectors have a totally filled or discharge groups and a vitality hole isolating the most elevated filled and least unfilled band. Semiconductors have a little vitality hole (E g < 2.0 eV).

Energy Bands in 3-D Solids 6 Si Cu 5 GaAs 4 3 2 Energy (eV) Direct Band Gap Indirect Ban Gap 1 Eg=1.42 eV Eg=1.12 e

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