ME 381R Lecture 11

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ME 381R Lecture 11 12 Free Electron Gas,
Electronic Specific Heat Thermal Conductivity
Dr. Li Shi Department of Mechanical Engineering
The University of Texas at Austin Austin, TX
78712 www.me.utexas.edu/lishi lishi_at_mail.utexas.
edu

• Reading 1-4 in Tien et al
• References Ch6 in Kittel

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Free Electron Theory for Metals

• Origin of Energy Bands

Na 1s22s22p63s1
Paulis Exclusion Principle
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Wave-Particle Duality of Electrons
The double slit experiment
Schrodinger eqn. for free electrons
? electron wave function ? Plancks
constant m electron mass
E electron energy
Electrons
Traveling wave solution to Schrodingers eqn
k wave vector 2p/l
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Electronic States
A metal ring with perimeter L
Metal
x
Energy
Born-vonKarman cyclic boundary condition
L
?(xL) ?(x)
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Fermi Wavevector
2-D projection of 3-D k-space
ky
dk

• Each state can hold 2 electrons
• of opposite spin (Paulis principle)
• To hold N electrons

k
kx
2p/L
kF Fermi wavevector he electron number density
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Fermi Parameters for Free Electron Metals
Vacuum Level
F Work Function
Fermi Energy, EF
Energy
Fermi Energy
Fermi Velocity
Fermi Temp.
Band Edge
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Effect of Temperature
Fermi-Dirac equilibrium distribution for the
probability of electron occupation of energy
level E at temperature T
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Number and Energy Densities
Summation over k-states
Integration over k-states
Transformation from k to E variable
Integration of E-levels for number and
energy densities
Number of k-states available between energy E and
EdE
Density of States
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Electronic Specific Heat and Thermal Conductivity
Specific Heat
Thermal Conductivity

• Electron Scattering Mechanisms
• Defect Scattering
• Phonon Scattering
• Boundary Scattering (Film Thickness,
• Grain Boundary)

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Thermal Conductivity of Cu and Al
Matthiessen Rule