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Lecture 4.0

Lecture 4.0. Properties of Metals. Importance to Silicon Chips. Metal Delamination Thermal expansion failures Chip Cooling- Device Density Heat Capacity Thermal Conductivity Chip Speed Resistance in RC interconnects. Electrical Current. Flow of Charged Particles due to applied voltage

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Lecture 4.0

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  1. Lecture 4.0 Properties of Metals

  2. Importance to Silicon Chips • Metal Delamination • Thermal expansion failures • Chip Cooling- Device Density • Heat Capacity • Thermal Conductivity • Chip Speed • Resistance in RC interconnects

  3. Electrical Current • Flow of Charged Particles due to applied voltage • Solids • Ions/holes are large and slow • electrons are small and fast • Electrons are often responsible for conduction

  4. Ohm's Law • Current density, J=I/A==/ • =electric field[V/cm] • =Conductivity, [=1/] =Resistivity • =ne, =mobility, e=electron charge, n=#/vol. • Resistance, R=  L/A • V=IR

  5. Drude’s theory electron scattering by lattice Mobility, e/me  = average time between collisions of electron with ions Bloch’s Quantum theory no electron scattering in perfect lattice only in a imperfect lattice Scattering lattice vibrations impurities dislocations Metal Conduction

  6. • • 1s 1s • • Remember Molecular Orbitals • New Energy • Bonding • Anti Bonding  

  7. Energy Bands

  8. Energy Bands Partially Filled

  9. Distribution of Electrons in Band • Fermi-Dirac distribution • Probability, • F(E)=1/(exp{[E-Ef]/kBT}+1) • Ef is the Fermi Energy

  10. Fermi Energy

  11. Work Function

  12. Fermi-Dirac Probability Distribution

  13. Density of States-3D Schrodinger Eq.

  14. ElectronFilling inBand-density of occupied states

  15. Eletrical Conductivity • =ne • =mobility, e=electron charge, n=#/vol. • =(N/V) F(E)G(E) e2/me,

  16. Thermal Properties - Chapter 7 • Thermal Conductivity • Thermal Expansion • Heat Capacity • Thermoelectric effect • thermocouple

  17. Thermal Properties - Chapter 7 • Thermal Vibrations-phonons • Displacement, xmax=(3kBT/Yao)1/2 • Y ao is the spring constant • Thermal Expansion • (l/lo)(1/T), also volume->(V/Vo)(1/T) • Heat Capacity • Cp=1/2 kBT per degree of freedom • 6 degrees of freedom per ion, Cp=3R • kinetic and potential • Variation of Conductivity with Temp. d  /dT

  18. Thermal Expansion

  19. Heat Capacity-Effect of Phonons/electrons • Einstein Model • Debye Model • Electrons • density of occupied states En=(n+1/2)h <E>= h/(exp(h/kBT)-1) g()= 2V/(22v3)

  20. Heat Capacity of Electrons

  21. Heat Capacity

  22. Thermal Conduction • Transport of Phonons (vibrations) • kthermal/(T)=constant • thermal conductivity scales with electrical conductivity • kthermal=kelectrons + kphonons

  23. Conductivities

  24. Thermal Conductivity-Phonon • kphonons= Ne Cp ph Vph/3 • Ne number e-/volume, • Cp=heat capacity of atoms =3kB • ph =mean free path, • Vph=velocity

  25. Thermal Conductivity - Electron • ke= Ne Ce e Ve/3 • Ne number e-/volume, • Ce=heat capacity of electrons • e =mean free path, • Ve=velocity

  26. Thermal Conductivity

  27. Phonon Interactions • With other phonons • With impurities • depends upon phonon wavelength • With imperfections in Crystal • depends upon phonon wavelength • Phonons travel at speed of sound

  28. Phonon Interactions

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