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Importance of Metal Properties in Silicon Chip Performance

Explore the significance of metal properties on silicon chips, including thermal expansion failures, chip cooling, heat capacity, thermal conductivity, and more. Delve into electrical current flow, resistance in interconnects, and the role of electrons in conduction. Learn fundamentals like Ohm's Law and Drude's theory for a comprehensive understanding.

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Importance of Metal Properties in Silicon Chip Performance

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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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