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Lecture 6.0

Lecture 6.0. Properties of Dielectrics. Capacitors On chip On Circuit Board Insulators Transistor gate Interconnects. Materials Oxides SiO 2 Boro-Silicate Glass Nitrides BN polymers. Dielectric use in Silicon Chips. Importance of Dielectrics to Silicon Chips. Size of devices

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Lecture 6.0

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  1. Lecture 6.0 Properties of Dielectrics

  2. Capacitors On chip On Circuit Board Insulators Transistor gate Interconnects Materials Oxides SiO2 Boro-Silicate Glass Nitrides BN polymers Dielectric use in Silicon Chips

  3. Importance of Dielectrics to Silicon Chips • Size of devices • Electron Tunneling dimension • Chip Cooling- Device Density • Heat Capacity • Thermal Conductivity • Chip Speed • Capacitance in RC interconnects

  4. Band theory of Dielectrics • Forbidden Zone–Energy Gap-LARGE Conduction Band Valence Band

  5. Difference between Semiconductors and Dielectrics kBT =0.0257 eV at 298˚K

  6. Fermi-Dirac Probability Distribution for electron energy, E • Probability, F(E)= • (e{[E-Ef]/kBT}+1)-1 • Ef is the • Fermi Energy

  7. Number of Occupied States Density of States Fermi-Dirac T>1000K only

  8. Probability of electrons in Conduction Band • Lowest Energy in CB • E-Ef Eg/2 • Probability in CB • F(E)= (exp{[E-Ef]/kBT} +1)-1 ) • = (exp{Eg/2kBT} +1)-1 •  exp{-Eg/2kBT} for Eg>1 eV @ 298K • exp{-(4eV)/2kBT}= exp{-100} @ 298K kBT =0.0257 eV at 298˚K

  9. Intrinsic Conductivity of Dielectric • Charge Carriers • Electrons • Holes • Ions, M+i, O-2 • = ne e e + nh e h • # electrons = # holes •   ne e (e+ h) • ne  C exp{-Eg/2kBT}

  10. Non-Stoichiometric Dielectrics • Metal Excess • M1+x O • Metal with Multiple valence • Metal Deficiency • M1-x O • Metal with Multiple valence • Reaction Equilibrium • Keq (PO2)±x/2 +3 +4 +2 +3

  11. Density Changes with Po2 SrTi1-xO3

  12. Non-Stoichiometric Dielectrics Excess M1+x O Deficient M1-x O

  13. Non-Stoichiometric Dielectrics Ki=[h+][e-] K”F=[O”i][V”O] Conductivity =f(Po2 ) Density =f(Po2 )

  14. Dielectric Conduction due to Non-stoichiometry • N-type P-type

  15. Dielectric Intrinsic Conduction due to Non-stoichiometry • N-type P-type + h + h Excess Zn1+xO Deficient Cu2-xO

  16. Extrinsic Conductivity • Donor Doping Acceptor Doping • n-type p-type Ed = -m*e e4/(8 (o)2 h2) Ef=Eg-Ed/2 Ef=Eg+Ea/2

  17. Extrinsic Conductivity of Non-stoichiometry oxides • Acceptor Doping • p-type p= 2(2 m*h kBT/h2)3/2 exp(-Ef/kBT) Law of Mass Action, Nipi=ndpd or =nndn @ 10 atom % Li in NiO conductivity increases by 8 orders of magnitude @ 10 atom % Cr in NiO no change in conductivity

  18. Capacitance C=oA/d =C/Co =1+e e = electric susceptibility

  19. Polarization P =  eE  e = atomic polarizability Induced polarization P=(N/V)q

  20. Polar regions align with E field P=(N/V)  Eloc i(Ni/V) i=3 o (-1)/(+2)

  21. Local E Field Local Electric Field Eloc=E’ + E E’ = due to surrounding dipoles Eloc=(1/3)(+2)E

  22. Ionic Polarization P=Pe+Pi Pe = electronic Pi= ionic Pi=(N/V)eA

  23. Thermal vibrations prevent alignment with E field

  24. Polar region follows E field  opt= (Vel/c)2 opt= n2 n=Refractive index

  25. Dielectric Constant

  26. Resonant Absorption/dipole relaxation Dielectric Constant imaginary number ’ real part dielectric storage ” imaginary part dielectric loss o natural frequency

  27. Resonant frequency,o Relaxation time,  Dipole Relaxation

  28. Relaxation Time, 

  29. Dielectric Constant vs. Frequency

  30. Avalanche Breakdown

  31. Avalanche Breakdown Like nuclear fission

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