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Understanding Dielectrics: Properties, Applications, and Importance in Silicon Chips

This lecture covers the essential properties of dielectrics and their pivotal role in semiconductor technology. Key topics include various dielectric materials such as oxides, nitride, and polymers, their use in capacitors and transistors, and the implications of dielectric behavior on silicon chip performance. We delve into electron tunneling, heat capacity, TC, and speed, exploring the impact of dielectrics on device density and functionalities. The lecture also covers the principles of band theory, Fermi-Dirac statistics, and conductivity variations in non-stoichiometric dielectrics, aiding the understanding of advanced electronic materials.

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Understanding Dielectrics: Properties, Applications, and Importance in Silicon Chips

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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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