Properties of Dielectrics

1
Lecture 6.0

• Properties of Dielectrics

2
Dielectric use in Silicon Chips

• Capacitors
• On chip
• On Circuit Board
• Insulators
• Transistor gate
• Interconnects

• Materials
• Oxides
• SiO2
• Boro-Silicate Glass
• Nitrides
• BN
• polymers

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 ZoneEnergy Gap-LARGE

Conduction Band
Valence Band
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Difference between Semiconductors and Dielectrics
kBT 0.0257 eV at 298K
Material Eg(eV)
Ge 0.67
Si 1.12
GaAs 1.43
SiO2 8
UO2 5.2
Ga2O3 4.6
Fe2O3 3.1
ZnO 3.2
NiO 4.2
Al2O3 8
6
Fermi-Dirac Probability Distribution for electron
energy, E

• Probability, F(E)
• (eE-Ef/kBT1)-1
• Ef is the
• Fermi Energy

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Number of Occupied States
Density of States
Fermi-Dirac
Tgt1000K only
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Probability of electrons in Conduction Band

• Lowest Energy in CB
• E-Ef ? Eg/2
• Probability in CB
• F(E) (expE-Ef/kBT 1)-1 )
• (expEg/2kBT 1)-1
• ? exp-Eg/2kBT for Eggt1 eV _at_ 298K
• exp-(4eV)/2kBT exp-100 _at_ 298K

kBT 0.0257 eV at 298K
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Intrinsic Conductivity of Dielectric

• Charge Carriers
• Electrons
• Holes
• Ions, Mi, O-2
• ? ne e ?e nh e ?h
• electrons holes
• ? ? ne e (?e ?h)
• ne ? C exp-Eg/2kBT

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Non-Stoichiometric Dielectrics

• Metal Excess
• M1x O
• Metal with Multiple valence
• Metal Deficiency
• M1-x O
• Metal with Multiple valence
• Reaction Equilibrium
• Keq? (PO2)x/2

3
4
2
3
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Density Changes with Po2
SrTi1-xO3
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Non-Stoichiometric Dielectrics
Excess M1x O
Deficient M1-x O
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Non-Stoichiometric Dielectrics
Kihe- KFOiVO
Conductivity ?f(Po2 ) Density f(Po2 )
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Dielectric Conduction due to Non-stoichiometry

• N-type P-type

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Dielectric Intrinsic Conduction due to
Non-stoichiometry

• N-type P-type

h
h
Excess Zn1xO
Deficient Cu2-xO
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Extrinsic Conductivity

• Donor Doping Acceptor Doping
• n-type p-type

Ed -me e4/(8 (??o)2 h2) EfEg-Ed/2
EfEgEa/2
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Extrinsic Conductivity of Non-stoichiometry oxides

• Acceptor Doping
• p-type

p 2(2? mh kBT/h2)3/2 exp(-Ef/kBT)
Law of Mass Action, Nipindpd or nndn _at_ 10 atom
Li in NiO conductivity increases by 8 orders
of magnitude _at_ 10 atom Cr in NiO no change in
conductivity
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Capacitance
C??oA/d ?C/Co ?1?e ?e electric
susceptibility
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Polarization
P ? ?e E ??? ?e atomic
polarizability Induced polarization P(N/V)q?
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Polar regions align with E field
P(N/V) ? Eloc ?i(Ni/V) ?i3 ?o (?-1)/(?2)
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Local E Field
Local Electric Field ElocE E E due to
surrounding dipoles Eloc(1/3)(?2)E
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Ionic Polarization
PPePi Pe electronic Pi ionic Pi(N/V)eA
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Thermal vibrations prevent alignment with E field
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Polar region follows E field
???? ?opt (Vel/c)2 ?opt n2 nRefractive index
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Dielectric Constant
Material ?(?0) ?optn2
Diamond 5.68 5.66
NaCl 5.90 2.34
LiCl 11.95 2.78
TiO2 94 6.8
Quartz(SiO2) 3.85 2.13
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Resonant Absorption/dipole relaxation
Dielectric Constant imaginary number ? real
part dielectric storage ? imaginary
part dielectric loss ?o natural frequency
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Dipole Relaxation

• Resonant frequency,?o

• Relaxation time, ?

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Relaxation Time, ?
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Dielectric Constant vs. Frequency
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Avalanche Breakdown
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Avalanche Breakdown
Like nuclear fission