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Lecture 6.0Lecture 6.0
Properties of Dielectrics
Dielectric use in Silicon ChipsDielectric use in Silicon Chips
Capacitors– On chip– On Circuit Board
Insulators– Transistor gate– Interconnects
Materials– Oxides
–SiO2
– Boro-Silicate Glass
– Nitrides–BN
– polymers
Importance of Dielectrics to Silicon ChipsImportance 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
Band theory of DielectricsBand theory of Dielectrics
Forbidden Zone–Energy Gap-LARGE
ValenceBand
ConductionBand
Difference between Difference between Semiconductors and Semiconductors and DielectricsDielectrics
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
kBT =0.0257 eV
at 298˚K
Fermi-Dirac Probability Fermi-Dirac Probability Distribution for electron energy, EDistribution for electron energy, E
Probability, F(E)=
(e{[E-Ef]/k
BT}+1)-1
–Ef is the
Fermi Energy
Number of Occupied StatesNumber of Occupied States
Fermi-Dirac
Density of States
T>1000K only
Probability of electrons in Probability of electrons in Conduction BandConduction Band
Lowest Energy in CBE-Ef Eg/2
Probability in CBF(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} @ 298KkBT =0.0257 eV
at 298˚K
Intrinsic Conductivity of DielectricIntrinsic 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}
Non-Stoichiometric DielectricsNon-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
)(2
122
)(2
2..'
222
gOVTiOTi
gOx
TiOTiO
OTiOTi
x
ONigOx
NiO
OZngOx
ZnO
x
x
12
12
)(2
)(2
+4
+2
+3
+3
Density Changes with PoDensity Changes with Po22
SrTi1-xO3
Non-Stoichiometric DielectricsNon-Stoichiometric Dielectrics
ExcessM1+x O
DeficientM1-x O
Non-Stoichiometric DielectricsNon-Stoichiometric Dielectrics
Ki=[h+][e-]
K”F=[O”i][V”O]
Conductivity=f(Po2 )
Density =f(Po2 )
Dielectric Conduction due to Non-stoichiometryDielectric Conduction due to Non-stoichiometryN-type P-type
Dielectric Intrinsic Conduction due to Non-stoichiometryDielectric Intrinsic Conduction due to Non-stoichiometryN-type P-type
ExcessZn1+xO
DeficientCu2-xO
+ h
+ h
Extrinsic ConductivityExtrinsic Conductivity
Donor Doping Acceptor Dopingn-type p-type
Ed = -m*e e4/(8 (o)2 h2)Ef=Eg-Ed/2 Ef=Eg+Ea/2
Extrinsic Conductivity of Non-stoichiometry oxidesExtrinsic Conductivity of Non-stoichiometry oxidesAcceptor Dopingp-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
ONiNiLiOx
NiOxOLix
xxx )(4
)1(2
322122
CapacitanceCapacitance
C=oA/d
=C/Co
=1+e
e =electric susceptibility
PolarizationPolarization
P = e E
e = atomic polarizability
Induced polarizationP=(N/V)q
Polar regions align with E fieldPolar regions align with E field
P=(N/V) Eloc
i(Ni/V) i=3 o (-1)/(+2)
Local E FieldLocal E Field
Local Electric Field
Eloc=E’ + E
E’ = due to surrounding dipoles
Eloc=(1/3)(+2)E
Ionic PolarizationIonic Polarization
P=Pe+Pi
Pe = electronic
Pi= ionic
Pi=(N/V)eA
Thermal vibrations prevent Thermal vibrations prevent alignment with E fieldalignment with E field
Polar region follows E fieldPolar region follows E field
opt= (Vel/c)2
opt= n2
n=Refractive index
Dielectric ConstantDielectric Constant
Material (=0) opt=n2
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
Resonant Absorption/dipole relaxationResonant Absorption/dipole relaxation
Dielectric Constantimaginary number
’ real part dielectric storage
” imaginary partdielectric loss
o natural frequency
Dipole RelaxationDipole Relaxation
Resonant frequency,o Relaxation time,
22"
22'
1
)(
1
opts
optsopt
22222
222"
22222
222'
)(
)(
o
o
io
opto
o
io
m
e
V
N
m
e
V
N
tiem
ex
dt
dx
dt
xd 202
2
Relaxation Time, Relaxation Time,
Dielectric Constant vs. Dielectric Constant vs. FrequencyFrequency
Avalanche BreakdownAvalanche Breakdown
Avalanche BreakdownAvalanche Breakdown
Like nuclear fission