Lecture 6.0
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Lecture 6.0 Lecture 6.0 Properties of Dielectrics
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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 - PowerPoint PPT Presentation
Transcript of Lecture 6.0
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
