lecture 6.0 properties of dielectrics. dielectric use in silicon chips capacitors –on chip –on...

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