1. Properties of Dielectrics
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 Zone–Energy Gap-LARGE
Conduction
Band
Valence
Band

5. Difference between Semiconductors and Dielectrics
kBT = eV
at 298˚K
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

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 298K
exp{-(4eV)/2kBT}= 298K
kBT = 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
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 =  e E  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 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

26. Resonant Absorption/dipole relaxation
Dielectric Constant
imaginary number
’ real part
dielectric storage
” imaginary part
dielectric loss
o natural frequency

27. Dipole Relaxation
Resonant frequency,o
Relaxation time, 

28. Relaxation Time, 

29. Dielectric Constant vs. Frequency

30. Avalanche Breakdown

31. Avalanche Breakdown
Like nuclear fission