Lecture 6.0 Properties of Dielectrics

Dielectric use in Silicon Chips Capacitors –On chip –On Circuit Board Insulators –Transistor gate –Interconnects Materials –Oxides –SiO 2 –Boro-Silicate Glass –Nitrides –BN –polymers

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

Band theory of Dielectrics Forbidden Zone–Energy Gap-LARGE Valence Band Conduction Band

Difference between Semiconductors and Dielectrics MaterialE g (eV) Ge0.67 Si1.12 GaAs1.43 SiO 2 8 UO Ga 2 O Fe 2 O ZnO3.2 NiO4.2 Al 2 O 3 8 k B T = eV at 298˚K

Fermi-Dirac Probability Distribution for electron energy, E Probability, F(E)= (e {[E-E f ]/k B T} +1) -1 –E f is the Fermi Energy

Number of Occupied States Fermi-Dirac Density of States T>1000K only

Probability of electrons in Conduction Band Lowest Energy in CB E-E f  E g /2 Probability in CB F(E)= (exp{[E-E f ]/k B T} +1) -1 ) = (exp{E g /2k B T} +1) -1  exp{-E g /2k B T} for E g >1 298K exp{-(4eV)/2k B T}= 298K k B T = eV at 298˚K

Intrinsic Conductivity of Dielectric Charge Carriers –Electrons –Holes –Ions, M +i, O -2  = n e e  e + n h e  h # electrons = # holes –   n e e (  e +  h ) –n e  C exp{-E g /2k B T}

Non-Stoichiometric Dielectrics Metal Excess M 1+x O Metal with Multiple valence Metal Deficiency M 1-x O Metal with Multiple valence Reaction Equilibrium K eq  (P O2 ) ±x/

Density Changes with Po 2 SrTi 1-x O 3

Non-Stoichiometric Dielectrics Excess M 1+x O Deficient M 1-x O

Non-Stoichiometric Dielectrics K i =[h+][e-] K” F =[O” i ][V” O ] Conductivity  =f(Po 2 ) Density =f(Po 2 )

Dielectric Conduction due to Non-stoichiometry N-type P-type

Dielectric Intrinsic Conduction due to Non-stoichiometry N-type P-type Excess Zn 1+x O Deficient Cu 2-x O + h

Extrinsic Conductivity Donor Doping Acceptor Doping n-type p-type E d = -m* e e 4 /(8 (  o ) 2 h 2 ) E f =E g -E d /2 E f =E g +E a /2

Extrinsic Conductivity of Non-stoichiometry oxides Acceptor Doping p-type p= 2(2  m* h k B T/h 2 ) 3/2 exp(-E f /k B T) Law of Mass Action, N i p i =n d p d or =n n d 10 atom % Li in NiO conductivity increases by 8 orders of 10 atom % Cr in NiO no change in conductivity

Capacitance C=  o A/d  =C/C o  =1+  e  e = electric susceptibility

Polarization P =   e E   e = atomic polarizability Induced polarization P=(N/V)q 

Polar regions align with E field P=(N/V)  E loc  i (N i /V)  i =3  o (  -1)/(  +2)

Local E Field Local Electric Field E loc =E’ + E E’ = due to surrounding dipoles E loc =(1/3)(  +2)E

Ionic Polarization P=P e +P i P e = electronic P i = ionic P i =(N/V)eA

Thermal vibrations prevent alignment with E field

Polar region follows E field   opt = (Vel/c) 2  opt = n 2 n=Refractive index

Dielectric Constant Material  (  = 0)  opt =n 2 Diamond NaCl LiCl TiO Quartz(SiO 2 )

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

Dipole Relaxation Resonant frequency,  o Relaxation time, 

Relaxation Time, 

Dielectric Constant vs. Frequency

Avalanche Breakdown

Like nuclear fission