Properties of Dielectrics Lecture 6.0 Properties of Dielectrics

Dielectric 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 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 Conduction Band Valence Band

Difference between Semiconductors and Dielectrics kBT =0.0257 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

Fermi-Dirac Probability Distribution for electron energy, E Probability, F(E)= (e{[E-Ef]/kBT}+1)-1 Ef is the Fermi Energy

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

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 eV @ 298K exp{-(4eV)/2kBT}= exp{-100} @ 298K kBT =0.0257 eV at 298˚K

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}

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

Density Changes with Po2 SrTi1-xO3

Non-Stoichiometric Dielectrics Excess M1+x O Deficient M1-x O

Non-Stoichiometric Dielectrics Ki=[h+][e-] K”F=[O”i][V”O] Conductivity =f(Po2 ) Density =f(Po2 )

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

Dielectric Intrinsic Conduction due to Non-stoichiometry N-type P-type + h + h Excess Zn1+xO Deficient Cu2-xO

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

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

Capacitance C=oA/d =C/Co =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)  Eloc i(Ni/V) i=3 o (-1)/(+2)

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

Ionic Polarization P=Pe+Pi Pe = electronic Pi= ionic Pi=(N/V)eA

Thermal vibrations prevent alignment with E field

Polar region follows E field  opt= (Vel/c)2 opt= n2 n=Refractive index

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

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

Avalanche Breakdown Like nuclear fission