Properties of Semiconductors Lecture 5.0 Properties of Semiconductors

Importance to Silicon Chips Size of devices Doping thickness/size Depletion Zone Size Electron Tunneling dimension Chip Cooling- Device Density Heat Capacity Thermal Conductivity

Band theory of Semiconductors Forbidden Zone – ENERGY GAP Conduction Band Valence Band

Silicon Band Structure - [Ne]3s23p2

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>0

Difference between Semiconductors and Insulators kBT =0.0257 eV at 298˚K Material Eg(eV) InSb 0.18 InAs 0.36 Ge 0.67 Si 1.12 GaAs 1.43 SiC 2.3 ZnS 3.6 NiO 4.2 Al2O3 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 eV @ 298K kBT =0.0257 eV at 298˚K

Variation of Conductivity with T =d/dT

Intrinsic Conductivity of Semiconductor Charge Carriers Electrons Holes = ne e e + nh e h # electrons = # holes   ne e (e+ h) ne  C exp{-Eg/2kBT} ne=2(2 m*e kBT/h2)3/2 exp(-Eg /(2kBT)) Ef=Eg/2+3/4kBT ln(m*h/m*e)

Mobilities

Semiconductor Photoelectric Effect Light Absorption/Light Emission (photodetector)/(photo diode laser) Absorption max =hc/Eg

Light Emitting Diode

Photodiode Laser Color depends on band gap, Eg  =hc/Eg Eg>3.0 transparent Pb 0.37 0.27 0.33 IR detectors

Diode Laser

Extrinsic Conductivity of Semiconductor Donor Doping Acceptor Doping n-type p-type N=nd+ni p= 2(2 m*h kBT/h2)3/2 exp(-Ef/kBT) Law of Mass Action, Nipi=ndpd or =nndn

Extrinsic Conductivity of Semiconductor Donor Doping Acceptor Doping

Electron Density Dopant Concentration effects Electron Density Electrical Conductivity

Conductivity Intrinsic Range Extrinsic Range = ne e e + nh e h Exponential with T Extrinsic Range Promoted to CB   Decreasing ,  Joins Intrinsic   Majority/minority Carriers = ne e e + nh e h

Majority/minority Carriers Conductivity = ne e e + nh e h n-type ne>>nh Low number of holes due to recombination. Law of Mass Action Nipi=ndpd (For p-type Nipi =nndn )

Extrinsic Conductivity of Semiconductor Donor Doping Acceptor Doping n-type p-type Ed = -m*e e4/(8 (o)2 h2) Ef=Eg-Ed/2 Ef=Eg+Ea/2

Effective Mass Holes Electrons

Wafer Sales Following PRIME GRADE Si wafers are all single-side polish $14.50 each for 25 wafers each $11.00 for 50 or more (we can double side polish) 4" P<111> 3.0-6.6 ohm-cm 4" N<100> 4.0-6.0 ohm-cm 4" P<111> 7.0-21.6 ohm-cm 4" P<100> 12.0-16.0 ohm-cm 4" P<111> 3.0-5.0 ohm-cm http://www.collegewafer.com/

GaP Wafer 2" Undoped (100) $180.00 each 2" S doped (111) $180.00 each

C&ENews 1/6/03