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 Valence Band Conduction Band

Silicon Band Structure - [Ne]3s 2 3p 2

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>0

Difference between Semiconductors and Insulators MaterialE g (eV) InSb0.18 InAs0.36 Ge0.67 Si1.12 GaAs1.43 SiC2.3 ZnS3.6 NiO4.2 Al 2 O 3 8 k B T = eV at 298˚K

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 k B T = eV at 298˚K

Variation of Conductivity with T  =d  /dT

Intrinsic Conductivity of Semiconductor Charge Carriers –Electrons –Holes  = n e e  e + n h e  h # electrons = # holes –   n e e (  e +  h ) –n e  C exp{-E g /2k B T} n e =2(2  m* e k B T/h 2 ) 3/2 exp(-E g /(2k B T)) E f =E g /2+3/4k B T ln(m* h /m* e )

Mobilities

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

Light Emitting Diode

Photodiode Laser Color depends on band gap, E g =hc/E g Pb IR detectors E g >3.0 transparent

Diode Laser

Extrinsic Conductivity of Semiconductor Donor Doping Acceptor Doping n-type 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 n N=n d +n i

Extrinsic Conductivity of Semiconductor Donor Doping Acceptor Doping

Electron Density Dopant Concentration effects Electron Density Electrical Conductivity

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

Majority/minority Carriers Conductivity  = n e e  e + n h e  h n-typen e >>n h Low number of holes due to recombination. Law of Mass Action –N i p i =n d p d –(For p-type N i p i =n n d n )

Extrinsic Conductivity of Semiconductor 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

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 ohm-cm –4" N ohm-cm –4" P ohm-cm –4" P ohm-cm –4" P ohm-cm

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

C&ENews 1/6/03