Lecture 5.0 Properties of Semiconductors. Importance to Silicon Chips Size of devices –Doping thickness/size –Depletion Zone Size –Electron Tunneling.

Lecture 5.0Lecture 5.0

Properties of Semiconductors

Importance to Silicon ChipsImportance 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 SemiconductorsBand theory of Semiconductors

Forbidden Zone – ENERGY GAP

ValenceBand

ConductionBand

Silicon Band Structure - [Ne]3sSilicon Band Structure - [Ne]3s223p3p22

Fermi-Dirac Probability Fermi-Dirac Probability Distribution for electron energy, EDistribution for electron energy, E

Probability, F(E)=

(e{[E-Ef]/k

BT}+1)-1

–Ef is the

Fermi Energy

Number of Occupied StatesNumber of Occupied States

Fermi-Dirac

Density of States

T>0

Difference between Difference between Semiconductors and InsulatorsSemiconductors and Insulators

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

kBT =0.0257 eV

at 298˚K

Probability of electrons in Probability of electrons in Conduction BandConduction Band

Lowest Energy in CBE-Ef Eg/2

Probability in CBF(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 TVariation of Conductivity with T=d/dT

Intrinsic Conductivity of Intrinsic Conductivity of SemiconductorSemiconductorCharge 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)

MobilitiesMobilities

Semiconductor Photoelectric EffectSemiconductor Photoelectric EffectLight Absorption/Light Emission

(photodetector)/(photo diode laser)

Absorption max =hc/Eg

Light Emitting DiodeLight Emitting Diode

Photodiode LaserPhotodiode Laser

Color depends on band gap, Eg

=hc/Eg

Pb 0.37 0.27 0.33 IR detectors

Eg>3.0 transparent

Diode LaserDiode Laser

Extrinsic Conductivity of SemiconductorExtrinsic Conductivity of Semiconductor

Donor Doping Acceptor Dopingn-type p-type

p= 2(2 m*h kBT/h2)3/2 exp(-Ef/kBT)

Law of Mass Action, Nipi=ndpd or =nndn

N=nd+ni

Extrinsic Conductivity of SemiconductorExtrinsic Conductivity of Semiconductor

Donor Doping Acceptor Doping

Electron DensityElectron Density

Dopant Concentration effects Electron

DensityElectrical

Conductivity

ConductivityConductivity

Intrinsic Range– Exponential with T

Extrinsic Range– Promoted to CB

– Decreasing , – Joins Intrinsic

Majority/minority Carriers

= ne e e + nh e h

Majority/minority CarriersMajority/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 SemiconductorExtrinsic Conductivity of Semiconductor

Donor Doping Acceptor Dopingn-type p-type

Ed = -m*e e4/(8 (o)2 h2)Ef=Eg-Ed/2 Ef=Eg+Ea/2

Effective MassEffective Mass

HolesElectrons

Wafer SalesWafer Sales

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C&ENews1/6/03