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www.nanohub.org

NCN

Lecture13:RecombinationGeneration

MuhammadAshrafulAlamalam@purdue.edu

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Outline

onequ r umsys ems

2) Recombinationgenerationevents

3) Steadystateandtransientresponse

4) Derivationof

R

G

formula

5) Conclusion

Ref.Chapter5,pp.134146

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CurrentFlowThroughSemiconductors

II G V=

V q n Av=

Depends

on

chemical

composition,

cr stalstructure tem erature do in etc.

arr er

Densityvelocity

QuantumMechanics+EquilibriumStatisticalMechanics Encapsulatedintoconceptsofeffectivemasses

Transportwithscattering,nonequilibriumStatisticalMechanics

andoccupation

factors

(Ch.

14)

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Encapsulatedintodriftdiffusionequationwith

recombinationgeneration(Ch.5&6)

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NonequilibriumSystems

ap er

vs.

I

V

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DirectBandtobandRecombination

Inrealspace Inenergyspace

Photon

Photon

GaAs,InP,

InSb

(3D)

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, , .

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DirectExcitonicRecombination

Inenergyspace

Photon(wavelength?)

CNT,InP,IDsystems

Inrealspace

Transistors,Lasers,Solarcells,etc.

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IndirectRecombination(Trapassisted)

Phonon

Ge,Si,.

Transistors,Solarcells,etc.

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AugerRecombination

Phonon(heat)

3

12

4

InP,GaAs,3

Lasers,etc.

1 2

4

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ImpactIonization AGenerationMechanism

1

4

3

2

Si,Ge,

InP

Lasers,Transistors,etc.

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Indirectvs.DirectBandgap

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same wavevector k for indirect bandgap material

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PhotonEnergyandWavevector

photonE

=

=

+

+ VV phot

hoton

n C

C

o

k k k

2a

photonk

2

1 21 in eV

=

photonE. /4

2 2

5 10 m

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Phonon EnergyandWavevector

=+E EE

=+ V phonon C k k k

2 2

phononk = =

4

2 2

=phonsound on

Phonon has large wavevector comparable to BZ,

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but negligible energy compared to bandgap

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LocalizedTrapsandWavevector

a

4

2 2

trap~k

Trap provides the wavevector

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Outline

onequ r umsystems

2) Recombinationgenerationevents

3) Steadystateandtransientresponse

4) Derivationof

R

G

formula

5) Conclusion

Ref.Chapter5,pp.134146

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Equilibrium,Steadystate,Transient

Equilibrium,

p)

Device time(

Transient

time(n,p

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DetailedBalance:SimpleExplanation

Theratesofexchangeofpeople(particles) between

everypairofcountries(energy levels)isbalanced.

Mexico USA2

.

Detailedbalanceisthepropertyofequilibrium

China

3 3

4

4

Thepopulationofeachofthecountries(energylevels)

remainsconstantunderdetailedbalance.

India

,

canbeusedformanythings(e.g.reducethenumber

ofunknownrateconstantsbyhalf,andderiveparticle

distributionslikeFermiDirac,BoseEinstein

istri utions,

etc.

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Allnumbersarepeople/unittime.

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SteadystateResponse

nonequilibriumconditions(needsenergy).

Unidirectionalforces(redlines)cancreatesuch

Nonequilibriumconditions.

Mexico USA32The

rates

of

exchange

of

people

(particles)

betweeneverypairofcountries(energy

4 6

5

,

anddeparturestoallcountriesiszero.

Theflux

at

steady

state

is

balanced

overall,

but

1

India

thefluxisNOTthesameasindetailedbalance

(e.g.12inand12outinSSvs.9inand9outfor

DetailedBalance,forexample).

Thepopulation

of

acountry

(energy

level)

remains

constantwithtimeaftersteadystateisreached.

17

necanuset erequ rementt atnet uxat

steadystatebezero tocalculatesteadystate

populationof

acountry

(Eq.

5.21)

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DetailedBalance,Transient,Steadystate

Mexico2

Mexico2 Mexico

USA

3

2

3 3 3 514 6

5

1

China 4 China 4China 4

India India1

In a1

9in9out

Populationconserved

(redlines)

disturbs

equilibrium

(e.g.9in/12outattimet1

localpopulationsnotconserved,

12in12out

Populationstabilized

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.

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Outline

onequ r umsystems

2) Recombinationgenerationevents

3) Steadystateandtransientresponse

4) Derivationof

R

G

formula

5) Conclusion

Ref.Chapter5,pp.134146

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IndirectRecombination(Trapassisted)

Phonon

Ge,Si,.

Transistors,Solarcells,etc.

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PhysicalviewofCarrierCapture/Recombination

(1)Beforeacapture

TT TN pn= +

(2)Afterelectroncapture(3)Afterholecapture

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CarrierCaptureCoefficients

th

=

T nthAdn nt p

21 32 2

*

thm kT = n tT n hnc cnp

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CaptureCrosssection

2

0nr = Zncapturemodel

e116 -2

2 10 cm

e2 h1

156 10

185 10

e3 147 10

h1

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Cascademodelforcapture

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Conclusions

1) Therearewidevarietyofgenerationrecombinationevents

that

allow

restoration

of

equilibrium

once

the

stimulus

is

removed.

2) Directrecombinationisphotonassisted,indirect

.

3) Conceptsofequilibrium,steadystate,andtransient

ynam css ou

ec ear y

un erstoo .

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