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www.nanohub.org
NCN
Lecture13:RecombinationGeneration
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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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