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MIT OpenCourseWarehttp://ocw.mit.edu
2.626 Fundamentals of Photovoltaics
Fall 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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ChargeSeparation:HowVoltageandCurrentAreFormed
Lecture6 2.626
Tonio Buonassisi
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ConceptQuizResults
Discussion
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GeneralAnnouncements
Books
PrintOuts
of
Lecture
Notes
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HomeworkAssignment
Read:MartinGreen,Chapter4
Read:PVCDROM:
Chapters
3and
4
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Books:Stickershock,anyone?
If
not,
well
call
in
the
order!
Images removed due to copyright restrictions. Please see the covers of:
Green, Martin A. Solar Cells: Operating Principles, Technology, and System
Applications. Englewood Cliffs, NJ: Prentice-Hall, 1982.
Green, Martin A. Silicon Solar Cells: Advanced Principles and Practice. Sydney,Australia: Centre for Photovoltaic Devices and Systems, 1995.
Wenham, Stuart A., et al.Applied Photovoltaics. Sterling, VA: Earthscan, 2007.
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Outline
Review:pn
junctions
Minoritycarriercurrent
Idealdiode
equation
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Review:
Diffusion
FromPVCDROM
Courtesy Christiana Honsberg and Stuart Bowden. Used with permission.
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Review:DriftCurrent
FromPVCDROMCourtesy Christiana Honsberg and Stuart Bowden. Used with permission.
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http://en.wikipedia.org/wiki/Pn_junction
Nicerfigureat
Wikipedia!
Image removed due to copyright restrictions. Please see
http://en.wikipedia.org/wiki/File:Pn-junction-equilibrium-graphs.png
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http://www.ecse.rpi.edu/~schubert/LightEmittingDiodesdot
org/chap04/chap04.htm
Pnjunctionunderbias
Image removed due to copyright restrictions. Please see
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpg.
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpghttp://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpghttp://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpg -
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BiasAcrossapnJunction
Builtin
pn
junction
potentialafunctionof
dopant concentrations.
Builtin
pn
junction
potentialafunctionof
dopant concentrations.
Image removed due to copyright restrictions. Please see
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpg.
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpghttp://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpghttp://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpg -
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BiasAcrossapnJunction
Builtin
pn
junction
potentialafunctionof
dopant concentrations.
Builtin
pn
junction
potentialafunctionof
dopant concentrations.
Image removed due to copyright restrictions. Please see
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpg.
i i
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpghttp://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpghttp://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap04/F04-01%20PN%20junction%20energies.jpg -
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The
potential
across
a
biased
pn
junction
device
is
BiasAcrossapnJunction
C i C i A J i
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CarrierConcentrationsAcrossapnJunction
Ln
(n),
Ln(p)
Distance,x
Transition
region
p=pp0 NA
n=np0 ni2/NA
n=nn0 ND
p=pn0 ni
2
/ND
Approximation1:Devicecanbesplitintotwotypesofregion:quasi
neutralregions(spacechargedensityisassumedzero)andthedepletion
region(where
carrier
concentrations
are
small,
and
ionized
dopants
contributetofixedcharge).
Width f h i
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Widthofspacechargeregion
Ln
(n),
Ln(p)
Distance,x
Transition
region
p=pp0 NA
n=np0 ni2/NA
n=nn0 ND
p=pn0 ni
2
/ND
Width f h i
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Ln
(n),
Ln(p)
Distance,x
Transition
region
p=pp0 NA
n=np0 ni2/NA
n=nn0 ND
p=pn0 ni2/NDWidthofthe
spacecharge
region
Widthofthe
spacecharge
region
NB:Actually
*o,
where
o,
thevacuumpermittivity,is
8.85x1012 F/mor
5.53x107 e/(V*m)
NB:Actually
*o,
where
o,
thevacuumpermittivity,is
8.85x1012 F/mor
5.53x107 e/(V*m)
Widthofspacechargeregion
Capacitance
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Ln
(n),
Ln(p)
Distance,x
Transition
region
p=pp0 NA
n=np0 ni2/NA
n=nn0 ND
p=pn0 ni2/ND
pnjunctionareapnjunctionareaDevice
capacitance
Device
capacitance
Capacitance
Capacitance
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Capacitance
Ln
(n),
Ln(p)
Distance,x
Transition
region
p=pp0 NA
n=np0 ni2/NA
n=nn0 ND
p=pn0 ni2/ND
Whenonesideof
thepnjunctionis
heavilydoped,
the
capacitancereduces
tothisexpression
Whenonesideof
thepnjunctionis
heavilydoped,
the
capacitancereduces
tothisexpression
Pn junction under zero bias
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Pnjunctionunderzero bias
Ln
(n),
Ln(p)
Distance,x
Transition
region
p=pp0 NA
n=np0 ni2/NA
n=nn0 ND
p=pn0 ni
2
/ND
Pn junction under forward bias
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Pnjunctionunderforward bias
Ln
(n),
Ln(p)
Distance,x
Transition
region
np0
pn0
p=pp0 NA
n=nn0 ND
npa
a b
pnb
Pn junction under forward bias
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Pnjunctionunderforward bias
Ln
(n),
Ln(
p)
Distance,x
Transition
region
np0
pn0
p=pp0 NA
n=nn0 ND
npa
pnb
Atzerobias:
a b
Current flow through the depletion region
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Ln
(n),
Ln(
p)
Distance,x
Transition
region
p=pp0 NA
np0
n=nn0 ND
pn0
npa
pnb
Forholes:
a
DriftcurrentDriftcurrent DiffusioncurrentDiffusioncurrentb
Currentflowthroughthedepletionregion
Current flow through the depletion region
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Currentflowthroughthedepletionregion
Ln
(n),
Ln(
p)
Distance,x
Transition
region
p=pp0 NA
np0
n=nn0 ND
pn0
npa
pnb
Forholes:
a
Approximation2:AssumeJhissmall!Approximation2:AssumeJhissmall!
b
Current flow through the depletion region
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Currentflowthroughthedepletionregion
Ln
(n),
Ln(
p)
Distance,x
Transition
region
np0
pn0
p=pp0 NA
n=nn0 ND
npa
a b
pnb
Integrating
Current flow through the depletion region
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Currentflowthroughthedepletionregion
Ln
(n),
Ln(
p)
Distance,x
Transition
region
np0
pn0
p=pp0 NA
n=nn0 ND
npa
pnb
Approximation3:
Only
caseswhereminority
carriershaveamuchlower
concentrationthanmajority
carrierswill
be
considered,
i.e.,ppa>>npa,nna>>pna
a b
Current densities
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Currentdensities
Je Jh
xba
x
J
Calculate(diffusive)currentsinquasineutralregion:
Current densities
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Currentdensities
Magnitudeofthechangeincurrentacrossthedepletionregion:
Keyassumption:WissmallcomparedtoLeandLh.Therefore,integralis
negligible.ItfollowsthatthecurrentJeandJhareessentiallyconstant
acrossthe
depletion
region,
as
shown
below.
Jtotal
Jh Je
Je Jh
xba
x
J
Ideal Diode Equation
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IdealDiodeEquation
Thisleadstotheidealdiodelaw:
Since
Jeand
Jhare
known
at
all
points
in
the
depletion
region,
wecancalculatethetotalcurrent:
NextClass
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Idealdiode
equation
discussion
Contacts
ReviewPart
1