Charge Separation

8/14/2019 Charge Separation

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2.626 Fundamentals of Photovoltaics

Fall 2008

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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


8/31

Review:

Diffusion

FromPVCDROM

Courtesy Christiana Honsberg and Stuart Bowden. Used with permission.


9/31

Review:DriftCurrent

FromPVCDROMCourtesy Christiana Honsberg and Stuart Bowden. Used with permission.


10/31


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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


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






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Builtin

pn

junction



Builtin

pn

junction





i i


15/31

The

potential

across

a

biased

pn

junction

device

is


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


22/31

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



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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



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Ln

(n),

Ln(

p)

Distance,x

Transition

region

np0

pn0

p=pp0 NA

n=nn0 ND

npa

a b

pnb

Integrating



27/31


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

Documents

Charge Separation