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www.nanohub.org

NCN

Lecture12:EquilibriumConcentrations

MuhammadAshraful Alamalam@purdue.edu

Alam ECE606S09 1

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Outline

arr erconcen ra on

2) Temperaturedependenceofcarrierconcentration

3) Multipledoping,codoping,andheavydoping

4) Conclusion

Ref. ADFChapter4,pages118128

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CarrierdensitywithUniformDoping

+

Abulkmaterialmustbechargeneutraloverall

D A

Furtherifthedopingis spatiallyhomogenous

0D A p n N N + + + =

FDintegral

vs.

FD

function

?

( ) ( )1 2 1 22 2

01 2 1 4

+ = + +F FD AF F E EV V A C ( E )D

)

A

( E

N N F E E

NN F

e eE E

01 2 1 4

+ =

+ +V B C B

D B A

F F

F BF

( E ) / k T ( E ) / k T

V A ( E ) / k T ( E

E E

E E )

D

/ k T

A N e N ee e

N N(approx.)

Alam ECE606S09 3

Once you know EF, you can calculate n, p, ND+, NA

-.

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IntrinsicConcentration

+ =D A

01 2 1 4

+ =

+ +

F V B C F B

F D B A F B

( E E ) / k T ( E E ) / k T

( E E ) / k T ( E E )V CA

k T

D

/

N

e

NN eN

e

e

( ) ( )0

+ = =c F v F E E E VE

Cn p e eN N

1 = + VG

F i

E E E l

Nn

Alam ECE606S09 4

C

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Outline

1) Intrinsiccarrierconcentration

2) Temperaturedependenceofcarrierconcentration

3 Multi ledo in ,

co

do in ,

and

heav

do in

4) Conclusion

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CarrierDensitywithDonors

0D A p n N N + + + =

Inspatiallyhomogenousfieldfreeregion

ssumeN-type doping

01 2 1 4

+ =

+ +F V B C F B

F D B A F B

( E E ) / k T ( E E ) / k T A

( E E ) / k T ( E E ) / k T

DCV

NN

e ee e

NN

n(willplotinnextslide)

Alam ECE606S09 6

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TemperaturedependentConcentration

Freezeout

ExtrinsicIntrinsic

D

n

N

1

in

Temperature

D

Alam ECE606S09 7

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PhysicalInterpretation

Freezeout

ExtrinsicIntrinsic

D

n

N

1

in

Temperature

D

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ElectronConcentrationwithDonors

= =FC FC( E )E E

C

E

CNn e e eN

1 2

+

=

+ DFD E

D

( E )N

e

N

=

c D

D

( E E )

N

n1

+

DN

n

CN N

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ElectronconcentrationwithDonors

+ =Dp n

01 2

F V B C F B

F D B

( E E ) / k T ( E E ) / k T DV C ( E E ) / k T

N N e N e

e

+ =

+

2

0 + =i Dn

n

Nn

2 = i p n n

+ N

Alam ECE606S09 10

.

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HighDonordensity/FreezeoutT2

0 + =i Dn N

n

1

+N

Freeze IntrinsicD i

DND

n

N

1

out Extrinsic

1

+N

n

Tem erature

i

D

n

N

0 + =D N N N n n 1 24

1 1

= + D

Nn

N N

Alam ECE606S09 11

2 e

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Freezeout/ExtrinsicT

( )C D E E / kT CD

N N e N

1 2

4 = D

N N

2 N

n

N 1

Freezeout Extrinsic

Intrinsic

N

i

D

n

N

21 1

2

+

D

N

TemperatureD

Alam ECE606S09 12

hole concentration by nxp=ni2

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Extrinsic/IntrinsicT

2for

1

+

=