8/8/2019 Principles of Semiconductor Devices-L14

1/22

www.nanohub.org

NCN

Lecture14:BulkRecombinationMuhammadAshrafulAlamalam@purdue.edu

Alam ECE606S09 1

8/8/2019 Principles of Semiconductor Devices-L14

2/22

Outline

1) Derivationof

SRH

formula

2) ApplicationofSRHformulaforspecialcases

3) DirectandAugerrecombination

4 Conclusion

.

,

,

.

Alam ECE606S09 2

8/8/2019 Principles of Semiconductor Devices-L14

3/22

SubprocessesofSRHRecombination

(1) (2)

(3) (4)

(1)+(3): oneelectronreducedfromConductionband&

(2)+(4): oneholecreatedinvalencebandand

Alam ECE606S09 3

onee ec roncrea e ncon uc on an

8/8/2019 Principles of Semiconductor Devices-L14

4/22

SRHRecombination

Physicalpicture Equivalentpicture

(1) (2) (1) (2)

(3) (4) (3) (4)

oneholereducedfromvalenceband

Alam ECE606S09 4

oneelectroncreatedinconductionband

8/8/2019 Principles of Semiconductor Devices-L14

5/22

ChangesinelectronandholeDensities

(1) (2)

1 2,

n

t

=

n Tc n p ( )1n T ce n f+

p Tc p n

+ p Te p f3 4,

p

t

=

Alam ECE606S09 5

8/8/2019 Principles of Semiconductor Devices-L14

6/22

DetailedBalanceinEquilibrium

(3) (4)

1 2,

n

t

=

0 0

n Tc n p

0+

Tne n

p Tc p n

p Te p+3 4,

p

t=

= 0 0 0T n Tn

0 0

1= Tn nn

n pnce c

0 0 0 p T T p

0 0

1

0

p T

p p

T

c p ne c p

p =

Alam ECE606S09 6

0T

( )0 0 0 10

= T Tn n p n nc

( )0 0 0 10 = T Tp p n p pc

8/8/2019 Principles of Semiconductor Devices-L14

7/22

Expressionsfor(n1)and(p1)

(1) (2)

0

1

0 0= T

T

n p

nn

0

1

0 0= T

T

p n

pp

0 0 0 0

1 1= T T

n p nn

pp

2

0 0= =

in p n

Alam ECE606S09 7

0 0T T

8/8/2019 Principles of Semiconductor Devices-L14

8/22

8/8/2019 Principles of Semiconductor Devices-L14

9/22

Dynamics ofTrapPopulation

1

(3)

(2)

(4)

Tn

t=

3 4,

p

t

+

1 2,

n

t

n Tc n p= n Te n p Tc p n p Te p+

Alam ECE606S09 9

1n T Tc np n n=

1 p T T c p n p p

8/8/2019 Principles of Semiconductor Devices-L14

10/22

Steadystate TrapPopulation

1

(3)

(2)

(4)

0T

t=

1n T Tc np n n= 1 p T T c p n p p

( ) ( ) ( )1

1

1 1

n T p T T n T T

n p

n c np n nc n n c p p

= = + + +

Alam ECE606S09 10

8/8/2019 Principles of Semiconductor Devices-L14

11/22

NetRateofRecombinationGeneration

(3) (4)

2 inp n

1= = p T T R c p n p p

dt

( ) ( )1 11 1 + + +

p T n T n n p p

c N c N

Alam ECE606S09 11

n

p

8/8/2019 Principles of Semiconductor Devices-L14

12/22

Outline

1) DerivationofSRHformula

2) ApplicationofSRHformulaforspecialcases3) Direct

and

Auger

recombination

4) Conclusion

Alam ECE606S09 12

8/8/2019 Principles of Semiconductor Devices-L14

13/22

Case1:LowlevelInjectioninptype

2

inp n

R

=

2 + + n nnn

1 1p n

( ) ( )0 1 0 1 =

+ + + + +p nn n pn p p

2

0

( ) ( )0 0

0 1 0 1

=+ + + + +

p nn n pn p p

0+p n

20n ( )

( )0

0

=

=

n n

p

p

n n

Alam ECE606S09 13

0 0

8/8/2019 Principles of Semiconductor Devices-L14

14/22

Case2:HighlevelInjection

2

inp n

R

= e.g. organic solar cells

( ) ( ) 20 0 + + in p npn

p n

0+n n

( ) ( )0 1 0 1 + + + + +p nn n pn p p

2

( ) ( )0 0

0 1 10

=+ + + + +

p n

nn n

n

p

n nn p p

0 0n p n

2

= =

+ +n n

n n

n

0p n

Alam ECE606S09 14

8/8/2019 Principles of Semiconductor Devices-L14

15/22

High/LowLevelInjection

0 0n p n high

nR

=+

n p

nlow

p= 0 0

whichoneislargerandwhy?

Alam ECE606S09 15

8/8/2019 Principles of Semiconductor Devices-L14

16/22

Case3:GenerationinDepletionRegion

2

inp nR

=

1 1p nn n p p + + +

2

in

= 1 1p n

1 1n n p p

Alam ECE606S09 16

8/8/2019 Principles of Semiconductor Devices-L14

17/22

Outline

1) DerivationofSRHformula

2) ApplicationofSRHformulaforspecialcases

3) DirectandAugerrecombination4) Conclusion

Alam ECE606S09 17

8/8/2019 Principles of Semiconductor Devices-L14

18/22

BandtobandRecombination

( )2i R B np n=

=Direct

recombination

at

low

level

injection

( )( )2

0 0 0

= + + i R B n p n Bppn n

0 0

Directgenerationindepletionregion

2 2

i i R B np n Bn= ,

Alam ECE606S09 18

8/8/2019 Principles of Semiconductor Devices-L14

19/22

AugerRecombination

2 22 2=

2 electron & 1 hole

29 610 cm /sec

n p i

n

i

pc ,c ~

Augerrecombination

at

low

level

injection

( ) ( )0 0 An n p p N = =

2

2

1

= =

p A auger R c N

c N

nn

Alam ECE606S09 19

8/8/2019 Principles of Semiconductor Devices-L14

20/22

EffectiveCarrierLifetime

Light

SRH direct Auger R R R R= + +

eff

tn 1 1 1n

= + +

SRH direct Auger

( )2n T D n ,auger Dn c N BN c N = + +

Alam ECE606S09 20

( )2

= + +eff n T D n ,auger Dc N BN c N

8/8/2019 Principles of Semiconductor Devices-L14

21/22

EffectiveCarrierLifetimewithallProcesses

ND2 eff n ,auger Dc N

21( )

12

= + +

eff n T D n ,auger Dc N BN c N Elec.Dev.

Lett.,

12(8),

1991.

8/8/2019 Principles of Semiconductor Devices-L14

22/22

Conclusion

SRHisanimportantrecombinationmechanismin

importantsemiconductorslikeSiandGe.

SRHformulaiscom licated,thereforesim lificationfor

specialcasesareoftendesired.

bedescribedwithsimplephenomenologicalformula.

T eseexpressions

or

recom ination

events

ave

een

widelyvalidatedbymeasurements.

Alam ECE606S09 22