Maura Pomoni, Athina Giannopoulou and Panagiotis Kounavis

Modulated photocurrent as a powerful method to Modulated photocurrent as a powerful method to reveal transport by the majority carriers of reveal transport by the majority carriers of disordered semiconductors and to resolve disordered semiconductors and to resolve

all the kinds of probed statesall the kinds of probed states

MauraMaura Pomoni, Pomoni, AthinaAthina Giannopoulou Giannopoulou

and and PanagiotisPanagiotis Kounavis Kounavis

Department of Engineering Sciences, University of Department of Engineering Sciences, University of Patras, Patras,

26504 Patra, Greece26504 Patra, Greece

Semic-LabSemiconductors Lab

Dep. of Eng. SciencesUniv. of Patras

Univ. of Patras

Possible contribution from both carriers complicates interpretation of photoconductivity measurements

This limitation is overcome in the modulated photocurrent (MPC)

Specific features in the MPC spectra can be used to reveal whether the transport of the majority carriers dominates

In this case, a DOS spectroscopy based on a general formula can be used to evaluate the DOS parameters of the various species of states with which the majority carriers interact



Univ. of Patras

)(sin

ENeGYac

ac

The essential parameter of the MPC is the

out of phase Y signal

Phase shift

Modulated

photoconductivity

Modulated light Generation rate

Mobility of the majority carriers

Out of phase MPC Y signal

Experimental setup



LEDModulated+ bias light

Lock-In

Osciloscope

Amplifier

Vdc

a-Si:Helectrodes

Phase shift

Φ amplitude ofMPC

Φ iac

iacreference

signalMeasured

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DOS

nn

acoutinac jYX

Gjnnn

pp

acoutinac jYX

Gjppp

2/122 )()( inpinnoutpoutnac pnpnAi

inpinn

outpoutn

pn

pn

tan

nYY

The analysis have shown that

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acaceGY

sin

pYY or

Y signal is related to the gap states with which the electrons and holes interact and contribute to Yn , Yp

nnnn YYYY 321

0.0 0.5 1.0 1.51011

1014

1017

1020

Etp

Etn E

ωn

EF

DO

S (e

V-1cm

-3)

Energy (eV)

ip

in

it pcnc

nnnn YYYY 321

ip

in

it pcnc

High Frequency (HF) regime Low Frequency (LF) regime

0.0 0.5 1.0 1.51011

1014

1017

1020

Etp

Eωn

Etn

EF

DO

S (e

V-1cm

-3)

Energy (eV)

Electrons the majority carriers n>>p

The states contributing Yn

In some cases Y2n + Y3n=0

and so Yn=Y1n



Y1n>>Y2n + Y3n and so Yn=Y1n

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Trapping & detrapping

Deep trapping

electrons

holes electrons

holes

1011

1014

1017

1020

0.0 0.5 1.0 1.5

Etp

Eωp

Etn

EF

DO

S (e

V-1cm

-3)

Energy (eV)

pp YY 1

ip

in

it pcnc

ppppp YYYYY 1321

ip

in

it pcnc

High Frequency (HF) regime Low Frequency (LF) regime

Holes the minority carriers

The states contributing Yp

Y1p>>Y2p+Y3p and so Yp=Y1p



1011

1014

1017

1020

0.0 0.5 1.0 1.5

Etp E

tnEωp E

F

DO

S (e

V-1cm

-3)

Energy (eV)

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holes

holes



tpp EE 0.5 1.0 1.5

1016

1018

Eωp

Etp

Etn

Eωn

EF

DO

S (e

V-1cm

-3)

Energy (eV)

kTEDcHYY pvv

pvtpp )(),(

21

kTEDcHYY ncc

nctnn )(),(

21

2/12

0lnit

i kTE

ip

in

it pcnc

HF regime

ntn EE ip

in

it pcnc

LF regime

1)arctan(2

1),(

iti

tH

12

),( it

itH

n>>p

ntn EE ptp EE

=1/τωn

Effective trapping rate of holes

Effective trapping rate of electrons

=1/τωp

10-3 10-1 101 103 105

107

108

109ω

t

vω

t

c

LF HF

ω<<ωt

i ω>>ωt

i

1/τωp

1/τωn

1/τ

(s-1)

ω (rad/s)

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Yn=1/τωn Reflects the DOS of the CB side

Yp=1/τωp Reflects the DOS of the VB sideYn, Yp

do not reflect the DOS

The so-called H function



n>>pnp

Y

/1/1

Majority carriers (electrons) dominate

μpτωp<< μnτωn

μpτωp>> μnτωn

μpτωp= μnτωn

npY

/1/1

ωn/1/1

Y

p

Minority carriers (holes) dominate

Mixed contributionsFrom both carriers

How can we know whether the majority

carriers dominate

A DOS spectroscopy is impossible

A DOS spectroscopy can be achieved

?

DOS model

Comparable densities below and above EF

0.0 0.5 1.0 1.5

1017

1019

1021

E (eV)

Dv(E) Dc(E)E

F

DO

S (c

m-3 e

V-1)

EF is abοve midgap so that electrons the majority carriers

μp=μn

μp<<μn

μp>>μn

10-1 101 103 105

108

109

Y

1/τωp1/τ

ωn

μn=μ

p

ω (rad/s)

Y (

s-1)

10-2 100 102 104 106

107

108

109

Y

1/τωp

1/τωn

μn=10μ

p

Y (

s-1)

ω (rad/s)

10-1 101 103 105

108

109

Yμ

p=10μ

n

1/τωp

1/τωn

ω (rad/s)

Y (

s-1)

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n>>p

Majority carriers (electrons) dominate Y signal

)arctan(2

1),(

HtH

tH

If the majority carriers dominate and Y signal follows 1/τωn

2/1),( ctH at ωt

Η=ωtc=ncn

c

This can be used to determine the

capture coefficient p

nHtc

n

ec

Bias light dependence

1),( ctH

kTEDcHY ncc

nct

n

)(),(2

1

kTEDcY ncc

n )(20

0),( YHY ct

),(0

HtH

Y

Y

Y moderate bias

0.1 1 10 1000.0

0.5

1.0

Y/Y0

Y

/Y0 (

r.u.

)

μnτ

ωn>>μ

pτ

ωp

H

ω/ωt

H (r.u.)

Y0 weak bias near dark equilibrium

Y follows 1/τωn

Two bias light levels

Normalized Y/Y0 spectrum

the normalized Y/Y0 ratio follows the universal H function

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Y signal drops by a factor of 2

…providing that the capture coefficient cnv of the states below EF for the

majority carriers is much lower than that cnc of the states above EF

1cn

vn

e c

cC

100 102 104

107

108

109

Y

Y0

2

1/τωn

ωt

c

ωt

H

μn=10μ

p

Y (

s-1)

ω (rad/s)

ct For

1cn

vn

e c

cC

1 10 1000.4

0.6

0.8

1.0

Y

/Y0 (

r.u.

)

μn=10μ

p

0.1 1 2

Ce

H

ω/ωt

H (r.u.)

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For

The decay of Y signal in the LF regime is steeper than 1/τωn

10-1 101 103 105

107

108

109

0.1

1/τωn

Ce

12

μn=10μ

p

Y (

s-1)

ω (rad/s)

The normalized Y/Y0 spectrum is below the universal spectrum of

H function for Ce=cnv/cn

c≥1

nnYY

1

1

In general,

),(0

HtH

Y

Y

0.0 0.5 1.0 1.51011

1014

1017

1020

Etp

Eωn

Etn

EF

DO

S (e

V-1cm

-3)

Energy (eV)

nnn YYY 321

electrons holes

032 nn YYRecombination through thestates below EF increases

nnnnn YYYYY

1

1321 cn

vn cc 0.0 0.5 1.0 1.5

1017

1019

1021

E (eV)

Dv(E) Dc(E)E

F

DO

S (c

m-3 e

V-1)

cn

vn cc Majority carriers (electrons)

dominate Y signal, but Y<1/τωn

if Y differs from the 1/τωn the normalized Y/Y0 ratio does not follow the universal H function

because

μpτωp<< μnτωn



Minority carriers(holes) dominate

Mixed contributions from electrons and holes

the normalized Y/Y0 ratio is above the universal H function for


),(0

HtH

Y

Y

),(0

HtH

Y

Y

μpτωp>> μnτωn

μpτωp= μnτωn

Majority carriers (electrons) do not dominate Y signal

Y does not follow 1/τωn

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μpτωp= μnτωn

μpτωp>> μnτωn

0YY

0YY

Ht For

Ht

0.1 1 10 1000.0

0.5

1.0

Y

/Y0 (

r.u.

)

H

ω/ωt

H (r.u.)

100 102 104

108

109

Y0

Y

2ω

t

H

μp=10μ

n

ω (rad/s)

Y (

s-1)

100 102 104 106

108Y

Y0

ωt

H

2

μn=μ

p

ω (rad/s)

Y (

s-1)

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DOS spectroscopy

This formula can be used for a

DOS spectroscopy

& Y follows 1/τωn

The majority carriers (electrons) dominate

If the normalized Y/Y0 ratio follows H function

kTEDcHY ncc

nct

n

)(),(2

1

kTHe

YED

Ht

Ht

pn

c

),(

2)(

0.1 1 10 1000.0

0.5

1.0

Y/Y0

Y

/Y0 (

r.u.

)

μnτ

ωn>>μ

pτ

ωp

H

ω/ωt

H (r.u.)

100 102 104

107

108

109

Y

Y0

2

1/τωn

ωt

c

ωt

H

μn=10μ

p

Y (

s-1)

ω (rad/s)

2/1),( ctH

at ωtΗ=ωt

c=ncnc

the capture coefficient is obtained coefficient from

p

nHtc

n

ec

and Y signal drops by a factor of 2

1.0 1.1 1.2 1.3 1.4

1015

1016

introduced DOS

E (eV)

DO

S (c

m-3eV

-1)

Alternatively ωtc can be

obtained from the DOS in the frequency regime

at ωtL/4 =ωt

c/4

is the onset of LF regime (plateau)

10-1 101 103 105

1015

1016

LF regime

ωt

c

ωt

L

4

(b)introduced DOS

ω (rad/s)

DO

S (c

m-3eV

-1)

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Experimental spectra of a-As2Se3

the normalized Y/Y0 ratio follows the universal H function

The majority carriers (holes) dominate and Y signal follows 1/τωp

at ωtΗ=ωt

c=ncnc

p

Ht

p

vp ec

and Y signal drops by a factor of 2

2.8 Ǻ

101 102 103 104 105

108

109

1010

10-1 100 101 102

0.5

1.0

ω (rad/s)

Y0

Y

2ω

t

H

(a)

Y (

s-1)

H(b)

ω/ωt

H (r.u.)

Y

/Y0

(r.u

.)

101 103 105

1017

1018

1019

0.5 0.6 0.71017

1018

ωt

H

(a)

DO

S (

eV-1cm

-3)

ω (rad/s)

(b)

DO

S (

eV-1cm

-3)

Eω-E

V (eV)

kTHe

YED

Ht

Ht

pp

v

),(

2)(

Neutral centers

Exponential dependence

(valence band-tail)

DOS spectroscopy

Capture radius

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Various species of states

100 102 104 106

10-2

10-1

100

ω (rad/s)

2Y

0

ωt

H

(a)

Y (

r.u.

)

0.0 0.5 1.0 1.51014

1016

1018

1020

EF

Dc(E)Dv(E)

Energy (eV)

DO

S (

cm-3eV

-1)

0.0 0.5 1.0 1.51014

1016

1018

1020

EF

Dhc(E)

Dc(E)Dv(E)

Energy (eV)

DO

S (

cm-3eV

-1)

DOS model Experimental spectra of a-Si:HAdditional states

having a 100 times higher capture

coefficient

scme

cp

nHthc

n /10 36

cn

hcn cc 100

10-1 101 103 105 107106

107

108

109

ω (rad/s)

Dc(E)

Y (

s-1)

10-1 101 103 105 107106

107

108

109

ω (rad/s)

Dhc(E)Dc(E)

Y (

s-1)

10-1 101 103 105 107106

107

108

109ω

t

Hωt

hc

ω (rad/s)

Dhc(E)Dc(E)

Y (

s-1)

p

nHthc

n

ec

From the decay of Y signal by the

factor of 2ωt

H is determined

hcn

hct

Ht nc

hcn

hct

Ht ncFrom

kTEDcHY cccn

ct

nn)(),(

2

1

kTEDcH hchchcn

hct n

)(),(2

The highest capture coefficient

the experimental Y signal follows 1/τωn

kTHe

YED

Ht

Ht

pn

c

),(

2)(

cn

ct

Lt nc

at ωtL/4 =ωt

c/4

is the onset of LF (plateau)

p

nLtc

n

ec

scme

cp

nLtc

n /102 39

cn

ct

Lt nc

From

scmccn /102 39Normal db’s

scmchcn /10 36

db’s with a Si-H back bond

or a three center Si-H-Si bond

LF

HF

0.7 0.6 0.5 0.4 0.31015

1016

1017

Dhc(E)

Dlc(E)EFn

DO

S (

eV-1cm

-3)

EC-E (eV)

100 102 104 106

1015

1016

1017

ωt

H

ωt

L

Dhc(E)

DO

S (

eV-1cm

-3)

ω (rad/s)

Provides the DOS of both species of states

DOS spectroscopy

model

Dc(Eωn)

Dhc(Eωn)

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a-Si:H

1.0 1.2 1.4 1.61014

1016

1018

10-1 101 103 1051014

1015

1016

Dc(E)

Dhc(E)

170K

200K

250K300K

D

OS

(cm

-3eV

-1)

Energy (eV)

ωt

lc Dc(E)

Dhc(E)

300K

ωt

L

4

DO

S (c

m-3eV

-1)

ω (rad/s)

HF

LF



The states with the lowest capture coefficient

Vertical line the signature ofvarious species

of states

Various species of states



ppY

/1/1 Mixed

contributions from electrons and holes

reasonable for the the lightly p-type doped material

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Experimental spectra from the literature where the majority carriers do not dominate

from the MPC measurements of Kleider & Longeaud Sol. St. Phen.44&46 596 (1995)

The normalized Y/Y0 ratio does

not follow the universal H

function

kTEDcHY cccn

ct n

)(),(2

a-Si:H lightly p-type dopedfrom MPC measurements of

Bruggemann J Mat. Sc.14, 629 (2003)

μc-Si:H

Y does not follow 1/τωn

10-2 10-1 100 10110-2

10-1

100H

Y/Y

0 (r.

u.)

ω/ωt

H

The normalized Y/Y0 ratio at lowest ω does not follow the

universal H function

Y does not follow

1/τωn at lowest ω

Mixed contributions from electrons and

holes

103 104 105 106

100

101

102

103

ω (rad/s)

Y (

r. u

.)

103 104 105 106

100

101

102

103

ω (rad/s)

Y (

r. u

.)

103 104 105 106

100

101

102

103

ω (rad/s)

Y (

r. u

.)

A DOS spectroscopy is impossible

102 103 104 10510-1

100

2

ωt

H

Y

Y0

Y (

r.u.

)

ω (rad/s)102 103 104 10510-1

100

2

ωt

H

Y

Y0

Y (

r.u.

)

ω (rad/s)

10-1 100 101 1020.1

1

153 K 183 K

(b)

H

Y/Y

0 (r.

u.)

ω/ωt

H (r.u.)

Y signal exponential dependence


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Conclusions

the transport of the majority carriers dominates giving the highest mobility effective trapping time

Y signal follows the effective trapping rate of the majority carriers into the probed states.

A DOS spectroscopy using a general formula gives

If the Y signal deviates from the universal frequency dependence

of H function,

The applicability of our analysis was demonstrated

in a-As2Se3, undoped and lightly p-doped a-Si:H samples and μc-Si:H.

If Y signal follows the universal H function around each ωt

i.

The states with the highest capture coefficient

The states with the lowest capture coefficient

then there are possible contributions from both carriers.

HF

LF

Documents

Maura Pomoni, Athina Giannopoulou and Panagiotis Kounavis