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Univ. of Patras. Modulated photocurrent as a powerful method to reveal transport by the majority carriers of disordered semiconductors and to resolve all the kinds of probed states. Maura Pomoni, Athina Giannopoulou and Panagiotis Kounavis.

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maura pomoni athina giannopoulou and panagiotis kounavis

Univ. of Patras

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

Maura Pomoni, Athina Giannopoulou

and Panagiotis Kounavis

Department of Engineering Sciences, University of Patras,

26504 Patra, Greece

slide2

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

slide3

The essential parameter of the MPC is the

out of phase Y signal

Univ. of Patras

Out of phase

MPC Y signal

Experimental setup

Phase shift

Measured

DOS

Mobility of the majority carriers

Modulated

photoconductivity

Modulated light

Generation rate

slide5

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

Electrons the majority carriers n>>p

Univ. of Patras

The states contributing Yn

High Frequency (HF) regime

Low Frequency (LF) regime

holes

holes

electrons

Trapping

& detrapping

electrons

Deep trapping

In some cases Y2n + Y3n=0

and so Yn=Y1n

Y1n>>Y2n + Y3n and so Yn=Y1n

slide6

The states contributing Yp

Univ. of Patras

Holes the minority carriers

High Frequency (HF) regime

Low Frequency (LF) regime

holes

holes

Y1p>>Y2p+Y3p and so Yp=Y1p

slide7

n>>p

Effective trapping rate of electrons

=1/τωn

Univ. of Patras

Effective trapping rate of holes

=1/τωp

HF regime

LF regime

The so-called H function

Yn=1/τωn

Reflects the DOS of the CB side

Yp=1/τωp

Reflects the DOS of the VB side

do not reflect the DOS

Yn, Yp

slide8

DOS model

μp=μn

μpτωp= μnτωn

Univ. of Patras

Comparable densities below and above EF

EF is abοve midgap so that electrons the majority carriers

n>>p

Mixed contributions

From both carriers

A DOS spectroscopy

is impossible

μp>>μn

μpτωp>> μnτωn

How can we know whether the majority carriers dominate

?

Minority carriers (holes) dominate

μp<<μn

μpτωp<< μnτωn

A DOS spectroscopy

can be achieved

Majority carriers (electrons) dominate

slide9

Majority carriers (electrons) dominate Y signal

n>>p

Univ. of Patras

at ωtΗ=ωtc=ncnc

Bias light dependence

Y signal drops by a factor of 2

This can be used to determine the capture coefficient

Two bias light levels

Y follows 1/τωn

Normalized Y/Y0 spectrum

Y moderate bias

Y0 weak bias near dark equilibrium

For

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

thenormalized Y/Y0 ratio follows the universal H function

…providing that the capture coefficient cnvof the states below EF for the majority carriers is much lower than that cncof the states above EF

slide10

For

Majority carriers (electrons) dominate Y signal, but Y<1/τωn

Univ. of Patras

μpτωp<< μnτωn

because

Recombination through the

states below EF increases

electrons

holes

The normalized Y/Y0 spectrum

is below the universal spectrum of H function for Ce=cnv/cnc≥1

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

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

In general,

slide11

Majority carriers (electrons) do not dominate Y signal

Univ. of Patras

μpτωp>> μnτωn

Bias light dependence

Y does not follow 1/τωn

μpτωp= μnτωn

For

Mixed contributions from electrons and holes

μpτωp= μnτωn

Minority carriers

(holes) dominate

the normalized Y/Y0 ratio

is above the universal H function for

μpτωp>> μnτωn

slide12

DOS spectroscopy

Univ. of Patras

If thenormalized Y/Y0 ratio follows H function

The majority carriers (electrons) dominate

& Y follows 1/τωn

the capture coefficient is obtained coefficient from

This formula can be used for a DOS spectroscopy

at ωtΗ=ωtc=ncnc

and Y signal drops by a factor of 2

Alternatively ωtc can be obtained from the DOS in the frequency regime

at ωtL/4 =ωtc/4

is the onset of LF regime (plateau)

slide13

Experimental spectra of a-As2Se3

The majority carriers (holes) dominate and

Y signal follows 1/τωp

Univ. of Patras

DOS spectroscopy

at ωtΗ=ωtc=ncnc

and Y signal drops by a factor of 2

Capture radius

2.8 Ǻ

Neutral centers

Exponential dependence

(valence band-tail)

thenormalized Y/Y0 ratio follows the universal H function

slide14

Various species of states

Univ. of Patras

DOS model

Experimental spectra of a-Si:H

Additional states having a 100 times higher capture coefficient

the experimental Y signal follows 1/τωn

From the decay of Y signal by the factor of 2

ωtH is determined

From

The highest capture coefficient

slide15

Various species of states

DOS spectroscopy

Provides the DOS of both species of states

Univ. of Patras

model

a-Si:H

LF

Vertical line

the signature of

various species

of states

Normal db’s

HF

Dc(Eωn)

LF

db’s

with a Si-H back bond

or a three center Si-H-Si bond

Dhc(Eωn)

HF

From

at ωtL/4 =ωtc/4

is the onset of LF

(plateau)

The states with the lowest capture coefficient

slide16

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

U. of Patras

μc-Si:H

a-Si:H lightly p-type doped

from MPC measurements of Bruggemann J Mat. Sc.14, 629 (2003)

from the MPC measurements of

Kleider & Longeaud Sol. St. Phen.44&46 596 (1995)

Y signal exponential dependence

Y does not follow 1/τωn

Y does not follow1/τωn at lowest ω

Bias light

dependence

The normalized Y/Y0 ratio does not follow the universal H function

Mixed contributions from electrons and holes

Mixed contributions from electrons and holes

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

reasonable for the the lightly p-type doped material

A DOS spectroscopy

is impossible

slide17

Conclusions

U. of Patras

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

If Y signal follows the universal H function around each ωti.

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

HF

The states with the highest capture coefficient

A DOS spectroscopy using a general formula gives

The states with the lowest capture coefficient

LF

If the Y signal deviates from the universal frequency dependence of H function,

then there are possible contributions from both carriers.

The applicability of our analysis was demonstrated

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