Semic-Lab
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
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
Semic-Lab
Semiconductors Lab
Dep. of Eng. Sciences
Univ. 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
Semic-Lab
The essential parameter of the MPC is the
Univ. of Patras
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
out of phase Y signal
Out of phase
MPC Y signal
Y  eGac
Experimental setup
Phase shift
sin 
 ac
Mobility of the
majority carriers
Modulated light
Generation rate
 N ( E )
Phase shift
LED
Modulated
+ bias light
Φ
amplitude of
MPC
Osciloscope
Measured
iac
reference
signal
Φ iac
Lock-In
DOS
Amplifier
electrodes
Modulated
photoconductivity
Vdc
a-Si:H
The analysis have shown that
Semic-Lab
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
Univ. of Patras
nac  nin  jnout 
pac  pin  jpout

Gac
X n  jYn
Gac

X p  jYp
iac  A ( nnout   p pout )  ( nnin   p pin )
2
n nout   p pout
tan   
n nin   p pin

2 1/ 2
Y  eGac
Y  Yn
or
sin 
 ac
Y  Yp
Y signal is related to the gap states with which the
electrons and holes interact and contribute to Yn , Yp
Univ. of Patras
Semic-Lab
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
Electrons the majority carriers n>>p
The states contributing Yn
High Frequency (HF) regime
Low Frequency (LF) regime
  ti  ncni  pcip
  ti  ncni  pcip
Yn  Y1n  Y2 n  Y3n
10
17
10
14
10
11
EF
Etp
Etn E
ωn
holes
electrons
0.0
-3
20
-1
10
DOS (eV cm )
-1
-3
DOS (eV cm )
Yn  Y1n  Y2n  Y3n
Trapping
& detrapping
Deep trapping
0.5 1.0 1.5
Energy (eV)
Y1n>>Y2n + Y3n and so Yn=Y1n
10
20
10
17
EF
Etp
holes
10
14
10
11
0.0
Etn
Eωn
electrons
0.5 1.0 1.5
Energy (eV)
In some cases Y2n + Y3n=0
and so Yn=Y1n
Semic-Lab
Semiconductors Lab
The states contributing Yp
Dep. of Eng. Sciences
Univ. of Patras
Univ. of Patras
Holes the minority carriers
High Frequency (HF) regime
Low Frequency (LF) regime
  ti  ncni  pcip
  ti  ncni  pcip
10
17
10
14
10
11
Etp
EF
Etn
-3
Eωp
-1
10
20
Yp  Y1 p
DOS (eV cm )
-1
-3
DOS (eV cm )
Yp  Y1 p  Y2 p  Y3 p  Y1 p
holes
0.0
0.5 1.0 1.5
Energy (eV)
10
20
10
17
10
14
Etp
EF
Etn
Eωp
11
10 0.0
Y1p>>Y2p+Y3p and so Yp=Y1p
holes
0.5 1.0 1.5
Energy (eV)
Yn  Y1n  H ( ,  )c D ( En )kT =1/τωn Effective trapping
rate of electrons
2
n>>p

2
c
t
    nc  pc
i
t
i
n
10
10
1

HF regime
ωt
9
10
Ep  Etp Etn  En
v
ωt
c
The so-called H function
ti
H ( ,  )  1  arctan( )  1


1/τωp
i
t
8
1/τωn
10
7
do not reflect
the DOS

1/ 2 

  ti  ncni  pcip
10
Yn, Yp
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
Eωn
0.5
1.0
1.5
Energy (eV)
1/τ (s )

i
t

16
-1
H ( ,  ) 

0
E i  kT ln 
2
i
   t
Etn
Eωp
i
p
2 
EF
Etp
Etp  Ep Etn  En
i
t
c
18
-1
LF regime
c
n
trapping
=1/τωp Effective
rate of holes
H ( , tv )c vp D v ( Ep )kT
-3
Yp  Y1 p 
DOS (eV cm )
Univ. of Patras
Semic-Lab

ω<<ωt
i
ω>>ωt
LF
-3
-1
1
3
Yn=1/τωn
Reflects the DOS
of the CB side
Yp=1/τωp
Reflects the DOS
of the VB side
i
HF
5
10 10 10 10 10
ω (rad/s)
2
Univ. of Patras
μpτωp= μnτωn
1 /  p  Y  1 /  n
-1
Y (s )
10
8
Y
μn=μp
10
-1
9
1
3
10 10 10
ω (rad/s)
1/τωn
Mixed contributions
From both carriers
5
-1
Y (s )
10
10
9
10
8
10
1
3
10 10 10
ω (rad/s)
10
0
μpτωp<< μnτωn
2
4
1.0
E (eV)
10 10 10 10
ω (rad/s)
Semic-Lab
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
1.5
Comparable densities below and above EF
EF is abοve midgap so that
electrons the majority carriers
n>>p
A DOS spectroscopy
is impossible
How can we know
whether the majority
carriers dominate
μp<<μn
1 /  p  Y  1 /  ωn
Y
μn=10μp
-2
0.5
Minority carriers (holes) dominate
5
1/τωn
1/τωp
7
D (E)
EF
1 /  p  Y  1 /  n
Y
μp=10μn
-1
0.0
μpτωp>> μnτωn
-1
Y (s )
10
10
17
c
v
D (E)
μp>>μn
10 1/τ
ωp
8
-1
μp=μn
1/τωp1/τωn
10
19
-3
9
21
DOS (cm eV )
10
DOS model
10
6
A DOS spectroscopy
can be achieved
Majority carriers (electrons) dominate
?
Majority carriers (electrons)
dominate Y signal
10
Bias light
dependence
Y0
8
2
Y
Two bias light
levels
at ωtΗ=ωtc=ncnc
0
2
Y moderate bias
ω (rad/s)
1 
Y
 H ( , tc )cnc D c ( En )kT
 n 2
Y0 weak bias near dark equilibrium
For   tc
 c c
H ( , tc )  1
Y0 
Y signal drops by a factor of 2
μn=10μp
10
2
H ( , tc )  1 / 2
c
7
10 1/τωn
10
n>>p
H
ωt
ωt
-1
Y (s )
10
9
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
cn D ( En )kT
10
4
This can be used to
determine the
capture coefficient
Y follows 1/τωn
c 
c
n
etH  n
p
Normalized Y/Y0 spectrum
1.0
Y  H ( ,  )Y0
c
t
Y
 H ( , tH )
Y0
If the majority carriers dominate and Y signal follows 1/τωn
Y/Y0 (r.u.)
Univ. of Patras
Semic-Lab
H
0.5
0.0
Y/Y0
μnτωn>>μpτωp
0.1 1
H
10 100
ω/ωt (r.u.)
H
the normalized Y/Y0 ratio follows the universal H function H ( ,  H )  1  2 arctan( t )
t


v
…providing that the capture coefficient cnv of the states below EF for the
cn
Ce  c  1
majority carriers is much lower than that cnc of the states above EF
cn
Y  Y1n  Y2 n  Y3n  Y1n 
cnv
Ce  c  1
cn
because
7
10
-1
10
-3
1
-1
Ce
0.1
1
2
8
DOS (eV cm )
-1
Y (s )
1/τωn
10
 n
Y2n  Y3n  0 Y1n  Y2 n  Y3n
9
10
1
μn=10μp
3
10 10 10
ω (rad/s)
Y  Y1n 
5
1
 n
10
20
10
17
10
14
10
11
17
0.0
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
D (E)
EF
0.5
1.0
E (eV)
1.5
Recombination through the
states below EF increases
EF
Etp
1.0
Etn
Eωn
holes
0.0
electrons
0.5 1.0 1.5
Energy (eV)
Y
 H ( , tH )
Y0
The decay of Y signal in the LF
regime is steeper than 1/τωn
In general,
10
Semic-Lab
c
v
D (E)
Y/Y0 (r.u.)
cnv  cnc
-1
μpτωp<< μnτωn
10
19
-3
Univ. of Patras
10
21
DOS (cm eV )
Majority carriers (electrons)
dominate Y signal, but Y<1/τωn
cnv  cnc
For
H
0.8
Ce
0.6
0.4
1
μn=10μp
0.1
1
2
10
100
H
ω/ωt (r.u.)
The normalized Y/Y0 spectrum
is below the universal spectrum of
H function for Ce=cnv/cnc≥1
if Y differs from the 1/τωn the normalized Y/Y0 ratio does
not follow the universal H function
10
Y0
For    H
t
H
Y
8
Y
 H ( , tH )
Y0
μp=10μn
10
0
2
10
10
ω (rad/s)
4
-1
Y (s )
μpτωp>> μnτωn
10
Y  Y0
H
ωt
Y
Y
 H ( , tH )
Y0
μn=μp
10
0
1.0
0.5
2
H
0.1 1 H 10 100
ω/ωt (r.u.)
2
8
μpτωp= μnτωn
0.0
Y0
Minority carriers
(holes) dominate
μpτωp>> μnτωn
Y  Y0
ωt
-1
10
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
Y does not follow 1/τωn
2
Y (s )
μpτωp= μnτωn
Bias light
dependence
9
Y/Y0 (r.u.)
Univ. of Patras
Mixed
contributions from
electrons and holes
Semic-Lab
Majority carriers (electrons)
do not dominate Y signal
4
10
10
ω (rad/s)
10
6
the normalized Y/Y0 ratio
is above the universal H
function for   tH
DOS spectroscopy
Y/Y0 (r.u.)
Univ. of Patras
Semic-Lab
1.0
If the normalized Y/Y0 ratio follows H function
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
H
0.5
0.0
Y/Y0
μnτωn>>μpτωp
0.1 1
H
ω/ωt (r.u.)
10
9
10
8
Y0
2
Y
2Y
c
This formula can be used for a
DOS spectroscopy
LF
regime
4
ωt
-3
-1
DOS (cm eV )
-3
-1
DOS (cm eV )
10
10
10
15
introduced
DOS
1.0
1.1
1.2
1.3
E (eV)
1.4
10
-1
1
10
ω (rad/s)
4
etH  n
p
Alternatively ωtc can be
obtained from the DOS in the
frequency regime
L
10
10
ω (rad/s)
10
and Y signal drops by a factor of 2
c 
(b)
introduced
DOS
10
μn=10μp
2
c
n
c
ωt
15
0
H ( , tc )  1 / 2
at ωtΗ=ωtc=ncnc
16
16
7
10 1/τωn
10
the capture coefficient is
obtained coefficient from
H
ωt
ωt
-1
Y (s )
The majority carriers (electrons) dominate
1 
Y
 H ( , tc )cnc D c ( En )kT
& Y follows 1/τωn
 n 2
p
D c ( En ) 
  etH H ( , tH )kT
10 100
at ωtL/4 =ωtc/4
3
5
10
is the onset of LF regime
(plateau)
Semic-Lab
Experimental spectra of a-As2Se3
The majority carriers (holes) dominate and
Y signal follows 1/τωp
Univ. of Patras
DOS spectroscopy
D v ( Ep ) 
10
ωt
8
10
1
and Y signal drops
by a factor of 2
H
Y
2
10
10
10
3
10
4
10
5
c
ω (rad/s)
v
p
p

e
H
t
p
10
18
10
17
10
1.0
ωt
1
10
-1
10
0
ω/ωt
10
H
Neutral centers
(b)
1
10
2
(r.u.)
the normalized Y/Y0 ratio
follows the universal H function
(a)
3
10
5
(b)
-3
H
-1
0.5
H
10
ω (rad/s)
Capture radius 2.8 Ǻ
DOS (eV cm )
Y/Y 0 (r.u.)
19
-3
10
2
-1
10
p
  etH H ( , tH )kT
2Y
at ωtΗ=ωtc=ncnc
(a)
Y0
9
DOS (eV cm )
-1
Y (s )
10
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
10
18
10
17
0.5
0.6
Eω-EV (eV)
0.7
Exponential dependence
(valence band-tail)
Various species of states
Semic-Lab
Semiconductors Lab
Y
Univ. of Patras
1
 n


2
H ( , tc )cnc D c ( E cn )kT 
-1
-3
0
v
D (E)
18
10
10
c
EF
D (E)
16
10
Y (r.u.)
c
n
DOS (cm eV )
c  100c
hc
n
20
10
hc
D (E)
14
10
0.0
0.5
1.0
1.5
Energy (eV)
    nc
H
t
hc
t
c 
hc
n
hc
n
etH  n
p
9
10
-1
Y (s )
From the decay of
Y signal by the
factor of 2
ωtH is determined
ωt
hc
ωt
H
8
10
7
10
2
H ( , thc )cnhc D hc ( E hcn )kT
Experimental
spectra of a-Si:H
DOS model
Additional states
having a 100 times
higher capture
coefficient

Dep. of Eng. Sciences
Univ. of Patras
hc
D (E)
ccc
D
D(E)
(E)
D
(E)
10
-1
10
-2
Y0
2
ωt
H
the
experimental
Y signal
follows 1/τωn
(a)
10
0
6
10 -1
1
3
5
7
10 10 10 10 10
ω (rad/s)
c 
hc
n
2
4
6
10
10
10
ω (rad/s)
H
hc
hc
From t  t  ncn
etH  n
p
 10 6 cm 3 / s
The highest capture
coefficient
Various species of states
DOS spectroscopy
Semiconductors Lab
p
D ( En ) 
  etH H ( , tH )kT
2Y
c
Univ. of Patras
-3
250K
300K
hc
D (E)
14
1.0
1.2
1.4
Energy (eV)
1.6
300K
15
10
hc
D (E)
14
10
tL  tc  ncnc
c 
c
n
10
-1
etL  n
p
10
1
3
10
10
ω (rad/s)
-3
-1
t
10
D (E)
cnc  2 10 9 cm3 / s
Normal db’s
10
HF
hc
D (E)
15
10
0.7
0.6
0.5
0.4
10
ωt
17
cnhc  10 6 cm3 / s
db’s with a Si-H back bond
0.3
EC-E (eV)
DOS (eV cm )
ωt
c
4 ω lc D (E)
16
EFn
lc
16
L
-1
is the onset of LF
(plateau)
10
-1
170K
-3
at ωtL/4 =ωtc/4
200K
16
HF
DOS (cm eV )
Dhc(Eωn)
c
10
DOS (eV cm )
-3
Dc(Eωn) LF
LF
17
D (E)
10
a-Si:H
18
-1
DOS (cm eV )
Vertical line
the signature of
various species
of states
Dep. of Eng. Sciences
Univ. of Patras
Provides the DOS of
both species of states
model
10
Semic-Lab
or a three center Si-H-Si bond
L
From
tL  tc  ncnc
10
10
5
The states with the lowest
capture coefficient
16
ωt
c 
c
n
hc
D (E)
15
10
H
0
2
10
10
4
ω (rad/s)
10
6
etL  n
p
 2 10 9 cm 3 / s
Experimental spectra from the literature where
the majority carriers do not dominate
Semic-Lab
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
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)
Y0
2
Y (r.u.)
ωt
Y
Y does not follow
H
-1
10
1
3
4
10
10
ω (rad/s)
10
5
Y
2
H ( ,  )c D ( E n )kT
c
t
c
n
c
c
10
3
10
2
10
1
10
0
Bias light
dependence
10
3
10
4
10
5
10
6
ω (rad/s)
H
(b)
Y/Y 0 (r.u.)
The normalized
Y/Y0 ratio does
not follow the
universal H
function
2
10

1/τωn at lowest ω
0
153 K
183 K
0.1
10
-1
0
1
2
10
10
10
H
ω/ωt (r.u.)
10
Mixed contributions
from electrons and
holes
1 /  p  Y  1 /  p
Mixed
contributions from
electrons and holes
reasonable for the
the lightly p-type
doped material
A DOS spectroscopy
is impossible
Y/Y 0 (r. u.)
Y does not follow
1/τωn
Y signal
exponential
dependence
0
Y (r. u.)
10
H
-1
10
-2
10 -2
10
-1
10
0
1
10
10
H
ω/ωt
The normalized Y/Y0 ratio at
lowest ω does not follow the
universal H function
Conclusions
Semic-Lab
Semiconductors Lab
Dep. of Eng. Sciences
Univ. of Patras
U. of Patras
If Y signal follows the universal H
function around each ωti.
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.
HF
A DOS spectroscopy using a
general formula gives
The states with the highest
capture coefficient
The states with the lowest
LF capture coefficient
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.