Article
pubs.acs.org/JPCC
Defect Characterization in Organic Semiconductors by Forward Bias
Capacitance−Voltage (FB-CV) Analysis
Biswajit Ray,† Aditya G. Baradwaj,‡ Bryan W. Boudouris,‡ and Muhammad A. Alam*,†
†
School of Electrical and Computer Engineering and ‡School of Chemical Engineering, Purdue University, West Lafayette, Indiana
47907, United States
S Supporting Information
*
ABSTRACT: Transport in organic semiconductors (OSCs)
generally is poorer relative to their inorganic counterparts,
mainly due to the high defect density that trap the free charge
carriers. In this article, we demonstrate a new defect
characterization method based on forward bias capacitance−
voltage (FB-CV) measurements, which is appropriate for a
broad range of low mobility OSCs with relatively large (>1.5
eV) band gaps. The characterization method, developed using
numerical modeling and experimental data, relates the
capacitance peaks in the FB-CV sweep to the deep level
defect states; these states are inaccessible to classical reverse
bias (RB) impedance spectroscopy. We validate the proposed technique by interpreting FB-CV data for organic photodiodes
made of a commonly used semiconducting polymers, poly(3-hexylthiophene) (P3HT), poly[2-methoxy-5-(2-ethylhexyloxy)-1,4phenylenevinylene] (MEH-PPV), and copper(II) phthalocyanine (CuPc). We find that P3HT and MEH-PPV contain both
shallow and deep level states, but deep traps in CuPc depend on process conditions, consistent with reports in the recent
literature. We demonstrate that these deep traps corrupt the interpretation of the classical Mott−Schottky analysis (of RB-CV
data), leading to an underestimation of the built-in voltage of a device.
O
for a P3HT photodiode, which shows a single transition
frequency corresponding to ωp ≈ 10 kHz. Therefore, classical
IS analysis has limited applicability for measuring the trap levels
of typical OSCs (e.g., poly(3-hexylthiophene) (P3HT), poly[2methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEHPPV), copper (II) phthalocyanine (CuPc)). The validity of IS
technique and the corresponding measurement window (ωmin,
ωdr) are dependent on the material, device, and the
measurement system.10,15,21−23
This failure of the widely used IS method led the community
to look for alternative techniques. For example, Nicolai et al.12
have developed a space charge limited current−voltage (SCLIV) measurement technique to determine the deep level defect
states in OSCs. Unfortunately, their results can be consistently
interpreted only for specialized test structures with relatively
small built-in voltages (Vbi). It is not clear if the technique can
be generalized to interpret defects in Schottky junction or PN
junction diodes. In addition, the SCL-IV method cannot
distinguish between deep and shallow level states and therefore
is not suitable for devices with mixed and/or distributed defect
levels.
In this work, we develop a new defect characterization
technique based on a FB-CV measurement, which is ideally
rganic semiconductors (OSCs) are widely used in many
applications such as light emitting diodes,1 solar cells,2−5
and transistors.6 As van der Waals solids,7 OSCs form
disordered films with weak lattice forces that results in a large
number of defect states8−10 within the energy band gap, Eg.
These defects scatter and trap free carriers, so that the carrier
mobility is reduced and recombination is enhanced.11−13 Thus,
it is important to understand the origin of these defects and
characterize the energy levels and the density of these defect
states. In this manner, the design of new OSCs with improved
transport properties will be facilitated.
The energy levels of defect states within the band gap of a
material generally are characterized by impedance spectroscopy
(IS) or, more specifically, capacitance−frequency (C-f)
measurements at zero bias (the horizontal line separating RB
and FB regions in Figure 1).14−18 The IS analysis correlates the
transition frequencies (ωi) with the defect energy levels (Ei)
according to the following relationship: Ei = kTln(ω0/ωi),
where ω0 is a material dependent constant,14 T is the
temperature, k is the Boltzmann constant, and Ei is referred
from the HOMO level of the OSC. For deep level states, ωi
values are exponentially suppressed below the measurement
window (W1 in Figure 1a). The shallow states can be measured
only if their ωi values are lower than dielectric relaxation
frequency (ωdr).19 For OSCs, however, ωdr values characteristically are very low, which precludes the use of IS analysis for
defect level characterization20 (see W4 in Figure 1a). As an
illustrative example, in Figure 1b we show the measured IS data
© 2014 American Chemical Society
Received: June 3, 2014
Revised: July 16, 2014
Published: July 16, 2014
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Figure 1. (a) Impedance measurement depends on voltage−frequency (V-f) range, which is depicted here by dividing the entire Vf-space in four
different windows. The measurement windows W1 and W4 are not accessible due to measurement noise and the dielectric relaxation frequency,
respectively. The forward bias window (W2) is accessible only in low mobility materials, and it contains information about the defect levels (Edp and
Esh). (b) Measured impedance spectroscopy (IS) plot (V = 0) for a P3HT diode (inset shows the device structure). The transition frequency (ωp) in
the plot corresponds to the dielectric relaxation frequency (ωdr) and does not provide any information about the defect energy levels.
Figure 2. Theory of the capacitance oscillation. (a) Energy band diagram of the metal−semiconductor Schottky junction at equilibrium (V = 0 and
Ef = Efn = Efp). The deep and shallow energy defect states are shown within the band gap and measured from the valence band. The space charge in
the depletion region is shown below the band diagram, emphasizing the fact that the space charge consists of both shallow and deep level defects.
The total capacitance is, thus, a parallel combination of two capacitances: one related to shallow defects (Csh) and the other related to deep states
(Cdp). (b) Energy band diagram in the forward bias (FB) illustrates that deep level states float above the hole quasi-Fermi level (Efp) and become
charge neutral as the diode is forward biased. Thus, the deep states no longer contribute to device capacitance explaining capacitance fall (or
oscillation) at FB.
defect states, which are otherwise inaccessible to classical RBCV methods. A few recent reports24,25 have highlighted the
importance of FB-CV for OSCs; however, the analysis is
generally qualitative and the validity of the technique (for a
specific OSC) has not been defined clearly. Our work makes
the FB-CV measurement approach quantitative by defining the
limits of validity of the technique in terms of the frequency and
voltage range of operation and suggests a quantitative
framework for identification of deep level trap information
from the FB-CV peaks. The theory has been used to interpret
the measured CV data of OSC-based Schottky diodes. The data
indicate that common OSCs (e.g., P3HT, MEH-PPV, CuPc)
not only contain shallow defects (usually called dopants), but
suited for a wide range of low mobility, wide band gap OSCs.
Classical CV measurements are performed in the reverse bias
(window W3 in Figure 1a; ωmin < ω < ωdr ,VA < 0) to calculate
the doping densities (NA,ND) and Vbi of semiconducting
devices.19 The FB-CV (window W2 in Figure 1a; ωmin < ω <
ωdr, VA ≥ 0) is excluded because the high conductivity of the
forward-biased devices (as reflected in high dissipation factor
(D)14,18) reduces the accuracy of the capacitance extracted.
In this article, we show that the limitation regarding FB-CV
measurement does not apply to low-mobility OSCs with μ ≈
10−3−10−6 cm2 V−1 s−1). For OSCs, the FB-CV window (W2 in
Figure 1a) allows for high-precision measurement of device
capacitance and provides additional information on deep level
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Figure 3. (a) Capacitance−voltage data for the P3HT diode in both forward and reverse bias. The measurement frequency (f) is 200 Hz. (b) The
corresponding Mott−Schottky plot of the capacitance data has two slopes: one in the reverse bias and other in the forward bias. The solid lines are
drawn according to eq 2 (reverse bias, red line) and eq 3 (forward bias, black line) to interpret the data and extract the defect density.
and shallow levels. The corresponding equation of the
capacitance in the reverse bias (CRB) is given by (a general
derivation is given in refs 28 and 29)
also contain a high density of deep level states. The defect
densities and the defect levels obtained by FB-CV are
consistent with SCL-IV method.12 In addition, we find that
the classical Mott−Schottky analysis on the RB-CV data of
organic Schottky diode underestimates the device Vbi due to the
high density of deep level states.
Classical Mott−Schottky (MS) analysis19,20,26,27 commonly
is used to calculate the total doping density (NA) and the builtin voltage (Vbi) of a semiconducting device. These values are
obtained from the slope and intercept of the C−2−V plot, based
on the following MS equation:
1
2
=
(Vbi − V )
2
qϵNA
C
1
2
=
(VbiRB − V )
qϵ(Ndp + Nsh)
C RB 2
(2)
Here Ndp and Nsh are the defect densities of the deep level and
shallow level states, respectively, and VRB
bi is the extrapolated
built-in voltage based on RB-CV data.
When a positive voltage is applied at cathode (moving from
W3 to W2 in Figure 1a), the energy bands move up so that the
deep states float above the hole quasi-Fermi level (Efp in Figure
2b). The deep states are now empty and charge neutral and
therefore no longer contribute to the total capacitance. Hence,
the capacitance abruptly falls to a lower value in forward bias
(see Figure 3a). Beyond this bias point, the capacitance
corresponds exclusively to the shallow defect states (Figure 2b).
The forward bias capacitance (CFB) can be written as
(1)
Here, ϵ is the dielectric constant and q is the charge of an
electron. Note that the MS analysis does not provide any
information about the energy levels of the dopants or the
defects because the theory assumes that only ionized shallow
dopants contribute to RB capacitance. In the early 1970s,
Crowell et al.28,29 generalized the classical MS theory to
account for multiple deep level defect states and found that,
under certain conditions,28 the FB-CV may contain signatures
of trap levels. We find that these conditions are generally
satisfied for organic Schottky diodes. In the following,
therefore, we adapt the Crowell−Mott−Schottky (CMS)
theory for an accurate characterization of defect states in
OSCs. The CMS theory accounts for all charges including the
mobile carriers; however, the mobile carrier density is small in
large band gap organic semiconductors. Therefore, the CMS
theory can be simplified by neglecting the contribution from
mobile carriers for organic semiconductors to develop a
simplified analytical theory as discussed below.
Figure 2 shows the energy band diagram and the space
charge regions of a metal−semiconductor Schottky diode in the
presence of both deep and shallow defects. We assume that
both the shallow and deep level states are acceptor-like states.
In principle, there may be a narrow distribution of states
around individual defect levels, but for simplicity we assume
that the defect levels are discrete. At the equilibrium conditions
(or reverse bias), both the deep and the shallow defects remain
below the hole quasi-Fermi energy level (Figure 2a). Thus, the
space charge consists of both the shallow (acceptor-like
dopants), and deep level states filled with electrons. The
measured capacitance, therefore, can be interpreted as the
parallel combination of the capacitances corresponding to deep
1
2
≈
(VbiFB − V )
qϵNsh
C FB 2
(3)
Here VFB
bi represents the built-in voltage extrapolated from the
FB-CV characteristics. Note that eq 3 is an approximate
description for FB-CV as it neglects the effects of mobile charge
carriers even in the forward bias regime. In the wide band gap
organic semiconductors, such as P3HT, the mobile carriers are
few and the space charge is mainly due to the dopants or
charged defect states. This assertion is confirmed by a detailed
and self-consistent numerical modeling of carrier transport in
the organic Schottky diodes; the results are summarized in
Figure S6 of the Supporting Information (SI, section 5).36 For a
precise analysis of FB-CV, we refer the readers to the initial
paper by Crowell et al.28 Thus, for organic semiconductors, eq
3 should be used with caution as an approximate guideline to
interpret the high forward bias data.
The energetic positions of the deep defect levels (Edp) and
shallow defect levels (Esh) are related to the voltages
corresponding to capacitance peaks (denoted as Vdp) and Vsh
in Figure 3a) as follows.
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Edp − Ef ≈ q(Vbi − Vdp)
(4a)
Esh − Ef ≈ q(Vbi − Vsh)
(4b)
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Here, Ef is the equilibrium Fermi level of the semiconductor
(see Figure 2a), and Vbi is the intrinsic built-in voltage. Note
that the energy levels obtained by eqs 4a and 4b are
approximate as we have neglected the effects of mobile charge
carriers and contact series resistance. A detailed numerical
simulation can be used to improve the precision of energy
levels obtained from the C−V data, and this topic has been
discussed in Figure S5c of the Supporting Information (section
6).
The derivation of eqs 2−4 neglects any contribution of
diffusion capacitance, which is valid because the Schottky
junction is a majority carrier device.19 Second, the analysis
assumes that the Schottky barrier forms only at the cathode−
organic junction. Because OSCs are generally p-type materials,
this assumption holds well for many OSCs. Third, eqs 2−4 are
derived assuming that bulk defect states dominate the
electrostatics of the device and that the contributions of the
contact states is relatively small. We justify this assumption by
numerical simulation in Supporting Information section 6.
Finally, the theory presented here assumes that deep level traps
respond to the relatively low measurement frequency (e.g., f ≈
200 Hz). This assumption holds because the charging of the
deep level traps takes place near the metal−semiconductor
interface where electrons can directly tunnel in the trap states
from the metal electrode instead of band-to-trap capture/
emission.30
We now apply the theory of RB-CV and FB-CV to interpret
the measured capacitance−voltage data for the P3HT-based
Schottky junction devices. The structure of the device is as
follows: tin-doped indium oxide (ITO) on glass (150 nm)/
PEDOT:PSS (50 nm)/regioregular P3HT (700 nm)/Al (100
nm). The P3HT layer is made deliberately thick to avoid any
effect of a fully depleted device.20,26 The device fabrication
steps are described in detail in the Supporting Information. The
CV response of other OSCs such as MEH-PPV and CuPc are
described in the Supporting Information (Figure S2).
In Figure 3a, we plot the low frequency ( f = 200 Hz) CV
characteristics of the P3HT-based Schottky diode. The
corresponding MS plot is drawn in Figure 3b. The figure
shows that the capacitance follows the MS theory (C−2 ∝ V) for
negative voltages (i.e., in reverse bias). In forward bias,
however, we observe an oscillatory behavior in the
capacitance−voltage characteristics not anticipated by classical
reverse bias MS analysis. Similar capacitance oscillations in FB
capacitance also were observed by Crowell et al.28,29 for siliconbased Schottky diodes in the presence of deep (Au) and
shallow (Cu) impurity levels (or defect states). According to ref
28, the first peak in the CV curve is due to the discharge of the
deep level defect states (Edp), and the second peak corresponds
to the discharge of shallow defects (Esh).
We now utilize eqs 2 and 3 to extract information from both
the FB-CV as well as RB-CV characteristics. In Figure 3b, we
plot eqs 2 and 3 as solid red and black lines, respectively, to fit
the data. From the slope of the FB-CV (eq 3), we find Nsh = 2
× 1015 cm−3. From the slope of the RB-CV, we calculate Nsh +
Ndp = 8 × 1015 cm−3. In other words, in this system, the deep
level defects outnumber the shallow defects in a 3:1 ratio.
Similarly, the capacitance peaks (Vsh ≈ 1.2 V and Vdp ≈ 0.25 V)
can be used with eqs 4a and 4b to find that Edp ≈ 1.3 eV and Esh
≈ 0.35 eV are above the HOMO level of P3HT (we use Ef ≈
0.35 eV above the HOMO level as calculated from total defect
density). These values are in agreement with previously
reported values.12,15 Thus, our analysis provides independent
confirmation of the presence of the deep defect levels in P3HT.
Note that the C-f characteristics shown in Figure 1b do not
saturate at low frequency indicating incomplete trap response,
in particular from the deep level traps. Thus, the slopes of
Mott−Schottky plots (measured at 200 Hz) underestimate the
actual defect density in the semiconductor.
Figure 3b shows that there are two built-in voltages: one
corresponds to RB-CV (VRB
bi ≈ 0.55 V) and the other to FB-CV
RB
(VFB
bi ≈ 1.2 V). Traditionally, Vbi is attributed as the built-in
voltage of the Schottky diode, provided that the capacitance
saturates to the geometric limit (Cgeo).18 Figure 3, however,
shows that the capacitance for the P3HT Schottky diode
FB
RB
saturates to Cgeo = 3 nF/cm2 after VFB
bi , where Vbi > Vbi .
estimates
the
intrinsic
device
built-in
voltage.
Therefore, VFB
bi
This anomaly in Vbi extraction by classical MS analysis is wellknown in the literature,28,29,31,32 but the difference for the
P3HT diode is dramatically accentuated due to high density of
deep level trap states.
The built-in voltage of a typical Schottky barrier generally is
dependent on the difference between the work function of the
metal (ΦAl) and the semiconductor’s Fermi level (i.e., Vbi =
HOMO − Ef − ΦAl). In P3HT, Ef ≈ 0.3 eV and HOMO ≈ 4.9
eV. Thus, the value of the extracted Vbi ≈ 1.3 eV suggests that
the metal (Al) work-function is modified significantly, and it is
pinned at the lowest unoccupied molecular orbital (LUMO)
level of the P3HT. This pinning of the metal work-function to
the molecular orbital of OSCs has been reported previously in
the literature,33,34 and this may be expected due to the thermal
evaporation-based deposition conditions used to generate the
diode structure.
For a highly conductive system, an accurate measurement of
the FB-CV characteristics is fundamentally limited by instrument precision. For high precision measurements, theoretical
analysis shows that the upper limit of the dissipation factor14,18
(D = 1/ωRC, R is the device resistance) should be in the range
of 10−20.14 Because the diode becomes very conductive in FB,
D increases sharply beyond the instrument precision, thereby
preventing accurate measurement of capacitance. In contrast,
the dissipation factor for organic diodes remains within the
accuracy limit even at a relatively high forward bias (the
measured D factors from several devices are plotted in Figure
S3 of the Supporting Information), because OSCs are
considerably less conductive due to poor charge carrier mobility
in the material. The results are therefore consistently reliable
and contain unambiguous signature of deep level traps. Because
D is inversely proportional to the measurement frequency (ω),
it is preferable to measure impedance at higher frequencies.
However, at very high frequencies, the traps cannot respond to
the applied field, and the oscillations of FB capacitance
observed in Figure 3a disappear (see Figure S3 of the
Supporting Information). Thus, a careful choice of the
measurement frequency (in this analysis, 200 Hz) is an
important prerequisite to capture the capacitance peaks at FBCV characteristics.
In addition to the dissipation factor, a few other experimental
precautions are necessary to extract meaningful information
from the measured impedance data. For example, the
capacitance must be extracted from the measured impedance
data by using the appropriate circuit model.35 In this analysis,
we use the hybrid circuit model (details given in Supporting
Information), which is shown to be appropriate for the entirety
of the frequency range.35 It is important to ensure that the
organic film thickness needs to be larger than the space charge
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region for the application of MS analysis.26 The thickness of the
P3HT film fabricated for this study is approximately 700 nm,
which is much larger than the space charge region (∼200 nm).
Finally, we emphasize that the technique is broadly applicable.
In Figure S2 in the Supporting Information, we show that the
approach has been used to identify shallow and deep traps in
MEH-PPV and CuPc, in addition to P3HT. For CuPc, it has
been suggested that the existence of deep traps depends on the
process conditions.24 This assertion is validated in Figure S2 as
well (Supporting Information). We speculate that the deep
traps are intrinsic to the semiconductor and the process
conditions, although the potential role of the contacts in
creating the deep traps cannot necessarily be ignored. To
identify the origin of the deep traps in the future, we anticipate
using the proposed technique to measure FB capacitance of a
series of test capacitors where a single OSC is sandwiched
between various contact metals, processed under nominally
identical conditions.
In summary, we have presented a new technique to
determine the energy levels of the deep defect states in the
OSCs. The technique is based on FB-CV measurements for an
organic photodiode. We have demonstrated that capacitance
oscillation in the FB-CV offers the signature of deep level traps,
the energy positions of which can be calculated from the FBCV data. The theory is verified by the FB-CV measurements of
a P3HT, MEH-PPV, and CuPc diodes, which confirms the
presence of deep level trap state; this also has been recently
demonstrated by SCL-IV measurement. Finally, we conclude
that the typical MS analysis in the presence of multiple defect
states underestimates the built-in voltages of the Schottky
junction. Therefore, the FB-CV measurement technique
provides a new approach to characterization of defect levels
in organic electronic devices, which are inaccessible to classical
impedance spectroscopy. As such, the approach should be very
useful for design and analysis of a wide variety of polymer
semiconductors for applications in flexible electronics.
■
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ASSOCIATED CONTENT
S Supporting Information
*
Detailed device fabrication and characterization, capacitance−
voltage response of CuPc, MEH-PPV, and P3HT samples,
capacitance characterization precautions, representative dark
current−voltage data of a P3HT sample, energy band and
charge distribution simulation, and characterization of interfacial vs bulk traps. This material is available free of charge via
the Internet at http://pubs.acs.org.
■
Article
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
Portions of this research were supported as part of the Center
for Re-Defining Photovoltaic Efficiency through Molecule Scale
Control, an Energy Frontier Research Center funded by the
U.S. Department of Energy (DOE), Office of Science, and
Office of Basic Energy Sciences (BES) under Award Number
DE-SC0001085. A.G.B. and B.W.B. gratefully acknowledge the
Air Force Office of Scientific Research (AFOSR) Young
Investigator Program (Grant Number: FA9550-12-1-0243;
Program Manager Dr. Charles Lee) for support to perform
device fabrication and characterization experiments.
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