Unification of the hole transport in polymeric field-effect transistors and light-emitting diodes.

Abstract

A systematic study of the hole mobility in hole-only diodes and field-effect transistors based on poly(2-methoxy-5-(3('),7(')-dimethyloctyloxy)-p-phenylene vinylene) and on amorphous poly(3-hexyl thiophene) has been performed as a function of temperature and applied bias. The experimental hole mobilities extracted from both types of devices, although based on a single polymeric semiconductor, can differ by 3 orders of magnitude. We demonstrate that this apparent discrepancy originates from the strong dependence of the hole mobility on the charge carrier density in disordered semiconducting polymers.

Full text

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Unification of the HoleTransport in Polymeric Field-Effect Transistors
and Light-Emitting Diodes
C. Tanase,1E.J. Meijer,2,3P.W. M. Blom,1and D. M. de Leeuw2
1Materials Science Centre and DPI, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
2Philips Research Laboratories, 5656 AA Eindhoven, The Netherlands
3Delft University of Technology, Faculty of Applied Sciences, Department of NanoScience,
Lorentzweg 1, 2628 CJ Delft, The Netherlands
(Received 26 February 2003; published 19 November 2003)
A systematic study of the hole mobility in hole-only diodes and field-effect transistors based on
poly?2-methoxy-5-(30;70-dimethyloctyloxy)-p-phenylene vinylene? and on amorphous poly(3-hexyl
thiophene) has been performed as a function of temperature and applied bias. The experimental hole
mobilities extracted from both types of devices, although based on a single polymeric semiconductor,
can differ by 3 orders of magnitude.We demonstrate that this apparent discrepancy originates from the
strong dependence of the hole mobility on the charge carrier density in disordered semiconducting
polymers.
DOI: 10.1103/PhysRevLett.91.216601PACS numbers: 72.80.Le, 73.61.Ph
In recent years solution-processible conjugated poly-
mers have had a significant impact in optoelectronic ap-
plications such as light-emitting diodes (PLEDs) [1] and
metal-insulator-semiconductor
(FETs) [2]. After the discovery of electroluminescence
in poly(p-phenylene vinylene) (PPV) and its derivatives,
attention has been focused on studying their electrical
transport properties [3,4]. One of the most widely studied
materials
poly?2-methoxy-5-(30;70-dimethyloctyloxy)-p-phenylene
vinylene? (OC1C10-PPV). It has been demonstrated that
the hole current in OC1C10-PLEDs is space-charge lim-
ited (SCL) and that it is governed by hole mobility, ?h,
which is dependent on both the temperature, T, and the
applied electric field, E [4]. At low electric fields, and at
room temperature, the hole mobility amounts to 5 ?
10?7cm2=Vs [4]. Its field and temperature dependencies
are well described by a 3D transport model based on
hopping in a correlated Gaussian disordered system [5,6]:
field-effecttransistors
is
? ? ?1exp
8
<
:?
?3?DOS
5kBT
?2
? 00:78
???DOS
kBT
?3=2?2
????????????
eaE
?DOS
s
9
=
;;
(1)
with ?1the zero-field mobility in the limit T ! 1,
?DOSthe width of the Gaussian density of states (DOS),
and a the intersite spacing. The hole mobility of
OC1C10-PPV is characterized by a ?DOS? 0:112 eV
and a ? 1:2–1:4 nm [7].
One of the first and most widely studied solution-
processed conjugated polymers in organic field-effect
transistors is poly(3-hexyl thiophene) (P3HT) [8].
Typical field-effect mobilities, ?FE, for spin-coated
amorphous
10?5–10?4cm2=Vs, whereas by ordering the polymer
in the film the field-effect mobility increased to about
10?1cm2=Vs [9]. The transfer characteristics of amor-
phous P3HT have been modeled as a function of tem-
perature and gate bias with variable range hopping in an
exponential density of states [10]. The value for ?FEat
room temperature amounts to 6 ? 10?4cm2=Vs for a
gate voltage Vg? ?19 V.
Apparently, the solution-processible conjugated poly-
mers developed for PLEDs and FETs have fundamentally
different properties. The reported hole mobilities differ
typically by more than 3 orders of magnitude [4,10].
Theoretically, the field- and temperature-dependent hole
mobility in PLED materials is described by hopping in a
Gaussian DOS, whereas for FET materials the tempera-
ture and gate bias dependencies are described by hopping
in an exponential DOS. It has recently been derived that
in disordered semiconductors the Einstein relation and,
thus, the charge transport properties are dependent on the
charge carrier density [11]. However, the dependence of
the hole mobility on charge carrier density has not been
experimentally addressed so far. In this Letter a unified
picture of the hole transport in the two classes of devices
is presented. We are able to establish the dependence of
the hole mobility in OC1C10-PPV and P3HT on charge
carrier density and to correlate the hole mobility obtained
fromdiodesandfield-effect transistors. It isdemonstrated
that the strong increase of the hole mobility, for both
materials, with increasing hole density is responsible for
the observed large mobility differences obtained from the
hole-only diodes and the field-effect transistors.
Although OC1C10-PPV and P3HT have often been
studied indiodes and field-effect transistors, respectively,
the field-effect mobility of OC1C10-PPV and the hole
mobility of P3HT in SCL sandwiched diodes have not
P3HT films are intherange of
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yet been determined. In the present study OC1C10-PPV
is used as an active semiconductor in a field-effect tran-
sistor, and current density versus voltage (J-V) mea-
surements have been performed on a P3HT-based diode.
On top of a highly doped n??-Si substrate (gate elec-
trode) a 200 nm thin film of SiO2was thermally grown
and used as the gate dielectric. Two gold electrodes
were evaporated onto the insulator to form the source
and drain contacts. The channel width, W, is 2500 ?m,
and the channel length, L, typically 10 ?m. The tran-
sistor is finished by spin coating the OC1C10-PPV layer
from toluene. The transfer characteristics have been
measured in the dark, in the linear operating regime of
the transistor, by using a drain voltage Vd? ?0:1 V,
which is much smaller than the applied gate voltage
(?1 to ?20 V). In the diode structures P3HT is spin
coated on top of a patterned indium tin oxide bottom
electrode used as an anode. The thickness of the polymer
layer amounts to 95 nm. As a top electrode an evaporated
gold contact is used.
The experimental transfer characteristics of the
OC1C10-PPVFETare presented for the temperature range
from 206 to 293 K in Fig. 1. From the transfer character-
istics the experimental field-effect mobility is directly
calculated by differentiating the channel current Idwith
respect to the gate voltage Vg[2]:
?FE?Vg? ?@Id
@Vg
L
WCiVd
:
(2)
A field-effect mobility of 4:7 ? 10?4cm2=Vs for
OC1C10-PPV at Vg? ?19 V at room temperature has
been obtained. Surprisingly, this value for the field-
effect mobility is approximately 3 orders of magnitude
larger thanthe mobility value determined from hole-only
diodes [4].
We establish a relation between the experimental field-
effect mobility and the volume charge density in the
transistor. The transfer characteristics have been mea-
sured in the linear regime using a drain bias much lower
than the gate bias. Hence the gradual channel approxima-
tion can be applied in which the distribution of charge
carriers needs to be described only in the direction per-
pendicular to the gate dielectric/semiconductor inter-
face, x. Using Ci? 17 nF=cm2and a dielectric constant
of the semiconductor of about 3, the charge carriers at the
interface p?0? can be calculated as a function of gate bias
[12]. Furthermore, from Eq. (2) the experimental field-
effect mobility is also determined as a function of gate
bias. In Fig. 2 the resulting dependence of the field-effect
mobility [Eq. (2)] on charge carrier density p?0? is pre-
sented in the range of 2 ? 1017to 2:9 ? 1019cm?3
(circles) for the OC1C10-PPV FET. It is observed that
in this range the field-effect mobility increases from
1 ? 10?5to 4:7 ? 10?4cm2=Vs.
In order to compare the field-effect mobility with that
derived from hole-only diodes, the transfer characteris-
tics are measured as a function of temperature and inter-
pretedwiththevariable rangehopping model proposedby
Vissenberg and Matters [13]. This hopping percolation
model in an exponential density of states yields an ex-
pression for the conductivity as a function of the charge
carrier density and the temperature.The conductivity can
be converted into charge carrier mobility by dividing by
ep, where e is the elementary charge and p the charge
carrier density:
?FE?p? ??0
e
??T0=T?4sin??T=T0?
?2??3Bc
?T0=TpT0=T?1;
(3)
where ?0is a prefactor for the conductivity, ??1is the
effective overlap parameter between localized states, T0
is a measure of the width of the exponential density of
FIG. 1.
effect transistor. Solid lines indicate the calculated drain cur-
rents. Inset: The chemical structure of OC1C10-PPV.
216601-2
Drain current vs gate voltage of OC1C10-PPV field-
FIG. 2.
and field-effect transistor for P3HT and OC1C10-PPV [Eq. (2)
(symbols) and Eq. (3) (lines)]. The dashed line is a guide to the
eye. Inset: The activation energy of the mobility in the
OC1C10-PPV based FET as a function of gate voltage (tri-
angles), together with the activation energy of 0.46 eV as
obtained from the diode at low densities (square).
Mobility as a function of hole density p in a diode
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states, and Bcis the critical number for the onset of
percolation.
The experimental transfer characteristics can now be
described with the variable rate hopping model by using
the equation Id? WVd=LRl
Using this equation the transfer characteristics could be
fitted with a single set of values for the three parameters
T0, ?0, ??1, namely T0? 540 K, ?0? 3:1 ? 107S=m,
and ??1? 0:14 nm (solid lines in Fig. 1). For Bca value
of 2.8 was used [14]. Inserting the obtained T0, ?0, and
??1in Eq. (3) provides the calculated power-law depen-
dence ?FE? pT0=T?1, as indicated by the solid line in
Fig. 2. This calculated ?FEvs p behavior is in good
agreement with the data obtained directly from Eq. (2)
(circles), demonstrating that the model is consistent with
the experiment.The same analysis has been applied to the
transfer characteristics of P3HT-FETs, which could be
fitted with T0? 425 K, ?0? 1:6 ? 106S=m, and ??1?
0:16 nm [10]. The resulting ? vs p relation for P3HT as
determined directly from ?FE?Vg? [Eq. (2)] (squares) and
from ?FE?p? [Eq. (3)] (solid line) is also plotted in Fig. 2
in a charge carrier density range of 2 ? 1018to 3:5 ?
1019cm?3. Surprisingly, Fig. 2 shows that when mea-
sured at the same high values of charge carrier density
per unit volume the field-effect mobility of OC1C10-PPV
is nearly equal to the field-effect mobility of P3HT.
Furthermore, the dependence of the field-effect mobility
on charge carrier density is stronger for OC1C10-PPV due
to a larger T0, which is indicative of a larger energetic
disorder as compared to P3HT.
In order to determine the hole mobility of P3HTat low
carrier densities J-V measurements have been performed
for a P3HT-based hole-only diode in a temperature range
of 215 to 294 K (see Fig. 3). The current density at room
temperature dependsquadratically on the appliedvoltage,
which is indicative of space-charge limited transport.The
derived hole mobility at room temperature is 2:8 ?
10?5cm2=Vs, which is more than an order of magnitude
lower than what is obtained in P3HT FETs (see Fig. 2).
The transport model of hopping in a correlated Gaussian
disordered system well describes the field and tempera-
ture dependence ofa P3HT hole-onlydiode (solid linesin
Fig. 3). Using Eq. (1) the width of the Gaussian energy
distribution ?DOS? 0:098 eV has been determined.
In the temperature range 255–294 K the current den-
sity of the P3HTdiode depends quadratically on the volt-
age for applied voltages up to 3 V. As a result, the hole
mobility is constant for low fields, and thus also indepen-
dent of the hole density.The lowest charge carrier density
in a space-charge limited diode is found at the noninject-
ing contact and is given by pL? 0:75?"0"rV=eL2?,
where L represents the thickness of the polymer, and
"0"ris the permittivity of the polymer [15]. The volt-
age range applied of 0.1 to 3 V corresponds to hole
densities of 1:4 ? 1015to 4:1 ? 1016cm?3. We note
that for voltages higher than 3 V (carrier densities
0ep?x???p?x??dx, where l
represents the thickness of the semiconducting film [13].
>4:1 ? 1016cm?3) the carrier density dependence of
?hcannot be discriminated from the field dependence
of ?h, due to the fact that in a space-charge limited
diode both carrier density and field are simultane-
ously increased. For an OC1C10-PPV hole-only device
with a thickness of 700 nm the mobility of ?h? 5 ?
10?7cm2=Vswasconstant fromanappliedvoltageof 1V
up to 10 Vat room temperature [4], which corresponds to
hole densities of 2:5 ? 1014to 2:5 ? 1015cm?3. The ex-
perimental mobilities from the hole-only diode measure-
ments and the field-effect mobilities from the transistors
are presented together in Fig. 2, for both OC1C10-PPV
and P3HT in the charge carrier density range of
1014–1019cm?3. Combination of the results from the
diode and field-effect measurements shows that typically
the hole mobility is constant for charge carrier densities
<1016cm?3and increases with a power law for densities
>1016cm?3. The large differences in mobility values
obtained from diodes and FETs, based on a single semi-
conducting polymer, are direct results of the large differ-
ences in charge densities in these devices. It should be
noted that in OC1C10-PPV the optical properties exhibit a
significant anisotropy, pointing to a preferential align-
ment of the chains in the plane of the film [16]. A possible
anisotropy in the charge transport properties would ob-
scure a direct comparison between diodes and FETs. A
strong indication for the absence of anisotropy is shown
in the inset of Fig. 2; the activation energy of the mobility,
Ea, which directly reflects the amount of disorder
[Eq. (1)], is plotted as a function of gate voltage from
?1 to ?19 V. Extrapolating towards zero gate voltage
yields an Eaof 0.46 eV , exactly equal to the activation
energy as obtained from the diode measurements.
The question that remains is whether the mobility
description at low carrier densities, using a Gaussian
FIG. 3.
characteristics of a P3HT hole-only diode, with thickness
95 nm and active area 10 mm2. The solid lines represent the
prediction from the space-charged limited model including the
field-dependent mobility [Eq. (1)]. Inset: The chemical struc-
ture of P3HT.
Temperature dependent current density vs voltage
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DOS, is fundamentally different from the mobility de-
scription at high carrier densities, which employs an
exponential DOS. In Figs. 4(a) and 4(b) the obtained
Gaussian DOS is plotted as a function of energy for
OC1C10-PPV and P3HT, respectively. For the total num-
ber of states per unit volume Ntwe have used a value of
3 ? 1020cm?3for both OC1C10-PPV and P3HT, which
corresponds to 1=a3(a ? 1:4 nm). Additionally, the ex-
ponential DOS of OC1C10-PPV and P3HT as obtained
from the FET characteristics are shown, which are de-
scribed by the characteristic temperature T0. Both Gauss-
ian and exponential DOS are presented in Fig. 4 in a
semilogarithmic plot. For the charge carrier density
range in which the OC1C10-PPV FEToperates the Fermi
level in the Gaussian, as indicated by the vertical dashed
lines, ranges from 0.4 to 0.16 eVwith respect to the center
of the Gaussian DOS. From Fig. 4(a) it appears that in
this energy range the exponential distribution with T0?
540 K is a good approximation of the Gaussian DOS with
?DOS? 0:112 eV.Similar behavior is observed forP3HT
in Fig. 4(b), in which the exponential distribution with
T0? 425 K approximates well the Gaussian DOS with
?DOS? 0:098 eVintheenergy rangefrom0.27to 0.13eV.
This unifies the two models, in the sense that the expo-
nential DOS accurately describes the Gaussian DOS in
the energy range in which the field-effect transistors
operate. Consequently, the field, temperature, and density
dependencies of the hole mobility in these disordered
conjugated polymers are unified in one single charge
transport model.
In conclusion, the large mobility differences reported
for conjugated polymers used in PLEDs (OC1C10-PPV)
and FETs (P3HT) have been shown to originate from the
strong dependence of the mobility on the charge carrier
density. The exponential density of states, which consis-
tently describes the field-effect measurements, is shown
to be a good approximation of the tail states of the
Gaussian in the energy range where the Fermi level is
varied.
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FIG. 4.
from the hole-only diode analysis (dashed lines) and the
exponential DOS as obtained from the field-effect transistors
(solid lines) as a function of energy for (a) OC1C10-PPV and
(b) P3HT. For both semiconductors the exponential density of
states is found to be an accurate approximation of the Gaussian
density of states, in the energy range in which the transistors
operate.
The Gaussian density of states (DOS), as obtained
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