University of Groningen
Ambipolar charge transport in organic field-effect transistors
Smits, ECP; Anthopoulos, TD; Setayesh, S; van Veenendaal, E; Coehoorn, R; Blom, PWM;
de Boer, B; de Leeuw, DM; Anthopoulos, Thomas D.
Published in:
Physical Review. B: Condensed Matter and Materials Physics
DOI:
10.1103/PhysRevB.73.205316
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Smits, ECP., Anthopoulos, TD., Setayesh, S., van Veenendaal, E., Coehoorn, R., Blom, PWM., de Boer,
B., de Leeuw, DM., & Anthopoulos, T. D. (2006). Ambipolar charge transport in organic field-effect
transistors.
Physical Review. B: Condensed Matter and Materials Physics
,
73
(20), [205316].
https://doi.org/10.1103/PhysRevB.73.205316
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Ambipolar charge transport in organic field-effect transistors
Edsger C. P. Smits,
1,2,3,
*
Thomas D. Anthopoulos,
4
Sepas Setayesh,
2
Erik van Veenendaal,
5
Reinder Coehoorn,
2
Paul W. M. Blom,
1
Bert de Boer,
1
and Dago M. de Leeuw
2
1
Molecular Electronics, Material Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
2
Philips Research Laboratories High Tech Campus 4 (WAG 11) 5656 AE Eindhoven, The Netherlands
3
Dutch Polymer Institute, Nijenborgh 4, 9747 AG Groningen, The Netherlands
4
Department of Physics, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom
5
Polymer Vision, Philips Technology Incubator, High Tech Campus 48, 5656 AE Eindhoven, The Netherlands
共Received 26 January 2006; published 9 May 2006
兲
A model describing charge transport in disordered ambipolar organic field-effect transistors is presented. The
basis of this model is the variable-range hopping in an exponential density of states developed for disordered
unipolar organic transistors. We show that the model can be used to calculate all regimes in unipolar as well as
ambipolar organic transistors, by applying it to experimental data obtained from ambipolar organic transistors
based on a narrow-gap organic molecule. The threshold voltage was determined independently from metal
insulator semiconductor diode measurements. An excellent agreement between theory and experiment is ob-
served over a wide range of biasing regimes and temperatures.
DOI: 10.1103/PhysRevB.73.205316 PACS number共s兲: 73.50.⫺h, 73.61.Ph, 73.43.Cd, 73.40.Qv
I. INTRODUCTION
Organic thin-film field-effect transistors 共FETs兲 have been
studied extensively over the past decade, and tremendous
progress has been achieved in device performance
1,2
Organic
FETs have generally been used as unipolar devices, and this
has limited the design of integrated circuits to unipolar logic.
From a performance point of view, complementary logic is
crucial. The advantages are low-power dissipation, good
noise margin and robust operation.
The first organic complementary logic circuits, 48-stage
shift registers, were created by combining discrete p-channel
and n-channel transistors.
3,4
Two different semiconductors
were used, one for the p-channel and one for the n-channel.
Both materials had to be deposited and patterned locally and
sequentially. With such an approach it is difficult to minimize
the parameter spread and match the n- and p-channel
transconductances. A step forward for the development of
complimentary logic is the realization of ambipolar transis-
tors based on a single semiconducting film and a single type
of electrode.
Numerous groups have now demonstrated ambipolar
transistors,
5–10
discrete inverters,
11–13
and simple circuits.
14
An analytical expression for the charge transport that can be
incorporated in circuit simulators is required for the design
of complementary-like logic. Here we present a model that
can be used to describe current transport in unipolar as well
as ambipolar transistors. The model predictions are tested
against experimental data obtained from ambipolar organic
transistors based on a narrow-gap organic molecule.
II. EXPERIMENTAL
Field-effect transistors were fabricated on a doped 共n
++
兲
silicon wafer acting as the gate electrode with a 200-nm-
thick layer of thermally grown silicon dioxide as gate dielec-
tric. The surface of the SiO
2
insulator was subsequently pas-
sivated by a hexamethyldisilazane 共HMDS兲 treatment. Gold
source and drain contacts were defined using standard pho-
tolithographic techniques. Titanium was used as an adhesion
layer. To minimize in-plane parasitic leakage currents, a cir-
cular device geometry was used.
15
The channel width of the
ring transistors was 1000
m and the channel length varied
from 2.5 to 40
m. Electrical characterization of the transis-
tors was performed using an Agilent 4155C Semiconductor
Parameter Analyzer under vacuum 共10
−7
mbar兲 and in dark.
Metal insulator semiconductor 共MIS兲 diodes were made
starting from the same oxidized silicon wafer as used for the
transistor test devices. The semiconductor was spin-coated
and subsequently 50 nm of gold was evaporated through a
shadow mask as the top electrode. The area of the top elec-
trode was varied from 0.07 to 0.38 cm
2
. The impedance mea-
surements were performed with an Schlumberger 1260 Im-
pedance Gain-Phase Analyzer under vacuum 共10
−7
mbar兲
and in dark.
16
As an ambipolar semiconductor, a small band-gap organic
molecule, nickel-dithiolene 共NiDT兲关see Fig. 1共a兲兴, was used.
This material was obtained from Sensient GmbH, Germany.
Cyclic voltammetry measurements in solution with Ag/Ag
+
as the reference electrode in acetonitrile reveal a narrow en-
ergy gap of 0.9 eV with the highest occupied molecular or-
bital 共HOMO兲 and lowest unoccupied molecular orbital
共LUMO兲 levels at 5.2 and 4.3 eV, respectively 关see Fig.
1共b兲兴. This value is in good agreement with the optical band
gap obtained from the solid-state absorption spectrum, where
a maximum absorption around a wavelength of 1160 nm
with the onset at around 1450 nm is observed. The Fermi
level of gold 共approximately 4.8 eV兲 is in between the
HOMO and LUMO energy levels of NiDT. This implies that
the barrier for injection of holes in the HOMO and for elec-
trons in the LUMO is expected to be smaller than 0.5 eV.
These small injection barriers explain the occurrence of am-
bipolar transport in the field-effect transistors.
Nickel dithiolene was found to be highly soluble in a
range of chlorinated organic solvents. Thin films were spun
from a solution of 5 mg/mL of NiDT in chloroform at
PHYSICAL REVIEW B 73, 205316 共2006兲
1098-0121/2006/73共20兲/205316共9兲 ©2006 The American Physical Society205316-1
500 rpm. The devices were then annealed at 60 °C for 1 h
under vacuum.
The transistors function in air and light. When stored in
ambient conditions, no sign of electrical degradation is ob-
served for the hole as well as the electron current for days.
However, the hysteresis between backward and forward
scans increases upon exposure to air. Therefore, electrical
characterization of both transistors and MIS diodes was per-
formed in dark and vacuum.
III. CHARGE TRANSPORT MODELING
Due to disorder and variation of interaction energies, thin
films of disordered semiconductors do not have two delocal-
ized energy HOMO and LUMO bands separated by an en-
ergy gap. Instead, a spatial and energetic spread of charge
transport sites will be present, often approximated in shape
by a Gaussian density of states 共DOS兲.
17
The use of that
approximation is supported by the observation of Gaussian-
shaped absorption spectra of disordered polymers. Further-
more, for disordered small-molecule systems, the electro-
static field from a random distribution of static or induced
dipoles leads to a Gaussian DOS function.
18
For a system
with both negligible background doping and at typical gate-
induced carrier densities, the carrier mobility resulting from
hopping in a Gaussian DOS can be approximated by the
mobility resulting from hopping in an exponential DOS.
19–21
The often observed almost linear relationship 共on a double-
log scale兲 between the field-effect mobility and the carrier
concentration at the gate-dielectric/semiconductor interface
21
suggests that an exponential DOS is nevertheless a good ap-
proximation for the DOS in the case of intermediate and high
carrier concentrations.
19
Therefore, our analyses of the I共V兲
characteristics of unipolar and ambipolar organic transistors
will be based on the mobility in an exponential DOS. In the
literature, such a dependency was also found for amorphous
silicon.
22,23
Electrical transport is described by hopping between the
localized states. With increasing carrier density, the filling of
tail states of the DOS increases. The charge carriers have
more transport states available at higher energy and thus also
the average mobility increases. For bulk conduction, a trans-
port model has been derived based on variable range hopping
and percolation.
19
This model gives an analytical description
for the bulk conductivity as a function of carrier density. In
an organic field-effect transistor 共OFET兲 in the linear regime,
where V
d
→ 0, the potential in the channel is to a good ap-
proximation uniform between source and drain. The model
combined with an exponential DOS was used to calculate the
current as a function of gate bias. For the linear regime, an
accurate description of the transport as a function of the tem-
perature and gate biasing has been demonstrated.
19–21,24
Here, we show that the formalism can be applied to a wide
range of bias conditions. This will be shown for both unipo-
lar and ambipolar OFETs.
A schematic layout of a field-effect transistor is presented
in Fig. 1共c兲, where L is the channel length, W is the channel
width in the y direction and t is the semiconductor thickness.
The x direction is the direction between source and drain and
the z direction is the direction perpendicular to the channel.
For the derivation of the current voltage I共V兲 characteristics,
we ignored the source and drain contact resistances. Further-
more, we consider long channels so that short channel effects
can be disregarded and contact resistance effects are mini-
malized. Finally, the gradual channel approximation is used.
The electric field in the z direction perpendicular to the film
is much larger than in the parallel x direction. In this way, the
transport can be treated independently in both directions.
First, we calculate the sheet conductance as a function of
local effective gate potential in the channel. The charge-
carrier density in the sheet as a function of effective gate
potential and position z can be solved analytically for an
exponential DOS. We substitute the relation between bulk
conductivity and charge-carrier density. The sheet conduc-
tance then follows from integration over the charge-carrier
FIG. 1. 共a兲 Molecular structure of nickel dithiolene 共bis关4-dimethylaminodithiobenzyl兴-nickel兲. 共b兲 Band diagam of nickel dithiolene. 共c兲
Schematics of a bottom gate and contact transistor similar to the one used for the experiments. The x, y, and z directions are indicated to
visualize the directions referred to in the text. 共d兲 Schematic representation of a MIS diode used in the experiments.
SMITS et al. PHYSICAL REVIEW B 73, 205316 共2006兲
205316-2
density profile. The source-drain current as a function of gate
bias is then obtained by integrating the sheet conductances
along the channel.
A. Unipolar transport
The drain bias, V
d
, gives rise to a nonzero value of the
local electrochemical potential at each point in the channel,
V
x
. The difference between this electrochemical potential and
the gate bias, V
g
, is the effective gate potential, V
eff
. This
effective potential determines the amount of induced charge
at position x. The effective potential is given by
V
eff
= V
g
− V
t
− V
x
, 共1兲
where V
t
is the threshold voltage.
20
The correction for the
threshold voltage is included to account for the presence of
trapped and static charges. To be specific, we focus here on
electron transport so that V
eff
⬎0 in order to have accumula-
tion. At each point x, the charge-carrier density decreases
with increasing distance from the insulator/semiconductor
interface, z. This charge distribution depends on the effective
gate potential. For an exponential DOS, this charge distribu-
tion, n共z兲, has been calculated from the Poisson equation
26
and is given by
n共z兲 =
2k
B
T
0
s
0
q
2
共z + z
0
兲
2
共2兲
with
z
0
=
2k
B
T
0
s
0
qC
i
V
eff
, 共3兲
where k
B
T
0
is the width of the exponential DOS, k
B
is the
Boltzmann constant,
0
is the relative permittivity of
vacuum,
s
is the dielectric constant of the semiconductor, C
i
is the gate capacitance per unit area, and q is the electron
charge. Equations 共2兲 and 共3兲 show that the carrier density
decreases with distance from the interface. Calculations of
the effective accumulation layer thickness, z
0
, show it is typi-
cally at most a few nanometers.
From percolation theory, the following expression for the
conductivity has been derived as a function of the carrier
density and temperature:
19
共n兲 =
0
冢
冉
T
0
T
冊
4
sin
冉
T
T
0
冊
共
2
␣
兲
3
B
c
冣
T
0
/T
n
T
0
/T
, 共4兲
where
0
is a conductivity prefactor,
␣
−1
is the wave function
overlap localization length, B
c
is the critical number for the
onset of percolation 共⬃2.8 for 3D amorphous systems兲, and
T is the temperature. A superlinear increase in conductivity is
observed for an exponential DOS with charge density.
19
This
expression holds for disordered semiconductors where trans-
port occurs solely through localized states and at tempera-
tures T well below T
0
.
For each value of the local effective potential, V
eff
, sub-
stitution of Eqs. 共2兲 and 共3兲 in Eq. 共4兲 gives the conductivity,
共z兲, as a function of the distance z from the interface. Inte-
grating this conductivity,
共z兲, over the layer thickness then
yields the sheet conductance, G
sh
共V
eff
兲,
G
sh
共V
eff
兲 =
冕
0
t
共z兲dz ⬵
T
2T
0
− T
q
FE
共V
eff
兲C
i
V
eff
共5兲
with
FE
共V
eff
兲 =
0
q
冢
冉
T
0
T
冊
4
sin
冉
T
T
0
冊
共2
␣
兲
3
B
c
冣
T
0
/T
冉
共C
i
V
eff
兲
2
2k
b
T
0
S
0
冊
共T
0
/T兲−1
,
共6兲
where
FE
共V
eff
兲 is the local field-effect mobility.
19
The right-
hand part of Eq. 共5兲 has been obtained assuming that the
carrier density is negligible at the top of the semiconductor
film, so that effectively t =⬁. The source-drain current I
sd
,
which is constant within the channel 共independent of the
position x兲, is given by
I
sd
=−WG
sh
共V
eff
兲
V
eff
共x兲
x
. 共7兲
Integrating over the length of the transistor and replacing V
eff
by V
g
−V
t
−V
x
gives
I
sd
=−
W
L
冕
0
V
d
G
sh
共V
g
− V
t
− V
x
兲dV
x
. 共8兲
The source-drain current then follows immediately by inte-
grating the sheet conductance, Eq. 共5兲, over the electro-
chemical potential between the source and drain bias, which
yields
I
sd
=
␥
W
L
T
2T
0
T
2T
0
− T
关共V
g
− V
t
兲
2T
0
/T
− 共V
g
− V
t
− V
d
兲
2T
0
/T
兴
共9兲
for V
g
−V
t
ⱖV
d
with
␥
=
0
q
冢
冉
T
0
T
冊
4
sin
冉
T
T
0
冊
共2
␣
兲
3
B
c
冣
T
0
/T
冉
1
2k
b
T
0
S
0
冊
共T
0
/T兲−1
C
i
共2T
0
/T兲−1
.
共10兲
We note that Eq. 共9兲 holds for V
g
−V
t
⬎V
d
. When V
g
−V
t
⬍V
d
, the transistor is operated in saturation. When V
d
is
exactly equal to V
g
−V
t
, the effective potential at the drain
contact is zero, V
eff
=0. Hence at the drain contact there is no
accumulation of charge carriers. In general, the channel is
pinched off when V
eff
is zero. This occurs when the electro-
chemical potential is equal to the applied gate bias. With
increasing drain bias, the position at which the pinchoff oc-
curs moves into the channel from the drain in the direction of
the source contact. When pinchoff occur, the accumulation
length is smaller than the channel length. We ignore this
channel shortening in the equations. Moreover, as is known
from the literature, the resistance of the depleted part of the
channel can be disregarded.
27
With these assumptions, the
source-drain current in saturation is derived from Eq. 共8兲 by
AMBIPOLAR CHARGE TRANSPORT IN ORGANIC¼ PHYSICAL REVIEW B 73, 205316 共2006兲
205316-3
replacing V
d
with V
g
−V
t
. The saturated source-drain current
is given by
I
sd
sat
= I
sd
共V
d
= V
g
− V
t
兲 =
␥
W
L
T
2T
0
T
2T
0
− T
共V
g
− V
t
兲
2T
0
/T
共11兲
for V
g
−V
t
⬍V
d
. A more general expression for the source-
drain current has been derived by Calvetti et al.
25
The deri-
vation included the diffusion current and the effect of a finite
semiconductor thickness, t. However, we find that our more
simplified approach provides a fully adequate description for
the transport regimes investigated in this paper. The deriva-
tion presented here yields the analytical expression Eq. 共8兲,
which will be crucial for deriving the ambipolar transport
model further on.
In the limit of a negligible drain bias 共V
d
兲, I
sd
is a linear
function of V
d
, Eq. 共8兲, and is consistent with results for this
regime given in the literature.
19,20
In the derivation, we used
a gate bias-dependent mobility. For most inorganic devices
and some organic single crystals, the mobility is constant as
a function of gate bias.
28
This corresponds to taking T=T
0
.
The classical metal oxide semiconductor field-effect transis-
tor 共MOSFET兲 equations are then obtained,
29
although the
mobility obtained from the percolation theory, Eq. 共6兲,isnot
expected to hold for this limit. The classical MOSFET equa-
tions have been used for modeling of 共ambipolar兲
OFETs.
27,30
The compact modeling given by Eqs. 共9兲–共11兲 is
valid for T ⬍T
0
. Several authors have proposed that for em-
pirically modeling OFETs, the same functional dependence
can be applied,
I
sd
= a关共V
g
− V
t
兲
b
− 共V
g
− V
t
− V
d
兲
b
兴共12兲
where a and b are fit constants.
31,32
Other authors have used
numerical simulations based on 共ambipolar兲 amorphous sili-
con theory
33
to model OFETs.
34
B. Ambipolar transport
Depending on the bias conditions, the current in an ambi-
polar transistor is due to electrons, holes, or both. The oper-
ating regimes are schematically presented in Fig. 2. For each
regime, the charge distribution in the channel and the output
curves are schematically given. When 兩V
g
−V
t
兩 ⬎ 兩V
d
兩 and
both are positive, the current is carried by electrons 共regime
1兲. The current as a function of bias voltages is then given by
Eq. 共9兲 as derived in the preceding section for a unipolar
electron-only transistor. Similarly, when 兩 V
g
−V
t
兩 ⬎ 兩V
d
兩 and
both are negative, the current is carried by holes 共regime 4兲.
The hole current as a function of bias voltage is given by the
same expression by replacing V
g
−V
t
by −V
g
+V
t
, V
d
by −V
d
,
and taking the source drain current to be negative. We note
that electrons transport through the unoccupied density of
states corresponding to the LUMO levels while the holes
transport through the occupied density of states correspond-
ing to the HOMO levels. This implies that for holes and
electrons, the parameters T
0
,
0
, and
␣
−1
are different. When
V
g
−V
t
is positive and V
d
theis negative 共regime 6兲, the ef-
fective gate potential is positive throughout the whole chan-
nel. The transistor operates as unipolar n-type transistor
where the source and drain are inverted. Therefore, the cur-
rent in regime 6 is given by Eq. 共9兲 in which V
g
is replaced
by V
g
−V
d
and V
d
is replaced by −V
d
, which gives Eq. 共9兲
again
I
sd
=
W
L
␥
e
T
2T
0,e
T
2T
0,e
− T
关共V
g
− V
t
兲
2T
0,e
/T
− 共V
g
− V
t
− V
d
兲
2T
0,e
/T
兴共13兲
for V
g
−V
t
⬍0.
Similarly, when V
g
−V
t
is negative and V
d
is positive 共re-
gime 3兲, the effective gate potential throughout the channel is
negative. The hole current is given by Eq. 共13兲 upon apply-
ing the appropriate substitutions. Ambipolarity can occur
when V
d
⬎V
g
−V
t
⬎0 共regime 2兲 and when V
d
⬍V
g
−V
t
⬍0
共regime 5兲. Under those bias conditions, a unipolar transistor
then operates in saturation. The channel is pinched off and
charges cannot be accumulated in the pinched off part of the
channel. In an ambipolar transistor, those bias conditions
give rise to a change of the sign of the effective gate poten-
tial at a certain position in the channel. Holes and electrons
are accumulated at opposite sides. A narrow transition re-
gion, which acts as a pn-junction, separates the accumulation
regions. We now develop a description of the charge trans-
port in this regime.
For simplicity, we assume bimolecular recombination of
electrons and holes with an infinite rate constant, and a con-
stant threshold voltage throughout the entire channel, i.e.,
equal threshold voltages in the electron and hole accumula-
tion region. For infinite recombination, electrons and holes
cannot pass each other without recombining. Therefore, re-
combination takes place at a single plane, x=x
0
, namely the
plane where the effective gate potential is zero. The ambipo-
lar transistor is then represented by a unipolar n-type transis-
FIG. 2. A sketch of all operating regimes for a typical ambipolar
transistor as a function of drain and gate biasing.
SMITS et al. PHYSICAL REVIEW B 73, 205316 共2006兲
205316-4
