|Título/s:||Electronic transport in sub-micron square area organic field-effect transistors|
|Fuente:||Applied Physics Letters. 102, 103301 (2013)|
|Autor/es:||Golmar, F.; Stoliar, P.; Gobbi, M.; Casanova, F.; Hueso, L. E.|
|Institución:||CIC nanoGUNE Consolider. Donostia – San Sebastián, ES |
INTI-Electrónica e Informática. Buenos Aires, AR
Laboratoire de Physique des Solids. LPS, CNRS. Orsay, FR
Escuela de Ciencia y Tecnología. Universidad Nacional de San Martín. ECyT, UNSAM. San Martín, Pcia. de Buenos Aires. AR
IKERBASQUE, Basque Foundation for Science. Bilbao, ES
|Editor:||American Institute of Physics|
|Palabras clave:||Transistores; Semiconductores; Nanoestructuras; Dispositivos electrónicos; Campo eléctrico|
| Ver+/- |
Electronic transport in sub-micron square area organic field-effect
F. Golmar, P. Stoliar, M. Gobbi, F. Casanova, and L. E. Hueso
Citation: Appl. Phys. Lett. 102, 103301 (2013); doi: 10.1063/1.4795014
View online: http://dx.doi.org/10.1063/1.4795014
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Electronic transport in sub-micron square area organic field-effect
F. Golmar,1,2 P. Stoliar,1,3,4 M. Gobbi,1 F. Casanova,1,5 and L. E. Hueso1,5,a)
1CIC nanoGUNE Consolider, Tolosa Hiribidea 76, 20018 Donostia-San Sebastian, Basque Country, Spain
2I.N.T.I.-CONICET, Av. Gral. Paz 5445, Ed. 42, B1650JKA, San Martın, Bs As, Argentina
3LPS, CNRS UMR 8502, Universite Paris Sud, 91405 Orsay, France
4ECyT, Universidad Nacional de San Martın, 1650 San Martın, Argentina
5IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Basque Country, Spain
(Received 5 January 2013; accepted 26 February 2013; published online 12 March 2013)
Scaling down organic field effect transistors to channel areas well below the micron square could
improve positively its speed and integration capabilities. Here, we report a careful study of the
electronic carrier transport for such nanoscale devices. In particular, we explore the validity of
standard analysis for parameters extraction in this size regime. We also study the effect of the
large longitudinal electric field and fringe currents, especially their influence on the ON/OFF
ratio. VC 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4795014]
Organic semiconductors can be integrated as active
channels in field-effect transistors (FETs), mostly with
the objective of producing low-cost or flexible electronic
applications.1–8 In the scientific literature, organic FETs
(OFETs) are devices whose channel lengths typically range
from the millimeter down to the micrometer level and very
commonly have interdigitated electrodes. These geometries
are necessary for producing a large, easily measurable, out-
put current since organic semiconductors have very low car-
rier density. Operative frequencies for these OFETs are also
limited to the kHz regime,9,10 due to the relatively low car-
rier mobility of the semiconductor channels (rarely much in
excess of 1 cm2/Vs (Refs. 3, 6, and 11)). In this scenario,
miniaturization and improvement of OFETs well down into
the sub-micrometer regime are very much sough-after tech-
nological improvement. Recent reports using organic cir-
cuits show that even a relatively modest improvement in
size and speed would be highly desirable for practical appli-
cations.12,13 Shortening the channel length in OFETs leads
to an increase in switching speed, since this parameter is
roughly inversely proportional to the square of the channel
length.9 Moreover, smaller devices with active areas below
100 nm2 could be integrated at a higher density, increasing
the overall functionality of a circuit per unit area. From
another perspective, sub-100 nm2 devices are going to be
most likely constituted by one single crystalline grain of the
organic material, so the undesirable role of defects and grain
boundaries on the electronic carrier transport will be
removed or at least greatly decreased.14–16
However, all these possible advantages are countered by
several problems. In nanometer-sized OFETs, transport is
commonly dominated by the contact resistance rather than
by the bulk of the organic material.17–19 In addition, reducing
the organic semiconductor area in an OFET generally leads
to a significant increase of the strength of the longitudinal
electric field along the channel and to significant fringe
currents.20–23 In this operational condition, the standard for-
mulas for studying carrier transport in OFETs do not longer
apply and consequently, the parameters extracted from them
In this letter, we present pentacene-based OFETs with
channel areas much below the lm2 in which spurious effects
in the carrier transport cannot be neglected. In this context,
we propose a method for calculating a corrective form-factor
for the standard expressions generally applied to transport in
OFETs. The use of such corrective factor allows us to extract
relevant physical parameters that are not correct without this
adjustment, such as the field effect mobility, the intrinsic
conductivity of the channel, and the ON/OFF ratio.
For our experiments, we fabricated bottom-gate, bot-
tom-contact OFETs with the geometry presented in Fig. 1(a).
Channel lengths (L) from 320 nm down to 120 nm were used
in this study. The metal contacts (palladium: 20 nm thick)
were defined by e-beam lithography (EBL) and lift-off on
highly doped p-type Si substrates that act as a common gate.
Channel widths were kept constant for the drain (W1:
100 nm) and source (W2: 500 nm). Different widths of the
electrodes were used for making our transistors geometry as
general as possible. The gate dielectric is a 150-nm-thick
thermally grown SiO2 layer. Pentacene was deposited by
organic-molecular beam deposition (OMBD) in UHV condi-
tions (base pressure <1 109 mbar; evaporation pressure
<1 108 mbar). Pentacene thickness was 58 nm, deposited
(through a shadow mask) at a rate of 1 nm/min on substrates
kept at room temperature and without primer. It is widely
accepted that, in general, both using a primer for the gate
dielectric, and functionalizing the channel electrodes largely
improve the response of organic transistors.17 Nevertheless,
here we choose to keep our devices as simple as possible for
studying the effect of the channel area reduction. Fig. 1(b)
shows a scanning electron microscopy (SEM) image of one
of the devices. The electrical measurements were performed
in a LakeShore probe station under vacuum (105 mbar) and
in the dark. We used two Source-Measure Units (SMUs) of a
Keithley 4200 Semiconductor Characterization System with
sub-femto preamplifiers for supplying the gate voltage (VGS)
and the channel bias voltage (VDS). Both the gate current
(IGS) and the drain current (IDS) were measured, but only thea)Electronic mail: email@example.com.
0003-6951/2013/102(10)/103301/5/$30.00 VC 2013 American Institute of Physics102, 103301-1
APPLIED PHYSICS LETTERS 102, 103301 (2013)
latter is reported here. The gate current was constantly moni-
tored to ensure that there was no significant leak through the
gate. The organic semiconductor morphology was checked
by means of atomic force microscopy (AFM, inset in
Fig. 1(c)). The pentacene films present pyramidal grains with
a characteristic size of 300 nm, as derived from the power
spectral density analysis (PSD) (Fig. 1(c)).24
In Fig. 2(a), we show the representation of IDS as a func-
tion of VDS for a transistor with a channel length of 260 nm.
Curves for other channel lengths are analogous and are not
shown. Nanoscale devices typically show current-voltage
curves with a linear behaviour at low source-drain bias, a
clear saturation at large source-drain voltages and very good
modulation for different gate voltages. These curves com-
pare favourably with those of transistors with micrometre
length channels widely available in the literature (see Refs.
6, 11, and references therein).
The modulation of the current in the semiconducting
channel is clear in the transfer characteristics, in which we
plot IDS versus VGS (see Fig. 2(c) for transistors with differ-
ent channel lengths). As expected,25 the ON/OFF ratio is
reduced with decreasing channel length, moving from more
than four orders of magnitude for a 320 nm channel to less
than one for transistors with 120 nm channels. Similar tran-
sistors with micrometric channel have ON/OFF ratios of six
orders of magnitude.26 It is also evident from the transfer
characteristics that the nanosized transistors do not switch
off completely, having a relatively large IDS,OFF current
(Fig. 2(b)). This is a usual feature for devices similar to those
reported here (see Ref. 25 and references therein). Transfer
characteristics are particularly useful for the extraction of the
For the sake of clarity, we must specify the criteria fol-
lowed in all the discussion. We consider the transistors to be
in OFF state when the positive gate bias stops modulating
the drain current; above L¼ 300 nm, the OFF current was
found to be below the sensitivity of the instrument. The ON
state is considered in the linear regime (jVGS-VTj< jVDSj),
where VT is the threshold voltage or voltage below which the
transistor is in OFF state. In both cases, we are at the limit of
the region for which the gradual channel approximation
holds and the devices present little or no short channel
effects, i.e., the transverse electric field generated by the gate
bias is larger than the longitudinal electric field generated by
the channel bias, and hereafter simply referred to as E.28,29
We first analyze the transistors in the OFF state.
Representative curves showing a linear relationship between
IDS,OFF (extracted from the transfer characteristics) and VDS
for different channel lengths are presented in Fig. 2(b). For
the geometries used here, the total current flowing through the
channel is larger than the values which would be expected by
considering the infinite-parallel-plate approximation. In the
literature, these extra currents are commonly referred to as
fringe currents.22,30 A form-factor that accounts for this differ-
ence in current can be numerically computed for our specific
FIG. 1. (a) Scheme of the nanometric OFET showing the nominal dimen-
sions as defined by electron-beam lithography. This specific geometry is
characterized by three parameters: the channel length (L) and the width of
the source (W1) and drain (W2) electrodes. (b) SEM image of fabricated me-
tallic electrodes, showing a nanogap. (c) PSD of an AFM image of a penta-
cene film. From the PSD, the typical grain size can be inferred. The inset
shows the AFM image of pentacene.
FIG. 2. (a) Source-drain current (IDS) as a function of source-drain voltage bias (VDS) represented for different gate-source (VGS) voltages. The main panel
shows the clear tendency to saturation of the current-voltage curves for relatively low voltage bias of around 15 V. The inset is a magnification of the main
panel for small source-drain voltages (VDS< 0.2 V). In this inset, the linear regime in the source-drain current is more evident. (b) Source-drain leakage current
(IDS,OFF) as a function of the channel bias normalized by L. (c) Transfer curves or representation of the source-drain current (IDS) as a function of gate-source
(VGS) for different channel lengths.
103301-2 Golmar et al. Appl. Phys. Lett. 102, 103301 (2013)
transistor geometry. This form factor kFF is the ratio between
the conductance G of a conductor with the shape proposed in
Fig. 1(a) and the ideal conductance calculated in the parallel-
plate-approximation with distance between the electrodes L
and width W1 (see supplemental material)37
kFFðLÞ ¼ Gproposed shapeðL;W1;W2 ¼ 5W1ÞGinfinite-parallel-plate approximationðL;W1Þ : (1)
Fig. 3 shows the computed potential distributions in the chan-
nel and the values obtained for kFF as a function of the chan-
nel lengths. Then, we express the linear behavior of IDS,OFF in
terms of a ohmic conductivity of the channel when the device
is in the OFF state, rOFF, by correcting the standard formula
for the conductivity of a homogeneous media by kFF as
IDS;OFF ¼ kFF VDS rOFF
; L < 300 nm; (2)
where t is the effective thickness of the semiconductor layer.
Note that our calculation of the electrostatic potential, as the
experimental results shown above, is as general as possible
since we consider two metallic electrodes with different
widths, W1 and W2¼ 5 W1. In the case of a more conven-
tional geometry with W1¼W2¼ 100 nm and L¼ 220 nm, the
calculation method leads to a kFF value of 3.43. In the
extreme case in which W/L tends to infinite, the fringe cur-
rent contribution is negligible and kFF tends to 1.
Following the characterization of the transistors in the
OFF state, we can proceed with the study of the device in the
ON state. The standard expression for long-channel crystal-
line OFETs in the linear regime has to be modified consider-
ing three different assumptions:28,31,32 first, it has to account
for the lack of validity of the infinite-parallel-plate approxi-
mation previously mentioned; second, the field-effect mobil-
ity should be corrected by the longitudinal electric field;20,21
third, the introduction of IOFF as an offset. We then propose
the following equation:
lCiðVGS VTÞVDS þ IDS;OFF; VGS VT > VDS;
where VT is the threshold voltage and Ci the dielectric
capacitance of the gate per unit area. The mobility
l ¼ l0FET expðb0
p Þ accounts for the Frenkel-Poole
dependence on the longitudinal channel electric field, being b0
the temperature-corrected field-dependent coefficient and
l0FET the zero field mobility.
The introduction of kFF must be supported by a linear de-
pendence of IDS vs. VDS. This is experimentally observed in
the low VDS region of the output characteristics presented in
the inset of Fig. 2(a). Also, a set of mathematical considera-
tions support this procedure.33,34 Besides, the carrier density
in the accumulation layer (formed by the gate bias in the ON
state) decays in the regions of the pentacene film relatively far
(in terms of L) from the most active part of the channel. This
would confine the extension of the fringe currents. The longer
current paths, therefore with lower net contribution, would be
modified with respect to the OFF state and require higher
order corrections in the kFF. In this work, we neglect this
effect. Note that kFF is a function of L and IDS,OFF is a func-
tion of VDS, even if here we are not making it explicit.
Once we have the expression for the IDS, we can differ-
entiate it in VGS and operate accordingly to obtain
kFFl0FET exp b0
where the left-hand side resembles the standard procedure
for extracting the field-effect mobility from the linear
region of the transfer characteristics.21,27 In order to obtain
FIG. 3. (a)-(c) Color-code representation of the electrostatic potential between
the source and drain electrodes, as calculated from the Laplace equation. In
the figure, which represents different channel lengths, it is clear how the small
channel length to channel width ratio distorts the electrostatic potential distri-
bution. The fringe current is, therefore, affected in a similar fashion following
the electrostatic potential. (d) Form factor KFF as a function of the transistor
channel length. The specific values represented in the figure arise from the
exact calculation of the current in the transistor geometry used in this manu-
script and cannot be readily extrapolated to other geometries.
FIG. 4. Procedure to extract the zero field mobility. (a) Slope of the transfer
characteristic (lkFF ¼ dIDS=dVGSðW1CiVDSÞ1L in log scale) as a function of
the applied voltage to the semiconducting channel. The extrapolation of the
curve allows the extraction of the uncorrected zero-field mobility (kFFl0FET).
(b) Zero-field mobility (l0FET) as a function of the organic transistor channel
length. For comparison, also kFFl0FET and kFFl are plotted.
103301-3 Golmar et al. Appl. Phys. Lett. 102, 103301 (2013)
the zero-bias field-effect mobility, we proceed in three
steps; first, we extract the slope from the linear region of
the transfer characteristics at several bias voltages; second,
l0FET kFF is obtained from the linear regression in the plot
ln½dIDS=dVGSðW1CiVDSÞ1L ¼ f ð
p Þ (Fig. 4(a)); and
third, each value is normalized by the proper value of kFF
for each specific L (Fig. 4(b)).
This procedure allows us to extract the real values of the
zero-field mobility, dealing with the fringe current contribu-
tion that is generally overlooked when extracting organic
semiconductor mobility values (see, for example, the values
listed in Ref. 25). For the sake of comparison, in Fig. 4(b), we
represent the corrected zero-field mobility values together
with those values that would be obtained without taking into
account the size and shape of the metal electrodes via the
form-factor kFF. With the proposed procedure, the mobility
values found (around 0.2 cm2/Vs) are consistent with the liter-
ature reports for the materials and fabrication techniques used
here. Even if the overall correction does not exceed one order
of magnitude, in our specific case, the uncorrected values are
in excess of 1 cm2/Vs and unrealistic for the materials and
fabrication methods reported here.11,24,35,36 Mobilities of the
order of 0.01 cm2/Vs were measured in transistors with inter-
digitated geometries and channel lengths of 2 lm, fabricated
simultaneously on the same substrate and following the same
procedures.21 For our nanometer-sized transistors, the depend-
ence of the zero-field mobility with L may be affected by two
factors; the detrimental effect of having an L comparable to
(or smaller than) the extension of the contact region,17 and the
beneficial effect of a channel with few grain boundaries. We
hypotheses that the scaling between these two factors results
in the slowly increasing zero-field mobility we experimentally
measure below 300 nm. For micrometer-sized channels, the
grain boundaries contribution is predominant.
Combining Eqs. (2) and (3), we can derive an expression
that describes the switching capabilities of our devices below
L¼ 300 nm, in the range for which our devices present a
strong decrease of the ON/OFF ratio (see Fig. 2(b))
ðVGS VTÞ: (5)
Equation (5) emphasizes the detrimental effect of the OFF
intrinsic conductivity of the organic film, while highlighting
the possibility of improving the ON/OFF ratio by reducing
the organic film effective thickness or by increasing the
dielectric capacitance of the gate. Beside these well-known
conclusions, we remark two further points which go beyond
the standard treatment applied to OFETs. First, the form-
factor kFF is not present in Eq. (5) indicating that the fringe
currents do not play a relevant role in the ON/OFF ratio.
This conclusion is actually true only when the device is in
the linear regime, since otherwise a corrective factor differ-
ent from kFF has to be introduced in Eq. (3) that will not
compensate the kFF in the IDS,OFF. Second, due to the
Frenkel-Poole-like dependence of the mobility, increasing
VDS (moderately) improves the ON/OFF ratio. This conclu-
sion has a limited practical use since VDS cannot be increased
beyond the linear regime, but puts in solid ground the
influence of the activation of the mobility at high longitudi-
nal electric fields.
In conclusion, we have reported pentacene field-effect
transistors with channel lengths in the order of 100 nm and
channel areas much below the lm2. The devices presented
show current-voltage curves with a linear behaviour at low
source-drain bias, a clear saturation at large source-drain vol-
tages and very good modulation for different gate voltages.
Transfer characteristics, in which the source-drain current is
represented as a function of the gate voltage, are typically
used for extracting the carrier mobility in the semiconducting
channel. Here, we show how the equations commonly
employed need to be treated carefully since the total current
flowing in a transistor is affected by potentially large fringe
currents if the channel width to channel length ratio (W/L)
approaches 1. We have computed the influence of the fringe
current in the mobility via a form-factor, which depends on
the specific geometry of the transistor channel. Finally, we
propose a general expression for the ON/OFF ratio in this
kind of devices.
This work was supported by the European Union 7th
Framework Programme under the European Research Council
Grant Agreement No. 257654 (SPINTROS), NMP project
(NMP3-SL-2011-263104- HINTS), and the Marie Curie
Actions (PIRG06-GA-2009-25647, ITAMOSCINOM). This
research was also partially funded by the Spanish Ministry of
Science and Education under Project No. MAT2009-08494 as
well as by the Basque Government Program PI2011-1.
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numerical procedures to calculate kFF.
103301-5 Golmar et al. Appl. Phys. Lett. 102, 103301 (2013)