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DOI: 10.1002/adfm.((please add manuscript number)) Determination of Threshold-Voltage Shifts in Organic Thin-Film Transistors due to Polarized Self-Assembled Monolayers at the Dielectric Surface** By Stefan Possanner, Karin Zojer, Peter Pacher, Egbert Zojer and Ferdinand Schürrer * [*] Prof. F. Schürrer, S. Possanner, K. Zojer
Institute of Theoretical and Computational Physics, Graz University of Technology Petersgasse 16, A-8010 Graz (Austria) E-mail: schuerrer@itp.tugraz.at
Prof. E. Zojer, P. Pacher
Institute of Solid State Physics, Graz University of Technology Petersgasse 16, A-8010 Graz (Austria)
[**] Supporting Information is available online from Wiley InterScience or from the author. Keywords: Organic Semiconductors, Transistors, Self-Assembled Monolayers, Thin Films
We simulate the hole transport in organic thin-film transistors (OTFTs) with dipole layers, i.e., self-
assembled monolayers (SAMs), at the semiconductor/dielectric interface by means of a two-
dimensional drift-diffusion model. Moreover, we analyze the simulated evolution of the electric
potential and the hole density with the help of Gauss law. By means the latter, simple expressions
for the shifts in the threshold voltage and the amount of accumulated charge in the channel are
derived. We demonstrate that the shift in the threshold voltage, that is equal to the potential drop
across the dipole layer, amounts to a few volts for realistically chosen intrinsic dipole moments of
corresponding SAM molecules. Thus, large threshold voltage shifts (> 45 eV) that were observed in
(SiO2/SAM/P3HT) OTFTs upon exposure to ammonia [P. Pacher et al., Adv. Mater., 2008, in
print] cannot be related to changes in dipole moments within a SAM. Furthermore, our simulations
reveal that the capacitance of the gate dielectric does not influence this shift, while it profoundly
influences the accumulated interface charge; thus, a decrease in the thickness of the gate oxide leads
to bigger drain currents. Based on the results of our simulations, we present criteria that any model
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has to fulfill in order to correctly describe the impact of interface dipole layers on the threshold
voltage.
1. Introduction
Over the past few years the organic semiconductor (OSC)/dielectric interface has been the subject
of numerous studies on the device performance of organic thin-film transistors (OTFTs). It is
known that organic transistors usually operate in accumulation mode and that charge transport takes
place mainly in the first few mono-layers of the OSC adjacent to the gate dielectric.[1,2] Therefore, it
appears that transistor performance is greatly influenced by the OSC/dielectric interface properties.
It was shown that the carrier mobility in polycrystalline materials such as pentacene strongly
depends on the morphology and the molecular ordering in the channel, which is governed by the
quality and the reactivity of the oxide surface.[3,4,5,6] Moreover, chemical reactions taking place at
the OSC/dielectric interface were reported to create/annihilate carrier trap states that can shift the
threshold-voltage by some 10 V,[7,8] or even lead to n-type conduction devices.[9] Yoon et al. have
presented a comprehensive experimental study on the correlation between the oxide surface
chemistry and the threshold-voltage, mobility, current on-off ratio and sub-threshold slope for
various p-type, n-type and ambipolar OTFTs.[10]
Recently, several groups reported that the electrical properties of organic transistors can be
controlled via self-assembled mono-layers (SAMs) with different functional groups that align on
the oxide surface. Pentacene as well as polymeric OTFTs with different organosilane-based SAMs
linked covalently to the SiO2 dielectric were investigated.[8,11,12,13] A significant dependence of the
threshold-voltage and the sub-threshold slope on the deposited SAM was observed. To give an
example of the typical behavior, the measured transfer characteristics of an OTFT made of spin-
coated poly(3-hexylthiophene) (P3HT) on an SiO2-dielectric with and without an organosilane-
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based SAM at the oxide surface is depicted in Figure 1 (data taken from Pacher et al.)[8]. The major
changes in the electrical characteristics are explained either by additional interface traps originating
from the interaction of the functional group with the OSC molecules, or by a change of the oxide
surface potential, caused by the intrinsic electric field of the organosilane layer, due to the uniform
arrangement of the dipole moments of the molecules in the SAM. It is known from simulation
studies that energetically distributed interface trap-states could be responsible for the observed
threshold-voltage shifts and changes in the sub-threshold slope.[14,15,16] By contrast, only
speculations exist regarding the possible magnitude of a threshold-voltage shift induced by a dipole
layer at the gate dielectric surface. Our goal is to clarify this situation by time-dependent numerical
simulation of the carrier transport in SAM-modulated OTFTs. We aim at reproducing the curves
from Figure 1, thereby defining possible parameter ranges for an interface dipole density and a
fixed surface charge density that could yield the observed changes. By checking on the evolution of
the electric potential from the case where mobile charges are completely absent (before injection) to
steady state, we are able to determine the threshold-voltage shifts due to dipole layers and fixed
charges at the OSC/dielectric interface from Gauss’ law. Besides, a relation between the upper
bound of accumulated charge in the channel and the gate voltage is obtained for both cases.
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2. Simulation model
The drift-diffusion model was shown to be well applicable to model the carrier transport in organic
devices.[2,14,15,16,18,19,20] In our approach, only p-type conduction is considered and electron transport
is assumed to be negligible. We simulate transistors made of wide band-gap materials with hole
injecting electrodes, i.e., the Fermi-level in the contacts is close to the highest occupied molecular
orbital (HOMO) of the OSC. Our drift-diffusion model is based on solving self-consistently a
system of three equations:
€
dpdt
+1e∇ ⋅ j+G − R = 0 (1)
€
j = epµ(p)∇ϕ − kBTµ(p)e
∇p (2)
€
∇ ⋅ ∇ εrϕ( )[ ] =eε0(NA − p + ntA ,occ − N fix ) (3)
Here, p is the hole density, j hole-current density, e elementary charge, G hole generation rate, R
hole recombination rate, µ(p) carrier concentration-dependent mobility, φ electric potential, kB
Boltzmann constant, T temperature, εr permittivity, ε0 dielectric constant, NA acceptor doping
density, ntA,occ density of occupied electron acceptor traps and Nfix is the density of permanent fixed
charges in the transistor. Equation (1) is the continuity equation for the hole density, (2) indicates
the drift-diffusion equation and the Poisson equation (3) governs the electric potential.
The numerical solution of the system (1)-(3) is computed on a two-dimensional grid with
appropriate geometry and boundary conditions. We focus on the top-contact transistor structure but
confirm our results to be valid for the bottom-contact design too. A schematic view of the
investigated top-contact geometry is depicted in Figure 2. We simulate either a two- or a three-
layer structure consisting of the organic semiconductor as the active material, a gate dielectric and
an optional polarized layer in between the two. Diriclet conditions are used at contact boundaries
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and zero-field Neumann conditions are applied at non-contact surfaces. The contact nodes are
assumed to be in thermal equilibrium, described by non-degenerate statistics, i.e., pcontact=NV exp(-
Δ/kBT), where NV is the effective density of states of the HOMO-level (monomer density) and Δ is
the hole injection barrier. The regions of the gate dielectric and the polarized layer are assumed to
be free of mobile charges. Additionally, no charge transfer is allowed from the organic
semiconductor to the adjacent region, which means that the equations (1) and (2) are solved in the
active domain only. The density of permanently occupied acceptor states NA is assumed to be 1016
cm-2, a value that was confirmed to be small enough not to cause depletion mode operation in the
regarded OTFT structures. The term Nfix in the Poisson equation allows us to place permanent fixed
charges anywhere in the device. The terms G and R in equation (1) together with the term ntA,occ in
equation (3) describe the dynamics of rechargeable, deep, acceptor-like electron traps. Details can
be found in the supporting information. In order to account for the peculiarities of charge transport
in organic materials we implement a carrier density dependent hole mobility. We use a model of
carriers hopping in a Gaussian density of states, elaborated by Pasveer et al.[21] Details are stated in
the supporting information.
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3. Results and discussion
3.1. Operation regimes of OTFTs
It is well known that organic transistors like the one described in Figure 2 work in p-accumulation
mode and that, in the gradual-channel approximation, the drain current ID (above threshold)
depends on the gate-source voltage VGS and the drain-source voltage VDS as[18]
€
ID =µWLCox (VGS −Vth −
VDS
2)VDS for VDS < VGS −Vth
µW2L
Cox (VGS −Vth )2 for VDS > VGS −Vth
(4)
where µ is a constant hole mobility, W channel width, L channel length, Cox=ε0εr/dox oxide
capacitance per unit area and Vth is the threshold-voltage. The first condition in (4) defines the linear
regime and the second one the saturation regime of OTFT-operation. These equations are widely
used by experimenters to obtain threshold voltages and carrier mobilities from measured transfer
characteristics (ID or ID1/2
vs. VGS at a fixed VDS). In an ideal p-accumulation device (no space
charges) with little unintentional acceptor doping (so that depletion operation is not possible), Vth
should in principle be the flat-band voltage VFB, that is the difference between the gate work
function and the HOMO-level of the OSC.[1] Applying VFB at the gate leads to a flat transport-level
and no channel is formed at the OSC/dielectric interface, i.e. the transistor is turned off. Possible
space charges and dipole layers at the OSC/dielectric interface will lead to a shift ΔVth of the
threshold voltage so that
€
Vth =VFB + ΔVth (5)
In order to determine the magnitude of such shifts we start with the investigation of the ideal case
ΔVth=0, i.e. no interface dipole layers and no permanent surface charge densities in the device. We
simulate a top-contact OTFT as depicted in Figure 2 with channel length L=10 µm, an organic layer
of thickness dosc=30 nm and a gate oxide with dox=100 nm. The hole-mobility is set to µ=4.0×10-4
cm2V-1s-1, which is a common value in polymeric organic materials. We chose the monomer density
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as the effective density of states, i.e. NV=2.0×1021 cm-3, and assume a hole-injection barrier of
Δ=0.1 eV between the contacts and the OSC. The flat-band voltage is set to zero, which in this case
leads to Vth=0. The dielectric constants of the OSC and the oxide are chosen as εr,osc=3.2 and
εr,ox=3.9, respectively. For all simulations we choose room temperature, T=298.15 K. The source
potential is set to VS=0 and the drain potential is held at VD=-20 V. The solutions of the Laplace
equation, i.e. (3) with the bracketed expression on the right-hand side being zero in the whole
device, are depicted for four different gate voltages in Figure 3. The images display the situation at
a time before charge carriers are injected into the device, i.e. shortly after setting the gate from flat-
band condition (0 V in this case) to the specific gate voltage. It is interesting to note that in all cases,
there is no electric field between source and drain at that stage. Instead, we find a large domain in
the active region (0<x<0.03 µm) where the potential is completely flat, thereafter referred to as the
zero-field domain. This is a consequence of the big aspect ratio of the regarded cross-section in
OTFTs, here L/d=10/0.13≈77. From figure 3d) we derive that the transistor is turned off when the
zero-field domain lies above the source potential, since then no holes can overcome the resulting
barrier and flow from source to drain. In the linear regime, depicted in 3a), charges will enter the
channel from both source and drain until a steady source-drain electric field has been established.
By contrast, in the saturation regime shown in 3b), the region under the drain contact immediately
gets depleted and charges are only injected from the source electrode. The steady state of the
electric potential and the hole density for both regimes is shown in Figure 4. The pinch-off
(depletion under the drain contact) in the saturation regime is clearly visible in the figures 4c) and
4d).
3.2 Fixed surface charges at the OSC/dielectric interface
In Figure 5 simulated transfer characteristics of the regarded transistor are displayed for different
permanent surface charge densities σif at the OSC/dielectric interface (x=x’ in figure 2). The
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simulations confirm the expressions (4) to be valid in principle, even though the macroscopic
mobility extracted from the slope of linear fits of ID or ID1/2 vs. VGS can differ from the microscopic
input mobility by about 20 %. We explain this by the omission of diffusion currents in the
derivation of the equations (4), but a sophisticated analysis is yet to be done. The threshold voltages
were determined in the saturation regime, as the intersection of a linear fit of ID1/2 vs. VGS with the
x-axis (indicated as the dashed line in figure 5). From figure 5 we obtain that permanent negative
interface charges have two effects: a) they shift the threshold voltage to positive values and b) they
increase the drain current in both the saturation and the linear regime. In order to understand this we
investigate the potential profile of the OTFT with σif=-6×1012 ecm-2 at VGS=0, depicted in Figure 6.
In the absence of mobile charges, the zero-field domain is found to be at a voltage that is different
from the one applied to the gate. We call it the effective gate voltage Veff. It can be derived from
Gauss’s law by taking into account that the displacement current D in the zero-field domain is
constant in the y-z-plane:
€
dDx
dx= ρ (6)
where Dx=εEx is the x-component of the displacement current and ρ is the charge density. Assuming
ρ=σif×δ(x-x’), where δ is the Dirac delta function and x’ is the position of the surface charge, and
integrating equation (6) over a small distance around x’, we obtain
€
Dox −Dosc =σ if (7)
Here, Dox and Dosc are the constant x-components of the displacement currents in the oxide and the
OSC, respectively. Since the simulation yields Dox=εox (VG-Veff)/dox in the oxide region and Dosc=0
in the zero-field domain due to the Neumann boundary condition at the transistor surface, we obtain
for the effective gate voltage
€
Veff =VG −σ if
Cox
(8)
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where Cox=εox/dox is the capacitance per unit area of the gate oxide. If VG is set to the flat-band
voltage, negative interface charges cause the transistor still to be on, because then, according to
equation (8), the zero-field domain is at a voltage below flat-band condition and charges are able to
enter the channel region from the source. The figures 4b) and 4d) reveal that the amount of
accumulated mobile charges at the OCS/dielectric interface reaches its maximum σmax under the
source contact. Above threshold, it is given by
€
σmax =VeffCox (9)
From the equations (8) and (9) we derive that, in case of permanent interface charges σif, the
occurring threshold voltage shift and the dependence of the maximally accumulated charges on the
gate voltage (above threshold) are described by
€
ΔVth = −σ if
Cox
(10)
€
σmax =VGCox −σ if (11)
The threshold voltage shifts predicted from equation (10) agree outstandingly well with the
simulated results from figure 5, as can be seen in Table 1. In organic transistors the magnitude of
fixed interface charges will in most cases not be constant, but will change with threshold voltage
due trapping/de-trapping of charge carriers into/from localized states in the transport gap. This
process and the meaning of equation (10) in this case will be addressed in another work.
3.3 Dipole layers at the OSC/dielectric interface
We simulate OTFTs with the same geometry and material parameters as in section 3.1, but now
assuming a polarized layer (e.g. a SAM) with different dipole densities γ at the OSC/dielectric
interface. The layer is realized by implementing two surface charge densities of the same magnitude
σ and opposite signs at x’ and x’’, respectively (see figure 2). The resulting dipole density γ=ddip×σ
is related to the dipole moment µdip of a single molecule of the SAM via
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€
γ = ddipσ =µdip
A (12)
where A is the area of a single molecule of the SAM. From equation (6), Gauss’ law, the potential
drop Δφdip over a dipole layer with a dipole density as in (12) and a permittivity εdip is calculated as
€
Δϕdip =ddipσεdip
=σCdip
(13)
where Cdip=εdip/ddip is the capacitance per unit area of the dipole layer. The simulations yield
threshold voltage shifts in very good agreement with the potential drop from equation (13), as is
demonstrated in Table 2. These results become obvious by examining the potential profile of an
OTFT with a dipole layer of γ=1.92×1016 Dcm-2 at the OSC/dielectric interface at VGS=0 in the
absence of mobile charges and in steady state, as depicted in Figure 7. The zero-field domain is
almost exactly at the potential Δφdip=31.4 V, calculated from equation (13), below the source
potential. Additionally, it is revealed that the accumulation of mobile charges at the interface does
not influence the potential drop over the dipole layer. The dependence of the maximally
accumulated interface charge σmax on the gate voltage can be derived from the curve at Δt=0.0 in
figure 8a). According to Gauss’ law, σmax relates to the interface potential V’ (above threshold) as
€
σmax =V '(Cosc + Cox ) (14)
where Cosc=εosc/dosc is the capacitance per unit area of the active organic layer. From Δφdip=V’’-V’
and V’Cosc=Dosc=Dox=(VG-V’’)Cox we derive that
€
V '= Cox
Cosc + Cox
(VG −Δϕdip ) (15)
By combining the equations (13), (14) and (15), we state that, in case of a SAM with a dipole
charge σSAM and a capacitance per unit area CSAM at the OSC/dielectric interface, the occurring
threshold voltage shift and the dependence of the maximally accumulated charges on the gate
voltage (above threshold) are described by
€
ΔVth =σ SAM
CSAM
(16)
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€
σmax = (VG −σ SAM
CSAM
)Cox (17)
where for σSAM, the dipole charge closer to the gate must be taken to yield the correct sign. In
contrast to the threshold voltage shift, the charge σmax and therefore the drain current do depend on
the oxide capacitance. This fact could be used in experiments to distinguish between influences of
dipole layers and surface charges on the electrical characteristics of an OTFT. Simulated transfer
characteristics of transistors with different oxide and organic layer thicknesses are displayed in
Figure 9. The relations (16) and (17) are confirmed.
3.4 Simulation of measured transfer characteristics
We aim at reproducing the experimental data from Pacher et al.,[8] displayed in figure 1. The
regarded top-contact OTFTs are made of 10 nm regioregular poly(3-hexylthiophene) (rr-P3HT) as
the active material deposited on an approximately 1 nm thick organosilane based SAM covalently
linked to 170 nm of SiO2 as the gate dielectric. The channel length was L=25 µm and the width was
W=7 mm. The other input parameters were chosen as in section 3.1, representing values describing
the above mentioned materials. The intrinsic dipole moments of organosilane molecules are known
to be of the order of some Debye. As was shown in the preceding section, this cannot be the reason
for the observed threshold voltage shift (see table 2).
In Figure 10 the result of a simulation with a constant mobility µ=4.0×10-4 cm2V-1s-1 and a
permanent negative interface charge σif=-5×1012 ecm-2 is displayed along with the experimental
curve and the most accurate simulation result. The latter is obtained by comprising rechargeable
acceptor interface trap states, which allows the regulation of the off-current and the sub-threshold
slope, and a hole density dependent mobility, which gives the non-linear ID(VG)-dependence in the
linear regime. The best value for the acceptor interface traps is a density of ntA=1014 cm-2 positioned
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at ΔE=0.25 eV above the HOMO level. In the Pasveer-model for the mobility, we chose µ0=1.0×10-
8 cm2V-1s-1 and the broadness of the Gaussian density of states to be ŝ=3.5 kBT.
4. Conclusions
We developed a drift-diffusion simulator for organic transistors and investigated the effect of
surface charges and dipole layers at the OSC/dielectric interface on the electrical characteristics of
OTFTs. The simulation results revealed that one can apply Gauss’ law to determine the occurring
threshold voltage shifts and the amount of accumulated charge at the interface. We found that the
dipole moments of SAM molecules are by far too small to cause the experimentally observed
threshold voltage shifts.
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_[1] T. Li, J. W. Balk, P. P. Ruden, I. H. Campbell, D. L. Smith, J. Appl. Phys., 2002, 91(7),
4312
_[2] M. A. Alam, A. Dodabalapur, M. R. Pinto, IEEE Trans. Electron. Devices, 1997, 44(8),
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_[15] Scheinert 1
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_[16] S. Scheinert, K. P. Pernstich, B. Batlogg, G. Paasch, J. Appl. Phys., 2007, 102, 104503-1
_[17] A. Rolland, J. Richard, J. P. Kleider, D. Mencaraglia, J. Electrochem. Soc., 1993, 140(12),
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_[22] M. Schwoerer, H. C. Wolf, in Organic Molecular Solids, Wiley-VCH, Weinheim, Germany
2007, Ch. 8.
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Figure 1. Semi-log plot of the measured drain current vs. gate voltage (transfer characteristics) of a P3HT-based OTFT with and without an organosilane-based SAM at the OSC/dielectric interface. Data is taken from Pacher et al.[8]
Figure 2. Schematic view of the simulated top-contact transistor structure. L is the channel length and d is the thickness of the device. Boundary conditions for the electric potential ϕ and the current density j are indicated. The regions of the gate dielectric and the polarized layer are assumed to be free of mobile charges. The latter is realized by two surface charge densities of opposite sign at x’ and x’’, respectively.
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Figure 3. Simulated electric potential profiles of a top-contact transistor with L=10 µm, dosc=30 nm and dox=100 nm before charge carriers (holes) enter the device (charge-neutrality). The source potential is set to 0 V and the drain potential to -20 V. The device is free of permanent space-charges. The flat-band voltage is assumed to be VFB=0. The gate potential is chosen to represent a) the linear regime (-50 V), b) the saturation regime (-12 V), c) the switch-on/off condition (0 V) and d) the off-state (+14 V).
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Figure 5. Square root and logarithm of the drain current vs. the gate voltage of the regarded top-contact OTFT with different permanent surface charge densities σif at the OSC/dielectric interface. The drain-source voltage is -20 V. The dashed line indicates the linear fit of the square root of the drain current in the saturation regime made to determine the threshold voltage.
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0246810121400.03
0.060.09
0.12
!5
!10
!20
!25
!15
0
source
y [µm]
gate die:ectric
drain
x [µm]
! [V
]
a= gate
>?@
interface
"t=0.0
0246810121400.03
0.060.09
0.12!20
!15
!10
!5
0
source
y [µm]
gate dielectric
drain
gate
x [µm]
! [V
]
b)
OSCinterface
steadC state
Figure 6. Simulated electric potential of the regarded top-contact OTFT with a fixed surface charge of σif=-6×1012 ecm-2 at the OSC/dieletric interface at zero gate voltage a) in absence of mobile charges and b) in steady state. The source potential is set to 0 V and the drain potential is -20 V.
0246810121400.03
0.060.09
0.12!30
!20
!10
0
10
20
source
y [µm]
3o4ari7ed 4ayer
gate die4ectric
gate
drain
x [µm]
! [V
]
a?
@AB
free of moDi4ecEarges
0246810121400.03
0.060.09
0.12!20
!10
0
10
20
30
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y [µm]
3ol5-i7ed l5:e-
d-5inx [µm]
! [V
]
=)
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ABC
ste5d:!st5te
Figure 7. Simulated electric potential a) in the absence of mobile charges and b) in steady state of the regarded top-contact OTFT with a polarized layer of γ=1.92×1016 Dcm-2 at the OSC/dieletric interface. Source and gate potentials are set to 0 V and the drain potential is -20 V. The layer was realized by two surface charge densities σ=±5.0×1014 ecm-2 of opposite sign at a distance ddip=0.8 nm.
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0 0.02 0.04 0.06 0.08 0.1 0.12
!(
0
(
10
1(
20
2(
30
x [µm]
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]
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gate
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0 0.02 0.04 0.06 0.08 0.1 0.12!30
!25
!20
!15
!10
!5
0
5
10
15
20
x [µm]
! [V
]
"t
y=6.75 µm
0.0, start of sim.9.1 µs16 µs130 µs, steady!state
transistorsurface
gate
AB
Figure 8. Simulated evolution of the electric potential perpendicular to the source-drain direction a) under the source contact and b) in the middle of the channel of the regarded OTFT with a dipole layer of γ=1.92×1016 Dcm-2 at the OSC/dieletric interface. Source and gate potentials are set to 0 V and the drain potential is -20 V.
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Figure 9. Simulated transfer characteristics of an OTFT with L=10 µm and a polarized layer with γ=8.1×1015 Dcm-2 at the OSC/dieletric interface for different thicknesses of the OSC and the gate oxide. We obtain that, in contrast to the drain current ID, the threshold voltage is independent of the oxide capacitance.
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!60 !50 !40 !30 !20 !10 0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
1.2
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!8
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log(
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best simulationexperiment
Figure 10. Comparison of the measured transfer characteristics of an OTFT with a SAM at the OSC/dielectric interface from Pacher et al. with simulation results.[8] The squared line is obtained with µ=4.0×10-4 cm2V-1s-1 and σif=-5×1012 ecm-2. The best simulation is obtained by comprising rechargeable interface traps and a carrier density dependent hole mobility. Table 1. Comparison of the threshold voltage shifts ΔVth_sim obtained from simulated transfer characteristics as shown in figure 5 with ΔVth_gau calculated from Equation (10) for an OTFT with dox=100 nm and εr,ox=3.9 and for different fixed surface charge densities σif at the OSC/dielectric interface. σif [1012 ecm-2] ΔVth_sim [V] ΔVth_gau [V]
+6.0 -28.6 -28.3
+4.0 -19.0 -18.9
+2.0 -9.3 -9.4
0.0 0.1 0.0
-2.0 9.5 9.4
-4.0 19.1 18.9
-6.0 28.7 28.3
Table 2. Comparison of the threshold voltage shifts ΔVth_sim obtained from simulated transfer characteristics of the regarded SAM-modulated OTFT with the potential drop Δφdip over a dipole density γ calculated from Equation (13). The absolute value of the corresponding dipole moment µdip of a single molecule of the layer is obtained from equation (12) assuming A=25 Å2. γ [1015 Dcm-2] ΙµdipΙ [D] Δφdip [V] ΔVth_sim [V]
19.19 47.97 -31.4 -31.1
3.84 9.59 -6.3 -6.2
1.92 4.80 -3.1 -3.0
-1.92 4.80 3.1 3.2
-3.84 9.59 6.3 6.3
-19.19 47.97 31.4 31.6
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The table of contents entry should be fifty to sixty words long, written in the present tense, and refer to the chosen figure. Keyword (see list) C. Author-Two, D. E. F. Author-Three, A. B. Corresponding Author*((same order as byline))<B>…<B> Title ((no stars)) ToC figure ((55 mm broad, 50 mm high, or 110 mm broad, 20 mm high)) Column Title: First author et al./Short title
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