Analytical Model of Apparent Threshold Voltage Lowering Induced by Contact Resistance in Amorphous Silicon Thin Film Transistors

Abstract

In this paper, we have shown that in a-Si TFT's the apparent threshold voltage extracted by conventional methods is lowered by the presence of the source/drain contact resistance, especially at short channel lengths and the analytical model presented to explain this effect is in good agreement with the experimental data. This model is particularly useful for AMOLED applications where the contact resistance has a crucial role in determining the driving current and thus the brightness of the pixels. In this abstract, we (i) show that this series resistance causes a large lowering of the "apparent" threshold voltage when it is extracted by conventional methods, and (ii) develop an analytical model to explain this effect. The model is supported by experimental data at different channel lengths and series resistances.

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Analytical Model of Apparent Threshold Voltage Lowering Induced by Contact Resistance
in Amorphous Silicon Thin Film Transistors

Bahman Hekmatshoar, Ke Long*, Sigurd Wagner and James C. Sturm

Princeton Institute for the Science and Technology of Materials (PRISM), Department of Electrical Engineering,
Princeton University, Princeton, NJ 08544
*Present address: Flexible Display Center, Arizona State University, Tempe, AZ 85284
Email: hekmat@princeton.edu

The interest in amorphous Si (a-Si) thin-film transistors (TFT’s) has increased recently due to active matrix
organic light emitting diode (AMOLED) display applications. Unlike active matrix liquid crystal display
(AMLCD) applications where the TFT only charges a capacitor, the DC driving requirement in AMOLED’s
makes the source/drain series resistance and modeling of current in saturation very important. It is well-known
from Si VLSI MOS technology that the presence of the drain/source contact resistance lowers the driving
current and as a result the “apparent” mobility extracted from the electrical characteristics is lower than the
“true” mobility especially at short channel lengths [1]. Amorphous Si TFT’s have a much larger series
resistance than VLSI FET’s because in addition to the metal/n+ contact, a-Si which is a low conductivity
material also contributes to the contact resistance. This is because in the TFT structure, the metal/n+ contact is
on top of the a-Si film while the channel is at the bottom. In this abstract, we (i) show that this series resistance
causes a large lowering of the “apparent” threshold voltage when it is extracted by conventional methods, and
(ii) develop an analytical model to explain this effect. The model is supported by experimental data at different
channel lengths and series resistances.

Conventionally, the apparent mobility and threshold voltage of a FET are extracted by plotting the
square root of the saturation current versus the gate voltage and a least square fit (LSF) calculation is
performed to approximate the square root of the drain current with a straight line. Fig. 1 shows that the values
of apparent threshold voltage extracted by this method are lower at shorter channel lengths and higher contact
resistances. To explain this behavior, we first assume that the contact resistance in a-Si TFT’s is a constant
voltage-invariant resistance as in MOSFET’s. Also, in our model, we assume that a-Si TFT’s are described by
MOS I-V characteristics, which is a relatively good approximation for hydrogenated a-Si TFT’s. As shown in
Fig. 2, an LSF to the saturation regime of the MOS-based characteristic results in an apparent threshold
voltage and mobility which are lower than their true values. However, the actual a-Si TFT problem is more
complicated, since the contact resistance is not constant, and has a gate-voltage dependent series component
that results from the presence of a-Si beneath the metallurgical junction [2] as shown in Fig. 3 for a typical
inverted-staggered a-Si TFT. The extracted values of contact resistance for our test TFT’s are plotted in Fig. 4.
It is observed that both components of the contact resistance increase with decreasing the overlap between the
gate and drain/source. By direct application of the MOS equation (the model given in Fig. 2) it can be shown
that the gate-voltage dependent component of the contact resistance lowers the apparent mobility but does not
change the apparent threshold voltage. By adding this effect, the apparent mobility and threshold voltage can
be evaluated analytically. This model is given in Fig. 5 and compared with the experimental I-V curves for two
different contact resistance values. Fig. 6 shows the variation of the apparent threshold voltage as a function of
contact resistance for different channel lengths. In Fig. 7, the model is compared with the experimental I-V
curves to show that changing the drain bias changes the extracted apparent threshold voltage and mobility by
changing the saturation to linear transition point and therefore changing the range over which the LSF is
calculated. Finally, the variation of the apparent threshold voltage is plotted versus the channel length in Fig. 8
and compared to the experimental data at two different drain biases.

In summary, we have shown that in a-Si TFT’s the apparent threshold voltage extracted by
conventional methods is lowered by the presence of the source/drain contact resistance, especially at short
channel lengths and the analytical model presented to explain this effect is in good agreement with the
experimental data. This model is particularly useful for AMOLED applications where the contact resistance
has a crucial role in determining the driving current and thus the brightness of the pixels.

[1] P. R. Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits, 3rd Edition, John Wiley & Sons, New York, NY 1993
[2] S. Luan and G. W. Neudeck, J. Appl. Phys. vol. 72, no. 2, July 1992, pp. 766-772
1-4244-1102-5/07/$25.00 ©2007 IEEE 131

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010 20304050607080 90 100
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
L (µm)
VTa (V)
{
{
dov=10µm
dov=1µm
data
data
model
model
W=80µm
VT=2.0V
µn=1.0cm2/Vs
VDS=20V

Fig.1. Apparent threshold voltage (VTa) extracted from
test TFT’s using the conventional method, for several
channel lengths (L) and two gate to drain/source
overlap lengths, dov (see Fig. 3). The shorter dov
corresponds to the higher contact resistance. It is
observed that VTa is lower at shorter L and also lower
for higher contact resistance (shorter dov).
VTa=1.0V
0246810
VGS (V)
1214 1618 2022
0
1
2
3
4
5
6
7
8
slope:
µna= 0.4cm2/Vs
LSF
RC = 500KΩ
ID,sat (µA)1/2
1000
RC = 100KΩ
RC = 50KΩ
RC = 0W/L=80µm/5µm
VT=2.0V
µn=1.0 cm2/Vs
VDS=20V
RC = ∞
Linear
Saturation

G
SD
RC
RC
Sint
Dint
Model:

I


−=
−=
satDC DSnti
=
DS
satD
I
C
R
GSnti GS
VV
IRVV
,,
,,
2
ID, sat
L
W
W
CkVV(k
oxnnTnti GSnsatD
µ
2
1
,)
2
,,
=−
L
CkVV(kI
oxna naTa GSnaLSF
µ
2
1
,)
2
=−=

Fig.2. Plot of the square root of the saturation current in a FET for several values of
contact resistance RC, when the current is calculated by a simple FET model plus RC at
the source and drain. Using a least square fit (LSF) to estimate the current results in an
apparent threshold voltage (and mobility) that is lower than its true value, i.e. VTa < VT
(and µna < µn), as shown for RC = 500KΩ. The LSF is calculated (and the result is valid)
only where VGS is low enough (for a given VDS) to ensure saturation. The saturation to
linear transition point occurs at VDS, int = VGS, int – VT.
Source / Drain
Gate
Undoped
a-Si
Gate
Nitride
n+ a-Si
Substrate
metal
i-Si
channel
extension
RC
metal/n+/a-Si



dov
Source / Drain
G
SD
RC (VGS)
RC (VGD)
Model
R0
()
TGSoxn
C
VVWC
RR
−
+=
µ
0
0
l
Sint
Dint

Fig.3. Cross-section of an inverted-staggered a-Si TFT. The contact resistance RC
is composed of a metal/n+Si/a-Si metallurgical junction and an a-Si region beneath
that junction. The latter component makes RC gate-voltage dependent [2].
{
R0 = 122KΩ
= 2.9µm
{
0l
510 15 20
100
200
300
400
500
600
700
800
RC (KΩ)
VGS (V)
dov=1µm
W/L = 80µm/5µm
VT = 2.0V
µn = 1.0 cm2/Vs
0 l
dov=2µm
R0 = 95KΩ
= 2.4µm
{
0 l
dov=10µm
dov=5µm
R0 = 69KΩ
= 1.9µm
{
0 l
R0 = 56KΩ
= 1.7µm
model
data

Fig.4. Gate voltage dependence of the contact resistance RC
for various gate to drain/source overlap dov. The RC values
are extracted from the I-V curve of the test TFTs following
the approach introduced in [2].

Fig.5. Comparison of our LSF-based model with the experimental data. The apparent
threshold voltage VTa (and µna) is lower for smaller dov (higher R0).The model
predicts that VTa is not affected by the gate-voltage dependent component of RC
(though µna is). In the model, Vf is the gate voltage at which the saturation to linear
transition occurs and α is the ratio R0 ID, sat / (VGS –VT) at the transition point, VGS = Vf .
7
VT = 2V
µn=1cm2/Vs
dov=1µm
1000
036912 15
0
1
2
3
4
5
3
VT = 2 V
VTa,10µm
VTa,1µm
ID,sat (µA)1/2
1000
VGS (V)
W/L=80µm/5µm
µn=1cm2/Vs
VT=2V
RC = 0
{
{
dov=10µm
dov=1µm
data
model
data
model
VDS=20V

()











+




−
−=






−+
×












−
×++=
n
TTa
nna
kR
VV
L
L
0
2
2
0
0
/
2
6
1
2 . 01
1
1/2
l
1
115
16
111/
α
α
α
α
α
αµµ
l







−+
++=
−
−−+
=
0
0
0
0
8
181
2
)(4
1)(41
Rk
RV
n
k
V
VV
VVR
VVR
n
DS
DS
Tf
Tf
Tf
α


0.8
103
1.0
1.2
1.4
1.6
1.8
2.0
VTa (V)
104
105
106
R0 (Ω)
L=80µm
L=20µm
L=40µm
L=10µm
L=5µm
VT=2.0 V
W=80µm
VDS=20V
model
data
dov=1µm
dov=2µm
dov=5µm
dov=10µm

Fig.6. Variation of VTa versus R0 for several values of
channel length, L. The extracted VTa is lower at shorter L
and higher R0, as predicted by the model.
02468101214 161820
0
1
2
3
4
5
6
Saturation
(VDS=5V)
Saturation
(VDS=10V)
Saturation
(VDS=20V)
VDS=20V
VDS=10V
VDS= 5V
{
data
24
model
W/L=80µm/5µm
VTa5
VTa10
VTa20
}
ID,sat (µA)1/2
VGS (V)

Fig.7. Variation of VTa for different drain biases. Reducing VDS shrinks the
saturation regime over which the LSF is calculated. The extracted VTa
(and µna) increases with reducing the drain bias as predicted by the model.

0.8
1.0
1.2
1.4
1.6
1.8
2.0
1
10100
VTa (V)
L (µm)
VDS=20V
VDS=10V
{
{
dov=10µm
dov=1µm
data
data
model
model
W=80µm
VT=2.0V
µn=1.0cm2/Vs

Fig.8. Variation of VTa versus L for two dov and VDS values and
comparison with the model. The extracted VTa is lower at shorter L,
higher R0 and higher VDS, as predicted by the model.
1-4244-1102-5/07/$25.00 ©2007 IEEE 132