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Compact Modeling Compact Modeling Approaches for Organic and Approaches for Organic and Oxide Thin Film TransistorsOxide Thin Film Transistors
Benjamin Iñiguez, Benjamin Iñiguez,
(*)DEEEA, Universidad Rovira i Virgili, Tarragona, Catalonia, Spain
Introduction● Organic (as well as polymer) and Amorphous Oxide (OTFTs and
AOS TFTs, respectively) will probably become essential devices in niche applications, related to flexible, printed or large area electronics and also transparent electronics (in the case of AOS TFTs). Examples of applications are electronic tags, drivers in AMLCDs, sensors
● Organic and amorphous oxide electronics allow flexible and low-cost substrates for large-area applications by relatively simple and low-temperature fabrication for disposable electronics
GIZO TFT structureOrganic (polymeric) TFT structure
Outline
Introduction
OTFT drain current model and parameter extraction
AOS TFT drain current model
Conclusions
OTFT drain current model
)(),(1 TGSFETFET VVToT
Etran
Ec=1.72
For organic TFTs, Qloc>>Qfree and DOS with only one exponential dependence
OTFT drain current model
1D Poisson’s equation has no analytical solution if a Gaussian DOS is used
An analytical solution is possible assuming an exponential DOS, as in a-Si:H TFTs
20
2exp
2
V
gaussNDOS
00exp exp
kTkTNDOS t
,002
2kTq
t eNdyd
OTFT drain current model
In [*] it was shown that for OTFTs, it can be considered that Qloc>>Qfree in above threshold regime and Poisson´s equation has analytical solution for the electric field and the induced sheet charge in the channel. The DOS is represented as:
TokEvEgEg
bdod
)(exp)(
[*] M. Estrada et all, Solid State Electronics, 52 (2008) 787.
OTFT drain current model
Mobility model development
t: channel thicnesswhere
The mobility expression is obtained from:
OTFT drain current model
The expression of the current obtained is:
where:
OTFT drain current model
If VDS
< VGS
-VFB
OTFT drain current model
22
1
22
),('TTo
FBGS
TTo
S
TTo
ioFET VVCToTP
1
22
),('TTo
S
TTo
io
aa
o CToTP
V
TTo
bTTo
b
VFodob
TbkVEFoE
Vb
TokToT
TokEE
gTkq
NTkqToTP
2)/sin(
exp
exp),('
)( TGSaa
oFET VV
V
22
TToand
The expression of mobility obtained is:
where:
OTFT drain current model
mm
TGSS
DSTGSFETi
DSDSTGSFETiDS
VVVVVC
LWR
VVVVCLWI 1
11
1
m and are fitting parameters related to the curvature and the saturation region of the curves, respectively
OTFT parameter extraction
nTGSDS VVI )(
)0
21
)(
)(
)(1
max
TGSGSDS
V
GSGSDS
GS VVVI
dVVI
VH
GS
An extraction procedure based on the properties of the integral function H1(VGS). was developed:
If ID can be represented as:
Our parameter extraction method is called UMEM (Unified Modelling and Extraction Method). It has been adapted and applied to several types of TFTs.
OTFT parameter extraction
1)(
1DSTGS
TGSFETi
FETi
DSlin VVVVVC
LWR
CLW
I
TGSGSlinDS
V
GSGSlinDS
GS VVVI
dVVI
VH
GS
21
)(
)(
)(1
max
0
)( TGSAA
oFET VV
V
If the measured transfer characteristic in the linear regime IDSlin, is represented as:
Where FET is modeled as a power dependence of the (VG-VT):
then
OTFT parameter extraction
1)(
1DSTGS
TGSFETi
FETi
DSlin VVVVVC
LWR
CLW
I
TGSGSlinDS
V
GSGSlinDS
GS VVVI
dVVI
VH
GS
21
)(
)(
)(1
max
0
)( TGSAA
oFET VV
V
If the measured transfer characteristic in the linear regime IDSlin, is represented as:
Where FET is modeled as a power dependence of the (VG-VT):
then
OTFT parameter extraction
2slope
1
TGSGSDSlinGS VVPAVIVy 11
)()(
slopeinterceptTV
STEP1: Calculate the slope and intercept of H1(n1):
STEP 2: Calculate the slope, PA, of the equation:
and VDS1 is the drain voltage at which the linear transfer curve was measured.
11
1
AA
DSoi
V
VCLW
PAWhere:
OTFT parameter extraction
TGS
DS
FET VVV
LWPA
1
1
1
1
DSiAA
o
VCLW
PAV
STEP 3: Calculate :
STEP 4: Calculate FET:
AAVo
OTFT parameter extraction
STEP 6: Calculate the slope Ps of the curve:
where IDsat is the transfer curve in saturation
22
11
PsPAVDS
SSTEP 7: Calculate S
STEP 5: Calculate R for the maximum measured VGS :
TGSFETiGSDSlin
DS
VVCLWVI
VR
maxmax
1 1
11
)()( GSDSsatGS VIVy
OTFT parameter extraction
A.1. Calculate the characteristic energy To of the DOS as:
2
2 TTo
A.2. Calculate gdo as:
ToT
i
ToT
CVToTqkToT
TkqNg aasb
sbVdo
22
22
sin
OTFT parameter extraction
Modeling the subthreshold regime
2
)tanh(12
)tanh(1 QDVVVIQDVVVII TGSDS
TGSsDSt
The subthreshold regime is expected to present an exponential increase with the gate voltage than can be written as:
VT+ DV is the value of gate voltage near which the exponential dependence of IDS starts and Io is the measured off current at a gate voltage sufficiently well below in the subthreshold region.The total drain current is the sum of the two components, in above and below threshold regimes. The tahh function is used to sew both terms.
3.2),(
SVV
DSTDSS
TGS
eVDVVIIoI
Improvement of the output conductance
In saturation above threshold:
Extended to the linear regime by replacing VGS
-VT with V
DSe
Results
Results
AOS TFT Drain Current Model
1
20
10 expexp
kTEEg
kTEEgg C
adC
ata
Conduction band energy
Tail acceptor density ofstates
The VGS variation abovethreshold modifies thepopulation of the tailstates.
Deep acceptor densityof states
The VGS variation in subthreshold modifiesthe population of thedeep states.
Distribution of acceptor type traps
TaT2
21
TbT2
22
AOS TFT Drain Current Model
Unified Model and Parameter Extraction Method (UMEM) where the mobility is calculated by solving:
• Poisson’s equation assuming an exponential DOS and Qfree<<Qloc
• Free carrier transport in AOS TFTs
Multiple Trapping and Release
AOS TFT Drain Current Model
1
mm
TGS
DSTGSFETi
DSDSTGSFETiDSGSab
VVVVVC
LWR
VVVVC
LWVVI /1
)(11
1,
a
aTGS
FET VaaVV
0
Channel length modulation
where
Saturation parameter
Empirical parameters defining thevariation of mobility with Vgs abovethreshold
Sharpness of the knee region
ABOVE THRESHOLD
AOS TFT Drain Current Model
1
In [*] extraction procedure based on the properties of the integral function H(VGS). was developed and applied, first, to a‐Si:H devices model :
TGSGSDS
V
GSGSDS
GSabove VVaVI
dVVIVH
GS
21
)(
)()(
max
0
Parameters extracted from the transfer curve in linear regime, and with the slope and the abscissa intercept of the H function.
a
a
Di
slope
VCLW
Vaa
1
1
1
Subsequently, parameters R, m, λ, α are extracted as indicated in:
‐A. Cerdeira, M. Estrada, R. Garcia, A. Ortiz‐Conde, and F.J.G. Sanchez, Solid‐St. Electron, vol.45, no. 7, pp.1077‐1080 (2001).
Now we can model the fielddependent mobility μFET
AOS TFT Drain Current Model
1
[*] L. Resendiz, M. Estrada, and A. Cerdeira, Solid State Electron 2003;47:135–1358.[**] A. Cerdeira, M. Estrada, B. S. Soto‐Cruz, and B. Iñíguez, Microelectron Reliab vol. 52, pp.2532‐2536 (2012).
SUBTHRESHOLD
To model the subthreshold region of devices, the drain current can be described as [*]:
γ b depends on the temperature T and on the characteristic temperature of the deep states distribution (T2)
22 2 TTb
Vbb is obtained as indicated in [**]
AOS TFT Drain Current Model
1
To join the subthreshold and the above threshold regions, an expression It1 is obtained where the tanh function is applied to sew Iab(VGS, VDS) and Ibt(VGS, VDS) .
-10 -5 0 5 101E-13
1E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
I DS (A
)
VGS
Measurement Iab Ibt It1
VT
Typical non‐stress transfer characteristic of a HIZO TFT in linear regime.
W=160 m. L=20 m. VDS=0.1 V
Experimental data is compared with It1, which is composed of the above threshold region (VGS > VT), modeled by Iab, and the subthreshold region, modeled by Ibt.
AOS TFT Results
1
GIZO TFT W=160 μm L=20 μm
0 5 10 15 20
0.0
2.0x10-4
4.0x10-4
6.0x10-4
VGS (V)
VGS = 4 V
VGS = 12 V
VGS = 20 V
I DS (A
) Measurements MOTFT in Mathcad MOTFT Verilog-A
VGS = 16 V
AOS TFT Results
0 5 10
0
2x10-5
4x10-5
I DS(A
)
VDS(V)
Measurements VGS=4V VGS=5V VGS=8V Model
0 2 4 6 8 100
2x10-6
4x10-6
6x10-6
8x10-6
Out
put c
ondu
ctan
ce (S
)
VDS(V)
Measurements VGS=4V VGS=5V VGS=8V Model
AOS TFT Results
0 1 2 3 4 5 6 7 8 9
10-9
10-8
10-7
10-6
10-5
10-4
I DS
(A)
VGS(V)
Measurements VDS=1V VDS=10V Model
10-8 10-7 10-6 10-50
1
2
3
4
5
6
7
8
9
10
g m/I D
S (1
/V)
IDS (A)
Measurements VDS=10V Model
Conclusions
A physically-based compact modelling framework for Organic and Amorphous Oxide TFTs has been presented ➢
For both OTFTs and AOS TFTs our models predict I-V characteristics above and below threshold., with a smooth transition between both regimes The extraction procedure (UMEM) is simple and well defined.
Mobility as function of both bias and temperature is also modeled.
DOS parameters (To and gdo) in OTFTs and for deep states in AOS TFTs can be determined.➢
Very good agreement is obtained with I-V experimental data from OTFTs and AOS TFTs fabricated with different technologies