compact modeling approaches for organic and oxide thin ... · approaches for organic and oxide thin...

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