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simulate organic transistors. In this study, we use ATLAS(Silvaco) simulator as a general software. This simulator isable to predict electrical properties of the device given itsphysical structure and operating bias condition by solvingPoisson’s and continuity equations and classic equations of carrier currents including drift and diffusion terms [5]. pq 2 (1)

p p p RG J qt

p .1(2)

Where,ε is dielectric constant,ψ is potential profile, p is holedensity,q is the unit charge,G p is carrier generation rate, R p isthe carrier recombination rate, and J p is the hole currentdensity. pqDF qp J p p p (3)

Where µ p is the mobility of holes,F is the electric field,and D p

is the hole diffusion constant.Since ATLAS simulator has been proposed initially to

simulate silicon devices, its capacity to simulate organicdevices is limited in some cases as it will be seen later. Usedparameters’ values for pentacene in this study were as thefollowing; Energy bandgap is 2.49 eV, electron affinity as 2.8eV, density of both conduction and valance band states as2 1021 cm-3and dielectric constant as 4 [2, 7, 8]. The acceptordoping concentration of pentacene is taken 31016 cm-3 [1].Pool-Frenkel mobility model is used for conduction channelof pentacene:

E KT KT

E

exp)( (4)

Where is the field effect dependent mobility, is the zero field

mobility, is the electric field, is the zero field activation energy,is the Pool-Frenkel factor, is the fitting parameter, is theBoltzman constant, and is the temperature [3].

C. Analytical Model for Organic Field-Effect TransistorsIEEE1620 Standard has suggested that drain current of

an organic transistor would be calculated using classic theoryof conventional non-organic transistors [9]:

2)(2 thGS i D V V C L

W I

for 0 DS thGS V V V (5)

DS thGS i D V V V C LW

I )(

for 0thGS DS V V V (6)WhereW and L are the channel width and channel length,

iC is the capacitance per unit area of the gate insulator, isthe mobility, and thV is the threshold voltage.

III. RESULTSANDDISCUSSION

The extracted and the other used parameters in both tsimulations and the analytical calculations in this paper, given in tables 2 and 3. In these simulations using ATLAsoftware, regarding the Pool-Frenkel mobility model pentacene, the zero field activation energy and the PoFrenkel factor, , are set to 0.1 eV, and 4.3510-5ev(cm/V)1/2

respectively and the fitting parameter, , was 10-5(cm/V)1/2.Regarding the interface trap state densities, their experimenvalues were used in the simulations [3].

In early simulations, in some cases, mismatch betweexperimental and simulated curves were observed. In orto resolve this problem, simulation programs must be firscalibrated. For calibration, we should add some fixed charat the semiconductor/oxide interface. This procedure cadjust the threshold voltage. After calibration, the electribehavior of simulated transistors became well. At tfollowing, we report similarities and differences exist betwanalytical results, simulation results and experimental d

regarding the four different mentioned subjects.TABLEI: PARAMETERS AND CHARACTERISTICS OF THE POLYMER DIELECTRICS

A. Sub-Threshold RegionConcerning equations (5) and (6), analytical model pred

that for VGS=Vth , the drain current vanishes and it will be zerfor all VGS < Vth. Therefore, such equations fail to measurcorrect value of drain current in sub-threshold region. Ibetter model [1], drain current in this region takes exponential dependency to the gate-source voltage as:

nkT qV kT qV oxFE D

GS DS eC K LW

I / / ).1( (7)

Where,K is a constant that depends on material type andevice structure, andn is an ideality factor. Both theseparameters must be adjusted to match with experiment anor simulation data.

In figure 3, transfer characteristics of sub-threshold regin logarithmic scale is shown regarding simulation methand analytical model in comparison with the experiment dGiven results of figure 3, it is concluded that sub-threshoslope of experiment data is always lower than that frosimulated curves. Similarly, for sub-threshold slope theoretical results, it is evident that their best fit, which adepicted in our figures, are different from simulation aexperiment data considerably. Thus it may be concluded teq.7 is not a proper model at all, because this equation wil

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a straight line with a fixed slope in logarithmic scale and it isunlikely to develop a continuous curve in vicinity of VGS> Vthregion (eq. 5, 6).

B. On-State Drain Current Transfer characteristics of our transistors from simulation

and from analytical model (equations 2 and 3) are shown infigure 4. Experiment data for such diagrams have not been inaccess.

As it is seen from figure 4, analytical results have beentuned so that they are matched at the beginning and the endof the bias range in each plot with the simulation results, butin spite to this, the results are not matched in intermediategate-source voltages and simulation results always representlower current in comparison with the analytical results. Thisdifference may be attributed to better modeling of mobilityand also due to considering horizontal and vertical fields inthe simulation method in comparison with the analyticalmethod which uses a fixed mobility and neglects the horizontaland vertical field dependencies.

C. Threshold Voltage

In analytical model, threshold voltage is a fixed valuewhich is calculated from physical specifications of thetransistor such as its insulator thickness (tox), insulatorpermittivity(ε ox) and doping profile of semi-conductorsubstrate. Empirically it has been shown that variousparameters affect threshold voltage of transistor and thereare different values for threshold voltage in linear andsaturated regions of transistor. In linear and saturation

90

Figure 3: Transfer characteristics in logarithmic scale for studied transistors using simulation method, analytical model and experimen

regions, threshold voltage is extracted from GS D V I andGS D V I curves, respectively..

In the simulation method, threshold voltage is not a givennumber, but it is a value which can be calculated from theresults as it is done in analytical model. Although this volt-age is a function of the drain-source voltage, but, it is ex-tracted in a certain drain-source voltage in linear and or saturated region. There are two major reasons for threshold volt-age dependency on the drain-source voltages: (a) mobilitythat follows the vertical field, and (b) horizontal and verticalfields interference. The former has been considered in theanalytical model, but the latter is considered only in the simu-lation method. Tables 2 and 3 represent results of simulationmethod and analytical methods. It is observed that the sec-ond column of table 3 is not matched with the expected be-havior. Threshold voltage can be written as the sum of twovoltages as shown in fig.5. 21 V V V th (8)Where, 1V is part of threshold voltage due to semiconductor,,and 2V is the contribution from the insulator.V 1 is notfunction of the insulator parameters, therefore, we have:

i

ssoxth

E t V V

1 (9)

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Figure 4: Transfer characteristics of the certain transistors from simulation method and analytical model

Considering the above formula, we see that, as mentionedbefore, the second column of tables 2 and 3 are matchedneither with experimental data nor with simulation results.The reason is the interface charges exist due to interfaceroughness and is neglected in both approaches

Figure 5: Potential graph in insulator/semiconductor interface

TABLEII: ELICITED RESULTS AND PARAMETERS FROMATLASSIMULATIONS

TABLEIII: OBTAINED RESULTS OF EXPERIMENTAL DATA

D. MobilityMobility is considered a fixed value in the analytical model,

but experimentally it has been proven that it depends on thegate-source and the drain-source voltages which are notconsidered in the analytical model. In fact, upon extractingthe mobility from the measurement data, it should be consid

ered as a voltage dependent quantity which is derived frsmall signal measurements. In the linear and saturated gions it can be calculated via eq. 10 and 11, respectively

GS

D

DS oxFE V

I

V WC

L (10)

22

GS

D

oxFE V

I

WC L

(11)

Fig.6: Output characteristic of organic field-effect transistor wiPMMA gate insulator obtained from simulation and analytical

model results and experiment valuesEffective mobility is shown in the third column of the tab2 and 3 which has been measured in a relatively high currpoint. Third column of table 2 has been obtained by eq

from saturation region of the simulation results. Meanwhthird column of table 3 shows experiment data. These tcolumns show different values for the mobility and this is main source of mismatch exists between diagrams of figu6 and 7, and as mentioned before, it is due to surface rouness which cannot be included in the current simulation sware easily.

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Figure 7: Output characteristics of the studied transistors with simulation and analytical model

REFERENCES

[1] Z. Bao, and J. Locklin,Organic Field-Effect Transistors , CRCPres, New York, 2007.[2] M. Kitamura and Y. Arakawa, “Pentacene-based organic field-effect transistors,” J. Phys. Condens. Matter., vol. 20, 2008.[3] W. Wondmagegn and R. Pieper, “Simulation of top-contactpentacene thin film transistor,” J. Comput Electron. , vol. 8, pp. 19-24, 2009.[4] K. N. Narayanan Unni, S. D. Seignon, A. K. Pandey and J. M.Nunzi, “Influence of the polymer dielectric characteristics on theperformance of a pentacene organic field effect transistor,”Solid-State Electron ., vol. 52, pp. 179-181, 2008.

[5] ATLAS, Silvaco International, Santa Clara, CA, 2005.[6] S. Scheinert, G. Paasch and T. Doll, “The influence of bulk

traps on the subthreshold characteristics of an organic field effecttransistor,”Synth. Met. Vol. 139, pp. 233-237, 2003.[7] E A. Silinish and V. Èápek,Organic Molecular Crystals: Their

Electronic States , New York, 1980.[8] L. Sebastian, G. Weiser and H. Bassler, “Charge transfertransitions in solid tetracene and pentacene studied byelectroabsorption,”Chem. Phys. , vol. 61, pp. 125-135, 1981.[9] IEEE standard test methods for the characterization of organictransistors and Materials, IEEE Std 1620-2004, 200

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