A Compact Model for Organic Field-Effect Transistors ... - IEEE Xplore

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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 60, NO. 3, MARCH 2013

A Compact Model for Organic Field-Effect Transistors With Improved Output Asymptotic Behaviors Chang Hyun Kim, Student Member, IEEE, Alejandra Castro-Carranza, Magali Estrada, Senior Member, IEEE, Antonio Cerdeira, Senior Member, IEEE, Yvan Bonnassieux, Gilles Horowitz, and Benjamin Iñiguez, Senior Member, IEEE

Abstract—Here, we propose an advanced compact analytical current–voltage model for organic field-effect transistors (OFETs), which can be incorporated into SPICE-type circuit simulators. We improved the output saturation behavior by introducing a new asymptotic function that also enables more precise low-voltage current and conductance fitting. A new expression for the subthreshold current was suggested to cover all operation regimes of OFETs. All model parameters were extracted by a systematic method, and the comparison of the modeled current with the experimental data on pentacene-based OFETs confirmed the validity of the model over a wide operation range. Index Terms—Asymptotic behaviors, circuit simulation, compact modeling, organic field-effect transistors (OFETs).

I. I NTRODUCTION

W

E HAVE seen impressive progress in the research related to organic field-effect transistors (OFETs), which make use of semiconducting property of small-molecular and polymeric materials [1], [2]. OFETs are not only entering into conventional applications as an alternative of inorganic counterparts but also creating various new applications by virtue of their multifunctionality. Solution-process compatibility and mechanical softness of organic materials are the key features that will enable cost-effective production of flexible electronic systems. Since the first demonstration of an organic transistor [3], major research efforts have been put into the device-level Manuscript received September 18, 2012; revised November 13, 2012; accepted January 4, 2013. Date of publication January 25, 2013; date of current version February 20, 2013. This work was supported in part by CONACYT under Project 127978, by the European Commission under Contract 247745 (FlexNet), by the Spanish Ministry of Science under Contract TEC200909551 and FPU Grant AP2008-02740, by URV under Grant PGIR/15, and by ICREA Institute (Catalonia, Spain) under the ICREA Award. The work of C. H. Kim was supported by the Vice Presidency for External Relations (DRE) in École Polytechnique through a Ph.D. fellowship. The review of this paper was arranged by Editor A. C. Arias. C. H. Kim, Y. Bonnassieux, and G. Horowitz are with the Laboratoire de Physique des Interfaces et des Couches Minces (CNRS UMR-7647), École Polytechnique, 91128 Palaiseau, France (e-mail: chang-hyun.kim@ polytechnique.edu). A. Castro-Carranza and B. Iñiguez are with the Departament d’Enginyeria Electrònica, Elèctrica i Automàtica (DEEEA), Universitat Rovira i Virgili, 43007 Tarragona, Spain (e-mail: [email protected]). M. Estrada and A. Cerdeira are with Sección de Electrónica del Estado Sólido (SEES), Departamento de Ingeniería Eléctrica, CINVESTAV, 07360 Mexico City, DF, Mexico. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2013.2238676

investigation to improve the electrical performance of OFETs. At the present time, however, device-to-system integration is considered as a central issue as people achieve sufficiently high performance and reliability of unit transistors. Recent reports on RFID tags [4], display backplanes [5], and largearea sensors [6] manifested great potential of those higher level circuit systems. A compact model is a mathematical description of an electrical component that can mimic the electrical behavior of that particular device [7], [8]. In more practical terms, a compact model makes a bridge between the transistor-level and the circuit-level outlooks, providing a way to analyze transistors and build more complex circuits in SPICE-based simulations. Hence, there is a strong need for an accurate compact OFET model for design and realization of organic circuit systems. However, it is difficult to find a widely accepted model and only a few reports dealt with specific model development for OFETs with different approaches [9]–[12]. There has been also another trend toward direct or modified utilization of MOSFET or amorphous silicon thin-film-transistor (TFT)-based models for describing OFET characteristics [13]–[15]. Over the past years, our group has developed the unified model and parameter extraction method (UMEM) for various transistor types [16]–[19] and recently suggested its application to OFETs with relevant physics of organic semiconductors [20]–[22]. In this paper, we propose an advanced compact model for OFETs based on the UMEM approach. The present model features three major improvements: 1) a modified asymptotic function for the saturation behavior that also improves the output conductance in the linear regime; 2) a new subthreshold-current model; and 3) an extended range of applications with the symmetry of source and drain electrodes. This model covers all operation regimes of OFETs from OFFto ON-state with a reasonable number of parameters and with smooth transition between the different regimes. Pentacene OFETs were analyzed to investigate the validity of the model, and we could fit the measured current–voltage characteristics very accurately with methodically extracted model parameters. II. E XPERIMENTAL Flexible OFETs were fabricated with the bottom-gate top-contact configuration shown in the inset in Fig. 1(b). An indium–tin–oxide (ITO)-coated poly(ethylene terephthalate) (PET) film was used as a substrate and a common gate

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KIM et al.: COMPACT MODEL FOR OFETS WITH IMPROVED OUTPUT ASYMPTOTIC BEHAVIORS

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III. I MPROVEMENT ON A SYMPTOTIC B EHAVIOR

Fig. 1. (a) Conceptual representation of the asymptotic saturation behavior. (b) Measured output curves with modeled above-threshold currents. (Inset) Device structure of a pentacene OFET. (c) Output conductance from the measured data and the model calculations.

electrode. The substrate was ultrasonically cleaned in isopropanol and treated with UV/ozone. A thin poly(3,4ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) layer was spin coated and annealed at 100 ◦ C for 10 min as a buffer layer for reduced gate leakage [23]. Poly(methylmethacrylate) (PMMA) dissolved in toluene at a concentration of 80 mg/mL was spin coated and cured at 120 ◦ C for 1 h as a polymeric gate insulator (970 nm). One hundred nanometers of pentacene was vacuum evaporated for a hole-transporting molecular layer, and 60 nm of Au was finally evaporated to define the source/drain electrodes. All fabrication steps were performed in a nitrogen-filled glove box to minimize chemical degradation. Current–voltage characteristics were recorded using a Keithley 4200 semiconductor characterization system in the dark at room temperature under ambient atmosphere.

Fig. 1(a) illustrates the concept of output asymptotes. In the ideal case, drain current IDS linearly increases at low drain voltage VDS and becomes saturated at a constant level. Ilin and Isat respectively denote linear and saturation currents, and Vsat indicates the saturation voltage here. For realistic devices, however, output curves are not perfectly flat at high VDS . This imperfect saturation is usually taken into account through a saturation coefficient λ, of which the physical origin can be attributed to several mechanisms. Channel length modulation is the most relevant; it correlates λ to the dependence of channel length reduction ΔL on VDS [8]. The space-charge-limited conduction through the depleted semiconductor bulk can be another reason, as explained in [10]. In this case, λ would mirror the dielectric property of the organic semiconductor. We infer that the electric field dependence of mobility, which is characteristic of disordered organic materials, can also have an effect on λ in connection with the degree of disorder in the distribution of states [24]. A standard way to model the finite output conductance behavior is to multiply the total current by (1 + λVDS ) [8]. The asymptotic equation by this conventional method is Ia1 = Isat (1 + λVDS ). A notable drawback is that Ia1 is not sufficiently close to real IDS , and this generally gives rise to inaccurate prediction of the low-voltage output conductance, as pointed out in [25]. To overcome this issue, we propose [1 + λ(VDS − Vsat )] as the multiplicative factor that leads to the shifted asymptote Ia2 = Isat [1 + λ(VDS − Vsat )]. As clearly shown in Fig. 1(a), Ia2 draws nearer to IDS and meets IDS at (Vsat , Isat ) point. This significantly raises the accuracy of the global fitting not only for the current IDS but also for the output conductance, which is an important requirement in analog circuit simulations. It is worth clarifying here that, by its definition, the asymptotic equation Ia1 or Ia2 does not represent the actual current, which is always lower than the corresponding asymptote but gradually approaches it when VDS becomes sufficiently high. Because the output conductance in the saturation regime is generally lower than that in the linear regime, the effect of an asymptotic function at low VDS is minimal. Our modified asymptotic expression prevents unexpected overestimation of low VDS conductance by reducing the contribution of the asymptotic term in the linear regime. IV. M ODELING AND PARAMETER E XTRACTION A. Above-Threshold Current We express the above-threshold drain current Iabove as multiplication of channel conductance gch , effective drain voltage VDSe , and new saturation asymptotic term [1 + λ(VDS − Vsat )] [19], [26]. gch embraces a contact voltage drop and is written as gch =

−KμFET (VGS − VT ) [1 − Rc KμFET (VGS − VT )]

(1)

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TABLE I E XTRACTED PARAMETERS F ROM THE M ODELED P ENTACENE F IELD -E FFECT T RANSISTOR

with the dependence of field-effect mobility μFET on gate voltage VGS as μ0 μFET = γ |VGS − VT |γ (2) Vaa

rent was also in good agreement with the experimental data, as shown in Fig. 1(c) with correct monotonous decrease at low |VDS |.

where K is (W/L)Ci , W is the channel width, L is the channel length, Ci is the insulator capacitance per unit area, VT is the threshold voltage, Rc is the contact resistance, γ is the characteristic mobility exponent, Vaa is the mobility enhancement voltage, and μ0 is the conversion mobility set to 1 cm2 /V · s. Equations (1) and (2) are written for the p-type operation, where VGS − VT < 0 in the above-threshold regime. VDSe enables a smooth linear-to-saturation transition by transition parameter m, and it is defined as m − m1 VDS (3) VDSe = VDS × 1 + Vsat

B. Subthreshold Current

which simply approximates to VDS when VDS Vsat and to Vsat when VDS Vsat . Now, we introduce the saturation modulation parameter αs for using Vsat = αs (VGS − VT ) and position the absolute-valued terms to write the complete new above-threshold equation as Iabove = −KμFET (VGS − VT )VDS [1 + λ(|VDS | − αs |VGS − VT |)] . m m1 DS [1 − Rc KμFET (VGS − VT )] 1 + αs (VVGS −VT ) (4) Here, we take the absolute values of VDS and Vsat terms in two brackets in order to extend the range of applications to both signs of VDS . This allows properly equal contributions of the transition term (grouped by m) and the asymptotic term (grouped by λ) to both positive and negative VDS . The mobility model in (2) has the same voltage dependence as the physical mobility model for OFETs that we developed based on the hopping charge transport between localized states, assuming an exponential density of states (DOS) [21], [27]. Identifying parameters between this physical mobility model and the mobility expression given in (2), we can extract the characteristic DOS temperature T0 and the density of localized states gd0 . The above-threshold parameters of a pentacene transistor were extracted according to the systematic procedure detailed in [20], [21], and [27] with W = 1000 μm, L = 40 μm, and Ci = 3.3 nF/cm2 . For λ, taking into account the modification made in this paper, we calculated by rearranging (4) with respect to λ. As shown in Fig. 1(b), the model well fits the measured output curves with the parameters listed in Table I. The output differential conductance from the modeled cur-

The subthreshold drain current Isub of OFETs is considered to have a similar mechanism to that of MOSFETs, which describes Isub as the diffusion current arising from the carrier concentration gradient between the source and drain [28]. The carrier concentration exponentially varies with the surface potential, and this predicts the exponential dependence of Isub on VGS . Here, we propose a simplified exponential model for Isub with the advantage of explicit appearance of the subthreshold swing S ln 10 (VGS − V0 ) Isub = I0 exp − (5) S where I0 is the off current, and V0 is the onset voltage. Equation (5) is devised to provide an easy parameter estimation, as illustrated in Fig. 2(a). V0 and I0 can be read in a transfer curve drawn on a semilogarithmic plot, and the inverse slope of a regression line on the exponential part directly gives S. The existence of deep traps can significantly lower the exponential slope because they act as additional capacitance that needs to be filled when the Fermi level moves toward the transport band edge. On that account, a physical correlation can be incorporated into (5) referring to the method in [29] and [30] by writing kT ln 10 q 2 Nt +1 (6) S= q Ci where q is the elementary charge, k is Boltzmann’s constant, T is the absolute temperature, and Nt is the deep trap density comprising interface and bulk traps. The extracted subthreshold parameters are listed in Table I. Note that, because of its diffusion nature, subthreshold current is practically independent of VDS as long as VDS is higher than a few kT /q [28]. The model (5) is based on this assumption and applicable to most unintentionally doped molecular semiconductors that are characterized by low thermal carrier density on the order of ∼1014 cm−3 [31]. Another situation might occur in polymeric OFETs, where the unintentional doping concentration can be much higher [32]. In this case, the subthreshold current can be influenced by the drift contribution of bulk dopant-induced carriers, which accompanies the VDS dependence, as exemplified by the data in [33]. For modeling this type of experimental results, one may extend (5) to include doping concentration and/or empirical VDS dependence.


Fig. 2. (a) A measured linear-regime transfer curve on a semilogarithmic plot with graphical instructions on the subthreshold parameters. (b) Effect of transition parameter B on the final model, including below-to-above-threshold transition.

C. Complete Model for All Regimes As depicted in Fig. 2(a), modeled Iabove and Isub can only describe its corresponding regime. A traditional method used for Si-based TFTs is to take [(1/Iabove ) + (1/Isub )]−1 as the combined equation [34]. It is found that this convention lacks the general applicability to OFETs, particularly when the below-to-above transition zone is spread over a wide voltage range. An alternative approach introduced in [10] makes use of a transition function for effective gate voltage, which is not compatible with our model with an independent model for Isub being defined. Here, we propose a hyperbolic tangent transition function as the suitable method for OFETs with a tunability of the position and the degree of transition. Another advantage is the mathematical continuity at the transition point of both the hyperbolic tangent function and its derivative. For a single compact expression for all operation regimes, we finally express the total drain current Itotal model as 1 [1 − tanh [B(VGS − VB )]] 2 1 + Isub × [1 + tanh [B(VGS − VB )]] + I0 2

Itotal = Iabove ×

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Fig. 3. Final comparison of the model and the experimental data on (a) transfer characteristics and (b) output characteristics.

center of transition in two hyperbolic tangent functions. A practical way is to select the voltage at which the vertical distance between Iabove and Isub is minimum [see Fig. 2(a)]. This generally requires a VB shifted from VT by a few volts toward the above-threshold direction. It is because, approaching VT , Iabove drops down too quickly, and as a consequence, choosing VT as VB cannot give a sufficiently smooth transition. The last parameter B dictates the degree of abruptness of transition around VB . B is best determined by iterative calculation and comparison to the experimental data, as shown in Fig. 2(b). Fig. 3 shows the final comparison of the compact model with the experimental data over a wide bias range. The proposed model precisely reproduces measured current–voltage characteristics over off, subthreshold, linear, and saturation regimes with a single set of the extracted parameters collected in Table I. The output curves in Fig. 3(b) show that the model correctly predicts the continuous change of current at VDS = 0 V as expected from the mathematical idea on (4) explained in Section IV-A. V. C ONCLUSION

(7)

in which two additional parameters, namely, transition voltage VB and transition parameter B, are introduced. VB fixes the

In this paper, we have introduced a new compact model for OFETs with improved output asymptotic behaviors. The above-threshold current model included this new asymptotic function and symmetric VDS terms for an extended range of applications. A simple three-parameter subthreshold equation

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with intuitive parameter extraction was suggested. The final fully analytical expression of total current was given by using hyperbolic tangent transition functions, and we have shown that our model fitted the experimental data on a pentacene transistor with high precision. We believe that the present model can be widely applied to OFETs with various materials and geometries and will serve as a practical and reliable tool for organic-based circuit developments. ACKNOWLEDGMENT C. H. Kim would like to thank the organization of a research visit at the Universitat Rovira i Virgili that led to this publication. R EFERENCES [1] D. Braga and G. Horowitz, “High-performance organic field-effect transistors,” Adv. Mater., vol. 21, no. 14/15, pp. 1473–1486, Apr. 2009. [2] H. Klauk, “Organic thin-film transistors,” Chem. Soc. Rev., vol. 39, no. 7, pp. 2643–2666, Jul. 2010. [3] A. Tsumura, H. Koezuka, and T. Ando, “Macromolecular electronic device: Field-effect transistor with a polythiophene thin film,” Appl. Phys. Lett., vol. 49, no. 18, pp. 1210–1212, Nov. 1986. [4] E. Cantatore, T. C. T. Geuns, G. H. Gelinck, E. van Veenendaal, A. F. A. Gruijthuijsen, L. Schrijnemakers, S. Drews, and D. M. de Leeuw, “A 13.56-MHz RFID system based on organic transponders,” IEEE J. Solid-State Circuits, vol. 42, no. 1, pp. 84–92, Jan. 2007. [5] S. Steudel, K. Myny, S. Schols, P. Vicca, S. Smout, A. Tripathi, B. van der Putten, J.-L. van der Steen, M. van Neer, F. Schütze, O. R. Hild, E. van Veenendaal, P. van Lieshout, M. van Mil, J. Genoe, G. Gelinck, and P. Heremans, “Design and realization of a flexible QQVGA AMOLED display with organic TFTs,” Org. Electron., vol. 13, no. 9, pp. 1729–1735, Sep. 2012. [6] T. Sekitani and T. Someya, “Stretchable, large-area organic electronics,” Adv. Mater., vol. 22, no. 20, pp. 2228–2246, May 2010. [7] R. Woltjer, L. Tiemeijer, and D. Klaassen, “An industrial view on compact modeling,” in Proc. ESSDRC, Montreux, Switzerland, Sep. 2006, pp. 41–48. [8] T. A. Fjeldly, T. Ytterdal, and M. Shur, Introduction to Device Modeling and Circuit Simulation. New York: Wiley, 1998. [9] M. Fadlallah, G. Billiot, W. Eccleston, and D. Barclay, “DC/AC unified OTFT compact modeling and circuit design for RFID applications,” Solid State Electron., vol. 51, no. 7, pp. 1047–1051, Jul. 2007. [10] O. Marinov, M. J. Deen, U. Zschieschang, and H. Klauk, “Organic thinfilm transistors: Part I—Compact DC modeling,” IEEE Trans. Electron Devices, vol. 56, no. 12, pp. 2952–2961, Dec. 2009. [11] M. J. Deen, O. Marinov, U. Zschieschang, and H. Klauk, “Organic thinfilm transistors: Part II—Parameter extraction,” IEEE Trans. Electron Devices, vol. 56, no. 12, pp. 2962–2968, Dec. 2009. [12] L. Li, M. Debucquoy, J. Genoe, and P. Heremans, “A compact model for polycrystalline pentacene thin-film transistor,” J. Appl. Phys., vol. 107, no. 2, pp. 024519-1–024519-3, Jan. 2010. [13] P. V. Necliudov, M. S. Shur, D. J. Gundlach, and T. N. Jackson, “Modeling of organic thin film transistors of different designs,” J. Appl. Phys., vol. 88, no. 11, pp. 6594–6597, Dec. 2000. [14] O. Yaghmazadeh, Y. Bonnassieux, A. Saboundji, B. Geffroy, D. Tondelier, and G. Horowitz, “A SPICE-like DC model for organic thin-film transistors,” J. Korean Phys. Soc., vol. 54, no. 925, pp. 523–526, Jan. 2009. [15] P. Stallinga and H. L. Gomes, “Modeling electrical characteristics of thinfilm field-effect transistors: II: Effects of traps and impurities,” Synth. Met., vol. 156, no. 21–24, pp. 1316–1326, Dec. 2006. [16] A. Cerdeira, M. Estrada, R. García, A. Ortiz-Conde, and F. J. García Sánchez, “New procedure for the extraction of basic a-Si:H TFT model parameters in the linear and saturation regions,” Solid State Electron., vol. 45, no. 7, pp. 1077–1080, Jul. 2001. [17] M. Estrada, A. Cerdeira, F. J. G. A. Ortiz-Conde, and B. Iñiguez, “Extraction method for polycrystalline TFT above and below threshold model parameters,” Solid State Electron., vol. 46, no. 12, pp. 2295–2300, Dec. 2002. [18] A. Cerdeira, M. Estrada, B. Iñiguez, J. Pallares, and L. F. Marsal, “Extraction method for polycrystalline TFT above and below threshold model parameters,” Solid State Electron., vol. 48, no. 1, pp. 103–109, Jan. 2004.

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Chang Hyun Kim (S’11) received the dual M.Sc. degree from Kyung Hee University, Seoul, Korea, and the École Polytechnique, Palaiseau, France, in 2010. He is currently working toward the Ph.D. degree at the École Polytechnique.


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Alejandra Castro-Carranza is currently working toward the Ph.D. degree at the Universitat Rovira i Virgili, Tarragona, Spain. Her research interests include the fabrication, characterization, simulation, and modeling of organic TFTs and MIS capacitors.

Yvan Bonnassieux received the Ph.D. degree from ENS Cachan, Cachan, France, in 1998. He is currently an Assistant Professor with the École Polytechnique, Palaiseau, France, where he is the Head of the Organic Electronics Research Team.

Magali Estrada (M’96–SM’98) received the Ph.D. degree from NW Leningrad Polytechnic Institute, Saint Petersburg, Russia, in 1977. She is currently a Full Professor with CINVESTAV, Mexico City, Mexico.

Gilles Horowitz received the Ph.D. degree from the University of Paris Diderot, Paris, France, in 1975. He is currently with the École Polytechnique, Palaiseau, France and is a Senior Research Fellow with the Centre National de la Recherche Scientifique.

Antonio Cerdeira (M’96–SM’98) received the Ph.D. degree from NW Leningrad Polytechnic Institute, Saint Petersburg, Russia, in 1977. He is currently a Full Professor with CINVESTAV, Mexico City, Mexico.

Benjamin Iñiguez (M’96–SM’03) received the Ph.D. degree from the University of the Balearic Islands (UIB), Palma, Spain, in 1996. He is currently a Professor with the Universitat Rovira i Virgili, Tarragona, Spain. His main research interest is the modeling of advanced electron devices.