Microelectronic Engineering 86 (2009) 2312–2315

Contents lists available at ScienceDirect

Microelectronic Engineering

journal homepage: www.elsevier .com/locate /mee

Numerical simulation of spin coated P3HT organic thin film transistorswith field dependent mobility and distributed contact resistance

Abdul Khaliq a,*, Feng Liang Xue a, Kody Varahramyan b

a Institute for Micromanufacturing, Louisiana Tech University, 911 Hergot Avenue, P.O. Box 10137, Ruston, LA 71272, USAb Indiana University – Purdue University Indianapolis, Office of the Vice Chancellor for Research, 755 West Michigan Street, UL 1140 Indianapolis, IN 46202, USA

a r t i c l e i n f o

Article history:Received 27 June 2008Received in revised form 7 March 2009Accepted 10 April 2009Available online 19 April 2009

Keywords:Polymer transistorDistributed contact resistanceNumerical modeling

0167-9317/$ - see front matter Published by Elsevierdoi:10.1016/j.mee.2009.04.009

* Corresponding author. Tel.: +1 318 257 4483; faxE-mail address: khaliq@latech.edu (A. Khaliq).

a b s t r a c t

P3HT thin film transistors (TFT) have been fabricated using inkjet printing technique. The present workaims at the systematic study of the impact of distributed contact resistance including field dependentmobility. The coupled analysis is not yet explored for polymer organic thin film transistors. Numericalsimulations are performed to study the coupled influence of field mobility and distributed contact resis-tance on the FET device behavior. Considering the influence of field mobility and distributed contactresistance, simulated results are consistent with our experimental results.

Published by Elsevier B.V.

1. Introduction

Organic microelectronics and optoelectronics have a rapiddevelopment due to the attractive properties and applications oforganic materials. P3HT is among popular organic materialsinvestigated [1,2]. Numerical solutions are used to study thephysics of organic devices, such as the effects of traps [3–6], fielddependent mobility models [7,8], device structures (bottom con-tact and top contact) [8,9], channel length [10], electrode contact[11], etc.

The impact of distributed resistance on the performance of theTFT has not been explored yet in conjunction with the field depen-dence mobility. In this paper, we report a two-dimensional simula-tion of electrical characteristics of P3HT TFTs. The objective of thework is to study the coupled influence of field mobility, and dis-tributed contact resistance on P3HT thin film transistors. The fielddependent mobility and contact resistance models are incorpo-rated in a numerical simulator for analysis. The technology com-puter-aided design (TCAD) tool Taurus-device (Synopsys�) isemployed to implement the simulation of the device characteris-tics. A field dependent mobility model is implemented in thenumerical simulator via the Taurus PMEI (physical model equationinterface) to include user defined mobility models. The simulationresults agree well with the experimental results.

B.V.

: +1 318 257 5104.

2. Device fabrication

Several devices were fabricated on heavily n-doped silicon,which also works as the gate electrode. A layer of 1000 Å thicksilicon oxide was thermally grown for the gate insulator. Thensource and drain (S/D) electrodes were deposited. After that,50 nm poly (3-hexylthiophene) (P3HT) was spin coated as a chan-nel material to form transistors as shown in Fig. 1. In this work,two types of contacting techniques were used. One is for longchannel (20 lm) using conducting polymer PEDOT-PSS as theelectrode material. The other is for short channel (5 lm) usinggold as the electrode material. We have found that by modifyingthe commercial PEDOT-PSS, its contact resistance with P3HT issignificantly lower than that of gold with P3HT. An n+-Si substratewith thermally grown 100 nm silicon oxide was used as the sub-strate. PEDOT-PSS was printed as the source and drain (S/D) elec-trodes. The gold S/D contact electrodes were formed bylithography and lift-off processes. Finally, The PEDOT-PSS usedwas modified to be highly conductive as compared to the com-mercial one [12]. The channel lengths are 20 lm and 5 lm for de-vices with PEDOT-PSS and gold contacts, respectively. In both ofthe devices, n+-Si serves as gate electrode. The devices were char-acterized on Keithley 236 source measure units at room temper-ature in air.

3. Measured device characteristics

The schematic of the P3HT TFT at room temperature are shownin Fig. 1. The on/off current ratio is measured above 103. Field effect

Fig. 1. Schematic structure of the fabricated P3HT TFTs. Lg is 20 lm and 5 lm forthe long and short channel devices, respectively.

A. Khaliq et al. / Microelectronic Engineering 86 (2009) 2312–2315 2313

mobility is calculated based on the following equation in satura-tion regime:

Ids ¼wCi

2LlðVgs � VthÞ2 ð1Þ

where Ids is the drain saturation current, l is the mobility, Vth is thethreshold voltage, and Ci stands for capacitance per cm2 of gateoxide, w and L are the channel width and channel length, respec-tively, and Vgs is the gate-to-source voltage. The mobility was deter-mined to be 1.2 � 10�2 and 1.0 � 10�2 cm2/v s for P3HT transistors.

4. Model description

Numerous analytical, numerical and empirical models havebeen investigated for organic semiconductors [6,13]. In the nextsection, a numerical implementation of mobility and distributedcontact resistance is presented. Field dependent mobility modelsare integrated with classical models in the software through a userinterface (the Taurus PMEI). This interaction allows a better insightof the device behavior for variety of mobility and contact resistancemodels. Models descriptions are presented in the subsequentsections.

4.1. Field dependent mobility

Unlike traditional inorganic semiconductors, organic semicon-ductors normally show the increase of carrier mobility with the in-crease of electric field for a bulk polymer piece sandwichedbetween two electrodes. The energy required for hopping fromone site to another is a distributed random variable, and the elec-tric field shifts the level in the distribution for the next hole hop[14]. The electric field dependence of mobility has been investi-gated [15–19] due to its application for polymer device physics.The application of the electric field (E) reduces the activation en-ergy by an amount eEq between two molecules spaced apart a dis-tance q.

This leads to the predicted electric field dependence of themobility:

l / exp ðeEq=kTÞ ð2Þ

The predicted field dependence on the mobility based on Eq. (2)establishes [23]:

l / exp ðEn=nþ1Þ ð3Þ

For n = 1

l / expffiffiffiEp

ð4Þ

This is similar to the Poole–Frenkel effect. The electron is ther-mally emitted over the top of the potential barrier which is low-ered by the electric field. The experimental observations of asquare root dependence of electric field were first reported byPai and Gill [20,21].

4.2. Distributed contact resistance

The effect of contact resistance in organic thin film transistorshas been studied [22–24]. The interface between contact and poly-mer is rough, and it leads to device degradation. The impact of dis-tributed contact resistance has not yet been investigated. For asimple voltage boundary condition, a single potential is associatedwith the entire electrode. Since the contact material has finiteresistivity, the electrostatic potential is not uniform at the metal-organic interface. To account for this effect, a distributed contactresistance can be utilized with any electrode in the simulation. Aresistance Ri is placed at each node linked with the contact of inter-est. The value of each Ri is calculated from contact resistance(in X-cm2) [25]:

Ri ¼ ðcon:resÞ=dc;i ð5Þ

where dc,i is the length of the contact associated with node i andcon.res is the contact resistance. An associated equation is addedfor each electrode node, unlike the lumped element case where asingle equation is related to the whole electrode. So for every nodei that is part of the contact [25],

1Ri

Vapplied � wi �kTq

lnNni

� �� �� �� In þ Ip þ Idisp

� �i ¼ 0 ð6Þ

where N is the doping concentration, ni is the intrinsic concentra-tion, Vapplied is the voltage applied, wi is the electric potential, In isthe electron current, Ip is the hole current, Idisp is the displacementcurrent and Ri is given by Eq. (5). The super linear characteristic ofthe short channel devices may be attributed to distributed contactresistance. The distributed resistance depends on external voltageas well, and therefore needs to be tuned up for each bias step.

5. Simulation

Numerical simulations were run with the 2D device simulatorTaurus-device (Synopsys�). The program solves simultaneouslythe Poisson equation for the electrical potential and the continuityequations for the hole and electron concentrations. The continuityequations do not depend on the type of the transport mechanismand are valid for hopping transport as well [26].

The applied field modulates the mobility of carriers as discussedearlier. The field dependence mobility has been implemented inthe numerical solver, and the solver has a physical model equationinterface to include user defined mobility models. The imple-mented mobility model based on Eq. (4) is given by:

l ¼ u0 exp ðAffiffiffiEpÞ ð7Þ

Where u0 is the zero field mobility and, A is the fitting parameter.The results with this model including distributed resistance wereconsistent with our experimental results. The results are show inFig. 2. The transfer characteristics for long channel device are shownin Fig. 3. Simulated and experimental results are matched well forthe long channel device using field dependent mobility model.

However, for the short channel device experimental and simu-lated results are not in agreement. The reason may be the in-creased contact effect at a short channel. The distributed contactresistance is added to include this phenomenon. The output char-acteristics for short channel device with and without distributedresistance are shown in Figs. 4 and 5. The distributed resistance

Fig. 2. Simulation of output characteristics of long channel device with fielddependence mobility model.

Fig. 3. Simulation of transfer characteristics of long channel device with fastinterface traps.

Fig. 4. Simulation of output characteristics of short channel device with fielddependence mobility without contact resistance.

Fig. 5. Simulation of output characteristics of short channel device with fielddependence mobility and contact resistance.

Table 1Material properties used for numerical simulations.

Material property Value

Metal work function 5 eVP3HT Electron Affinity 3.5 eVP3HT Bandgap 1.7 eVP3HT HOMO Level 5.2 eVP3HT LUMO Level 3.5 eVP3HT (Nv, Density of states) 2 � 1021 cm�3

P3HT Permittivity 3.0

Fig. 6. Band diagram at organic semiconductor and metal before contact.

2314 A. Khaliq et al. / Microelectronic Engineering 86 (2009) 2312–2315

is optimized for each bias step. The simulated and measure resultsare in good agreement. The band diagrams of metal and organicsemiconductor and material properties of metal contact and organ-ic semiconductor are listed in Table 1 (see Fig. 6).

6. Summary and conclusions

The P3HT organic thin film transistors were fabricated usinginkjet printing method and current voltage characteristics weremeasured. The devices were characterized on Keithley 236 sourcemeasure units at room temperature in air. A systematic study ofthe impact of distributed contact resistance including field depen-dent mobility was developed. A coupled analysis of these twoparameters was explored in depth. The model parameters were in-cluded into a commercially available Synopsys TCAD tools. An

A. Khaliq et al. / Microelectronic Engineering 86 (2009) 2312–2315 2315

exhaustive literature search was done to find out the optimalmaterial properties to include in the simulator.

The field mobility model is developed through the ‘‘physicalmodel equation interface (PMEI)” provided by the Synopsys TCADpackage. This interface allowed custom models to be included intothe package which are more appropriate for the system understudy. The field mobility model expressed in Eq. (7) is incorporatedthrough the PMEI into the simulation software. The contact resis-tance was enabled to evaluate its influence on the simulation.

A thorough review of the simulated behavior of devices withchannel lengths less than short channel showed increased depen-dence on coupled field mobility and distributed contact resistance.The simulated behavior of devices with channel lengths more thanlong channel device showed negligible dependence on distributedcontact resistance but field based mobility still plays a major role.The coupled effects of field dependent mobility and distributedresistance to the device characteristics were demonstrated bycomparing with the experimental results. The experimental andnumerical results were in good agreement both for long and shortchannel devices.

The presented numerical model (coupled field mobility andcontact resistance) was evaluated with devices which captured abroad range of useful channel lengths such that the discussedmethodology may be applied to similar devices. This consolidatesour premise that field mobility and contact resistance are impor-tant parameters to model the organic TFT’s accurately.

References

[1] A. Assadi, C. Svensson, M. Willander, O. Inganas, Applied Physics Letters 53 (3)(1988) 195–197.

[2] Yong Suk Yang, Seong Hyun Kim, Sang Chul Lim, Jeong-Ik Lee, Jung Hun Lee,Lee-Mi Do, Taehyoung Zyung, Applied Physics Letters 83 (19) (2003).

[3] G. Horowitz, P. Delannoy, Journal of Applied Physics 70 (1991) 469–475.[4] S. Scheinert, G. Paasch, M. Schrodner, H.-K. Roth, S. SensfuB, Th. Doll, Journal of

Applied Physics 92 (2002) 330–337.[5] S. Scheinert, G. Paasch, T. Doll, Synthetic Metals 139 (2003) 233–237.[6] R. Bourguiga, F. Garnier, G. Horowitz, R. Hajlaoui, P. Delannoy, M. Hajlaoui, H.

Bouchriha, The European Physical Journal: Applied Physics 14 (2001) 121–125.

[7] M.A. Alam, A. Dodabalapur, M.R. Pinto, IEEE Transactions on Electron Devices44 (1997) 1332–1337.

[8] P.V. Necliudov, M.S. Shur, D.J. Gundlach, T.N. Jackson, Journal of AppliedPhysics 88 (2000) 6594–6597.

[9] Y. Roichman, N. Tessler, Applied Physics Letters 80 (2002) 151–153.[10] L. Torsi, A. Dodabalapur, H.E. Katz, Journal of Applied Physics 78 (1995) 1088–

1093.[11] T. Li, P.P. Ruden, I.H. Campbell, D.L. Smith, Materials Research Society

Symposium Proceedings 725 (2002) P10.2.[12] F. Xue, Y. Su, K. Varahramyan, IEEE Transactions on Electron Devices 52 (2005)

1982–1987.[13] Gillies Horowitz, Journal of Applied Physics 67 (1) (1989) 528–532.[14] L.B. Schein, A. Peled, D. Glatz, Journal of Applied Physics 66 (2) (1989) 686–

691.[15] Beat Ruhstaller, Tilman Beierlein, Heike Riel, Siegfried Karg, J. Campbell Scott,

Walter Riess, IEEE Journal of Selected Topics in Quantum Electronics 9 (3)(2003).

[16] D.H. Dunlap, P.E. Parris, V.M. Kenkre, Physics Review Letters 77 (3) (1996).[17] H.C.F. Martens, J.N. Huiberts, P.W.M. Blom, Applied Physics Letters 77 (12)

(2000).[18] L. Bozano, S.A. Carter, J.C. Scott, G. Malliaras, P.J. Brock, Applied Physics Letters

74 (8) (1999).[19] S.M. Silence, J.C. Scott, F. Hache, E.J. Ginsburg, P.K. Jenkner, R.D. Miller, R.J.

Twieg, W.E. Moerner, Journal of the Optical Society of America B 10 (12)(1993).

[20] Damodar M. Pai, Journal of Chemical Physics 52 (5) (1970) 2285–2291.[21] W.D. Gill, Journal of Applied Physics 43 (12) (1972) 5033–5040.[22] A. Bolognesi, A. Di Carlo, P. Lugli, Applied Physics Letters 81 (24) (2002) 4646–

4648.[23] M.A. Baldo, S.R. Forrest, Physical Review B 64 (August) (2001).[24] Kannan Seshadri, C. Daniel Frisbie, Applied Physics Letters 78 (7) (2001).[25] Taurus MediciTM, Taurus-DeviceTM, User Guide, Version W-2004.09, September

2004, SYNOPSYS�.[26] P.H. Nguyen, S. Scheinert, S. Berleb, W. Brutting, G. Paasch, Organic Electronics

2 (2001) 105–120.