38 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 56, NO. 1, JANUARY 2009 SPICE Optimization of Organic FET Models Using Charge Transport Elements Vaibhav Vaidya, Jungbae Kim, Joshua N. Haddock, Bernard Kippelen, and Denise Wilson Abstract—We report on a modeling technique that uses charge transport equations to calculate channel current in organic field effect transistors (OFETs) by numerical solution in the SPICE simulation program. SPICE is also used to optimize the model and achieve a fit to measured characteristics within 5% error. The overall modeling technique is a bridge between physical models of charge transport and a SPICE model useful in circuit simula- tion without requiring a closed-form drain-current equation. The automatic optimization of the simulation to measured curves will also allow, in the future, the empirical weighing of various charge transport effects in search of physical device operation, given sufficient empirical data. This modeling technique was applied to the measured characteristics of an OFET using pentacene in which the mobility was dependent on the voltage in the channel. The accuracy of the fit was better than 5% for 40 V >V DS > 7 V and better than 20% for V DS < 7 V. Simulation was completed within 3 min for this optimization on a modern personal computer. Index Terms—Charge transport, organic electronics, or- ganic field effect transistor (OFET), OTFT, SPICE, SPICE optimization. I. INTRODUCTION O RGANIC FIELD effect transistor (OFET) technology is at a stage where useful commercial electronic circuits are possible for applications such as active matrix displays [1], [2] and flexible systems [3], and future applications such as printable RFID tags are under active development [4]. As circuit applications of OFETs are researched, a pressing need for accurate models of the OFETs for use in electronic circuit simulators is evident. Along with the development of the fabrication processes for OFETs, various such physical and empirical models have been developed to explain OFET behavior [5]–[12]. Since OFET physics is still an actively researched topic, these models are mathematically devised for single device calculations and present a significant difficulty for adapting to circuit simulators such as SPICE. Furthermore, Manuscript received June 10, 2008; revised October 10, 2008. Current version published December 19, 2008. This work was supported in part by the National Science Foundation under Agreement DMR 0120967 through the STC program and in part by the Office of Naval Research. The review of this paper was arranged by Editor J. Kanicki. V. Vaidya is with the Distributed Microsystems Laboratory, Department of Electrical Engineering, University of Washington, Seattle, WA 98195 USA. J. Kim is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA. J. N. Haddock is with the PixelOptics Inc., Roanoke, VA 24017-1911 USA. B. Kippelen is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA. D. Wilson is with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195 USA (e-mail: denisew@u.washington.edu). 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.2008.2008164 Fig. 1. Multielement channel model of OFET charge transport. since the actual physical mechanisms underlying OFET opera- tion have not yet achieved consensus, present literature shows a large variation in the type and scope of OFET models. Given the increasing advancement of organic devices in commercial markets, the need for useful circuit models is obvious. Inherent differences between the OFET and the silicon-based MOSFET, however, pose some challenges to developing effective models for widespread use in the circuit community. In this paper, we propose a basic model that enables flexibility and accuracy in matching physical equations to measured OFET characteristics; this approach is important in developing practical models for a wide variety of OFETs for use in SPICE-based simulation. The model is based on utilizing the ability of SPICE to numer- ically calculate node voltages to evaluate boundary conditions in a finite-element approach to modeling the OFET channel. Details of the model and performance for pentacene OFETs are presented herein. II. MODEL DESCRIPTION The model for charge conduction used in this paper divides the OFET channel into a finite series of elements, each of length ΔL = L/N (Fig. 1). An assumption that the electric field and material properties such as mobility are constant across the length of each element is then made. With this assumption, charge transport in each element can now be described as a function of basic physical parameters such as mobility and switch-on voltage for the FET, and circuit parameters such as gate and terminal voltage. This approach is similar to the ana- lytical derivation of the gradual channel approximation model for FETs. However, whereas the analytical method seeks a closed-form solution for the current in the channel, the element- based SPICE model arrives at this solution numerically as a by-product of simulation. Essentially, SPICE calculates the boundary conditions for the elements such that the current through them is the same and that this same current is also 0018-9383/$25.00 © 2009 IEEE Authorized licensed use limited to: IEEE Xplore. Downloaded on January 9, 2009 at 16:19 from IEEE Xplore. Restrictions apply.