(Invited) Compact Model for Short-Channel Organic Thin-Film Transistors with Extension for Non-Quasistatic Circuit Simulation and Variability Analysis
Authors: Kloes Alexander , Prüfer Jakob , Leise Jakob , Nikolaou Aristeidis , Darbandy Ghader , Klauk Hagen 
Published: July 2021

We present a compact model for organic thin-film transistors (TFTs) that covers both below-threshold and above-threshold operation with a single charge-based current expression [1]. The effect of hopping transport is included by a power-law mobility model. Contact resistances for staggered and coplanar device structures (Fig. 1) are considered, which can be nonlinear in the case of work-function mismatch between contacts and organic semiconductor [2]. Short-channel effects in submicron transistors, such as threshold-voltage roll-off and drain-induced barrier lowering (DIBL), are included [3].
From the expression for the accumulated channel charge, a closed-form model for the drain-current variability due to carrier-number and correlated mobility fluctuations has been derived, relating these statistical variations to the trap density in the channel [4].
Furthermore, by applying a partitioning scheme, charges are explicitly attributed to the source and drain contacts, allowing the derivation of a charge-based capacitance model valid for quasi-static operation [5]. Charges in the gate-to-contact overlap regions have been included.
Utilizing this device model in a transmission-line approach, a circuit simulation including non-quasistatic effects is possible [6]. In the circuit-simulation netlist, the TFT is replaced by a macro model consisting of a finite number of n single transistors, whereby each single transistor represents a section of the intrinsic channel capacitance and a segment of the intrinsic channel resistance. This model is able to capture the charging and discharging of the channel capacitance of each segment through the channel resistance of the adjacent transistors. In this way, the frequency dependence of the node-to-node capacitances of the full device is obtained.
The compact model has been implemented in the hardware description language Verilog-A and verified using results of measurements performed on organic p-channel TFTs fabricated on flexible polyethylene naphthalate (PEN) substrates by stencil lithography (Figs. 2, 3). The TFTs consist of 25-nm-thick aluminum gate electrodes, a 5.3-nm-thick hybrid AlOx/SAM gate dielectric, 30-nm-thick gold (Au) source and drain contacts coated with a pentafluorobenzenethiol (PFBT) monolayer, and a 25-nm-thick vacuum-deposited layer of the small-molecule organic semiconductor DPh-DNTT [7,8]. The transmission-line approach has been verified with good accuracy by comparison with frequency-dependent admittance measurements and numerical simulations of the transient switching behavior of organic TFTs. For a transient analysis, the optimum number of segments required to achieve good agreement between the results from the model and those from TCAD simulations is approximately n=6.
In conclusion, the model presented here is fully capable of providing accurate results in dc, small-signal ac, and transient circuit simulations, including short-channel effects. Furthermore, the same set of equations allows an estimation of the drain-current variability due to charge trapping.

Acknowledgements: This project was funded by the German Federal Ministry of Education and Research ("SOMOFLEX", No. 13FH015IX6), German Research Foundation (DFG) under Grant KL 1042/9-2 (SPP FFlexCom), and EU H2020 RISE ("DOMINO", No. 645760). We acknowledge AdMOS GmbH, Germany for support.

References:

[1] Hain et al., “Charge based, continuous compact model for the channel current in organic thin-film transistors for all regions of operation,” Solid-State Electronics, vol. 133, p. 17, 2017.
[2] Pruefer et al., “Compact modeling of non-linear contact resistance in staggered and coplanar organic thin-film transistors,” Proceedings Int’l Conf. Org. Electronics 2018, Grenoble, 2018.
[3] Pruefer, et al., "Compact Modeling of Short-Channel Effects in Staggered Organic Thin-Film Transistors," IEEE Trans. Electron Devices, vol. 67, no. 11, pp. 5082-5090, September 2020.
[4] Nikolaou, et al., "Charge-Based Model for the Drain-Current Variability in Organic Thin-Film Transistors due to Carrier-Number and Correlated-Mobility Fluctuation," IEEE Trans. Electron Devices, vol. 67, no. 11, pp. 4667-4671, September 2020.
[5] Leise et al., "Charge-Based Compact Modeling of Capacitances in Staggered Multi-Finger OTFTs," IEEE Journal of the Electron Devices Society, vol. 8, pp. 396-406, March 2020
[6] Leise, J. Prüfer, A. Nikolaou, G. Darbandy, H. Klauk, B. Iniguez, and A. Kloes, "Macro model for AC and Transient Simulations of Organic Thin-Film Transistor Circuits Including Nonquasistatic Effects," IEEE Trans. Electron Devices, vol. 67, no. 11, pp. 4672-4676, September 2020.
[7] W. Borchert et al., “Small contact resistance and high-frequency operation of flexible low-voltage inverted coplanar organic transistors,” Nature Commun., vol. 10, p. 1119, Mar. 2019.
[8] Zaki et al., “Accurate capacitance modeling and characterization of organic thin-film transistors,” IEEE Trans. Electron Devices, vol. 61, p. 98, January 2014.

Figure 1