(Invited) Parametrization of Gaussian Disordered Model with Fully Spatial and Energetic Disorders for Organic Thin Film Transistors
Authors: Lee Yongjeong , Jung Sungyeop , Jung Sungjune , Plews Andrew , Nejim Ahmed , Simonetti Olivier , Giraudet Louis , Baranovskii Sergei D. , Horowitz Gilles , Bonnassieux Yvan 
Published: December 2020

So far, the most widely addressed hopping transport model for organic disordered semiconductors (ODSs) is the so-called extended Gaussian disordered model (EGDM) [1] based on numerical simulations within the cubic lattice without spatial disorder. As known since 1973 [2] and confirmed recently [3], the EGDM is based on the parametrization of transport coefficients in the framework of the irrelevant set of parameters. Parameters responsible for the effects are not in the equations, while parameters in the equations are not responsible for the effects [3]. The deficiencies of the EGDM are particularly pronounced for systems with spatial disorder. Therefore, the study of Gaussian disordered model (GDM) with spatial disorder is necessary to provide a simulation tool for transport coefficients of charge carriers in real organic thin film transistors (OTFTs) and organic light-emitting diodes (OLEDs) based on materials with spatial disorder.
In this study, we examine the GDM which contains both spatial and energetic disorders and propose a physical parametrization for OTFTs. We determine all the parameters by adjusting the localization length and the attempt-to-escape frequency to satisfy experimentally measured mobility. For the localization length, the concept of effective localization length [4] is adopted which has the order of a molecular diameter, because assumption of the very low localization length (commonly order of 10-8 cm) induces very low mobility due to the strong localization of the each state. The large effective localization length can alleviate the strong localization and so it can predict the similar scale of mobility with experimentally measured one. In addition, the proper value of the attempt-to-escape frequency is estimated from comparison between a direct calculation of Miller-Abrahams (MA) transition rate and theoretical estimations of the hopping transition rate based on MA and Marcus theories. We show that its value should be increased by more than two orders of magnitude than conventional value to simulate high mobility device.
Then, we validate our parametrization of GDM through comparison between experimentally measured and numerically calculated transfer curves and charge carrier mobility of OTFTs at various temperature (Fig. 1). The staggered pentacene-based OTFT device was fabricated and measured at different temperatures T = 329, 293, 258 and 233 K. The charge carrier mobility was extracted by the transmission line method (TLM). For numerical simulation, we implemented the GDM by Baranovskii [3] into the commercial TCAD simulation tool, Silvaco ATLAS. Then, the numerical solver calculated Poisson’s, continuity and drift-diffusion equations in a self-consistent manner with characteristics of ODSs such as Gaussian density-of-states, generalized Einstein relation and GDM by Baranovskii. Numerical simulation with a single set of parameters makes an accurate fit with experimentally measured transfer curves (Fig. 1a) and charge carrier mobility (Fig. 1b) at every temperature condition.
In conclusion, we propose physically based parametrization of GDM with fully spatial and energetical disorder for OTFTs. It is confirmed that the localization length and the attempt-to-escape frequency are key parameters for the practical fitting with experimental result. In addition, we can expect that the electronic design automate (EDA) industry can be promoted by providing rigorous transport model and its parametrization for OTFTs within commercial simulation software.
[1] W. F. Pasveer, J. Cottaar, C. Tanase, R. Coehoorn, P. A. Bobbert, P. W. M. Blom, M. De Leeuw, and M. A. J. Michels, Phys. Rev. Lett. 94, 206601 (2005).
[2] B.I. Shklovskii Sov. Phys.-Semicond. 6, 1964 (1973).
[3] S. D. Baranovskii, Phys. Status Solidi Appl. Mater. Sci. 215, 1700676 (2018).
[4] A. V Nenashev, J. O. Oelerich, and S. D. Baranovskii, J. Phys. Condens. Matter 27, 093201 (2015).

Figure 1