(Invited) Generic Compact Model for Variability and Low-Frequency Noise in Organic Thin-Film Transistors
Authors: Kloes Alexander , Darbandy Ghader , Iniguez Benjamin , Nikolaou Aristeidis 
Published: August 2024

In organic thin-film transistors (OTFT), low-frequency noise (LFN) is dominated mainly by grain-boundary traps and mobility fluctuation [1]. Accurate LFN modeling of OTFTs has been successfully demonstrated in [2] by adopting the theory of carrier-number and correlated mobility fluctuations (ΔN noise) [3,4,5] and the empirical Hooge approach accounting for mobility fluctuation due to percolative effects (Δµ noise) [6,7]. Furthermore, OTFTs are sensitive to process variability. Charges being trapped in the channel region cause a local variation of the accumulated charge density, having impact on the threshold voltage of the device [8,9] and reducing the effective carrier mobility in the channel by Coulomb scattering. As a result, the drain-current variability is also correlated to carrier-number and correlated mobility fluctuations and therefore allows for a similar modeling approach as for ΔN noise [9].
Based on the results published in [2,9], we present a generic physics-based modeling approach for drain-current fluctuations by carrier-number and correlated mobility fluctuations, which leads to similar expressions for drain-current variability and ΔN noise in OTFTs. The model is based on the charge-based compact model for OTFTs presented in [10]. Starting from the local fluctuation of the current in the channel, closed-form model equations have been derived for the fluctuation of the total device current. The final expressions (1) for drain-current variability and (2) for ΔN noise show the same bias dependent part B*(qch) given by equation (5). An individual bias-independent prefactor C* is obtained. In case of drain-current variability this factor in equation (3) depends on the density Nt of trapped charges. For ΔN noise, in (4), NT is the density of traps per energy available for capture and release of charge carriers.
Measurements performed on fabricated OTFTs in staggered (C10-DNTT) or coplanar (Dph-DNTT) architectures (Fig. 1) show that the drain-current variability in the subthreshold regime is dominated by carrier-number fluctuations, whereas for above threshold operation the mobility-fluctuation effect by correlated Coulomb scattering comes to the fore (Fig. 2) [9]. In case of LFN, measurements on staggered DNTT OTFTs have shown that ΔN noise alone is not sufficient to describe the noise spectra in the deep subthreshold regime of operation (Fig. 3) [2]. Here, LFN due to mobility fluctuation (Δµ noise) must be included with equations (6-8), which results in an additional and different bias dependent expression with a prefactor including the empirical Hooge parameter. The total LFN is given by (9).
In conclusion, following a generic modeling approach, the combined equations for carrier-number and correlated mobility fluctuations and for percolative mobility fluctuation allow consideration drain-current variability and LFN noise in a charge-based compact model of OTFTs in all regions of operation and is in good agreement with results from measurements.

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), the Spanish Ministry of Science (PRX21/00726), and the EU EIC-PATHFINDER (BAYFLEX, no 101099555). We acknowledge AdMOS GmbH, Germany, for support, and Max Planck Institute for Solid State Research Stuttgart, Germany, for fabrication of devices.

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Figure 1