Most compact models for organic field-effect transistors (OFETs) are based on a two-piece description: a set of equations for above threshold operation is combined with a current model valid in subthreshold region by means of an analytical smoothing function [1]. Thereby the threshold voltage is introduced as fitting parameter without any relation to physical parameters. In [2] a charge-based current model with a continuous equation valid in all regions of operation has been presented. While solving Poisson’s equation the model preserves a close link to physical parameters like shallow and deep trap densities and avoids the introduction of a threshold voltage and subthreshold slope as model parameters.
However, from a circuit designer’s perspective a model providing a close link to electrical device parameters is desirable because parameters as threshold voltage and slope can easily be extracted from I/V curves and are performance measures of a device. In this paper an improvement of the model from [2] is presented which leads to a charge-based C∞-continuous current model with threshold voltage and slope as model parameters, while still keeping a single expression valid from below to above threshold operation.
To include the effect of hopping transport the empirical power-law mobility model [3] and a contact resistance [4] have been incorporated in the effective mobility. Channel length modulation effects have been included according to [5]. Furthermore, from physical parameters given by trap densities the threshold voltage and subthreshold slope of the device can be calculated.
In the case of co-planar device structures the output characteristics in the linear operation regime show a superlinear behaviour due to non-linear injection effects. If the barrier height between source electrode and the channel material is not negligible the channel current is limited by the source injection current. The Schottky barrier height is modulated by the gate and drain potential. A strong electric field causes thinning of the barrier, allowing more carriers to enter channel.
An analytical equation for the electric field at the injection barrier has been derived by applying the conformal mapping technique. The bias-dependent lowering of the Schottky barrier, and hence the maximum injection current can be calculated. An equivalent resistance of the Schottky barrier is calculated from the voltage drop Vds and the maximum possible injection current. To arrive at a closed-form current equation for the intrinsic device together with the injecting Schottky barrier this equivalent resistance is incorporated in the current equation by a first order approximation which is commonly used for the consideration of parasitic resistances. In this case the equivalent resistance is bias dependent and reduced with increasing Vds due to Schottky barrier lowering.
The model has been validated vs. measurements on devices with small molecule organic semiconductors (Fig. 1, 2). The results show good agreement, even for the 1st and 2nd derivatives of the transfer characteristics.
Acknowledgements: This project was funded by the German Federal Ministry of Education and Research contract No.03FH013PX2 (FhProfUnt). This project was also funded by the Horizon 2020 Programme of the European Union under contract RISE 2014 645760 ("DOMINO"). We acknowledge CEA-Liten (Grenoble) and Max Planck Institute for Solid State Research (Stuttgart) for providing measurement data. We thank AdMOS GmbH for support and Keysight Technologies for license donation of IC-CAP.
References:
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