Investigation of the Influence of the Source / Drain Barrier Height on the I / V Characteristics of OFETs by Using a 2 D Analytical Model for the Injection Current

The interest in organic semiconductors, especially organic field-effect transistors has grown enormously during the last years. They feature properties far beyond these of their inorganic counterpartners essential for devices like flexible displays or printable electronics. However, analytical compact models of organic semiconductors are rarely to find and mostly not able to describe the physical and chemical facts clearly. In the most cases they just exist for semiconductors with a well matching HOMO level. In dependence of different source and drain materials, varying workfunctions, HOMO-, LUMOand trap-levels the parasitic contact resistance effects became a major problem in organic transistors [1], [2]. So the source semiconductor junction was considered to be the limiting factor for the charge carriers. Exemplarily for the case of bottom-contact, bottom gate OFETs we present an analytical model for the electrostatic potential, the electric field as well as the source and drain injection current which is able to describe typical characteristics in the output and transfer curves. These are, for instance, an s-like shape in the output characteristic or kinks in the transfer characteristic (Fig. 2,4) especially of devices fabricated with organic semiconductors whose HOMO level does not match well with the electrode’s workfunction. In general the charge injection into organic semiconductors is described by the thermionic driftdiffusion theory. Mostly tunneling processes are neglected. In our model we combine thermal diffusion and tunneling processes to describe the injection into a random hopping system. The organic semiconductor data set is leaned on Pentacene but kept variable regarding the barrier height for holes ΦBp. A band-like transport within the semiconductor is assumed in this step, as well as a gate-bias dependent mobility [3]. As it is most commonly used, we assumed gold as source and drain electrode’s material. In accordance with the different charge transport mechanisms we separated the whole device into different subparts: The source semiconductor contact, whose properties highly influence the charge carrier injection, the transistor channel itself and the drain semiconductor contact. Each of these parts can limit the total device current. We assumed three operational states clearly to be separated and influenced just by the barrier height ΦBp (Fig. 1). At first if the gate and drain biases are low and the bands at the source-channel and the channel-drain junction are bent upwards (p-semiconductor). Secondly when the drain bias raises the bands at the source-channel junction bend downwards and finally the bands on both junctions bent downwards for high VGS and comparatively low VDS. If we assume that the injection current consists of a diffusion and a tunneling contribution the band bending has to be derived at the junctions. This is done by computing the electric field on the basis of a 2D potential solution analytically by solving the Poisson equation via the conformal mapping technique [4], [5]. The total device current is calculated by superposition, where IsTE, IsTU, IdTE, and IdTU, are the source or drain related thermionic and tunneling currents, respectively (Fig. 3):