The conduction in polycrystalline organic material is represented laterally and vertically. Lateral conduction is expected in between two electrodes, such as the source and the drain electrodes in an organic thin-film transistor (OTFT), consisting of a number of grains and grain boundaries. Considering the effects of an external voltage applied laterally, the formation of grains and grain boundaries depend mainly on two conduction mechanisms, namely drift and diffusion. In the case of organic semiconductors, these terms are developed as quasi- drift and quasi- diffusion. It is said that the exponential distribution of states in the grain boundary defines a potential in the grains. The further the grain boundaries are from each other, the lower the potential barrier exists at the centre of the grain. The difference in energy between the grain centre and the Fermi level is therefore reduced and conduction at the centre of the grain dominates.
From one grain boundary to another, the potential barrier progressively drops till the centre of the grain. The concentration gradient observed in this case is similar to the diffusion mechanism. In the case of drift mechanism, the difference between the energy of Fermi level and the transport level stays the same. Combination of both these mechanisms provides a good idea of the flux across the grain boundaries. The derivation of flux is therefore used to model a polycrystalline organic material for devices such as organic lateral diodes or TFT devices.
Vertical conduction is expected in vertical Schottky diodes between the ohmic and Schottky contacts. A vertical representation is important to determine the grains and grain boundaries across the thickness of the organic layer. The polycrystalline organic layer in this case is thin. Thinner organic layers lead to an extension of the depletion region across the thickness of the organic layer. Assuming that only a single layer of grain and grain boundaries exist, a 2- Dimensional model based on the potential variation in grains due to exponential distribution of traps is proposed in this thesis. The charge conduction is thus dependent on the exponential DOS in the grain boundaries and the conduction mechanisms are not considered. The disordered grain boundaries form a potential barrier to current flow due to the distribution of traps.
To solve this two dimensional problem, the grains and the grain boundaries are considered as two one-dimensional issues that at right angle to each other. In the vertical direction, Poisson’s equation is used to define the variation of potential in the grain boundary. A term in the z- direction is thus developed. Accordingly, this causes the grains to see a variation in potential at the grain edge such that the grains can be constructed. The potential variation in grains is developed by the use of Poisson’s equation applied at the grain edge. A few assumptions are made to construct the grain and consequently, the variation of potential in the whole of the grain is defined in the x-direction. A novel term for the potential at grain centre is established which provides the maximum number of carriers for charge conduction. Ultimately using drift currents, a new expression corresponding to the current density at the grain centre in the forward characteristics is established.
Laplace L1 DOS is a new approach used to describe the density of states in the grain boundaries of an organic polycrystalline material. Laplace DOS is considered a suitable representation for the distribution of states in a polycrystalline material as prediction of current density for a higher range of energy levels is possible with Laplace DOS. A number of reasons are provided to back the claim made in this thesis. In the case of devices such as a Schottky diode, the drop across the exponential region in the forward electrical characteristics is much more than the Meyer Neldel energy. Consequently, Laplace distribution is believed to be a better representation of the DOS instead of the vastly followed Gaussian DOS. Finally, by taking the exponential L1 distribution and the Maxwell-Boltzmann statistics into account, an expression to identify the carrier concentration is finally developed.
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