Modified Lampert triangle in an organic field effect transistor with traps

Abstract

Applying the surface-charge formalism, we developed a simple theory of trap-filling transitions in organic thin films in a planar field effect transistor geometry. We derived numerical as well as approximate analytical expressions for the current-voltage characteristics and for the saturation current as a function of the gate voltage (saturation transfer curve) in the presence of a discrete set of traps. We show that all single-carrier conduction possibilities in organic field effect transistors with discrete trapping levels are limited within a triangular region of the saturation transfer curve in the logarithmic scale. This region is bounded by the Ohm's law, a trap-free square law, and a trap-filled limit curve which has a voltage threshold and is characterized by a step rise of the saturation current. This ``triangle'' is equivalent to the Lampert's triangle of the simple space-charge limited conduction theory for one-dimensional charge transport between two Ohmic electrodes. Finally, we show that two of the bounding sides of this triangle were experimentally observed in tetrabenzoporphyrin-based organic field effect transistors reported in the literature [P. B. Shea, J. Kanicki, and N. Ono, J. Appl. Phys. 98, 014503 (2005)] with the calculated third side fitting the experimental data very well.