Space charge layers in organic field-effect transistors with Gaussian or exponential semiconductor density of states

Abstract

Space charge layers (SCLs) in metal-insulator-semiconductor (MIS) structures are critical for the operation of field-effect transistors (FETs). For many organic semiconductors, transport takes place as hopping in Gaussian or exponentially distributed states. However, existing theoretical descriptions of a SCL and advanced device simulation programs suppose a density of states other than a Gaussian or an exponential, employing often the nondegenerate limit for the concentrations. We present results of a simulation study for the MIS structure as the basic module of the FET and for a thin semiconducting layer on a metal substrate. The second system was extensively investigated by photoelectron spectroscopy to characterize the metal-organics interface occurring at the source/drain contact of FETs and as anode and cathode in organic light emitting diodes. For broader distributions, the densities deviate strongly from the nondegenerate limit which leads indeed in a MIS structure to a strong deviation of the dependence of the surface electric field (and, hence, the areal charge) on the surface potential. However, as one can control only the gate voltage directly, the dependency on this quantity determines device operation. For the variations of the layer thickness and gate insulator thickness, and doping in the wide range of interest, this dependency deviates only slightly from the nondegenerate approximation, essentially in the depletion region by a flatband voltage shift. In the accumulation region, which is determinative for FET operation, the remaining deviation can be removed almost perfectly by considering this flatband voltage shift. For the thin organic layer on a metal substrate, numerical simulations confirm the applicability of an analytical approximation for band bending and floating potential [G. Paasch et al., J. Appl. Phys. 93, 6084 (2003)] for the nondegenerate case and for the exponential distribution. Indeed, for small barriers at the interface, a band bending of up to the order of 100 meV can occur within the first 2 nm near the interface. In the interpretation of photoemission data such contribution will appear as part of the measured interface dipole.