Abstract
This paper discusses the use of an approximated charge carrier density to model an organic thin-film transistor (OTFT) using a double exponential density of states. Traditionally, published work employs a single exponential density of states and Gaussian density of states. On the contrary, this paper employs a double exponential density of states in the Fermi integral to evaluate the charge carrier density for the OTFT. We consider two exponential density of states, one rateled to the tail region and one to a deep region, in addition to various associated parameters. The distribution of localized trap states between the highest and lowest orbital is expressed as a density of states, one for the tail states and one for the deep states. Tail states are better described by the Gaussian function, while deep states are better described by the exponential density of states. Therefore, if we require that the two regions be defined by a single function, then the function should be a sum of the two, the exponential and the Gaussian, to more accurately describe the complete region. The double exponential density of states is employed to evaluate and approximate the Fermi integral using various mathematical methods, so that the error is lower for various parameters.