This paper discusses an approach to use an approximated charge carrier density for organic thin-film transistor (OTFT) using a double exponential density of states. Traditionally the literature has been published using a single exponential density of states and Gaussian density of states but this paper deals with using a double exponential density of states in the Fermi Integral to evaluate the charge carrier density for the OTFT. There are two exponential density of states related to the Tail region and Deep region and various parameters associated with it. The distribution of localized trap states between the highest and lowest orbital is expressed as a density of states. There are two states deep states and tail states. Tail states are better described by the Gaussian function, while Deep states are better described by the Exponential density of states. So, 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 accurately describe the complete region. The double exponential density of states is considered to evaluate and approximate the Fermi Integral using various Mathematical Methods, so that the error is lower for various parameters.

This paper discusses an approach to use an approximated charge carrier density for organic thin-film transistor (OTFT) using a double exponential density of states. Traditionally the literature has been published using a single exponential density of states and Gaussian density of states but this paper deals with using a double exponential density of states in the Fermi Integral to evaluate the charge carrier density for the OTFT. There are two exponential density of states related to the Tail region and Deep region and various parameters associated with it. The distribution of localized trap states between the highest and lowest orbital is expressed as a density of states. There are two states deep states and tail states. Tail states are better described by the Gaussian function, while Deep states are better described by the Exponential density of states. So, 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 accurately describe the complete region. The double exponential density of states is considered to evaluate and approximate the Fermi Integral using various Mathematical Methods, so that the error is lower for various parameters.