Calculating the trap density of states in organic field-effect transistors from experiment: A comparison of different methods

The spectral density of localized states in the band gap of pentacene (trap DOS) was determined with a pentacene-based thin-film transistor from measurements of the temperature dependence and gate-voltage dependence of the contact-corrected field-effect conductivity. Several analytical methods to calculate the trap DOS from the measured data were used to clarify, if the different methods lead to comparable results. We also used computer simulations to further test the results from the analytical methods. Most methods predict a trap DOS close to the valence-band edge that can be very well approximated by a single exponential function with a slope in the range of 50\char21{}60 meV and a trap density at the valence-band edge of $\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{21}\text{ }{\text{eV}}^{\ensuremath{-}1}\text{ }{\text{cm}}^{\ensuremath{-}3}$. Interestingly, the trap DOS is always slightly steeper than exponential. An important finding is that the choice of the method to calculate the trap DOS from the measured data can have a considerable effect on the final result. We identify two specific simplifying assumptions that lead to significant errors in the trap DOS. The temperature dependence of the band mobility should generally not be neglected. Moreover, the assumption of a constant effective accumulation-layer thickness leads to a significant underestimation of the slope of the trap DOS.