Statistical modelling of organic thin film transistor behaviour

Three analyses of the expressions describing the electrical characteristics of organic thin film transistors (OTFT's) are presented. The first is the field-independent approach to mobility originally used for inorganic semiconductor materials, often referred to as the Square Law (SQL). The second is appropriate for both the Multiple Trapping and Release (MTR) and the Variable Range Hopping (VRH) descriptions of mobility, where dependence on a transverse field is consistent with the Universal Mobility Law (UML). The third is appropriate for the Extended Gaussian Disorder (EGD) description where an exponential dependence of mobility on the transverse field occurs. In each case master equations have been derived, including Schottky contact effects, where the polarity of the voltage drop across the source and drain contacts is correctly taken into account for the first time. The effect of the bulk semiconductor material beyond the accumulation layer is also accounted for, and defines the sub-threshold performance in a low-voltage regime. A new statistical modelling procedure has been developed to extract the key parameters of these expressions simultaneously from experimental data. For the analysis of TRANSFER data, no more than five parameters are used in the SQL, UML and EGD treatments. All three models are considered so that the effect the choice of model has on the extracted parameters can be revealed; analysis of data from different metallophthalocyanines is used to illustrate the different effects. When the contact resistances correctly take into account possible Schottky-like behaviour, all three descriptions provide equally excellent fits to the data from TRANSFER experiments. In a following report, a family of copper phthalocyanine-related semiconductors will be examined in detail using these new analysis procedures to explore the effect of non-peripheral substituent bulk, and aza-nitrogen replacement by CH, on mobility.