Experiments in organic semiconductors (polyacenes) evidence a strong super quadratic increase of the current-voltage (I-V) characteristic at voltages in the transition region between linear (Ohmic) and quadratic (trap free space-charge-limited-current) behaviours. Similarly, excess noise measurements at a given frequency and increasing voltages evidence a sharp peak of the relative spectral density of the current noise in concomitance with the strong super-quadratic I-V characteristics. Here we discuss the physical interpretation of these experiments in terms of an essential contribution from field assisted trapping-detrapping processes of injected carriers. To this purpose, the fraction of filled traps determined by the I-V characteristics is used to evaluate the excess noise in the trap filled transition (TFT) regime. We have found an excellent agreement between the predictions of our model and existing experimental results in tetracene and pentacene thin films of different length in the range $0.65 div 35 mu m$.
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