  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 $0.65 \div 35 \ \mu m$.
