  Graphene devices for analog and RF applications are prone to Low Frequency
Noise (LFN) due to its upconversion to undesired phase noise at higher
frequencies. Such applications demand the use of short channel graphene
transistors that operate at high electric fields in order to ensure a high
speed. Electric field is inversely proportional to device length and
proportional to channel potential so it gets maximized as the drain voltage
increases and the transistor length shrinks. Under these conditions though,
short channel effects like Velocity Saturation (VS) should be taken into
account. Carrier number and mobility fluctuations have been proved to be the
main sources that generate LFN in graphene devices. While their contribution to
the bias dependence of LFN in long channels has been thoroughly investigated,
the way in which VS phenomenon affects LFN in short channel devices under high
drain voltage conditions has not been well understood. At low electric field
operation, VS effect is negligible since carriers velocity is far away from
being saturated. Under these conditions, LFN can be precicely predicted by a
recently established physics-based analytical model. The present paper goes a
step furher and proposes a new model which deals with the contribution of VS
effect on LFN under high electric field conditions. The implemented model is
validated with novel experimental data, published for the first time, from CVD
grown back-gated single layer graphene transistors operating at gigahertz
frequencies. The model accurately captures the reduction of LFN especially near
charge neutrality point because of the effect of VS mechanism. Moreover, an
analytical expression for the effect of contact resistance on LFN is derived.
This contact resistance contribution is experimentally shown to be dominant at
higher gate voltages and is accurately described by the proposed model.
