  Channel length scaling in graphene field effect transistors (GFETs) is key in
the pursuit of higher performance in radio frequency electronics for both rigid
and flexible substrates. Although two-dimensional (2D) materials provide a
superior immunity to Short Channel Effects (SCEs) than bulk materials, they
could dominate in scaled GFETs. In this work, we have developed a model that
calculates electron and hole transport along the graphene channel in a
drift-diffusion basis, while considering the 2D electrostatics. Our model
obtains the self-consistent solution of the 2D Poisson's equation coupled to
the current continuity equation, the latter embedding an appropriate model for
drift velocity saturation. We have studied the role played by the
electrostatics and the velocity saturation in GFETs with short channel lengths
L. Severe scaling results in a high degradation of GFET output conductance. The
extrinsic cutoff frequency follows a 1/L^n scaling trend, where the index n
fulfills n < 2. The case n = 2 corresponds to long-channel GFETs with low
source/drain series resistance, that is, devices where the channel resistance
is controlling the drain current. For high series resistance, n decreases down
to n= 1, and it degrades to values of n < 1 because of the SCEs, especially at
high drain bias. The model predicts high maximum oscillation frequencies above
1 THz for channel lengths below 100 nm, but, in order to obtain these
frequencies, it is very important to minimize the gate series resistance. The
model shows very good agreement with experimental current voltage curves
obtained from short channel GFETs and also reproduces negative differential
resistance, which is due to a reduction of diffusion current.
