To get this eletric field information I ran a simulation with Vd=0.5V and Vg from 0 to 6V, (Id x Vg characteristic) and then I saved the structure file to check how the eletric field behave. I am very doubtful because for me it doesn't make any sense all the structures having similar eletric field, but the structure and the curves Id x Vg seem to be Ok and according to what I expect.

Fernanda, it is not that easy to understand the electric field distribution from your images.because of the color profiles. It would be of some help showing the field along some specific cutlines, say the horizontal and vertical median lines and a couple of vertical lines at 0.5 om from the aluminum/semiconductor junctions (both source and drain). Al, at FIXED Vd and Vg (+0.5 V and +6V as per your simulations) and grounded source.

By the way I can not see any junction in the device body, apart from the two (Schottky-type) S and D ones at the horizontal bourders.

I can anticipate that no significant differences should be expected between mono- and poòysilicon if both are intrinsic. apart from mobility that is more or less affected by grain boundary scattering when grain size is much smaller than the whole polysilicon wire size.

At fixed external fields, current in germanium is larger than in silicon (both intrinsic) simply because the intrinsic carrier concentration is 1000+ times larger in the former. The same may be expected of course comparing a doped silicon (your "graphene") with the intrinsic case. A detailed behaviour, however, would require the knowledge of the transconductance, that is any "net resistance" modulation induced by tha gate voltage, case by case.

Just show up the cutlines I cited above and the Id vs Vg curves, if you like.