  The metal-graphene contact resistance is one of the major limiting factors
toward the technological exploitation of graphene in electronic devices and
sensors. A high contact resistance can be detrimental to device performance and
spoil the intrinsic great properties of graphene. In this paper, we fabricate
graphene field-effect transistors with different geometries to study the
contact and channel resistance as well as the carrier mobility as a function of
gate voltage and temperature. We apply the transfer length method and the
y-function method showing that the two approaches can complement each other to
evaluate the contact resistance and prevent artifacts in the estimation of the
gate-voltage dependence of the carrier mobility. We find that the gate voltage
modulates the contact and the channel resistance in a similar way but does not
change the carrier mobility. We also show that the raising temperature lowers
the carrier mobility, has negligible effect on the contact resistance, and can
induce a transition from a semiconducting to a metallic behavior of the
graphene sheet resistance, depending on the applied gate voltage. Finally we
show that eliminating the detrimental effects of the contact resistance on the
transistor channel current almost doubles the carrier field-effect mobility and
that a competitive contact resistance an be achieved by the zig-zag shaping of
the Ni contact.
