Simplified evaluation of the electrostatic effect of gate voltages on a graphene layer

We present a numerical method which allows an approximate but fast computation of the potential profile in a graphene sample subject to the electrostatic action of biased gates, including the effect of different contributions, such as those from doping or from charged impurities. The procedure is applied to the evaluation of the effect of a biased probe, coupled to the graphene flake through a space-dependent geometrical capacitance, for two realistic potential landscapes, corresponding to a series of tunnel barriers and to a disordered sample.