Simple model of Coulomb disorder and screening in graphene

We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration N/2 in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates the two-dimensional concentrations n(0)similar to N(2/3) of electrons and holes in the graphene sample. Electrons and holes reside in alternating in space puddles of the size R(0)similar to N(-1/3). A typical puddle has only one or two carriers in qualitative agreement with the recent scanning single electron transistor experiment.