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 two-dimensional concentration n0∼N2/3 of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size R0∼N−1/3. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.
@article{arxiv.0706.4425,
title = {A simple model of Coulomb disorder and screening in graphene},
author = {B. I. Shklovskii},
journal= {arXiv preprint arXiv:0706.4425},
year = {2009}
}