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To estimate the effect of a dielectric film placed on top of graphene, we have considered the standard scattering problem for a Coulomb potential V(q)1/qε. Here, ε is the effective dielectric function that, because of a finite thickness D of the film, is dependent on the in-plane electron wave vector q and is given by ε(q)=F(q)2G(q) with F(q)=κ+κS- [(κ-1)(κ-κS)(κ+1)]exp(-2qD) and G(q)=1+[κ- 1κ+1]exp(-2qD). This formula is a straightforward solution for the three media electrostatic problem with a charge placed at the interface between the SiO2 substrate (dielectric constant κS) and the film. One can check that this yields ε=(κS+1)/2 and ε=(κS+κ)/2 for D=0 and ∞, respectively.
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