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I am trying to understand how the sheet resistance would vary between a suspended sheet of graphene and a sheet of graphene on an insulating substrate (say SiO2). I am not looking for a law telling me how it varies, I just would like to understand if the sheet resistance increases when the graphene is bounded to an insulating substrate as I intuitively expext. And if yes, what is the physical reason? If you have any reference showing experimental measurements it would be appreciated (I haven't found anything so far).

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  • $\begingroup$ Why would you expect the resistance to decrease? $\endgroup$ – CuriousOne May 14 '16 at 9:37
  • $\begingroup$ Because of what I was reading here: researchgate.net/post/… . In some sense I think adding a substrate reduces the constraints on the k vector in one of the direction and therefore it makes it similar to a bulk material which usually has higher resistivity compared to their 2D counterpart. $\endgroup$ – Worldsheep May 14 '16 at 11:19
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    $\begingroup$ Did I just understand you wrong? Do you mean that the free graphene should have the lower resistance? The argument going from 3d to 2d materials gets you to the suspended graphene and I think it is, at least intuitively, correct. By bonding it to a substrate, we are still coupling to (some) of the substrate phonons and I would expect an increase in resistance and the effective dielectric constant relative to the free graphene. I could be wrong... I hope someone who knows can get the answer. $\endgroup$ – CuriousOne May 14 '16 at 11:33
  • $\begingroup$ Yes I am thinking only at an intuitive level (and looking for a better founded argument). I think we mean the same thing. Coupling the graphene to an insulating substrate should increase the resistance. I'll edit the question, it is not super-clear $\endgroup$ – Worldsheep May 14 '16 at 11:40
  • $\begingroup$ Sorry about the misunderstanding. I would, intuitively, agree. The 2.5d system (or whatever one wants to call it) should have an increased resistance. Having said that... who knows that really happens when quantum mechanics throws a wrench in there and the lattices line up into a special configuration that makes the ballistic transport even more efficient? See e.g. "Exceptional ballistic transport in epitaxial graphene nanoribbons" Jens Baringhaus et al. Nature 506, 349–354 (20 February 2014) ... surprise! $\endgroup$ – CuriousOne May 14 '16 at 11:46
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Citing one of the original works on suspended graphene by Bolotin et al., scattering of charge carriers in substrate-supported graphene may result from a number of sources, including

[...] charged impurities on top of graphene or in the underlying substrate, corrugation of the graphene sheet, [...] or remote interfacial phonons in the substrate. The formation of electron and hole puddles can further contribute to scattering at low carrier density.

Which mechanism dominates may depend on the details of the setup.

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