3D graphene is graphite. Vertical electron transport between 2D graphene and something else (e.g. another graphene) could be realised as quantum tunnelling. In this case vertical mobility is not defined.

Graphene is, by definition, a 2D material. Which mobility would one expect in 3rd dimension?

I presume out-of plane vibration, bending is thought of. Which is quite reasonable. I wonder whether Ram can be used to detect suc a motion. I would expect low frequency mode (similar to puckering or torsion). Surely there are higher frequency out of plane vibrations as well, but these are probebly local. I alos assume that the porbability of graphene bending would strongly depend on the perfection of the surface of the adherend and on the coverage of the surface.

Are you talking about charge transfer across the bilayer? For a transistor, we might expect spontaneous hopping between layers but this will also be modulated by the gate-induced electric field since in many cases, a bandgap will open. But in any case, I don't think a "vertical" mobility is the proper term here, especially if you're concerned with a ballistic device. The Fermi velocity should be large, so it's important to have a high quality bilayer.

Thanks

For mono layer Graphene, I think we can define another mobility except its common mobility. About devices like FET base transistor, due to its surface transferring, it isn't important to define another mobility. But for bipolar ones, as we know that carriers experience vertical transmission, if we implant graphene(even single layer) in some places, carriers sense extra scattering which can cause another mobility.

3D graphene is graphite. Vertical electron transport between 2D graphene and something else (e.g. another graphene) could be realised as quantum tunnelling. In this case vertical mobility is not defined.

Thanks

I have an extra question

As you mentioned above, which parameters differentiate quantum tunneling in different material or cases?(mean its velocity or lattice constant and ...)

quantum tunnelling usually has a peculiar nonlinear I(V), sometimes with resonances if there are well defined single quantum states.

Tunnelling current mainly depend on the barrier width and height. Width of the barrier is a geometrical property of a particular device. Height of the barrier is a property of the material used as the barrier layer (e.g. BN).

A good example of quantum tunnelling between 2 graphene layers can be found here: L. Britnellar al., Field-Effect Tunneling Transistor Based on Vertical Graphene Heterostructures, http://www.sciencemag.org/content/335/6071/947.short

Recently article published on how current flows in 2D materials

http://phys.org/news/2013-07-scientists-electric-current-multilayer-d.html#nwlt

http://pubs.acs.org/doi/abs/10.1021/nl401831u