I want to design a structure with tunability. I want to know if there is any restriction to increase that
The chemical potential of graphene can be tuned using an electrostatic field or with static charge bring by chemicals on the surface.
With electric field; the limit is set by the maximum field before breakdown occurs in the dielectric. In solid state this limit is about 1V/nm which leads to charge density of a few 10^13 electrons per cm^2. This is equivalent to a chemical potential shift of a hundred of meV. To reach significant shifts (eV range), other means have to be employed such as ionic liquid gating or chemical adsorption at the risk of modifying the graphene by chemical reaction. Still it is hard to move that chemical potential in the eV range.
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