# How is graphene a 2D substance?

How is graphene a 2D substance? It has length, width and some thickness to it, else it would be invisible. Why is it considered a 2D substance?

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I bet someone could write a really good and comprehensive answer to this explaining wave propagation in atomic layers. Unfortunately I don't have time right now. – David Z Jul 12 '13 at 23:10

Anyhow, the thickness of the sheet is around one atom, which means that in the direction normal to the sheet the electrons are confined within a potential well of around 1 atom in width. Consequently the energy spacings for excitations normal to the layer are going to be around atomic energy levels, which are typically a few eV. At room temperature electron energies are going to be of order $kT$, or about 0.025eV, so no excitations in the direction normal to the sheet are possible. That's why the electrons can be treated as moving in a two dimensional system.
If you increase the temperature then $kT$ increases as well, and at some point the material will stop behaving as a purely 2D material. However I'd guess you'd need several thousand degrees before this became significant.