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We built graphene nanoflakes doped or not with $C$ atoms in the $sp^3$hybridization or with $Si$ atoms. These nanoflakes are isolated, i.e. are notconnected to any object (substrate or junction). We used a modified tightbinding method to compute the $\pi$ and $\sigma$ density of states. Thenanoflakes are semiconducting (due to the armchair geometry of theirboundaries) when their are pure but the become conducting when doped becausedoping removes the degeneracy of the density of states levels. Moreover, weshowed that the $\pi$ Fermi level and the Fermi level of both $\pi$ and$\sigma$ electrons are not superimposed for small isolated nanoflakes.

Pure, $Si$ and $sp^3$-doped Graphene nanoflakes: a numerical study of density of states