Work function of single-walled and multiwalled carbon nanotubes: First-principles study

Abstract

Carbon nanotubes can be viewed as rolled-up graphene sheets. As such, their work functions should be closely related to those of graphene due to geometric and structural similarities. In this paper, we have systematically investigated the work functions of single-walled and multiwalled carbon nanotubes by density functional calculations. The work functions of single-walled carbon nanotubes (SWCNTs) are very close to those of graphene in the armchair conformation, while for the zigzag and chiral conformations, the work functions are close to those of graphene as the diameter is larger than a certain threshold. When the diameter of the tube is smaller than $10\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, the work functions of zigzag and chiral tubes increase dramatically as the diameter decreases. The deviation in the work function from that of graphene for small tubes can be explained and qualitatively estimated by the downshift of the Fermi level due to the curvature effect. For multiwalled carbon nanotubes (MWCNTs), we only consider zigzag and armchair MWCNTs. We find that the work functions of all armchair and zigzag MWCNTs with inner tube diameters larger than $10\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ are very close to those of graphene. The work functions of zigzag MWCNTs with inner tube diameters smaller than $10\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ exhibit significant variations depending on the diameters of the inner and outer tubes. Using a very simple model, we find that the work functions of MWCNTs can be successfully estimated from the work functions and electronic structures of the constituent SWCNTs.