The adsorption effect of C$_6$H$_5$ on density of states for double wall carbon nanotubes by tight binding model

A theoretical approach based on a tight-binding model is developed to study the effects of the adsorption of finite concentrations of C$_6$H$_5$ gas molecules on double-walled carbon nanotube (DWCNT) electronic properties. To obtain proper hopping integrals and random on-site energies for the case of one molecule adsorption, the local density of states for various hopping integrals and random on-site energies are calculated. Since C$_6$H$_5$ molecule is a donor with respect to the carbon nanotubes and their states should appear near the conduction band of the system, effects of various hopping integral deviations and on-site energies for one molecule adsorption are considered to find proper hopping and on-site energies consistent with expected $n$-type semiconductor. We found that adsorption of C$_6$H$_5$ gas molecules could lead to a (8.0)@(20.0) DWCNT $n$-type semiconductor. The width of impurity adsorbed gas states in the density of states could be controlled by adsorbed gas concentration.