Finite-concentration gas molecule adsorption on carbon nanotubes investigated by a tight-binding approach

A theoretical approach based on tight-binding model is developed to study the effects of finite concentrations of adsorption of diatomic gas molecules (in the general form denoted by $X_2$) and also triatomic gas molecules (in the general form denoted by $Y{X}_2$) on the single-walled carbon nanotube (SWCNT) 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. We found, for some specified values of hopping integrals and random on-site energies, adsorbed molecule bound states located inside the (10,0) SWCNT energy gap, where it is consistent with the reported experimental results for ${\mathrm{O}}_2$ and $\mathrm{N}{\mathrm{O}}_2$ adsorption, while for other values, there are no bound states inside of energy gap. The last case is similar to the ${\mathrm{N}}_2$ and $\mathrm{C}{\mathrm{O}}_2$ adsorption on semiconductor SWCNTs. Then, by using these obtained parameters and coherent potential approximation, we investigate the effects of finite gas molecule adsorption on the average density of states. Our results could be used to make a $p$-type or $n$-type semiconductors by finite-concentration adsorption of gas molecules.

Figure 1

(Color online) General form of diatomic gas adsorption by a (10,0) SWCNT.

Figure 2

(Color online) General form of triatomic gas adsorption by a (10,0) SWCNT.

Figure 3

(Color online) Comparison of the local density of states of a pure (10,0) SWCNT with respect to the local density of sates of $A_1$ subsite of site 0, where a diatomic gas molecule is adsorbed. The hopping deviations and on-site energy are chosen to be $\delta 1=+0.08t$, $\delta 2=-0.08t$, and $ϵ=-0.14t$, respectively. In this case, a $p$-type semiconducting (10,0) SWCNT has been produced.

Figure 4

(Color online) Comparison of the local density of states of a pure (10,0) SWCNT in the case when $A_1$ subsite of site 0 adsorbed a diatomic molecule. The hopping integral deviations and on-site energy are $\delta 1=-0.08t$, $\delta 2=+0.08t$, and $ϵ=+0.14t$. The adsorption led to an $n$-type semiconductor (10,0) SWCNT.

Figure 5

(Color online) Comparison of the local density of states of a pure (10,0) SWCNT with respect to case where a diatomic gas molecule is adsorbed by $A_1$ subsite of site 0. The hopping deviations and on-site energy are $\delta 1=-1.68t$, $\delta 2=-1.2t$, and $ϵ=-4.8t$. In this case, there are no adsorption gas molecule bound states inside the energy gap of semiconducting (10,0) local density of states.

Figure 6

(Color online) Local density of states at $A_1$ subsite of site 0 where two diatomic gas molecules are adsorbed by $A_1$ and $B_1$ subsites of site 0 of a (10,0) SWCNT. The hopping integral deviations and on-site energy are $\delta 1=+0.08t$, $\delta 2=-0.08t$, and $ϵ=-0.14t$, respectively. The density of states illustrates a $p$-type semiconductor.

Figure 7

(Color online) Local density of states at $A_1$ subsite of site 0 where two diatomic gas molecules are adsorbed by $A_1$ and $B_1$ subsites of site 0 of a (10,0) SWCNT. The hopping integral deviations and on-site energy are $\delta 1=-0.08t$, $\delta 2=+0.08t$, and $ϵ=+0.14t$, respectively. The density of states illustrates an $n$-type semiconductor.

Figure 8

(Color online) A (10,0) SWCNT when both $A_1$ and $B_1$ subsites of site 0 have adsorbed a diatomic gas molecule. Location of sites 1, 2, and 10 are defined.

Figure 9

(Color online) [(a)–(c)] Comparison of the local density of states of a pure (10,0) SWCNT with respect to the local density of states at $A_1$ subsites of sites 0, 1, and 10 indicated in Fig. 8. The hopping integral deviations and on-site energy are $\delta 1=+0.08t$, $\delta 2=-0.08t$, and $ϵ=-0.14t$ respectively. As expected, by increasing the distance from host site 0, the adsorbed bound state peak is decreased and finally disappears.

Figure 10

(Color online) [(a) and (b)] Comparison of the local density of states of a pure (10,0) SWCNT with respect to the local density of states at $A_1$ subsite of site 0 for two cases: first, both molecules are adsorbed by $A_1$ and $B_1$ subsites of site 0 and, second, one of them by $A_1$ subsite of site 0 and the other by $A_1$ subsite of site 10. The hopping integral deviations and on-site energy are $\delta 1=+0.08t$, $\delta 2=-0.08t$, and $ϵ=-0.14t$, respectively.

Figure 11

(Color online) Comparison of a pure (10,0) SWCNT density of states with respect to the $A_1$ subsite of site 0 local density of states, where each subsite ($A_1$ and $B_1$) of site 0 adsorbed a triatomic gas molecule. The hopping integral deviations and on-site energies are $ϵ1=-0.08t$, $ϵ2=-0,065t$, $\delta 1=0.13t$, $\delta 2=0.065t\delta 3=-0.8t$, and $\delta 4=-0.065t$, respectively. The local density of states illustrates a $p$-type semiconductor.

Figure 12

(Color online) Comparison of a pure (10,0) SWCNT density of states with respect to the $A_1$ subsite of site 0 local density of states, where each subsite ($A_1$ and $B_1$) of site 0 adsorbed a triatomic gas molecule. The hopping integral deviations and on-site energies are $ϵ1=+0.08t$, $ϵ2=+0.065t$, $\delta 1=-0.13t$, $\delta 2=-0.065t$, $\delta 3=+0.8t$, and $\delta 4=+0.065t$, respectively. The local density of states illustrates an $n$-type semiconductor.

Figure 13

(Color online) [(a), (b), and (c)] The density of states of a diatomic gas adsorbed (10,0) SWCNT for several gas molecule concentrations $c=0.004$, 0.008, and 0.012, respectively. The hopping integral deviations and on-site energy, are $\delta 1=+0.08t$, $\delta 2=-0.08t$, and $ϵ=-0.14t$, respectively. The average density of states illustrates an $n$-type semiconductor.

Figure 14

(Color online) [(a), (b), and (c)] The average density of states of a diatomic gas adsorbed (10,0) SWCNT for adsorbed gas molecules concentrations $c=0.004$, 0.008, and 0.012, respectively. The hopping integral deviations and on-site energy are $\delta 1=-0.08t$, $\delta 2=+0.08t$, and $ϵ=+0.14t$, respectively. The average density of states illustrates a $p$-type semiconductor, where the height and width of the acceptor band increased by increasing the adsorbed gas concentration.

Figure 15

(Color online) [(a), (b), and (c)] The density of states of a gas adsorbed (10,0) SWCNT for gas molecule concentrations of 0.004, 0.008, and 0.012, respectively. The hopping integral deviations and on-site energies are $ϵ1=+0.08t$, $ϵ2=+0.065t$, $\delta 1=-0.13t$, $\delta 2=-0.065t$, $\delta 3=+0.8t$, and $\delta 4=+0.065t$, respectively. The average density of states illustrates an $n$-type semiconductor.

Figure 16

(Color online) [(a), (b), and (c)] The density of states of a gas adsorbed (10,0) SWCNT for gas molecule concentrations of 0.004, 0.008, and 0.012, respectively. The hopping integral deviations and on-site energies are $ϵ1=-0.08t$, $ϵ2=-0.065t$, $\delta 1=0.13t$, $\delta 2=0.065t$, $\delta 3=-0.8t$, and $\delta 4=-0.065t$, respectively. The local density of states illustrates a $p$-type semiconductor.