Nonequilibrium Green’s function study of ${\text{Pd}}_4$-cluster-functionalized carbon nanotubes as hydrogen sensors

Pd-cluster-functionalized carbon nanotubes (CNTs) have been shown experimentally to be effective hydrogen sensors. Semiconducting CNTs exhibit much higher sensitivity than ensemble (mixed) ones. Using the nonequilibrium Green’s function method combined with the density-functional theory, we simulate and contrast the (8,0) semiconducting and the (5,5) metallic CNT model systems. We find that the electron localization effect plays a crucial role in determining electron transport. Pd clusters and hydrogen adsorption cause opposite effects on electron localization in the CNT backbone for the semiconducting CNT-based systems. Consequently Pd functionalization dramatically increases the conductance, but then it is strongly suppressed by hydrogen absorption. For the metallic CNT-based systems, there is a tiny shift of the transmission peak near the Fermi energy. These results offer a consistent explanation for the experiments.

Figure 1

(Color online) Geometric structures of the semiconducting (8,0) CNT-based systems (a) doped only with palladium, (b) with hydrogen molecule physisorbed on palladium, and (c) with hydrogen molecule chemisorbed on palladium. Yellow atoms are Au in leads; green atoms are carbon; magenta atoms are palladium; and white atoms are hydrogen. The top right inset of each panel shows the local structure of Pd cluster from front view. The dotted line shows the H-H bond.

Figure 2

(Color online) Geometric structures of the metallic (5,5) CNT-based systems (a) doped only with palladium, (b) with hydrogen molecule physisorbed on palladium, and (c) with hydrogen molecule chemisorbed on palladium. Yellow atoms are Au in leads; green atoms are carbon; magenta atoms are palladium; and white atoms are hydrogen. The top right inset of each panel shows the local structure of Pd cluster from front view. The dotted line shows the H-H bond.

Figure 3

(Color online) Transmission spectra of (a) pure CNTs within gold leads (without any Pd or hydrogen doping), (b) metallic (5,5) CNT-based systems, and (c) semiconducting (8,0) CNT-based systems. “Pd only” indicates Pd-cluster-doped CNT system without hydrogen adsorption; “Physi” indicates hydrogen-physisorbed system; and “Chemi” indicates hydrogen-chemisorbed system. $E_F$ is aligned at 0.0 eV in all figures.

Figure 4

(Color online) DOSs around $E_F$ projected onto CNT backbone for the pure and Pd-cluster-doped CNT systems without gold leads. $E_F$ is aligned at 0. Panel (a): metallic (5,5)-based systems; panel (b): semiconducting (8,0)-based systems.

Figure 5

(Color online) DOSs of model systems without gold leads projected onto CNT backbone: (a) metallic (5,5) CNT-based systems; (b) semiconducting (8,0) CNT-based systems. $E_F$ is aligned at 0.

Figure 6

(Color online) Hartree potentials averaged over the $xy$ cross section of the device region along the $z$ axis for (a) (5,5)-based model systems and (b) (8,0)-based model systems. The two panels should not be compared directly against each other. The curves within each panel, however, are directly comparable. The labels “Pd only,” “Physi,” and “Chemi” have the same meanings as in Fig. 3.

Figure 7

(Color online) LDOSs of metallic (5,5) CNT-based systems. The contour is taken at LDOS of $1.0\times {10}^{-4}$. The figure shows only one of the two CNT-cluster units for simplicity and clearness purposes. (a) Pd-cluster-doped CNT without hydrogen adsorption; (b) Pd-cluster-doped CNT with hydrogen chemisorption.

Figure 8

(Color online) LDOSs of semiconducting (8,0) CNT-based systems. The contour is taken at LDOS of $1.0\times {10}^{-4}$. The figure shows only one of the two CNT-cluster units for simplicity and clearness purposes. (a) Pd-cluster-doped CNT without hydrogen adsorption; (b) Pd-cluster-doped CNT with hydrogen chemisorption.

Figure 9

(Color online) Transmission spectra of reference system A for (a) (5,5) metallic CNT-based systems and (b) (8,0) semiconducting CNT-based systems. “Pd-only” denotes the system without hydrogen adsorption; “Physi” denotes the system with hydrogen physisorbed on the cluster; and “Chemi” denotes the system with hydrogen chemisorbed on the cluster.

Figure 10

(Color online) Transmission spectra of reference system B for (a) (5,5) metallic CNT-based systems and (b) (8,0) semiconducting CNT-based systems. “Pd-only” denotes the system without hydrogen adsorption; “Physi” denotes the system with hydrogen physisorbed on the cluster; and “Chemi” denotes the system with hydrogen chemisorbed on the cluster.