Modulation of the Work Function of Capped Single-Walled Carbon

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Modulation of the Work Function of Capped Single-Walled Carbon Nanotube by Alkali-Metal Adsorption: A Theoretical Study Shun-Fu Xu,† Guang Yuan,*,†,‡ Chun Li,† Wei-Hui Liu,† and Hidenori Mimura‡ † ‡

Department of Physics, School of Information Science and Engineering, Ocean University of China, Qingdao 266100, China Research Institute of Electronics, Shizuoka University, Hamamasu 432-8011, Japan ABSTRACT: The influence of alkali-metal (Li/Na/Cs) adsorption on work functions of (5, 5) and (9, 0) single-walled carbon nanotubes (CNTs) with a capped edge was investigated by first-principles calculations. After alkali-metal adsorption, the work functions of (5, 5) and (9, 0) CNTs decrease and vary linearly with the electronegativity of the element, but the positions where the alkali atom is adsorbed considerably influence the work functions. However, any vacancy defect on the cap raises the work functions of the CNTs. The variations in the work functions are mainly attributed to changes in the Fermi levels induced by charge redistributions. Additionally, alkali-metal adsorption can improve the electric conductivity of a CNT mixture.

1. INTRODUCTION Carbon nanotubes1 (CNTs) have received considerable attention as potential candidates for future nanoelectronics as they boast unique geometries and prominent electronic properties. Specifically, the potential of CNTs has been demonstrated in vacuum microelectronic devices.2,3 CNTs with indices (n, m) can exhibit metallic or semiconducting properties, depending on whether n
m is an integral multiple of three. In addition to electrical conductivity, the work function is another significant physical property of interest. Multiwalled carbon nanotubes (MWCNTs) have work functions between 4.30
4.95 eV,4
7 while single-walled carbon nanotubes (SWNTs) have values (4.80
5.05 eV) slightly higher than that of the graphite.8
10 First principles calculations show that the work functions of SWNTs are close to the work function of graphite and depend on the chirality and diameter, especially when the diameter is less than 1 nm.11
14 Besides chirality and diameter, the work function is influenced by the dipole of CNTs when CNTs form a bundle.15 The work functions of MWCNTs can be simply estimated from the work functions and electronic structures of the constituent SWCNTs.13,16 Decreasing or modulating the work functions of the CNTs is of great importance to control the interface properties between CNTs and other materials and considerably impacts device performance, including the field emission properties.17 Both experimental and theoretical calculations indicate that the work functions of CNTs are dramatically reduced upon alkali-metal (Li/K/Rb/ Cs) adsorption, which leads to a significant enhancement in the r 2011 American Chemical Society

field emission. The work functions of SWCNTs and MWCNTs after the treatment of cesium drastically decrease to about 2.0
3.1 and 3.0 eV, respectively.18
20 Moreover, lithium and potassium have been shown to decrease the work function of CNTs and improve the field electron emission.21
23 Theoretical calculations10,24
26 have demonstrated that adsorption or intercalation of alkali metals dramatically decreases the work functions of CNTs. It should be mentioned here that the calculated work functions strongly depend on the exchange and correlation functional. However, issues regarding the work functions of CNTs adsorbed with alkali metals remain. In this Letter, we report the results of work functions in the axial or radial directions of capped (5, 5)/(9, 0) single-walled CNTs with different alkali metals (Li/Na/Cs) based on first principles calculations. The calculation results show that the electronegativity of the alkali metal is a crucial parameter in determining the work functions of CNTs with alkali-metal adatoms. The effects of vacancy defects and adsorption positions of different alkali metals (Li/Na/Cs) are also investigated.

2. THEORETICAL METHODS Figure 1 shows the calculation models of the capped CNTs. We assumed single-walled armchair (5, 5) and zigzag (9, 0) Received: January 27, 2011 Revised: March 17, 2011 Published: April 15, 2011 8928

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Figure 1. Side and top views of (a) (5, 5) P-CNT and (b) (9, 0) P-CNT marked with the adsorption positions. Yellow and blue balls represent C and H atoms, respectively.

CNTs with a capped edge because they are energetically favored with respect to opened CNTs even in strong electric fields.27 The armchair (5, 5) CNT was simply constructed by a five-layer (50 atoms) stem. Similarly, (9, 0) CNT was modeled by seven layers of carbon rings (63 atoms) along the tube axis. On the basis of experimental observations,28 the (5, 5) and (9, 0) CNTs were capped by a hemisphere of C60 at one end, and the dangling bonds at the other end were saturated by hydrogen atoms. To increase the chemical stability of the structures and emulate infinite CNTs, the two layers of carbon atoms at the bottom terminated with hydrogen atoms were fixed throughout the simulation.29 Other research groups have employed similar models.30
32 A vacancy defect was created by removing a carbon atom from the pentagon (for the (5, 5) CNT) or hexagon (for the (9, 0) CNT) on the cap. Alkali-metal adatoms (Li/Na/Cs) were initially located at various positions above the center of the pentagons or hexagons (which are labeled as P1
P4 in Figure 1a for the (5, 5) CNT and P1
P5 in Figure 1b for the (9, 0) CNT) on the caps for a perfect CNT (P-CNT) or vacancy defects (for the defective CNTs (D-CNTs)). Our calculations were performed within first-principles desnity functional theory (DFT) under the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE).33 An ultrasoft pseudopotential with a plane-wave basis set up to a kinetic energy cutoff of 30 Ry was used for the wave functions. The Brillouin zone was sampled using the Γ-point approximation. The atomic positions were optimized until the maximum force on any atom was less than 1.0  10
4 au. The CNTs were constructed within the same tetragonal supercell employing a vacuum width of 20 Å in the axial direction and a separation of

Figure 2. (a) Axial and radial work functions of (5, 5)/(9, 0) P- and D-CNTs with Li/Na/Cs on P1 vs electronegativity. (b) Axial and radial work functions of the (5, 5) P-CNT with Li/Na/Cs on P2
P4 vs electronegativity.

12 Å in the radial direction to avoid interactions between adjacent CNTs. The work function was defined as the minimum energy necessary to extract an electron far from CNTs into the vacuum level, WF = φ
Ef, where φ represents the vacuum level and Ef denotes the Fermi level. In our calculations, the vacuum level was determined from the electrostatic potential in the vacuum region and was a sufficient distance from the carbon nanotubes in the Z/X direction that the value converged. All calculations were performed using the QUANTUM ESPRESSO suite of programs.34,35

3. RESULTS AND DISCUSSIONS In the present calculations, the work function of the (5, 5) P-CNT along the axial direction (Z-axis, Z-WF) is 4.20 eV, which is smaller than that of other calculation results (4.78 eV).12 In contrast, the Z-WF of (9, 0) P-CNT is 4.29 eV, which is slightly larger than the previous calculation (4.14 eV).12 After Li/Na/Cs adsorption, the work functions of both the P- and D-CNTs along the Z-axis and the X-axis (X-WF) significantly decrease. The X-WF of the (5, 5) P-CNT with alkali-metal adatoms are smaller than that of the (9, 0) P-CNT with alkali-metal adatoms. In contrast, the X-WF of the (5, 5) D-CNT with alkali-metal 8929

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Table 1. Slopes of the Linear Curves for (5, 5)/(9, 0) P- and D-CNTs with Alkali-Metal Adatoms Z-WF of (5, 5)

X-WF of (5, 5)

Z-WF of (5, 5)

X-WF of (5, 5)

Z-WF of (9, 0)

X-WF of (9, 0)

Z-WF of (9, 0)

P-CNT

P-CNT

D-CNT

D-CNT

P-CNT

P-CNT

D-CNT

3.01

2.13

3.13

2.37

2.75

2.02

2.38

X-WF of (9, 0)

Z-WF of (5, 5)

X-WF of (5, 5)

Z-WF of (5, 5)

X-WF of (5, 5)

Z-WF of (5, 5)

X-WF of (5, 5)

D-CNT

P-CNT-P2

P-CNT-P2

P-CNT-P3

P-CNT-P3

P-CNT-P4

P-CNT-P4

1.90

2.54

1.96

1.87

2.25

1.46

1.75

adatoms are larger than that of the (9, 0) D-CNT with alkalimetal adatoms. Figure 2 summarizes the work functions of (5, 5)/(9, 0) P- and D-CNTs with alkali-metal adatoms on the top plotted against the electronegativity of the alkali-metal element. All the axial and radial work functions of (5, 5)/(9, 0) CNTs increase linearly with electronegativity. Table 1 lists the slopes of these linear curves. The slopes are very close to those from the Gordy
Thomas equation (WF = 2.3χ þ 0.34), which is a linear relationship between the work function and electronegativity of an element.36,37 Compared to the axial work functions, the radial work functions (X-WF) of the D-CNTs are more consistent with the Gordy
Thomas equation.36,37 Similarly, the axial and radial work functions of (5, 5) P-CNT with alkali-metal adatoms on different positions (P2
P4) in Figure 2b exhibit a linear relationship with electronegativity. The slopes of these linear curves depend on the chirality, whether a vacancy defect is present, and the site where the alkali atom is absorbed. When the adsorption position shifts from P1 to P4, the slopes for the axial work functions of (5, 5) P-CNT with alkali-metal adatoms decrease markedly. However, the largest slope for the radial work function occurs at P3. Therefore, the adatom-P-CNT systems have the lowest work functions with alkali-metal adatoms on P1 in the axial direction and on P3 in the radial direction. The linear curves in Figure 2 can also predict the work functions of CNTs adsorbed with another alkali atom such as potassium. It is noteworthy that the work functions of CNTs adsorbed with potassium reported by Ha et al.23 agree well with the linear dependence of the work functions and electronegativity. These results suggest that the GGA framework can reliably calculate the work functions of adatom-CNT systems. Moreover, other metal adatoms, including other alkali-metal adatoms (K/Rb), are presumed to have similar effects as Li, Na, and Cs on decreasing or increasing the axial and radial work functions of CNTs. The linear dependence of the work functions of CNTs on the electronegativity of the adatom implies that the work function of CNTs can be simply modulated by adsorption of different elements. The work functions can be changed by either an enhanced (reduced) surface dipole moments or a lowering (rising) of the intrinsic bulk Fermi levels as ΔWF = Δφ
ΔEf.11 Our results show that the changes of the work functions are mainly due to the shifts in the Fermi levels. For example, the shift in the Fermi levels after Li/Na/Cs adsorption on P1 is 0.69/0.79/1.11 eV for the (5, 5) P-CNT, and the corresponding variations in the Z-WF and X-WF are 0.86/0.97/1.42 eV and 0.65/0.74/1.05 eV, respectively. Figure 3a plots the Fermi levels of (5, 5)/(9, 0) P- and D-CNTs with alkali-metal adatoms on P1 versus electronegativity. All the Fermi levels of the P-CNTs and D-CNTs adsorbed with Li/Na/Cs increase linearly with electronegativity, indicating the changes in the Fermi levels are dominated by the electronegativity of alkali-metal adatoms. The Fermi levels of the

Figure 3. (a) Fermi levels and dipole moments along the Z axis of (5, 5)/(9, 0) P- and D-CNTs with alkali-metal adatoms on P1 plotted against electronegativity. (b) Relation between the variations in the vacuum levels and induced dipole moments along the Z-axis of the (5, 5)/(9, 0) P-CNT with Li/Na/Cs on P1
P4/P1
P5.

(5, 5) P-CNT with alkali-metal adatoms are slightly higher than that of the (9, 0) P-CNT with alkali-metal adatoms. However, the Fermi levels of the (5, 5) D-CNT with alkali-metal adatoms are slightly lower than that of the (9, 0) D-CNT with alkali-metal adatoms. Figure 3a also shows the dipole moments along the Zaxis of CNTs with alkali-metal adatoms plotted as a function of electronegativity. All the dipole moments increase linearly with the electronegativity, suggesting that the changes in the dipole moments are dominated by the electronegativity. Figure 3b presents the variations in the vacuum levels as a function of the induced dipole moments along the Z-axis for (5,5)/(9,0) P-CNTs with alkali-metal adatoms on P1
P4/ P1
P5. The variations in the vacuum levels increase linearly as the induced dipole moments increase from P1 to P4 or 8930

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Figure 4. Contours of differential charge density distributions of (a) (5, 5) Li
P-CNT and (b) (5, 5) Li
D-CNT. Black, green, and red balls represent carbon, hydrogen, and Li atoms, respectively. Blue and yellow represent positive and negative charge distributions, respectively. Differential charge density distribution is defined as C = C(CNTs þ Li)
C(CNTs)
C(Li).

Figure 5. Density of states (DOS) of the (5, 5) P-CNT and D-CNT before and after Li adsorption on P1. The inset shows DOS of the (5, 5) P-CNT and D-CNT before and after Na adsorption. Fermi levels are set to 0 eV.

from P1 to P5 for all the adatom-P-CNT systems, indicating that the changes in the vacuum levels in the axial direction are mainly due to the changes in the dipole moments along the tube axis. After alkali-metal adsorption, the induced dipole moments influence the vacuum levels, leading to small changes in the work functions. The relationship between these physical quantities for the Cs
P
CNT system and adatom-D-CNT systems is similar to the adatom-P-CNT systems. Because the electronegativity of an alkali-metal atom is less than carbon, the alkali-metal adatoms on the CNTs are easily ionized, and the electrons are transferred from the alkali-metal adatoms to CNTs. Figure 4 illustrates the differential charge density distributions (DCDD) of the (5, 5) P-CNT and D-CNT adsorbed with one lithium atom on the top position (P1). The charges accumulate between Li and the six nearest-neighbor carbon atoms on the caps, exhibiting the features of a π-orbital for C atoms. Compared to the Li-P-CNT systems, there is an asymmetric contour of the DCDD for the Li-D-CNT systems. Therefore, Li adatom is predicted to almost completely donate its outer electrons with higher energy to the P- or D-CNT and elevate the Fermi level of the P- or D-CNT. The redistributions or charge transfer will also decrease the vacuum levels due to the induced dipole moments. The DCDD of the Na/Cs-P-CNT and Na/Cs-D-CNT systems is similar to that of the Li-P-CNT and Li-D-CNT systems. However, the Na/Cs adsorption is more efficient in charge transfer and elevation of the Fermi levels due to the smaller electronegativity of the Na/Cs adatom. Because the diameters of Li/Na/Cs atoms are comparable to that of the hexagon or pentagon rings of CNTs, alkali metals can reduce the spatial extensions of the p electrons into the vacuum by forming chemical bonds with CNTs and assist CNTs in keeping their electrons, resulting in a repulsion among the energy states.24 Here, we choose the (5, 5) P-CNT with the Li adatom as an example. Figure 5 shows the density of states (DOS) of the (5, 5) P-CNT and D-CNT before and after Li adsorption on P1. Usually the opened (5, 5) P-CNT presents metallic characteristics, while the capped (5, 5) P-CNT exhibits semiconducting properties.38 As shown in Figure 5, the DOS of the (5, 5) P-CNT shifts toward the low-energy side after Li adsorption, reflecting a

greater occupation of CNT states; that is, the highest occupied molecular orbital shifts toward a higher energy. Adsorption of the Li atom enhances the value of DOS at the Fermi level for the (5, 5) P-CNT, transforming the pristine semiconductor into a metal. This is consistent with the above-mentioned shift in the Fermi level of the P-CNT. The (5, 5) D-CNT shows metallicity and the DOS near the Fermi level does not change significantly after Li adsorption. The DOS of the Na/Cs-P-CNT and Na/CsD-CNT systems (the inset shows DOS of the (5, 5) P-CNT and D-CNT before and after Na adsorption) is similar to that of the Li-P-CNT and Li-D-CNT system. This phenomenon indicates that alkali-metal adsorption may resolve the two questions mentioned above (decreased high work function and improved electric conductivity of a CNT mixture). The projected density of states (PDOS) should provide detailed information about the electronic structure of the adsorption systems. Figure 6 shows the PDOS of the Li atom (on P1) and carbon atoms in the first layer of the (5, 5) P-CNT and the (5, 5) D-CNT. After Li adsorption, augmentation of the DOS value near the Fermi level is mainly attributed to the 2pz and 2px þ 2py orbitals of the carbon atoms and the 2px þ 2py orbitals of the Li atom for the Li-P-CNT system. This result indicates a charge transfer from the 2s orbital of the Li atom to the 2pz and 2px þ 2py orbitals of the carbon atoms on the tip of the P-CNT. When the Li atom is adsorbed on the (5, 5) P-CNT, its 2px þ 2py states are partly occupied and a broad resonance with 2pz state of carbon atoms exists near the Fermi level. This result implies that the Li-CNT interaction and the decrease in work function originate mainly from hybridization of the two states. However, after Li adsorption, the PDOS of the carbon atoms in the first layer for the Li-D-CNT system are not augmented. The 2px þ 2py peak of the carbon atom from the P-CNTs is smaller than that of the carbon atom from the D-CNT near the Fermi levels due to the influence of the vacancy defect. These characteristics are consistent with the charge redistributions in Figure 3. Furthermore, the charge transfer from the Li atom to the P-CNT increases the Fermi levels and decreases the vacuum levels. Similar results of PDOS are found for Na/Cs-CNT systems. 8931

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fund from National Natural Science Foundation of China (Grants 41076057 and 60907007).

’ REFERENCES

Figure 6. PDOS for the Li atom (on P1) and carbon atoms in the first layer of (a) the (5, 5) P-CNT, and (b) the (5, 5) D-CNT.

4. CONCLUSIONS The first principles calculations show that the work functions of CNTs can be distinctly modulated by alkali-metal adsorption and the electronegativity of the alkali atom plays a dominant role in the work functions of adatom-CNT systems. After alkali-metal adsorption, the semiconducting properties of capped (5, 5) P-CNT are converted into metallic properties. The work functions of the sidewalls of the CNTs are slightly higher than the axial work functions. The variations in the work functions are chiefly ascribed to the changes in the Fermi levels caused by charge redistributions, while the changes in the vacuum levels only have a small part of contribution. ’ AUTHOR INFORMATION Corresponding Author

*Tel./Fax: þ86-0532-66781204. E-mail: [email protected].

’ ACKNOWLEDGMENT We acknowledge the developers of XCrySDen39,40 (a crystalline and molecular structure visualization program) and VESTA41,42 (a three-dimensional visualization system for electronic and structural analysis). This work is supported by the

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