The enhanced field emission properties of K and Rb doped (5,5) capped single-walled carbon nanotubes

Abstract

The field emission properties of alkali metal K and Rb (AM) doped (5,5) capped single-walled carbon nanotubes (CNTs) have been investigated using first-principles theory. Our results showed the work function of (5,5) capped CNTs doped with AM at the cap (3.60–4.00 eV) decreases significantly in comparison with pristine CNTs (4.44 eV), due to a rise in the Fermi level (mainly) and a drop in the vacuum level. The reduction of the work function in AM-doped CNTs was more evident than when doped with N. All doped (5,5) capped CNTs were semiconductors and their energy gaps (0.12–0.55 eV) were considerably smaller than those of pristine CNTs (1.14 eV). The HOMO and LUMO of pristine (5,5) capped CNTs were evenly distributed at the side wall of the tube. However, the HOMO and LUMO of CNTs doped with AM at the cap were concentrated in the cap of the tube. The emission current of CNTs doped with AM at the cap was increased, because the LDOS (of the cap) at the Fermi level was increased and there emerged new localized states near the Fermi level. The abovementioned results suggest that the field emission properties of (5,5) capped CNTs can be enhanced significantly by doping K and Rb at the cap. Our research findings provide a new dopant that can reduce the work function of CNTs more effectively.

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1. Introduction

Because of their high-quality pictures and ultra-thin structure, field emission displays (FED) have become the research focus in the design and development of the new generation of displays. Also, carbon nanotubes (CNTs) have been considered promising field emission electron source materials (cold cathode materials) to be used in FED, because they have a high aspect ratio, high chemical stability and high current density.^1–4 Experimentally, large areas of vertically arranged CNTs have been proved to grow on substrates using a chemical vapour deposition method, including carbon nanotube–graphene composites.^5–11 Also, FED based on these vertically aligned CNTs have been fabricated and exhibit excellent field emission properties.^5–10 The work function is a key parameter for assessing the performance of field emission in materials. However, their high work function (about 4.7 eV) is a drawback of CNTs as cathode materials in FED.¹² For a cathode material in FED, we hope it has a low work function, which can lower the potential barrier for electrons to escape from the surface of the material and make electron emission easier. Therefore, it is important and meaningful to study how to reduce the work function of CNTs when using them to design FED. Previous investigations have found nitrogen (boron) doping can decrease (increase) the work function of CNTs^13–15 and the field emission properties of CNTs can be enhanced by doping with nitrogen or boron atoms,^14–18 coating with copper phthalocyanine,¹⁹ and capping with a ZnO nanotip.²⁰ Multi-walled carbon nanotubes–MoS₂ and CNTs–graphene composites have also been proved to have remarkable field emission properties.^8,21–23

Recently, some researchers found that the field emission properties of CNTs can also be enhanced by decorating with metal particles.^7,9 Moreover, it was also found that the work function of CNTs can be reduced by adsorbing the alkali metals Li or Cs (theoretically).²⁴ Potassium-doped CNTs and Li salt-functionalized multi-wall carbon nanotubes have very low turn-on voltages for FED (experimentally).^25,26 These findings aroused our interest to investigate the field emission properties of alkali metal-doped CNTs. As far as we know, there have been no theoretical studies about the field emission properties of CNTs doped with alkali metals. In this work, we investigated the field emission properties of K and Rb-doped (d-K and d-Rb) (5,5) capped CNTs. Our results showed the field emission properties of (5,5) capped CNTs can be enhanced significantly by doping with AM (AM represents the alkali metals K and Rb), and the work function of CNTs doped with AM is reduced more significantly than when doped with N.

2. Model and calculation method

2.1. The model

In our study, armchair (5,5) capped CNTs, as shown in Fig. 1, were chosen as the research objects. The (5,5) capped CNTs were represented by nine layers of carbon rings along the tube axis with one end capped by half of a C₆₀ molecule. The dangling bonds at the other end were saturated by hydrogen atoms in order to increase chemical stability and avoid boundary effects. The size of the periodic boundary condition is 15 Å × 15 Å × 20 Å, which is large enough to avoid interaction of adjacent repeated cells. The work function was calculated with a vacuum of 30 Å along the Z axis. A similar model has also been employed in previous studies.^14,24,27 The first and second layers have five carbon atoms, respectively; the layers from the third to the ninth have ten carbon atoms. In the present work, we consider carbon atoms in different atom layers being substituted by AM atoms (one carbon atom was substituted by one AM atom), to study the effects of different doping positions and impurity atoms on the work function of (5,5) capped CNTs.

Fig. 1 The geometrical structure of pristine (5,5) capped CNT and AM-doped (5,5) capped CNT at different atom layers (represented by numbers 1, 2, 3, 4, 5 and 6). The atom layers 1, 2, 3, 4, 5 and 6 represent doping positions 1, 2, 3, 4, 5 and 6, respectively.

2.2. Calculation method

All calculations were carried out using first principles based on density functional theory (DFT), which was provided by the DMOL³ code,^28,29 available from Accelrys Inc. The local density approximation (LDA) was employed to optimize the geometrical structures of AM-doped CNTs with the Perdew–Wang (PWC) parameterization of local exchange correlation energy.³⁰ The generalized gradient approximation (GGA) was adopted to study the electronic properties of these doped CNTs with the Perdew–Burke–Ernzerhof (PBE)³¹ correlation gradient correction. As LDA can underestimate the energy gap of a semiconductor, GGA can provide more reliable results for the calculation of electronic properties. The same calculation method (LDA for the optimization of the geometrical structure and GGA for the calculation of electronic properties) has been used in previous papers.^15,27 The electronic wave function was expanded in a double-numeric polarized (DNP) basis set with an orbital of 6.0 Å for K and 6.5 Å for Rb. The type of treatment of core electrons was all-electron forms for K and DFT semi-core pseudopots for Rb. Geometry optimization was performed with a self-consistent field (SCF) convergence criterion of 1.0 × 10⁻⁶ Ha (1 Ha = 27.2114 eV), a maximum force of 0.002 Ha Å⁻¹ and a maximum displacement of 0.005 Å. Brillouin zone integration was carried out using 1 × 1 × 8 k-points according to the Monkhorst–Pack approximation³² for superlattice geometry. Calculations using more k-points did not have any significant effects on the results.

3. Results and discussion

3.1. Binding energy and structure

The binding energy (E_b), work function (W_f) and energy gap (E_g) of AM-doped (5,5) capped CNTs are shown in Table 1. The binding energy is defined as:^33,34

E_b = E_t − u(C)n(C) − u(H)n(H) − u(AM) (1)

where E_t is the total energy of an AM-doped (5,5) capped CNT; u(C), u(H) and u(AM) are the chemical potentials of single C, H and AM atoms, respectively; and n(C) and n(H) are the number of C and H atoms, respectively. The binding energy can predict the relative stability of doped CNTs; those with a more negative binding energy should be more stable. Table 1 shows the binding energies of all AM-doped (5,5) capped CNTs are negative. We also found that CNTs doped with Rb are more stable than those doped with K, and the stability of CNTs is almost independent of the doping position for the same doping atom. Fig. 2 shows the final structure of (5,5) capped CNTs doped with AM at position 1 after geometry optimization. The doped CNTs have a protruding structure at the doping position; this is because the diameter of AM is much bigger than that of C. The structures of CNTs doped with AM at other positions are similar and not given here.

Table 1 The binding energy (eV per atom), work function (eV) along the Z-axis and energy gap (eV) of AM-doped (5,5) capped CNTs

Doping position	Binding energy		Work function/energy gap
	d-K	d-Rb	d-K	d-Rb
Pristine	—	—	4.44/1.14	4.44/1.14
1	−7.331	−7.787	3.62/0.54	3.60/0.55
2	−7.333	−7.890	3.80/0.53	3.76/0.53
3	−7.345	−7.801	4.00/0.40	3.95/0.41
4	−7.344	−7.800	4.03/0.31	4.00/0.31
5	−7.335	−7.791	4.57/0.12	4.54/0.13
6	−7.336	−7.792	4.60/0.27	4.57/0.29

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Fig. 2 The highest occupied molecular orbital (HOMO) of: (a) pristine (5,5) capped CNT, (b) d-K at position 1, and (c) d-Rb at position 1. The lowest unoccupied molecular orbital (LUMO) of: (d) pristine (5,5) capped CNT, (e) d-K at position 1, and (f) d-Rb at position 1. All the structures are the final structure after geometry optimization.

3.2. Work function and energy gap

The work function (W_f) is defined as:

W_f = φ − E_f (2)

where φ and E_f represent the vacuum level and the Fermi level, respectively. Our calculation results show the work function of pristine (5,5) capped CNTs is 4.44 eV, which is very close to other calculation results (4.2 eV,²⁴ 4.5 eV,¹³ 4.65 eV (ref. 12) and 4.78 eV (ref. 35)). This means the calculation method in our work is practicable. We found the work function of (5,5) capped CNTs doped with AM can be modified by changing the doping position. When AM was doped at the cap of CNTs (corresponding to the doping positions 1, 2, and 3), their work function (about 3.60–4.00 eV) decreased significantly. CNTs with a doping position closer to their tip will have a lower work function: from doping position 3 to 2 and then to 1, the work function decreases gradually (CNTs doped with AM in the first layer have the smallest work function). This is different from a previous investigation, which found the best doping position was the fourth and fifth layers for N-doped CNTs.¹⁵ However, when AM was doped in the side wall of CNTs (corresponding to the doping positions 4, 5, and 6), their work function does not vary significantly. We also found that CNTs doped with Rb have a smaller work function than those doped with K for the same doping position. Compared with previous investigations, which found the work function of CNTs doped with nitrogen is only 0.18 or 0.60 eV lower than that of pristine CNTs.^13,14 Our results suggest that the work function of CNTs can be reduced more effectively (by about 0.44–0.84 eV) by doping with AM at the tube cap. Therefore, the field emission properties of (5,5) capped CNTs can be enhanced remarkably after AM is doped at the tube cap, due to the marked reduction in their work function.

All AM-doped (5,5) capped CNTs were semiconductors, and their energy gaps (LUMO (lowest unoccupied molecular orbital)–HOMO (highest occupied molecular orbital) energy gap) are listed in Table 1. The Fermi level is defined as the HOMO. The energy gap of a C₆₀ molecule from GGA calculations is 1.655 eV. This is a little smaller than the estimated energy gap of 1.7 eV for C₆₀.³⁶ The energy gap of pristine (5,5) capped CNTs in our calculations is 1.14 eV, which is very close to previous calculation results of 1.41 eV.²⁷ However, the energy gap of (5,5) capped CNTs doped with AM (about 0.12–0.55 eV) decreased significantly when compared with pristine CNTs. The reduction in the energy gap means an increasing probability of electron excitation from the occupied levels to the unoccupied levels, and then more electrons can escape from the surface of the CNTs to the vacuum. This suggests the field emission properties of (5,5) capped CNTs can be improved by doping with AM.

3.3. Fermi level and vacuum level

According to eqn (2), a reduction in work function can be induced by either a rise in the Fermi level or a drop in the vacuum level. In order to further understand the reduced work function of (5,5) capped CNTs doped with AM at the cap, we studied the Fermi level, vacuum level and additional dipole moment of these doped CNTs, as well as the Mulliken charge of the AM atom. As shown in Table 2, we found the Fermi level rose strongly and the vacuum level fell slightly after (5,5) capped CNTs were doped with AM, which resulted in the work function of AM-doped (5,5) capped CNTs undergoing a marked reduction. This is because the electronegativity of an AM atom is smaller than that of C, so charge will transfer from AM to an adjacent C when AM replaces C in CNTs. The Mulliken charge in Table 2 shows there are about 0.8 electrons transferred from AM to CNTs. This charge transfer will induce a rise in the Fermi levels of AM-doped (5,5) capped CNTs. In addition, the charge transfer destroyed the original charge distribution of pristine CNTs, so it would induce an additional dipole moment in AM-doped (5,5) capped CNTs. The direction of the additional dipole moment being toward the positive Z axis, it should lead to a fall in the vacuum level and thus a decrease in the work function. Table 2 also shows a larger additional dipole moment can bring about a lower vacuum level for the same dopant. Our results indicate that the reduction in the work function of AM-doped (5,5) CNTs is mainly due to the increase in the Fermi level. In addition, when doping (5,5) capped CNTs with AM at the same position, the Fermi level of Rb-doped CNTs rose the most and the vacuum level of Rb-doped CNTs fell the most. Therefore, Rb-doped CNTs have the lowest work function (3.60 eV) for all AM-doped (5,5) capped CNTs.

Table 2 The Fermi level (eV), vacuum level (eV), additional dipole moment (a.u.) along the Z-axis and the Mulliken charge (e) of the AM atom of AM-doped (5,5) capped CNTs at the cap (positions 1, 2 and 3). The additional dipole moment equals the dipole moment of AM-doped (5,5) capped CNTs minus the dipole moment of pristine (5,5) capped CNTs

Doping position	Fermi level/vacuum level		Additional dipole moment/Mulliken charge
	d-K	d-Rb	d-K	d-Rb
Pristine	−4.59/−0.15	−4.59/−0.15	—	—
1	−3.97/−0.35	−3.93/−0.33	5.12/0.85	5.26/0.75
2	−4.08/−0.28	−4.03/−0.27	3.84/0.85	3.99/0.75
3	−4.23/−0.23	−4.18/−0.23	3.54/0.89	3.63/0.81

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3.4. HOMO, LUMO and LDOS

In order to further understand the field emission properties of AM-doped (5,5) capped CNTs doped at the cap, we chose AM-doped (5,5) capped CNTs doped at position 1, which has the lowest work function, as the research object. We further investigated their HOMO, LUMO and local density of states (LDOS). Previous studies revealed that the emission current of CNTs is mainly derived from localized states (especially the localized states at the tube cap).^37–40

Fig. 2 shows the HOMO and LUMO of pristine and AM-doped (5,5) capped CNTs doped at position 1. The HOMO and LUMO of pristine (5,5) capped CNTs are evenly distributed on the side wall of the tube. After doping with AM, both the HOMO and LUMO are concentrated at the cap of CNTs. The HOMO and LUMO of other CNTs doped with AM at the cap are similar and not given here. The states localized at the tip of CNTs are conducive to their field emission properties.

Fig. 3 shows the LDOS of the first three layers (the cap) of (5,5) capped CNTs before and after doping with AM at position 1. As the electronic states close to the Fermi level primarily contribute to the electron field emission, we concentrate on discussing the electronic states near the Fermi level. The LDOS of pristine (5,5) capped CNTs only has two peaks near the Fermi level: one is at the Fermi level and the other is at about −0.7 eV. The LDOS of AM-doped (5,5) capped CNTs also have peaks at the Fermi level and at about −0.7 eV, and the LDOS at the Fermi level is increased in comparison with that of the pristine (5,5) capped CNTs. In addition, there emerge three new peaks (at about −0.2 eV, 0.55 eV and 0.9 eV) in the LDOS for AM-doped (5,5) capped CNTs. The increased LDOS at the Fermi level and the new localized states appearing near the Fermi level suggest that CNTs doped with AM at the cap could provide a higher emission current density in the field emission process than pristine CNTs. Therefore, the field emission properties of AM-doped (5,5) capped CNTs are preferable to those of CNTs without dopant. Our calculated results provide a theoretical support for previous experimental investigation which found K-doped CNTs have a much lower emission threshold (work function) and higher emission current density than undoped CNTs.²⁵ The LDOS (of the tube cap) of other doped CNTs with AM at the cap are similar and not plotted here.

Fig. 3 The LDOS of the first three layers (the cap) of pristine and AM-doped (5,5) capped CNTs at position 1. The Fermi level is set at zero.

4. Conclusions

In summary, we have investigated the field emission properties of (5,5) capped CNTs doped with K and Rb using first-principles theory. Our results indicate the field emission properties of (5,5) capped CNTs can be effectively enhanced after AM is doped at the cap of the tube, because (1) there was an evident decrease in work function when compared with pristine CNTs, mainly due to a rise in the Fermi level; (2) the energy gaps decreased drastically in comparison with the undoped CNTs; (3) the HOMO and LUMO of doped CNTs were localized at the cap of the tube, whereas the HOMO and LUMO of pristine CNTs were evenly distributed at the side wall of the tube; (4) compared with the undoped CNTs, the localized states at the tube cap near the Fermi level increased significantly. Our theoretical results provide a new dopant that can more significantly reduce the work function of CNTs.

Acknowledgements

This work was supported by the Natural Science Foundation of Fujian Province of China (grant no. A0220001). This work was also supported by the high performance computing platform of South China Normal University.

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