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. 2021 May 27;6(22):14559–14565. doi: 10.1021/acsomega.1c01671

Reduction in Work Functions of Transition-Metal Carbides and Oxycarbides upon Oxidation

Wataru Hayami †,*, Shuai Tang ‡, Ta-Wei Chiu ‡, Jie Tang ‡
PMCID: PMC8190902  PMID: 34124479

Abstract

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Herein, the work functions of group 4 and group 5 transition-metal (Ti, Zr, Hf, V, Nb, and Ta) carbides and transition-metal oxycarbides (TMCOs) were investigated by first-principles calculations for their potential application as electron emitters. The work functions of both groups decreased as the substitution of carbon atoms with oxygen proceeded, and the reduction in group 4 was more than that of group 5. In particular, ZrC1–xOx and HfC1–xOx (x ≥ 0.25) exhibited work functions of less than 3 eV, which were comparable with those of LaB6- and ZrO-coated tungsten. The reduction in the work functions could be explained by the rigid-band model of the electronic density of states. The increase in valence electrons increased the Fermi energy, while it demonstrated a less significant influence on the vacuum potential, resulting in a reduction in the work functions. The phonon dispersion curves indicated that the NaCl-type group 5 TMCOs were less stable than the group 4 TMCOs. This agrees with the experimental findings that TaC1–xOx was not synthesized and NbC1–xOx was synthesized only for smaller values of x (i.e., x < 0.28). From the viewpoints of the work functions and structural stabilities, group 4 (Ti, Zr, and Hf) TMCOs exhibit better potential for application as electron emitters than group 5 (V, Nb, and Ta) TMCOs.

Introduction

Electron emission from solid surfaces has been a fundamental phenomenon known since the 19th century.1,2 The electron gun was devised to generate an electron beam by accelerating the emitted electrons. It has been utilized in various instruments, such as cathode-ray tubes, electron microscopes, and electron beam lithography. The major types of electron guns are thermionic emission (TE), Schottky emission (SE), cold field emission (CFE), and thermal field emission (TFE). The electron source material has the most important role in electron guns, for which a variety of materials have been used. Currently, tungsten (W) (TE, CFE), LaB6, and CeB6 (TE), and tungsten coated with zirconium oxide (W/ZrO) (SE) are commercially used.3−6

The performance of electron guns is characterized by emission current (A), brightness (A/m2/sr), stability, energy spread of the beam (eV), and the dimension of the emitter tip, which limits the image resolution. These factors are determined mainly by the work function of the electron-emitting material, the emitter tip profile, and the surface structure. Fundamentally, a lower work function and a sharper tip lead to better performance. The energy spread of the electron beam originates from the statistical distribution of the electron energy in the material. A material with a low work function enables the emitter to operate at low temperature, having a small energy spread.

The work functions of currently utilized W, LaB6, and W/ZrO source materials are approximately 4.6,7 2.6,8 and 2.7 eV,5 respectively. From these values, LaB6 and W/ZrO appear to be more advantageous than W. However, they are not suitable for CFE because their emission currents are not stable. An LaB6 tip sharpened by electrochemical etching or other methods may be used for TFE.9 For W/ZrO, the tip can be sharply pointed; however, when coated with ZrO, it undergoes dulling during operation.10 For this reason, W is mainly used for the tip of a CFE-type emitter, whose dimensions must be less than 100 nm to generate a sufficiently intense electric field.

Despite the difficulty in precision fabrication, LaB6 was successfully synthesized in the nanowire form by chemical vapor deposition (CVD),11 the thickness of which was less than 100 nm. When applied to an electron emitter, the LaB6 nanowire produced a stable CFE.12,13

LaB6 is an excellent material that can produce a high-current and high-brightness electron beam. On the other hand, other materials that may show better performance and have lower production costs have been investigated for years. Metal carbides and nitrides are good candidates because they, like metal borides such as LaB6, have metallic, covalent, and ionic bonds simultaneously.14 There have been attempts to apply group 4 and 5 transition-metal carbides (TMCs) to an electron emitter.15−22 Similar attempts have been made for transition-metal nitrides (TMNs).23−30

The probable reason why the LaB6 nanowire was obtained using the CVD method is that LaB6 has a cubic crystal structure whose surface energies greatly differ depending on the surface indices. The difference in the surface energy caused LaB6 to grow along a specific direction ⟨100⟩.12,13 In an analogous manner to LaB6, we expected that group 4 and 5 TMCs could be made into nanowires because they also have a cubic structure (NaCl-type). Thus, we succeeded in fabricating HfC and ZrC nanowires growing in the ⟨100⟩ direction.31−36

When HfC and ZrC nanowires were applied to the electron emitters, they produced a stable CFE current. Notably, we found that the work function of the emitting surface {100}, which was originally approximately 3.6 eV for HfC18 and ZrC,17 greatly decreased when the wires were exposed to an oxygen atmosphere.32,33 The work functions became approximately 2.5 eV for HfC32 and 3.06 for ZrC,33 which are close to the values for LaB6 and W/ZrO. We also found that the emission currents of oxidized HfC and ZrC were stable for a long operation time (∼5 h). HfC and ZrC, therefore, have good potential as electron emitters.

Our previous studies showed that the surfaces of HfC and ZrC were partially oxidized, forming transition-metal oxycarbides (TMCOs) as they maintained the NaCl structure.32,33 HfC and ZrC were spontaneously oxidized when exposed to an oxygen atmosphere at a high temperature. This implies that the compositions of oxycarbides can be controlled by the partial pressure of oxygen and the temperature of the sample. It is known that oxygen atoms can replace carbon atoms by up to approximately 50% in group 4 and 5 TMCs.37−47 First-principles calculations showed that Hf and Zr oxycarbides could have lower work functions than those of the original carbides.32,33 The stability of the emission current was probably caused by the passivation of the step edge, which prohibited further dissociative adsorption of residual gas molecules.

Thus far, we have investigated HfC and ZrC both experimentally and theoretically.32,33 It is natural to extend the study to other group 4 (TiC) and 5 (VC, NbC, and TaC) TMCs to determine whether they show similar or better performance for electron emitters. In this study, we investigated these using first-principles calculations and found that there is a large difference in the work function and the structural stability between group 4 and group 5 TMCs. The difference and the mechanism of the reduction in work functions are discussed in terms of their atomic and electronic structures, and phonon dispersion relations, which will be provided in detail in the following sections.

Results and Discussion

The work functions of TMCs and TMCOs were calculated using slab models, as depicted in Figure 1. In these models, the work functions were calculated on the (001) surfaces (top layers), which are intended to represent the {100} surfaces. Each model consists of (2 × 2 × 6) unit cells (96 atoms) and a vacuum space of 15 Å along the z direction (upward in the figure). The “x” in the figure denotes the ratio of oxygen in the chemical formula TMC1–xOx. In the TMCO models (x = 0.25 and 0.5), each layer has 16 atoms (8 TM and 8 C or O atoms), where the O atoms, denoted by red spheres in the figure, are uniformly distributed such that every layer has the same number of O atoms. The lattice constants and atomic positions were optimized for both TMC and TMCO when the lattice symmetry was constrained to an orthorhombic symmetry.

Figure 1.

Figure 1

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Slab models adopted in the calculations of the work functions of TMC1–xOx. Green, black, and red spheres depict TM, C, and O atoms, respectively. The work functions were calculated on the (001) surfaces (top layers), which represent the {100} surfaces.

Figure 2 shows the calculated work functions of the {100} surface of TMC1–xOx (TM = Ti–Ta) at x = 0, 0.25, and 0.5. The calculated values for TMCs (x = 0) are within approximately ±0.5 eV from experimental values,48 and ±0.2 eV from theoretical values.49−54 The differences from the experimental values are likely to be attributed to carbon defects in TMCs.52−54 In the early stage of oxidation as x increases from 0 to 0.25, the work function greatly reduces for all these TMCs, which agrees well with our experimental results that the work function of HfC and ZrC reduces from 3.6 to 2.5 eV and from 3.6 to 3.02 eV, respectively.32,33 In the case of HfC1–xOx, x was estimated to be approximately 0.2.32 In the experiments,31−36 the ⟨100⟩ oriented nanowires were sharpened by field evaporation when surfaces other than the {100} surface may have appeared. Even if other surfaces are involved in electron emission, the tendency would be the same because the reduction in work function is brought about mostly by the increase of the Fermi energy, as shown later in Figure 3.

Figure 2.

Figure 2

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Calculated work functions of the {100} surfaces of TMC1–xOx.

Figure 3.

Figure 3

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Fermi energies, vacuum potentials (Vvac), and work functions of ZrC1–xOx and NbC1–xOx.

As oxidation proceeds from 0.25 to 0.5, the work functions continue to decrease, but not as much as in the lower x range. Exceptionally, in the case of Ta, the work function increases slightly. This is probably related to its structural instability. In fact, the synthesis of NaCl-type TaCO has yet to be reported. The instability of TaCO is compared with that of HfCO later in terms of phonon dispersion curves (Figure 6).

Figure 6.

Figure 6

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Calculated phonon dispersion curves of HfC1–xOx and TaC1–xOx. Imaginary modes are represented by negative frequency values.

Before oxidation, the group 4 TMCs tended to have a higher work function than the group 5 TMCs in the same row of the periodic table, which is consistent with the results of previous studies.49−51 However, the work functions of group 4 TMCOs were reduced by oxidation more effectively and became lower than those of group 5. On this point, group 4 TMCOs appear to be more advantageous than group 5 TMCOs.

To elucidate the difference in work function between group 4 and 5 TMCOs, the Fermi energies (Efs), vacuum potentials (Vvac), and the work functions of ZrCO and NbCO were compared, as shown in Figure 3. The absolute value of the vacuum potential is not significant because it is dependent on the structural model adopted in the calculations. However, in the process of the oxidation of the TMCs, the same structural model was employed, except for the oxygen concentration. Thus, the relative change in the vacuum potential can be expected to reflect the change in the electric field due to the substitution of carbon by oxygen.

It was observed that for both ZrCO and NbCO, as x increased from 0 to 0.25, the Ef values increased, while the vacuum potentials were nearly the same. Because the work function is calculated from eq 1 in the Computational Methods section, the reduction in work function is caused for the most part by the increase in Ef in this x range. On the other hand, in the x range from 0.25 to 0.5, the increase in Ef is not as large as in the lower x range. At the same time, the vacuum potentials slightly increase, which cancels the increase in Ef in eq 1. Consequently, the work functions do not reduce significantly in the x range from 0.25 to 0.5.

The reason why the increase in Ef differs depending on x and the metal atoms can be explained by the densities of states (DOSs). We chose ZrCO and NbCO to represent group 4 and 5 TMCOs, and plotted their DOSs in Figure 4. The Ef values were set to zero. In the case of ZrCO (Figure 4, top), ZrC (x = 0) is semimetallic, and Ef is located at the bottom of the pseudogap. The DOSs at x = 0.25 and 0.5 appear to be similar to that at x = 0, except for the O 2p states in the region of −8 to −6 eV. The substitution of C with O atoms increases the number of valence electrons and accordingly increases Ef. The integrated DOSs from the bottom of the pseudogap to Ef (shadowed area) are 2.2 at x = 0.25 and 4.2 at x = 0.5, which nearly correspond to the increase of the valence electrons by the substitution. Therefore, the rigid-band model is valid for this substitution range.

Figure 4.

Figure 4

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DOSs of ZrC1–xOx (top) and NbC1–xOx (bottom). The Fermi energies are set to zero.

When x = 0, because the DOS at Ef is low, the increase in valence electrons rapidly increases Ef. As Ef increases, the DOS at Ef gradually increases; therefore, the increase rate of Ef declines for the same increase in valence electrons. This explains the tendency of Ef in ZrCO shown in Figure 3.

The DOSs of NbCO (Figure 4, bottom) appear to be similar to those of ZrCO, and the rigid-band model still holds. The difference is that NbCO has one more valence electron, and accordingly has a higher Ef than ZrCO. Because the DOS at Ef is approximately 2.5 times higher than that in ZrCO, the increase rate of Ef for the increase in valence electrons should be 2.5 times lower than that in ZrCO, which explains the work function changes shown in Figure 2.

In Figure 3, it is observed that the vacuum potentials are nearly the same at x from 0 to 0.25, but slightly increase at x from 0.25 to 0.5. This behavior can be qualitatively explained by the electric field caused by the surface dipole moment. As shown in Figure 1, the {100} surface of the TMCs has the same number of TM and C atoms. The geometrically optimized {100} surface has C atoms located slightly outside the TM atoms. The relative z coordinates (RZC) of C and O to that of TM (Zr and Nb) are plotted in Figure 5, where the z direction is taken to be the outward direction normal to the surface. Because C and TM atoms have negative and positive charges, respectively, they generate inward electric dipole moments.

Figure 5.

Figure 5

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RZC of surface atoms (a), and the surface dipole moments (b) for ZrC1–xOx and NbC1–xOx.

At x = 0.25, the RZC of C-TM is larger than that at x = 0, while that of O-TM is smaller than that of C-TM at x = 0 (Figure 5a). Therefore, the increase in the dipole moment is suppressed to a certain extent because the charges of the O and C atoms are comparable. In contrast, at x = 0.5, both the RZCs of C-TM and O-TM become larger than those of C-TM at x = 0, which greatly enhances the dipole moments. Taking the RZCs, electric charges, and atomic densities into account, the total electric dipole moments generated by the surface atoms are plotted in Figure 5b. The negative (inward) dipole moments generate an electric field that increases the vacuum potential, as shown in Figure 3.

At x from 0 to 0.25, the vacuum potentials are nearly unchanged (Figure 3), although the dipole moments slightly decrease. This difference probably originates from the electric field in the subsurface and the bulk, which we do not discuss in detail.

The RZCs for NbCO are larger than those for ZrCO (Figure 5a), which implies that NbCO (group 5) is less stable than ZrCO (group 4). This is understandable from their DOSs (Figure 4). Ef of NbC is located above the pseudogap, where the states have an antibonding character. TMC1–xOx, therefore, becomes less stable as x increases. In fact, the maximum x values for group 5 TMC1–xOx (V, Nb, and Ta) obtained in experiments are 0.49 (V),44 0.28 (Nb),45 and 0 (Ta). TaCO was observed only at the interface of TaC and TaO, but not in the bulk phase.47 The instability of group 5 TMCOs is confirmed in terms of the phonon dispersion curves.

Figure 6 shows the phonon dispersion curves of HfC1–xOx and TaC1–xOx. Before oxidation (x = 0), both HfC and TaC are stable, showing no imaginary phonon modes. As oxidation proceeds, HfC1–xOx exhibits no imaginary modes until x = 0.5, whereas TaC1–xOx has imaginary modes (presented by negative values) even at x = 0.25. The NaCl-type TaC1–xOx is, therefore, unstable at x > 0.25, which agrees with the fact that the synthesis of bulk TaC1–xOx has not been reported.47

Regarding VCO and NbCO, although their phonon dispersion curves have imaginary modes at x = 0.25 and 0.5 as observed in TaCO, oxygen substitution seems to be allowed to some extent. The maximum x for NbC1–xOx is 0.28,45 and that for VC1–xOx is 0.49.44 The value for VC1–xOx is much larger than 0.25, and appears to be contradictory to the results of the phonon dispersion curves. This can probably be attributed to the nature of VC, in which the original VC has approximately 20% carbon defects.44 The carbon defects, not included in the calculations, would help to stabilize the NaCl structure because the reduction in valence electrons lowers Ef toward the bottom of the pseudogap.

Conclusions

The work functions of group 4 (Ti, Zr, and Hf) and 5 (V, Nb, and Ta) TMCOs were investigated by first-principles calculations. For both groups, the work functions were reduced by the substitution of C atoms with O atoms, and those of group 4 reduced more than those of group 5. In particular, ZrC1–xOx and HfC1–xOx (x ≥ 0.25) exhibited a work function of less than 3 eV, suggesting that these materials have good potential as electron emitters.

The reduction in the work function is explained by the rigid-band model of the DOSs. As C atoms are replaced by O atoms, the number of valence electrons increases while the DOS spectrum maintains almost the same shape, which accordingly increases the values of Ef. In contrast, the vacuum potential was less influenced than Ef. As a result, the work function was reduced.

The phonon dispersion curves show that the NaCl-type group 5 TMCOs are less stable than the group 5 TMCOs. This agrees with the experimental findings that TaC1–xOx has not been reported and NbC1–xOx is reported only for small x < 0.28. Taking the work functions and stability into consideration, group 4 TMCOs have better potential for electron emitters than group 5 TMCOs.

Computational Methods

The electronic structures of TMCs and TMCOs were calculated using the Quantum ESPRESSO code,55,56 based on density functional theory with plane waves and pseudopotentials. Scalar-relativistic ultrasoft pseudopotentials57 for metals, carbon, and oxygen were adopted from the library.58 The generalized-gradient-approximation functional of Perdew, Burke, and Ernzerhof was employed.59 An energy cutoff of 60 Ry for plane waves and 600 Ry for electron density was sufficient to provide convergence of the total energy. The DOSs, work functions, and phonon dispersion curves were calculated following the optimization of the lattice parameters and the atomic structures using the Monkhorst–Pack k-point sampling60 with an (8 × 8 × 8) mesh per cubic unit cell. The calculated lattice parameters for the TMCs were within an error of 1% from the corresponding experimental values.

The work function ϕ was estimated using the following formula61

graphic file with name ao1c01671_m001.jpg 1

where Vvac and Ef are the electrostatic potential of the vacuum and the Fermi energy, respectively.

The phonon dispersion curves were calculated based on the density functional perturbation theory62 using the PHonon package in the Quantum ESPRESSO suite.

Acknowledgments

The authors would like to thank Shigeki Otani for the valuable input and insightful comments. This work was supported partially by the NIMS-DENKA Center of Excellence for Next Generation Materials.

The authors declare no competing financial interest.

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