Rich interfacial chemistry and properties of carbon-doped hexagonal boron nitride nanosheets revealed by electronic structure calculations

The substitution of B or N with a carbon atom provides half-filled flat midgap states, as reported in Ref. 16. A balanced substitution of B and N with multiple carbon atoms results in intrinsic semiconductors. Here, we calculated structures with odd-number substitution with multiple carbon atoms. Typical examples of odd-number substitutions are shown in Fig. 1. Figures 1(a) and 1(b) show the single atom substitutions of B and N, respectively. Figures 1(c) and 1(d) show the substitutions of three B atoms with three C atoms and of three N atoms with three C atoms, respectively. Figures 1(e) and 1(f) show the substitution of one B atom and two N atoms with three C atoms, and that of two B atoms and one N atom with three C atoms, respectively. The electronic band structures of these hypothetical materials are shown in Fig. 2. Figures 2(a)–2(f) correspond to Figs. 1(a)–1(f), respectively. The band structures in Fig. 2 are all metallic, as expected from the odd numbers of electrons in the unit cell. The Fermi levels indicated by horizontal broken lines are strongly dependent on which atom, B or N, is replaced more. It means that the work function values of these materials are switchable in a wide range of 2–3 eV, which is an intriguing feature of the materials. Moreover, the band dispersion widens with increasing number of C atoms. The small but finite band dispersion in Figs. 2(a) and 2(b) is different from the dispersion of the previously reported flat impurity bands of single-atom doping.¹⁵⁾ The discrepancy is due to the interaction between C atoms beyond the periodic boundary in the present calculation, the supercell of which is smaller than those in previous calculations.

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To determine the effect of carbon dopants laterally propagating, two-dimensional ELF (2D-ELF) was calculated for further analysis. ELF is frequently used to visualize chemical bonds explicitly.^31,32) Figure 3 shows the ELF distributions of the monolayers shown in Fig. 1 in addition to pure h-BN (designated as "BN" in Fig. 3). In pure h-BN, B and N atoms have totally different distributions of electrons, i.e., the red area (high density of electron pairs) included N atoms, while the blue area (low density of electron pairs) included B atoms, which reflect the difference in the nuclear charge. In structure (a), the electron density around the embedded carbon atom is intermediate between those around boron and nitrogen atoms. In the opposite situation in structure (b), in which a carbon atom substituted a nitrogen atom, a high electron density similar to that of nitrogen atoms is observed around the carbon atom. In structures (c) and (d), the three carbon atoms are separately embedded in the h-BN system. The 2D-ELF distributions around carbon atoms in (c) and (d) are very similar to those in (a) and (b), which means that the three carbon atoms have rather isolated electronic states. It is consistent with the band structures that show small dispersions of carbon-derived bands. The last two 2D-ELF distributions shown in Figs. 3(e) and 3(f) correspond to those of the hybrid structures shown in Figs. 1(e) and 1(f), respectively. In Fig. 3(e), the electron pair distribution around the carbon structures shows a totally different shape from the rest of the BN network, which means that the embedded carbon structures form a new π-conjugated electron system. Furthermore, the electron pair distributions around the B and N atoms adjacent to the C atoms are also modified. These correspond to the band dispersion modified in the LUMO − 1 and HOMO bands in Fig. 2(e). Similar features can be observed in Fig. 3(f).

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In the analysis above, the hybrid h-CBN systems with an unbalanced substitution show a metallic nature with very different electron affinities or work function values. This finding implies that a spontaneous electron transfer occurs by stacking differently doped h-CBN. In the next section, we will examine such a transfer.

We examined the electronic structures of C-doped h-BN double layers. In the ordinary h-BN (P6₃/mmc), atoms in each layer overlapped along the c-axis, and B and N atoms are stacked alternately. Figure 4 shows the double-layered h-CBN structures after the structural optimization. Figure 4(a) shows the case of the shortest interlayer C–C distance, denoted as the "2C-i" structure, in which two carbon atoms substitute for a B atom in the upper layer and for an N atom in the lower layer. C atoms are stacked at the same position along the plane. Figures 4(b) and 4(c) depict the structures of "2C-ii" and "2C-iii", respectively. The difference among "2C-n" (n = i, ii, iii) is in the distance between carbon atoms. In 2C-ii and -iii, the C atom in the lower layer is shifted toward the ($1\bar{1}0$) direction by one atom and two atoms, respectively.

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The optimized structures in single-atom substitution per layer are markedly different, as shown in Fig. 4. In the 2C-i structure [Fig. 4(a)], in which the carbon height difference in a different layer is smallest, carbon atoms come together up to a distance of h₂ = 1.67 Å. The bond lengths of nearest intralayer distances of C–N and C–B in the top and bottom layers are 1.47 and 1.56 Å, respectively. In the intermediate 2C-ii structure [Fig. 4(b)], the doped carbon in the top layer deviated from the layer by h₁ = 0.69 Å toward the lower layer, while that in the bottom layer did not shift significantly, resulting in an interlayer distance at the shortest point of h₂ = 2.71 Å. In the 2C-iii structure [Fig. 4(c)], the doped carbon in the top layer significantly deviated by h₁ = 0.82 Å from the top layer, while the carbon atom in the bottom layer showed no changes. Instead, a B atom in the bottom layer shifted toward the top layer by h₃ = 0.67 Å. This B atom in the bottom layer is just beneath the C atom in the top layer, while the N atom in the top layer is directly above the C atom in the bottom layer. It seems that this difference is the cause of the apparent asymmetry of the behavior of C atoms. The interlayer C–B distance of the shifted pair is 1.76 Å. On the basis of the structural information, we can conclude that 2C-i and 2C-iii have direct chemical bonds between layers. The interlayer C–C distance in 2C-i (1.67 Å) is shorter than the interlayer C–B distance in 2C-iii (1.76 Å), suggesting that the C–C bond is more stable than the C–B bond.

We also calculated the structure with three doped carbon atoms per layer. "6C-i" [Fig. 4(d)] has C atoms in the top and bottom layers that are facing each other, similarly to 2C-i. The shortest interlayer C–C distance in 6C-i is 1.67 Å, which is the same as that in 2C-i. The bond lengths of C–N and C–B in the top and bottom layers are 1.47 and 1.53 Å in the 6C-i, respectively, which are similar to those in 2C-i. In the 6C-ii [Fig. 4(e)], the deviations of C from the layers are smaller than those in 2C-ii. The displacement of C atoms from both layers is less than 0.1 Å, which is slightly smaller than that in 2C-ii. The structure with three carbon atoms per layer corresponding to 2C-iii was not calculated because of the limitation of the supercell.

The band gaps of all the structures are listed in Table I, which were determined by the band structure calculation (shown in Fig. 5). In the 2C-i and 6C-i shown in Figs. 5(a) and 5(b), respectively, the band gaps are larger than those in other structures (3.75 and 3.25 eV, respectively). This result means that by stacking two kinds of metallic layers (B- and N-rich h-CBN layers), free electrons will pair up. The band dispersions of 2C-ii and 6C-ii are shown in Figs. 5(c) and 5(d), respectively. Both 2C-ii and 6C-ii show small band gaps of values of 0.36 and 0.61 eV, respectively. The band gaps are much smaller than those of the 2C-i and 6C-i structures. Although the carbon content increased from 2 to 6, the band gap of 6C-ii increased from that of 2C-ii, which is different from the general tendency of monolayers or 2C-i and 6C-i. Both 2C-ii and 6C-ii are nonmetallic because neither of them has energy levels crossing the Fermi level. Figure 5(e) shows the band dispersion of the 2C-iii structure. The band gap is indirect; the HOMO-band top is located at the Γ-point while the LUMO-band bottom is located at the K-point. The band gap is 2.69 eV. This band gap is also smaller than that of 2C-i (3.75 eV), but larger than that of 2C-ii (0.32 eV). Interestingly, in the band dispersion of the 2C-iii structure, the HOMO crosses the Fermi level, which means that the 2C-iii structure is metallic and that unpaired electrons exist in this structure. From the analysis so far, the resemblances of electronic structures of 2C-i and 6C-i and of 2C-ii and 6C-ii are apparent. Therefore, we will focus on these "2C-n" (n = i, ii, iii) structures below.

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The wave function distributions of HOMOs and LUMOs are shown in Fig. 6. Figures 6(a) and 6(b) exhibit the HOMO and LUMO of the 2C-i structure, respectively. The HOMO of 2C-i is located on N atoms. LUMO is mainly located on B atoms, while a small part is located on C atoms. The HOMO and LUMO are mainly from B and N atoms adjacent to the C atoms. This means that the C atoms change the electronic structure of neighboring B and N atoms, and make them more active than other B and N atoms located far away. In the monolayers, HOMO and LUMO are located on the C atoms, however, in 2C-i, the contribution of C atoms is weak. This finding can be explained by considering that the sp³ carbon atoms formed by interlayer bonding in 2C-i have more stable electronic structures. The HOMO and LUMO of 6C-i (not shown) have similar features to those of 2C-i.

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The HOMO and LUMO of 2C-i are shown in Figs. 6(c) and 6(d), respectively. In 2C-ii, the HOMO and LUMO are mainly located on the C atoms. Both C atoms contribute to both HOMO and LUMO, which means that C atoms are active and can serve as electron donors and acceptors. This mixed contribution of C atoms to both HOMO and LUMO seems important as the mechanism of narrowing band gaps with decreasing carbon content. This point will be discussed later on the basis of the charge and ELF distributions. Finally, Figs. 6(e) and 6(f) respectively show the HOMO and LUMO of 2C-iii. In this figure, HOMO is mainly distributed in the top layer, around the N atoms adjacent to the doped C atom. On the other hand, LUMO is distributed in the bottom layer, around the C atom and the N atom adjacent to the C atom and N atoms around the displaced B atom. In the top layer, the doped C atom contributes to neither the HOMO nor the LUMO. Considering the displacement of the C atom in the top layer, this C atom might have an sp³ configuration, which has deep levels.

To directly show the modification of the electronic structure and the distributions of electrons, especially the interlayer electron transfer, ELF was calculated, and the results are shown in the following figures. In 2C-i shown in Fig. 7, a large ELF cloud can be clearly observed between two doped carbons along the C–C direction. It is the typical electron distributions, in σ-bonds, which means that, in this 2C-i structure, C atoms exist as sp³ carbons. It is reasonably considered that the band gap of 2C-i is large because sp³ carbon atoms have large energy gaps and do not contribute to the narrowing of the band gap.

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In the ELF distribution of 2C-ii shown in Fig. 8, the C atom in the top layer (marked "a") has an electron cloud, which is localized on the p_z-orbital (z is perpendicular to the layer), in addition to the three electron clouds along the three neighboring N atoms. On the other hand, the C atom in the bottom layer (marked "a"), has no electrons located at the p_z-orbital. These observations suggest that one electron is transferred from "a" in the bottom layer to "a" in the top layer. Indeed, the electron count indicates that 0.415 e⁻ is donated from the bottom layer to the top layer. In other words, 2C-ii is a kind of a charge-transfer (CT) complex. The narrow band gap is naturally explained because it is one of the important features of the CT complex.³⁴⁾

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Since the band gap of 6C-ii (0.61 eV) is greater than that of 2C-ii (0.36 eV) but still much smaller than that of BN (4.53 eV), the tunability of the CT complex was examined by taking another example in 6C-ii. In 6C-ii, the shape of the electron distributions between C–C (Fig. 9) means that aside from the σ bonds, C–C is also derived from π-electron structures. The doped C atoms form two π-electron structures separately in different layers. From this ELF distribution, it is hard to tell where the new electron pair is located and which direction is the electron transfer in. In 6C-ii, the electrons around C atoms are delocalized. The new electron pair contributes to π-electron structures among the three carbons in the same layer. By close analysis, it was found that the electron transfer was from the bottom layer to the top layer (N-rich layer to B-rich layer), and the amount of transfer was 0.32 e⁻ in this extended unit cell. This charge difference indicates that the spontaneous electron transfer behavior still exists in the 6C-ii structure, but is weakened. It is consistent with the band gap of 6C-ii being larger than that of 2C-ii. Multiple (odd numbered) doped C atoms tend to form more stable electronic structures in their own layers than isolated C atoms do.

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In the ELF distribution of 2C-iii shown in Fig. 10, the existence of an electron cloud between the C atom and the underlying B atom means that these two atoms directly bond together. Both of C and B atoms exist in the stable sp³ state. This is the reason why this C atom does not contribute to the HOMO or LUMO. The B atom, as a new electron donor, forms a covalent bond with the C atom. However, an unpaired electron is still located at the C atom in the bottom layers (N-rich layer), which makes the C atom more active than the C atom in the top layer. This is the reason for the metallic features. The interlayer charge transfer exists in 2C-iii, but the amount of transfer is 0.17 e⁻, which is much smaller than those in type ii (i.e., 2C-ii and 6C-ii).

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Finally, we examined the double-layered h-CBN with even-carbon-number doping. The results are not shown in the figures, but the distance between the two layers after optimization was 3.4 Å without any significant changes in the vertical direction from pure double-layered h-BN. The doped carbon atoms also did not show a significant position shift. On the basis of the optimized structures, the two layers are independent. The band gap was 3.09 eV. Noted that all the band dispersion curves are composed of two almost parallel curves, which is due to the layered structure with a very weak interaction.

Now we would like to comment on the comparison of the present calculation results with the experimental results. h-CBN can be synthesized by CVD or plasma CVD but its electronic structures are sensitive to growth conditions.^35–37) We found that the electronic structures are very sensitive to the geometry of doping (e.g., number of C atoms and arrangement). This sensitivity can account for the difficulty in controlling the electronic structures of materials. In the future, some methods of synthesizing h-CBN as designed at the atomic level need to be developed, which will pave the way to obtaining a variety of physical properties of this group of materials. We hope that the present work will stimulate further experiments on the electronic structure of the h-CBN system as well as on their applications. Once well-defined hexagonal B–C–N structures can be synthesized, they will be applied as photocatalysts using tunable band gaps, catalysts using partially localized electrons, and sensors with partial chemical bonding with adsorbed molecules on these structures. Various experimental methods are now being developed^25,38–40) for the controlled synthesis of these structures.