Two-dimensional borocarbonitrides for photocatalysis and photovoltaics

Abstract

We have designed two-dimensional borocarbonitrides (poly-butadiene-cyclooctatetraene framework BC₂N) with hexagonal unit cells, which are stable according to the cohesive energy, phonon dispersion, ab initio molecular dynamics, and elastic modulus results. They are n-type semiconductors with strain-tunable direct band gaps (1.45–2.20 eV), an ultrahigh electron mobility (5.2 × 10⁴ cm² V⁻¹ s⁻¹ for β-BC₂N), and strong absorption (an absorption coefficient of up to 10⁵ cm⁻¹). The intrinsic electric field due to the Janus geometry of α-BC₂N reduces the recombination of photo-generated carriers. The band edge positions of α-BC₂N and β-BC₂N are suitable for photocatalytic hydrogen production, achieving high solar-to-hydrogen efficiencies of 17% and 12%, respectively, in excess of the typical target value of 10% for industrial application. Both γ-BC₂N and δ-BC₂N can be used as electron donors in type-II heterostructures with two-dimensional transition metal dichalcogenides, and the power conversion efficiency of a solar cell based on these heterostructures can be as high as 21%, approaching the performance of perovskite-based solar cells.

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1. Introduction

Increasingly serious environmental pollution, climate abnormalities, and growing energy shortage call for a transition from the current fossil-fuel economy to a low-carbon (or even zero-carbon) economy¹ with a large share of green energy resources such as wind, solar, and hydrogen.² Being one of the most promising resources, great scientific efforts have been directed toward the development of environmentally friendly and efficient materials for converting solar energy.³ Two-dimensional (2D) materials have emerged as outstanding candidates in this endeavor.^4,5

Photocatalytic water splitting aims at the production of hydrogen and oxygen. The solar-to-hydrogen (STH) efficiency of a photocatalyst is determined jointly from the efficiency of light harvesting and separation of the photogenerated carriers. For many photocatalysts the STH efficiency falls short of the aspired 10%⁶ due to low absorbance and carrier recombination. 2D materials, on the other hand, can provide strong absorption of solar radiation and can generate high electrical currents beyond the reach of bulk materials.⁷ In addition, their atomic thickness is suitable for photocatalysis, because the distance that the photogenerated carriers have to overcome to participate in chemical reactions (on the surface) is much shorter than in bulk materials. Due to efficient light harvesting and carrier utilization, high STH efficiencies are reported for 2D materials, for example, 10.0% and 6.7% for the ferroelectric and paraelectric phases of AgBiP₂Se₆, respectively.⁸ The 2D Janus materials B₂P₆, Pd₄S₃Se₃, Pd₄S₃Te₃, and Pd₄Se₃Te₃ even achieve STH efficiencies of 28.2–38.6%.^9,10

Conversion of solar to electrical energy is another efficient technology for solar energy harvesting. The power conversion efficiency (PCE) achieved by state-of-the-art silicon solar cells is as high as ∼30% and that of perovskite solar cells is as high as ∼26%.¹¹ Excitonic thin-film solar cells based on 2D van der Waals heterostructures hold the promise of high efficiency due to high carrier mobility and strong absorption of visible light.^12,13 Examples include MoS₂/p-Si (PCE = 5.23%),¹⁴ graphene/GaAs (PCE = 18.5%),¹⁵ and CdS/GeSe (PCE = 1.48%)¹⁶ solar cells. Theoretical studies show PCEs as high as 20.1% in δ-CS/MoTe₂¹⁷ and 20% in 2D fullerene/CBN¹⁸ solar cells.

Borocarbonitrides, recently added members of the family of 2D materials, are of interest for application in a variety of cutting-edge technologies due to appealing sizes of the provided band gaps.^19–21 Based on the first-principles calculations, we therefore designed new 2D borocarbonitrides, namely, poly-butadiene-cyclooctatetraene framework BC₂N (PBCF-BC₂N), employing elemental mutation of poly-butadiene-cyclooctatetraene framework-graphene (PBCF-graphene)²² and then systematically investigated their stability, electronic structure, and optical properties. Excellent stability is inferred from the obtained cohesive energies, phonon dispersions, and elastic moduli as well as from ab initio molecular dynamics simulations. The materials are found to be direct band gap semiconductors with band edge positions suitable for photocatalytic water splitting. We also study the application potential of heterostructures formed from PBCF-BC₂N and transition metal dichalcogenides.

2. Methods

First-principles calculations are performed using the plane-wave Vienna ab initio simulation package with projector-augmented wave pseudopotentials.²³ The Perdew–Burke–Ernzerhof (PBE) functional is used for both the structure optimization and calculation of the material properties. The Heyd–Scuseria–Ernzerhof (HSE06) functional with a mixing parameter of 0.25 and a screening parameter of 0.2 Å⁻¹ for the Hartree–Fock exchange is adopted to rectify the band gap sizes and band edge positions, because both GW²⁴ and self-interaction-corrected²⁵ calculations are computationally much too expensive. The optical absorption spectrum is calculated by means of the random phase approximation method. The plane-wave cutoff energy is set to 500 eV and 9 × 9 × 1 Monkhorst–Pack meshes are utilized for Brillouin zone integrations. Vacuum slabs of 25 Å thickness are applied to generate 2D models. A total energy convergence of 1 × 10⁻⁸ eV per atom and an atomic force convergence of 0.001 eV Å⁻¹ are achieved. The phonon spectra are calculated using density functional perturbation theory (Phonopy²⁶ and Vienna ab initio simulation package) and a 3 × 3 × 1 supercell. Ab initio molecular dynamics simulations at 1000 K are carried out for 10 ps (time step 1 fs) using a 3 × 3 × 1 supercell and a canonical ensemble.²⁷

3. Results and discussion

3.1 Structure and stability

Starting from the structure of PBCF-graphene,²² we design four ternary structures of PBCF-BC₂N by replacing half of the C–C pairs with B–N pairs, see the optimized structures in Fig. 1 and structural details in Table 1. In each case, the primitive hexagonal unit cell contains six B, twelve C, and six N atoms. It turns out that α-BC₂N, β-BC₂N, γ-BC₂N, and δ-BC₂N have space groups P6mm (no. 183), P3̄m1 (no. 164), P6̄₂m (no. 189), and P3̄₁m (no. 162), respectively, with optimized lattice constants of 6.99, 7.05, 7.14, and 7.13 Å. The orthorhombic lattice constants are 6.99 Å (armchair direction) and 12.11 Å (zigzag direction) for α-BC₂N, 7.05 Å and 12.21 Å for β-BC₂N, 7.14 Å and 12.37 Å for γ-BC₂N, and 7.13 Å and 12.35 Å for δ-BC₂N. The sandwich-like structures are 2.47 to 2.53 Å thick. The top and bottom layers of α-BC₂N and β-BC₂N are connected by B–N bonds while those of γ-BC₂N and δ-BC₂N are connected by C=C bonds. α-BC₂N realizes a pronounced Janus geometry. In each case, the hexagonal unit cell comprises six C–C, six B–N, twelve C–B, and twelve C–N bonds. The C=C bond lengths of 1.36 to 1.39 Å are slightly shorter than those in graphene (1.42 Å), whereas the B–N bond lengths of 1.44 to 1.46 Å closely resemble the value for h-BN (1.45 Å). The relatively short C=C and B–N bond lengths represent strong covalent bonds. The C–B and C–N bond lengths range from 1.53 to 1.60 Å and from 1.45 to 1.48 Å, respectively.

Fig. 1 Top and side views of the atomic structures of (a) α-BC₂N, (b) β-BC₂N, (c) γ-BC₂N, and (d) δ-BC₂N. The primitive hexagonal unit cell is shown by gray solid lines and the orthorhombic unit cell is shown by red dashed lines. The orange, green, and blue spheres represent C, B, and N atoms, respectively.

Table 1 Space groups, lattice constants (a), thickness (h), bond lengths (l_C−N, l_C−B, and l_B−N), cohesive energy (E_coh), and band gaps (E^PBE_g and E^HSE06_g)

	Space group	a (Å)	h (Å)	l C–C (Å)	l C–N (Å)	l C–B (Å)	l B–N (Å)	E coh (eV per atom)	E ^PBEg (eV)	E ^HSE06g (eV)
α-BC2N	P6mm	6.99	2.53	1.36/1.39	1.48	1.53	1.46	6.25	0.75	1.97
β-BC2N	P3̄m1	7.05	2.51	1.37	1.45	1.59	1.44	6.31	1.10	2.20
γ-BC2N	P6̄2m	7.14	2.53	1.36	1.46	1.60	1.44	6.33	0.46	1.45
δ-BC2N	P3̄1m	7.13	2.47	1.36	1.46	1.59	1.44	6.31	0.66	1.68

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To analyze the chemical bonding in PBCF-BC₂N, we calculate the electron localization function, as plotted in Fig. 2. Localized electrons between the atoms represent covalent C=C, B–N, C–B, and C–N bonds. The obtained Bader charges agree with the electronegativities of the involved atoms: for α-BC₂N the C and B atoms on the (001) side show values of +1.29 and −1.96 e, respectively, while the C and N atoms on the (001̄) side show values of −0.64 and +1.31 e. For β-BC₂N, γ-BC₂N, and δ-BC₂N, respectively, we obtain Bader charges of −1.90, −1.94, and −1.96 e for the B atoms, +0.25, +0.28, and +0.28 e for the C atoms, and +1.40, +1.38, and +1.40 e for the N atoms. Hence, the chemical bonding in PBCF-BC₂N is governed by strongly polarized covalent bonds.

Fig. 2 Electron localization function (isosurface value 0.8) of (a) α-BC₂N, (b) β-BC₂N, (c) γ-BC₂N, and (d) δ-BC₂N.

The cohesive energy per atom, E_coh = [xE(B) + yE(C) + zE(N) − xE(B_xC_yN_z)]/(x + y + z), where E(B), E(C), E(N), and E(B_xC_yN_z) are the total energies of a B atom, a C atom, a N atom, and a unit cell of PBCF-BC₂N, respectively, follows the trend γ-BC₂N (6.33 eV) > β-BC₂N (6.31 eV) = δ-BC₂N (6.31 eV) > α-BC₂N (6.25 eV). It is lower than in the cases of graphene (7.85 eV) and h-BN (7.07 eV) but higher than in the cases of (experimentally existing) N-graphdiyne (6.02 eV),²⁸B-graphdiyne (5.85 eV),²⁹ and g-C₃N₄ (5.71 eV),³⁰ demonstrating pronounced stability. The obtained phonon spectra and densities of states in Fig. 3 demonstrate dynamical stability. The maximal phonon frequencies turn out to be 46.6, 44.4, 45.2, and 44.9 THz for α-BC₂N, β-BC₂N, γ-BC₂N, and δ-BC₂N, respectively. The high-frequency phonons are due to the presence of sp²-hybridized C atoms, whereas the B and N atoms contribute below 40 THz. Our ab initio molecular dynamics simulations, see Fig. 3 for the potential energy as a function of the time and the final atomic structure, demonstrate the absence of bond breaking.

Fig. 3 Phonon spectra and densities of states (left; colors correspond to the atomic species) as well as results of ab initio molecular dynamics simulations (right; at 1000 K) of (a) α-BC₂N, (b) β-BC₂N, (c) γ-BC₂N, and (d) δ-BC₂N.

The mechanical properties of PBCF-BC₂N are investigated by calculating the in-plane elastic constants, Young's modulus, Poisson's ratio, and the strain–stress relationship. The hexagonal lattice results in isotropic in-plane elasticity and the elastic energy accumulated under strain ε_ij can be expressed as

Perfect parabolic dependencies under uniaxial and biaxial strain (Fig. S1, ESI†) demonstrate reliability of the employed calculation method. Fulfilling the relations C₁₁ = C₂₂ and 2C₄₄ = C₁₁ − C₁₂ we obtain the elastic constant C₁₁, C₁₂, and C₄₄ values of 236, 100, and 68 N m⁻¹ for α-BC₂N; 230, 84, and 73 N m⁻¹ for β-BC₂N; 237, 73, and 82 N m⁻¹ for γ-BC₂N; and 223, 62 and 80 N m⁻¹ for δ-BC₂N, respectively. Therefore, the Born criteria (C₄₄ > 0 and C₁₁C₂₂ − C₁₂² > 0)³¹ of mechanical stability are satisfied. The in-plane Young's modulus Y = (C₁₁² − C₁₂²)/C₁₁ and Poisson's ratio v = C₁₂/C₁₁ amount to 194 N m⁻¹ and 0.42 for α-BC₂N; 199 N m⁻¹ and 0.37 for β-BC₂N; 215 N m⁻¹ and 0.31 for γ-BC₂N; and 206 N m⁻¹ and 0.28 for δ-BC₂N. The Young's modulus is thus lower than that in graphene (344 N m⁻¹)³² but much higher than those in MoS₂ (123 N m⁻¹)³³ and black phosphorene (83 N m⁻¹),³⁴ indicating mechanical robustness.

Strain–stress curves under biaxial strain are shown in Fig. 4(a). When the strain increases, the stress is found to increase first linearly and afterwards nonlinearly. The fracture strength and strain turn out to be 23.6 N m⁻¹ and 16% for α-BC₂N; 18.7 N m⁻¹ and 18.5% for β-BC₂N; 18.1 N m⁻¹ and 16.5% for γ-BC₂N; and 15.6 N m⁻¹ and 13% for δ-BC₂N. In contrast to α-BC₂N, β-BC₂N, and γ-BC₂N, we find for δ-BC₂N, a sudden drop in stress under high strain (between 13.5% and 14%). Comparison of the electron localization functions of δ-BC₂N under 13.5% and 14% strain in Fig. 4(b) and (c) points to the strengthening of the inter-layer B–N bonds at the cost of intra-layer bonds, resulting in structural collapse. The calculated phonon spectra of α-BC₂N, β-BC₂N, γ-BC₂N, and δ-BC₂N (Fig. S2, ESI†), on the other hand, show no imaginary frequencies under 8%, 18%, 16%, and 12% strain, respectively (while showing imaginary frequencies under 8.5%, 18.5%, 16.5%, and 12.5% strain), which correspond to fracture strengths of 18.3 N m⁻¹, 18.7 N m⁻¹, 18.1 N m⁻¹, and 15.5 N m⁻¹, respectively.

Fig. 4 (a) Strain–stress curves under biaxial strain (orange = α-BC₂N; blue = β-BC₂N, green = γ-BC₂N, and gray = δ-BC₂N). Electron localization function (isosurface value = 0.8) of δ-BC₂N under (b) 13.5% and (c) 14% biaxial strain.

3.2 Electronic properties

Fig. 5 shows the electronic band structures and partial densities of states of PBCF-BC₂N obtained using the PBE and HSE06 functionals. In each case we find a direct band gap with the conduction band minimum (CBM) and valence band maximum (VBM) located at the center of the Brillouin zone (Γ point). The size of the band gap of α-BC₂N, β-BC₂N, γ-BC₂N, and δ-BC₂N is found to be 1.97 (0.84), 2.20 (1.13), 1.45 (0.54), and 1.68 (0.70) eV using the PBE (HSE06) functional, respectively. The CBM of α-BC₂N (β-BC₂N) is dominated by the C (B) atoms and the VBM is dominated by the B (N) and C atoms. The CBM of both γ-BC₂N and δ-BC₂N is dominated by B atoms (with contributions of the N atoms) and the VBM by the C atoms.

Fig. 5 Electronic band structures (black = PBE and red = HSE06) and partial densities of states (PBE; in units of 1/eV; orange = C; green = B; blue = N) of (a) α-BC₂N, (b) β-BC₂N, (c) γ-BC₂N, and (d) δ-BC₂N.

For the HSE06 functional, the effect of biaxial strain on the size of the band gap is shown in Fig. 6(a) (see Fig. S3, ESI† for the electronic band structures). With the exception of α-BC₂N, the strain tunes the size of the band gap effectively. For the PBE functional, the carrier effective mass is obtained by fitting the electronic band structure at the respective band edge as m* = ℏ²/(∂²E/∂k²)⁻¹; see the results in Fig. 6(b) and (c). The electron (hole) effective masses of PBCF-BC₂N turn out to be isotropic with values of 0.37 (0.49), 0.44 (0.80), 0.47 (0.77), and 0.60 (1.04) m₀ for α-BC₂N, β-BC₂N, γ-BC₂N, and δ-BC₂N in the absence of strain, respectively. The electron effective masses increase slowly under strain, while the hole effective masses show a more complex behavior.

Fig. 6 (a) Band gaps, (b) hole effective masses and (c) electron effective masses of PBCF-BC₂N under biaxial strain (orange = α-BC₂N; blue = β-BC₂N, green = γ-BC₂N, and gray = δ-BC₂N).

The carrier mobility is calculated using the Bardeen–Shockley deformation potential theory as

where C_2D denotes the in-plane elastic constant and E denotes the (direction-dependent) deformation potential constant. The results should be understood as upper limits, since the carrier mobility tends to be overestimated. The band edge positions under strain along the armchair and zigzag directions are shown in Fig. 7. Table 2 summarizes the obtained in-plane elastic constants, deformation potential constants, and carrier mobilities at 300 K. We find virtually no anisotropy for electron mobilities and only a minor anisotropy for hole mobilities. All the materials show significantly larger electron mobilities than hole mobilities, where the particularly high electron mobility of β-BC₂N is a consequence of a small deformational potential constant. The hole mobilities of α-BC₂N and β-BC₂N exceed those of 2D MoS₂ (armchair direction: 2.0 × 10² cm² V⁻¹ s⁻¹ and zigzag direction: 1.5 × 10² cm² V⁻¹ s⁻¹)³⁵ by more than a factor of two and all the electron mobilities exceed those of 2D MoS₂ (armchair direction: 7.2 × 10¹ cm² V⁻¹ s⁻¹ and zigzag direction: 6.2 × 10¹ cm² V⁻¹ s⁻¹ in the)³⁶ by about two orders of magnitude, resembling few-layer black phosphorus.³⁶ The electron mobility of β-BC₂N is even comparable to that of 2D Ca₃Sn₂S₇ (6.7 × 10⁴ cm² V⁻¹ s⁻¹),³⁷ suggesting its great potential for application in nano-electronic devices.

Fig. 7 Valence and conduction band edges of (a) α-BC₂N, (b) β-BC₂N, (c) γ-BC₂N, and (d) δ-BC₂N under biaxial strain.

Table 2 Carrier effective mass (m*), in-plane elastic constants (C^2D), deformation potential constants (E_armchair and E_zigzag), and carrier mobilities at 300 K (μ_armchair and μ_zigzag)

	Carrier type	m* (m0)	C ^2D (N m^−1)	E armchair (eV)	E zigzag (eV)	μ armchair (cm^2 V^−1 s^−1)	μ zigzag (cm^2 V^−1 s^−1)
α-BC2N	Electron	0.37	236	3.28	3.29	4.8 × 10^3	4.8 × 10^3
β-BC2N		0.44	230	0.82	0.83	5.2 × 10^4	5.2 × 10^4
γ-BC2N		0.47	237	3.86	3.86	2.1 × 10^3	2.1 × 10^3
δ-BC2N		0.60	223	1.54	1.54	7.8 × 10^3	7.8 × 10^3
α-BC2N	Hole	0.49	236	6.39	6.51	7.2 × 10^2	6.9 × 10^2
β-BC2N		0.80	230	5.02	5.21	4.2 × 10^2	3.9 × 10^2
γ-BC2N		0.78	237	7.62	7.93	2.1 × 10^2	1.9 × 10^2
δ-BC2N		1.04	223	6.28	6.57	1.5 × 10^2	1.4 × 10^2

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3.3 Photocatalytic properties

To investigate the photocatalytic potential for water splitting, we determined the positions of the band edges with respect to the vacuum level using the HSE06 functional. One of the fundamental requirements of a photocatalytic semiconductor is band edges (CBM and VBM) enclosing the redox potentials of water, i.e., the CBM must exceed the reduction potential of H⁺/H₂ (−4.44 eV at pH = 0 and −4.03 eV at pH = 7) and the VBM must not exceed the oxidation potential of O₂/H₂O (−5.67 eV at pH = 0 and −5.26 eV at pH = 7).³⁸ To determine the positions of the band edges, we have shown the electrostatic potential in Fig. 8. Due to its Janus geometry, the value is different for the two sides of α-BC₂N (specifically: 0.76 eV higher for the (001) side than the (001̄) side).

Fig. 8 Electrostatic potential of (a) α-BC₂N, (b) β-BC₂N, (c) γ-BC₂N, and (d) δ-BC₂N.

Strain engineering is an effective approach to modulate the electronic properties of materials,^39–41 and the effect of strain on the positions of the band edges is shown in Fig. 9(a)–(e). For α-BC₂N we find that the (001) side is suitable only for the oxygen evolution reaction and the (001̄) side is suitable only for the hydrogen evolution reaction, see Fig. 9(f). Photocatalytic water splitting is possible for β-BC₂N (from pH = 0 to pH = 7), while for γ-BC₂N and δ-BC₂N it is possible only under at least 6% strain. Strong optical absorption from the visible to ultraviolet spectral range is another key requirement of a high-efficiency photocatalytic semiconductor. The optical spectra in Fig. 10, calculated by random approximation (RPA) with the polarization being parallel to the 2D material, show that PBCF-BC₂N fulfills this requirement even though the RPA does not include excitonic effects^42,43 (renormalization of the peak intensities, redshifting of the spectra due to electron–hole interaction, etc.) and these effects can be significant in 2D materials.

Fig. 9 Positions of the band edges relative to the vacuum level of (a) (001) side of α-BC₂N, (b) (001̄) side of α-BC₂N, (c) β-BC₂N, (d) γ-BC₂N, and (e) δ-BC₂N under biaxial strain. (f) Intrinsic electric field of α-BC₂N.

Fig. 10 Optical spectra of (a) α-BC₂N, (b) β-BC₂N, (c) γ-BC₂N, and (d) δ-BC₂N (gray = PBE + RPA; red = HSE06 + RPA; polarization parallel to the 2D material).

We next quantify the photocatalytic performance. The STH efficiency is estimated from η_sth = η_ab × η_cu, where η_ab is the efficiency of absorption and η_cu is the efficiency of carrier utilization. We have

where E_g is the optical gap (1.97 eV for α-BC₂N and 2.20 eV for β-BC₂N) and P(ℏω) is the AM1.5 solar energy flux at photon energy ℏω, resulting in η_ab = 37.7% for α-BC₂N and 28.2% for β-BC₂N. Furthermore, we havewhere ΔG = 1.23 eV for water and E_min (minimum energy of the photons that can be utilized for the redox reactions) can be determined aswhere χ(H₂) and χ(O₂) represent the overpotentials of the hydrogen and oxygen evolution reactions, respectively. Considering that the intrinsic electric field of a Janus material reduces the recombination of the photo-generated carriers, the STH efficiency is corrected aswhere ΔΦ is the electrostatic potential difference between the two sides of the materials. We find χ(H₂) = 0.78 eV, χ(O₂) = 0.72 eV, E_min = 1.97 eV, ΔΦ = 0.76 eV, and η_cu = 49.4% for α-BC₂N and χ(H₂) = 0.43 eV, χ(O₂) = 0.53 eV, E_min = 2.27 eV, and η_cu = 40.8% for β-BC₂N. Thus, the STH efficiency and corrected STH efficiency of α-BC₂N turn out to be 19% and 17%, respectively, approaching the conventional theoretical limit (∼18%). The STH efficiency of β-BC₂N turns out to be 12%, which is comparable to the values reported for GeN₃ (12.6%)⁴⁴ and AgBiP₂Se₆ (10.2%),²⁶ exceeding the target value for industrial application (10%).¹⁹ Both α-BC₂N and β-BC₂N therefore emerge as economically viable photocatalysts for water splitting.

3.4 Photovoltaic properties

Due to their moderate direct band gaps of 1.45 and 1.68 eV, respectively, and excellent absorption of solar radiation, γ-BC₂N and δ-BC₂N are potential candidates for heterostructure solar cell materials. We study heterostructures with hexagonal 2D MX₂ (M = Mo and W; X = S, Se, and Te), which also show direct band gaps and strong absorption.^45–47Table 3 summarizes the structural and electronic parameters of 2D MX₂ (M = Mo and W; X = S, Se, and Te) obtained using the HSE06 hybrid functional with spin–orbital coupling (SOC) being included (see Fig. S4, ESI† for the electronic band structures). The positions of the valence and conduction band edges relative to the vacuum level are illustrated in Fig. 11(a). The band edges of γ-BC₂N and δ-BC₂N enclose those of WTe₂, leading to type-I band alignment, while they are interlaced with those of MoS₂, MoSe₂, MoTe₂, WS₂, and WSe₂, leading to type-II band alignment. Due to the lower electron affinity as compared to 2D MX₂ (M = Mo and W; X = S, Se, and Te), both γ-BC₂N and δ-BC₂N act as electron donors in the heterostructure. For γ-BC₂N (δ-BC₂N), we obtain conduction band offsets of 0.84 (0.98), 0.48 (0.62), 0.31 (0.45), 0.43 (0.57), 0.12 (0.26), and 0.14 (0.28) eV relative to MoS₂, MoSe₂, MoTe₂, WS₂, WSe₂, and WTe₂, respectively.

Table 3 Lattice constants (a; space group P6̄m2), thickness (h), bond lengths (l_M–X), positions of the band edges with respect to the vacuum level (E^HSE06+SOC_VBM and E^HSE06+SOC_CBM), band gaps (E^HSE06+SOC_g), and spin–orbit splitting in the valence band (Δ^HSE06+SOC)

	a (Å)	h (Å)	l M–X (Å)	E ^HSE06+SOCVBM (eV)	E ^HSE06+SOCCBM (eV)	E ^HSE06+SOCg (eV)	Δ^HSE06+SOC (eV)
MoS2	3.18	3.13	2.41	−6.27	−4.25	2.02	0.21
MoSe2	3.32	3.34	2.54	−5.60	−3.89	1.71	0.28
MoTe2	3.55	3.61	2.73	−4.99	−3.72	1.27	0.35
WS2	3.18	3.14	2.42	−5.83	−3.84	1.99	0.55
WSe2	3.32	3.35	2.55	−5.17	−3.53	1.64	0.62
WTe2	3.55	3.62	2.74	−4.59	−3.55	1.04	0.68

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Fig. 11 (a) Band alignments and (b) PCE (in %).

The maximum PCE of a solar cell is given using the following expression

where we assume a fill factor of β_FF = 0.65. The open circuit voltagecan be obtained from the optical gap of the donor (E^d_g ∼ 1.45 eV for γ-BC₂N and 1.68 eV for δ-BC₂N) and conduction band offset (ΔE_CBM) considering an empirical loss of 0.3 eV. The short circuit current (limit of external quantum efficiency) is given using the following expression

As shown in Fig. 11(b), PCE_max values in excess of 20% are achieved by the γ-BC₂N/WSe₂ and γ-BC₂N/WTe₂ heterostructures, which are comparable to those of organic solar cells (18.2%)¹¹ and the δ-CS/MoTe₂ heterostructure (20.1%).¹⁷ They approach the performances of state-of-the-art perovskites (25.5%), silicon (27.6%), and GaAs (30.5%) solar cells,¹¹ pointing toward their great application potential.

4. Conclusion

Using comprehensive first-principles calculations, we have proposed 2D hexagonal borocarbonitrides (α-BC₂N, β-BC₂N, γ-BC₂N, and δ-BC₂N) with cohesive energies of 6.25–6.33 eV per atom combined with dynamical, mechanical, and thermal (at 1000 K) stability. High fracture strengths and strains are interesting for nano-mechanical applications. Moderate direct band gaps of 1.45–2.20 eV (HSE06) and isotropic small carrier effective masses are found. It also turns out that the size of the band gap can be effectively tuned using strain. Electronic applications can benefit from the discovered ultrahigh electron mobilities. Both α-BC₂N and β-BC₂N show potential in photocatalytic water splitting with excellent absorption of solar radiation. In particular, the intrinsic electric field induced by the Janus geometry of α-BC₂N separates the photo-generated electrons and holes, therefore minimizing their recombination. The electrons and holes migrate to opposite sides of the two-dimensional material to take part in the redox reactions for water splitting. The high efficiency of carrier utilization (49.4%) resulting from the intrinsic electric field leads to an outstanding solar-to-hydrogen efficiency of 17%. According to the band alignments, γ-BC₂N and δ-BC₂N act as electron donors in heterostructures with 2D MX₂ (M = Mo and W; X = S, Se, and Te). It turns out that such heterostructures can show a PCE of up to 21%.

Author contributions

W. Zhang, M. Sun, and U. Schwingenschlögl conceived the study. C. Chai and M. Sun performed the calculations and analyzed the data. W. Zhang and Q. Fan wrote the manuscript guided by M. Sun, M. Palummo, and U. Schwingenschlögl. C. Chai and Y. Yang provided equipment support.

Conflicts of interest

The authors declare no competing interests.

Acknowledgements

The authors acknowledge financial support from the National Natural Science Foundation of China (no. 61974116 and no. 61804120), the China Postdoctoral Science Foundation (no. 2019TQ0243 and no. 2019M663646), and the Key Scientific Research Project of Education Department of Shannxi-Key Laboratory Project (no. 20JS066). M. P. acknowledges CN1 (Spoke6) - Centro Nazionale di Ricerca (High-Performance Computing Big Data and Quantum Computing and TIME2QUEST-INFN projects). Xidian University provided computational resources and support. The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST).

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Footnote

† Electronic supplementary information (ESI) available: Elastic energies under uniaxial and biaxial strain, phonon spectra under extreme biaxial tensile strain, electronic band structures under biaxial tensile strain, and electronic band structures of 2D transition metal dichalcogenides. POSCAR files. See DOI: https://doi.org/10.1039/d2tc05268g

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