C₃N₂: the missing part of highly stable porous graphitic carbon nitride semiconductors

Abstract

Two-dimensional (2D) porous graphitic carbon nitrides (PGCNs) with semiconducting features have attracted wide attention because of built-in pores with various active sites, large surface area, and high physicochemical stability. However, only a few PGCNs have been synthesized, covering a 1.23–3.18 eV band gap. We systematically investigate two new 2D PGCN monolayers, T-C₃N₂ and H-C₃N₂, including possible pathways for their experimental synthesis. Based on first-principles calculations, the mechanical, electronic, and optical properties of T-C₃N₂ and H-C₃N₂ have been systematically investigated. These two architectural frameworks exhibit contrasting mechanical characteristics owing to their structural differences. Both T-C₃N₂ and H-C₃N₂ monolayers are predicted to be intrinsic semiconductors. Exceptionally, the stacking bilayers of T-C₃N₂ can transform into a rare 2D nodal-line semimetal structure. The narrow bandgap (0.35 eV) of the T-C₃N₂ monolayer and its extraordinary transformation in the bilayer electronic structure fill the vacancy of PGCNs as electronic devices in the middle/long wave infrared region. C₃N₂ structures possess ultrahigh anisotropic carrier mobilities (×10⁴ cm² V⁻¹ s⁻¹) and exceptional absorption coefficients (×10⁵ cm⁻¹) in the near-infrared and visible light regions, suggesting its possible optoelectronic applications. The findings expand the scope of 2D PGCNs and offer guides for their experimental realization.

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New concepts

Two-dimensional (2D) porous graphitic carbon nitrides (PGCNs) with semiconducting features have attracted wide attention since g-C₃N₄ was synthesized. However, only a few PGCNs have been synthesized. Herein, we systematically investigate two 2D PGCNs, namely, H-C₃N₂ and hitherto unreported T-C₃N₂. According to the synthetic methods of reported PGCNs, such as C₂N-h2D (Nat. Commun., 2015, 6, 6486–6492), the realization of H-C₃N₂ is quite feasible in the experiment. More notably, first-principles calculations show T-C₃N₂ has much lower cohesive energy than H-C₃N₂, which leads to the higher stability of the former. It also implies a possibility of experimental realization of T-C₃N₂. Both T-C₃N₂ and H-C₃N₂ monolayers are predicted to be intrinsic semiconductors with 0.35 eV and 1.97 eV bandgap, respectively. The proposal for T-C₃N₂ not only enriches PGCN semiconductors but also introduces a clear direction for the experimental realization of more highly stable PGCNs. Another novel feature is that the stacking bilayers of T-C₃N₂ can transform into a rare 2D nodal-line semimetal, which expands its optoelectronic application. Besides, two C₃N₂ structures possess ultrahigh anisotropic carrier mobilities (×10⁴ cm² V⁻¹ s⁻¹) and exceptional absorption coefficients (×10⁵ cm⁻¹) in the near-infrared and visible light regions, further suggesting its possible optoelectronic applications.

1. Introduction

The first synthesized two-dimensional (2D) porous graphitic carbon nitride (PGCN) was g-C₃N₄, reported in 2009, with a band gap of about 2.70 eV.¹ This carbon nitride allotope, with a layered structure analogous to graphite, was found to be more stable than the other four carbon nitride allotropes of the same stoichiometry, namely a-C₃N₄, b-C₃N₄, cubic C₃N₄, and pseudocubic C₃N₄, all of which exhibit three-dimensional structures of various types. The discovery of graphitic g-C₃N₄ has triggered considerable research interest owing to its high physicochemical stability, various active sites, built-in pore distribution, and large surface area.² However, its relatively poor conductivity has limited its electronic and electrochemical applications. Nevertheless, its unique optical properties, suitable conduction band minimum, and valence band maximum make g-C₃N₄ useful as a photocatalyst for hydrogen evolution by water splitting and for the degradation of some pollutants at room temperature.^1,3

The successful synthesis of g-C₃N₄ by the thermal polycondensation of the nitrogen-rich symmetrical hexaminoheptazaphenalene (commonly abbreviated as “heptazine”) with ammonia elimination led to the experimental and theoretical investigation of other PGCNs. Theoretically, the assembly of suitably chosen nitrogen-rich organic monomers through covalent bond formation is feasible. Thus several PGCNs have been successfully synthesized in recent years by polycondensation reactions between suitably chosen oligomers (Scheme 1). For example, C₃N₅, with a band gap of 1.76 eV, was obtained in 2018 by combining an azo unit (linker) with the hexagonal heptazine motif in the form of hexaminoheptazaphenalene (node).⁴ In 2019, C₃N₅ was synthesized as a low bandgap semiconductor for photocatalytic, photovoltaic, and adsorbent applications.⁵ Apart from g-C₃N₄ and C₃N₅, the three most representative PGCNs, namely the highly symmetrical t-C₃N₄,⁶ C₂N-h2D,⁷ and C₃N₃,⁸ were synthesized and studied experimentally owing to their moderate band gaps (2.40 eV, 2.47 eV and 3.18 eV, respectively) and architectural features similar to g-C₃N₄. The pyridinic nitrogen atoms surrounding the PGCNs pores provide sites for the absorption of metal ions through coordination. Consequently, the PGCNs can be used as electrode materials for metal-ion batteries.⁹ Double-layered C₂N-450 in lithium-ion (Li-ion) battery was found experimentally to display high reversible capacities of 933.2 (383.3) and 40.1 (179.5) mA h g⁻¹ at 0.1 and 10 C. Furthermore, its monolayer is predicted to exhibit the maximum theoretical capacities of 2939 mA h g⁻¹ among PGCNs.^10–12

Scheme 1 The main synthetic progress of reported PGCN, C₃N₂, and their synthetic precursors. Yellow and magenta balls correspond to carbon and nitrogen atoms, respectively.

Limited efficient synthetic methods and the instability of the PGCNs prevent them from being more widely synthesized and studied experimentally, despite the publication of many theoretical predictions.^12–22 The main bottleneck is the lack of suitable organic molecule building blocks. Theoretically, the possibility of experimental synthesis of a given structure is determined by its thermodynamic stability.²³ Recently, our group proposed that the coexistence of graphitic and pyridinic nitrogen atoms in PGCNs could lead to more stable structures thermodynamically.¹² The crucial role of the coexistence of graphitic and pyridinic N in determining the stability of PGCNs has been theoretically confirmed by Searles et al.¹¹ with subsequent experimental proof by the synthesis of C₃N₅ and g-C₃N₄. Analogous to the synthesis of covalent organic frameworks (COF),^24,25 the key to the successful synthesis of PGCNs is the availability of suitable organic building blocks meeting the above requirement.

In connection with the synthesis of PGCNs, we propose two feasible nitrogen-containing building blocks, namely 2,3,6,7,10,11-hexamine dipyrazino quinoxaline (HADQ) and 1,4,7,9b-tetraazaphenalene (TAPA). These building blocks can be used to synthesize three novel C₃N₂ allotropes with hexagonal pores, namely, T-C₃N₂, TH-C₃N₂, and H-C₃N₂. First principle calculations confirm that T-C₃N₂ with the highest graphitic nitrogen concentration exhibits the highest stability. The mechanical, electronic, and transport properties of C₃N₂ allotrope monolayers with and without graphitic nitrogen are explored and compared in this paper. The band gaps, carrier mobilities, and optical properties are discussed in order to illustrate their promising applications in nanoelectronic and photovoltaic devices.

2. Computational details

All simulations, including structural search and property calculations, were performed by the density functional theory (DFT) method implemented in the Vienna ab initio simulation package (VASP).²⁶ The electron–ion interaction was considered in the projected augmented wave (PAW)²⁷ method, and the exchange–correlation term was treated using Perdew–Burke–Ernzerhof (PBE)²⁸ parametrization involved in the generalized gradient approximation (GGA).²⁹ The kinetic energy cutoff was set to 700 eV with optimized structures of 20 Å vacuum region between the adjacent images in the z-direction to avoid the interaction between neighboring layers. Meanwhile, the total energy and atomic force converged on each atom when they were less than 10⁻⁶ eV and 1 meV Å⁻¹, respectively. The Brillouin zone was sampled with a resolution of 0.03 × 2π Å⁻¹. These studies were followed by using the Heyd–Scuseria–Ernzerh of hybrid functional (HSE06)³⁰ to obtain more accurate band gaps of T-C₃N₂ monolayers in electronic calculations. van der Waals's interaction was considered using the semiempirical DFT-D2 approach³¹ in the bilayer structures of PGCNs. Phonon dispersion calculations were carried out in the supercell with at least 96 atoms for T-C₃N₂, as used in the Phonopy code.³² Molecular dynamics (MD) simulations in the NVT ensemble were used to estimate the thermal stability of T-C₃N₂. Evaluation of the energetic stabilities of monolayers and the bilayers with different stackings was based on calculations of the cohesive energies (E_c) of the carbon nitride monolayers and the binding energies (E_b) of the bilayers H-C₃N₂ and T-C₃N₂ using the equations:respectively, where E_C3N2, E_c, E_n, and E_bilayer are energies of the monolayer C₃N₂, a carbon atom, a nitrogen atom, and the C₃N₂ bilayer, respectively. The quantities n and m are the numbers of atoms in the corresponding structure. To evaluate the synthesis possibility of two new C₃N₂ allotropes, a particle swarm optimization (PSO)³³ algorithm is used to search the low-energy structure for the ratio of C : N = 3 : 2.

3. Results and discussion

3.1. Design and feasibility for experimental realization of C₃N₂ monolayers

Similar to t-C₃N₄⁶ and g-C₃N₄,¹ H-C₃N₂ and T-C₃N₂ allotropes could be also synthesized by different organic unit molecules (details in the Design scheme). As shown in Scheme 1, the s-heptazine, triazine, and hexaaminobenzene (HAB) trihydrochloride are the basic building blocks of the synthesized CN compounds (i.e., C₃N₅, g-C₃N₄, t-C₃N₄, C₃N₃, C₂N-h2D, and C₃N).^{1,5,6,8,34,35} HAB reacts with the other hexaketocyclohexane (HKH) octahydrate organic molecule to produce C₂N-h2D,³⁵ where the carbonyl group reacts with amino leaving N atoms.³⁵ Thus, we propose that α-C₃N₂¹² (also labeled H-C₃N₂) monolayer could be synthesized through a possible synthesis scheme between HADQ³⁶ and HKH (Fig. 1c and Fig. S2 in the ESI†). HADQ was just synthesized for the first time in 2021 and used to prepare 2D metal–organic framework (MOF) Co₃(HADQ)₂,³⁶ similar to 2D MOF Co₃(HAB)₂³⁷ based on the HAB and transition metal Cobalt. The similar structural feature between HADQ and HAB opens the possibility for the experimental realization of H-C₃N₂. In addition to HADQ, another one containing-N organic unit 1,4,7,9b-tetraazaphenalene (TAPA)^38,39 is proposed to construct a new allotrope C₃N₂ monolayer (labeled T-C₃N₂). According to the synthetic process of tricycloquinazoline, which was used to prepare covalent quinazoline networks (CQNs), T-C₃N₂ allotrope could be synthesized^40,41 (Fig. 1a and Fig. S3, ESI†). Apart from H-C₃N₂ and T-C₃N₂, the combination of TAPA and HAB also forms another allotrope labeled TH-C₃N₂ (Fig. 1b and Fig. S4, ESI†).

Fig. 1 (a–c) The possible synthesis pathways and structures of H-C₃N₂, HT-C₃N₂, and T-C₃N₂ monolayers. (d) The cohesive energy comparison for the three proposed C₃N₂ monolayers and the reported pc-C₃N₂. (e) The convex hull of the synthesized CNs and theoretical predicted C₃N₂ monolayers. Cyan spheres and black squares represent highly stable and metastable structures, respectively. Heptazine, TAPA, and HAB are fundamental building blocks composed of pyridinic and graphitic N.

From the experimental perspective, the synthesis reaction between HADQ and HKH to form H-C₃N₂ is quite feasible because the dehydration reaction between amino and carbonyl usually occurs in the synthesis of COFs, such as aza-COF-2,^42–45 FA-PON,^42,46,47 TQBQ-COF,⁴⁸ and F-COF.⁴⁹ Solvents and catalysts are sometimes different, but primary monomers are unchanged. According to the synthesis of C₂N-h2D,^10,35 aza-COF-2,^42,43 and FA-PON^46,47,50(Fig. S2, ESI†) and their same edge functional group (i.e. amino), we propose that using the main organic reactants (i.e. HADQ and HKH) and N-methyl-2-pyrrolidone (NMP) in the presence of a few drops of sulfuric acid (H₂SO₄) as catalysts could produce preliminary materials via a bottom-up wet-chemical reaction, where the reaction mixture needs to be heated 175–185 °C under argon or N₂ atmosphere. Similarly, in the synthesis of mCQN and CQN-1, Zinc chloride (ZnCl₂) was always used as the solvent and catalyst and reacted with 2-aminobenzonitrile (ABN) and 2,5-diamino-1,4-benzenedicarbonitrile (DBDN) for the condensation of aromatic ortho-aminonitriles to produce tricycloquinazoline linkages (Fig. S3a and b, ESI†).⁴¹ For T-C₃N₂, thus, we predict mixing 1,2-diamino-1,2-dicyanoethylene (DDE) and anhydrous ZnCl₂ under 300–400 °C could yield preliminary materials. Furthermore, by comparing the cohesive energy of three C₃N₂ monolayers with the result of PSO (ESI†), T-C₃N₂ has the lowest cohesive energy and its synthesis is thermodynamically reliable.²³ Therefore, T-C₃N₂ and H-C₃N₂ are the focus of our research.

The lattice parameters of T-C₃N₂ monolayer are A₁ = B₁ = 8.36 Å, which is smaller than those of H-C₃N₂ (A₃ = B₃ = 12.29 Å).¹² Both T-C₃N₂ and H-C₃N₂ monolayers have regular periodic hexagon holes, the diameter of which is 5.53 Å for the former and 9.72 Å for the latter. According to the atomic chemical environment and symmetry, the nitrogen atoms have different arrangements in H-C₃N₂ and T-C₃N₂, exhibiting a hexagonal lattice and a kagome lattice, respectively. The pores of H-C₃N₂ are surrounded by pyridinic nitrogen atoms bonded to two carbon atoms (Fig. 1c). In comparison, the pore of T-C₃N₂ is surrounded by six fringed pyridinic nitrogen atoms and six graphitic nitrogen bonded with three carbon atoms within TAPA to form the kagome lattice (Fig. 1a). The space groups P6/m of C_6h symmetry and P6/mmm of D_6h symmetry are found for T-C₃N₂ and H-C₃N₂, respectively. T-C₃N₂ can be seen as the combination of C₃N³⁴ with graphitic nitrogen, as well as C₂N-h2D³⁵ with pyridinic-nitrogen and the same hexagon-hole (Fig. S5, ESI†). The optimized C–C and C–N bond lengths of the C₃N₂ allotropes and related carbon nitrides are compared in Table 1.

Table 1 The optimized space groups, lattice parameters, and C–C and C–N average bond lengths of H-C₃N₂, T-C₃N₂, HT-C₃N₂, C₂N-h2D, and C₃N

	Space group	Lattice parameter (Å)	Average bond lengths
			C–C (Å)	C–N (Å)
T-C3N2	P2/m	8.63	1.45/1.40	1.31/1.42
HT-C3N2	P6̄	10.39	1.47/1.43	1.34/1.34
H-C3N2	P6/mmm	12.29	1.48/1.45	1.32/1.35
C2N-h2D	P6/mmm	8.33	1.47/1.43	1.34
C3N	P6/mmm	4.86	1.40	1.40

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Fig. 1d shows that H-C₃N₂, TH-C₃N₂, and T-C₃N₂ have increasingly larger cohesive energies than pc-C₃N₂,¹⁶ suggesting that the coexistence of graphitic and pyridinic nitrogen leads to more stable structures.⁵¹ The cohesion energy of the three C₃N₂ monolayers increases sequentially with decreasing graphitic nitrogen concentration. Higher concentrations of graphitic nitrogen further stabilize the structures in PGCNs compared to pyridinic nitrogen. It explains why the most stable CN monolayer experimentally is hole-free C₃N in which all nitrogen atoms are graphitic.

Considering the cohesive energy of the T-C₃N₂ monolayer and the synthesized carbon nitrides, C₃N₅, g-C₃N₄, and T-C₃N₂ monolayers are on the cyan global stability line, suggesting that the coexistence of graphitic and pyridinic nitrogen are identified to be much more stable PGCNs. However, the metastable structures t-C₃N₄, C₂N-h2D, and C₃N₃, which were constructed with only pyridinic N, are not on the stability lines in the convex hull (Fig. 1e).²³ It signifies that metastable C₂N-h2D (C₃N₃) monolayer could decompose into C₃N₂. The C₂N-h2D (C₃N₃) monolayer has been synthesized, which further strengthens the synthesis feasibility of C₃N₂ monolayers.⁵² The graphitic nitrogen concentration in the stable structures increases from 0.1 in C₃N₅ to 1 in C₃N (Fig. S6, ESI†), suggesting that a likely growing trend of graphitic nitrogen concentration exists in highly stable PGCNs.

The electron localization function (ELF) in Fig. S7a (ESI†) clearly shows that the bonds between graphitic carbon atoms and graphitic(pyridinic) nitrogen atoms are strongly covalent for T-C₃N₂. The nonbonding lone electron pairs of the pyridinic nitrogen atoms surround the hexagon-holes uniformly, suggesting strong chemisorption capacity. No imaginary frequency is observed in the phonon spectra of the T-C₃N₂ monolayer. The phonon mode also exhibits good stability for T-C₃N₂ (Fig. S7b, ESI†). The highest phonon mode (47.99 THz) of T-C₃N₂ is larger than those of H-C₃N₂ (47.57 THz),¹² C₂N-h2D (46.98 THz),⁵³ and g-C₃N₄ (45 THz)⁵⁴ monolayers and only less than that of C₃N (49.16 THz).⁵⁵ First-principles molecular dynamical simulations are used to survey the thermal stabilities in a 3 × 2 supercell of T-C₃N₂ at the selected temperatures of 500 K, 750 K, and 1000 K (Fig. S7c and d, ESI†). The original framework at 750 K is retained even up to 1000 K indicating that the T-C₃N₂ monolayer maintains stability under high temperatures.

3.2. Mechanical performance of C₃N₂ monolayers

In order to explore the mechanical performance of C₃N₂ monolayers, the linear elastic constants were calculated for the most stable such monolayer, namely T-C₃N₂. The 2D linear elastic constants were found to be C₁₁ = 180 N m⁻¹, C₂₂ = 180 N m⁻¹, C₁₂ = 40 N m⁻¹ and C₄₄ = 70 N m⁻¹, all of which are larger than those in H-C₃N₂.¹² These satisfy the Born–Huang criteria for a rectangular cell, namely C₁₁C₂₂ − C₁₂² > 0 and C₄₄ > 0.¹⁵ Thus T-C₃N₂ is also mechanically stable. The orientation-dependent Young's modulus Y and Poisson's ratio ν of T-C₃N₂ and H-C₃N₂ monolayers are plotted in Fig. 2a and b and Fig. 2d and e, respectively, according to the expressions of eqn (S1) and (S2) (ESI†). Compared to the maximum Y of H-C₃N₂, T-C₃N₂ shows greater robustness. The robustness difference between T-C₃N₂ and H-C₃N₂ mainly results from the graphitic nitrogen within the TAPA unit and the pyridinic nitrogen of HADQ. The sp²-hybridization with three σ bonds between the graphitic nitrogen atoms and the three adjacent carbon atoms separated by 120° solidifies the structure in three directions owing to its strong electronegativity (Fig. 2c). The pyridinic nitrogen atoms are bonded to only two adjacent carbon atoms, including two σ bonds and one π bond, to form the swing hinge (Fig. 2f). The maximum Y of T-C₃N₂ is 177 N m⁻¹, close to g-C₃N₄ (172 N m⁻¹),¹⁵ larger than C₃N₅ (38 N m⁻¹),¹⁵ C₂N-h2D (159 N m⁻¹),⁵⁶ and smaller than C₃N (341 N m⁻¹).⁵⁷

Fig. 2 Polar diagram for (a and d) Young's modulus, (b and e) Poisson's ratio, and the strain–stress relation (g and h) of T-C₃N₂ and H-C₃N₂. θ is the angle to a direction. Diagram of forces of (c) graphitic N in TAPA unit and (f) pyridinic N in HADQ unit. The strain–stress relation and diagram of (g and i) T-C₃N₂ and (h and j) H-C₃N₂ with applying the uniaxial (a and b directions) strain, respectively.

The stress variation to the uniaxial tensile strains is calculated and plotted in Fig. 2g–j. The ideal tensile strengths of T-C₃N₂ are 69.12 and 68.13 GPa nm, corresponding to the critical strains of 14% and 13% upon uniaxial strain along the a and b directions, respectively. The critical strains of T-C₃N₂ are similar to those of C₂N-h2D,⁵⁸ larger than those of C₃N₅ (12%) and g-C₃N₄ (11%).¹⁵ The ideal tensile strengths of T-C₃N₂ are greater than those of H-C₃N₂, whereas the critical strains along two directions are smaller than the latter, indicating that H-C₃N₂ has better flexibility. Although the maximum critical strain (17%) of H-C₃N₂ can withstand only 3% larger than that of T-C₃N₂, it can be significant from a macroscopic point of view. The flexibility of H-C₃N₂ is derived from the flexible hinges formed by the pyridinic nitrogen atoms bonded to two C atoms in the zigzag (a) direction, where the direction of the uniaxial strain force is parallel to the open and close direction of the hinge. In the armchair (b) direction of H-C₃N₂, the uniaxial strain force is not parallel to the hinge but to the C–C bond, thereby inhibiting the flexibility in the corresponding direction. The flexibility of H-C₃N₂ leads to a Poisson's ratio of H-C₃N₂ (C₁₂/C₁₁ = 0.49)¹² larger than those of the T-C₃N₂ (0.22) and C₂N-h2D (0.28)⁵⁸ monolayers. The high sturdiness of T-C₃N₂ and the flexibility of H-C₃N₂ provide more candidates for PGCNs used as nanomechanical, microelectronic, and optoelectronic materials.

3.3. The electronic structures of C₃N₂ monolayers and bilayer

Optoelectronic detectors' detection range depends on the band gap of a semiconductor. The electronic structures of H-C₃N₂ and T-C₃N₂, along with the high symmetry path (Γ–M–K–Γ), are shown in Fig. 3. In the PBE level, according to the orbital-projected band structures and partial charge densities in Fig. 3a and b, e and f, the valence band maximum (VBM) of T-C₃N₂ has contributions mainly from p_z orbitals of C and pyridinic N atoms. In contrast, the conduction band minimum (CBM) of T-C₃N₂ mainly consists of p_z orbitals of C and graphitic N atoms. The H-C₃N₂ can be seen as a new structure by adding an ethanedinitrile (C₂N₂) unit to each side of the built-in hexagonal hole in the C₂N-h2D monolayer. Adding ethanedinitrile brings valence bands closer to the Fermi energy level in the electronic structure, creating a lower band gap (Fig. S8a and e, ESI†). This bandgap change is caused by C-p_x+y (N-p_x+y) coupling of the ethanedinitrile (C₂N₂) unit with C-p_x+y (N-p_x+y) of the other C (N) atoms, which make up the VBM of H-C₃N₂ (Fig. 3c and d, i and Fig. S8b and c, f and g, ESI†). The CBM of H-C₃N₂ is composed of the C-p_z and N-p_z orbitals similar to the C₂N-h2D monolayer (Fig. 3c and d, h and Fig. S8d and h, ESI†).

Fig. 3 The orbital-projected band structures of T-C₃N₂ (a and b) and H-C₃N₂ (c and d) monolayers based on C and N atoms at PBE method. Partial charge densities (top view) of the CBM (e and h) and VBM (f and i) of T-C₃N₂ and H-C₃N₂ (isovalue 0.004 e bohr⁻³). Electronic structures of T-C₃N₂ (g) and H-C₃N₂ (j) at the HSE06 method, along with the high symmetry path (Γ(0,0,0)–M(0,0.5,0)–K(−0.333,0.667,0)) of the first Brillouin zone. The transverse dotted line is the Fermi energy.

Accurate band gaps of T-C₃N₂ and H-C₃N₂ were calculated using the HSE06 method. The resulting band gaps for H-C₃N₂ and T-C₃N₂ of 1.97 eV and 0.35 eV were approximately twice those obtained by the PBE method. The band gap of more than 1.23 eV for H-C₃N₂ meets the primary requirement of catalytically entirely splitting water. The CBM of H-C₃N₂ was found to be lower than the reduction potential of hydrogen and higher than the oxidation potential of O₂/H₂O, and its VBM is lower than the oxidation potential of O₂/H₂O (Fig. S9, ESI†). The band edges of CBM and VBM only support the oxidation potential of O₂/H₂O. The band gap of 0.35 eV for T-C₃N₂ conforms to the gap in the mid-infrared region of the series of carbon nitride semiconductors as photoelectronic detectors, where band gaps of C₃N, C₃N₅, t-C₃N₄, C₂N-h2D, g-C₃N₄, and C₃N₃ monolayers are 1.23 eV,⁵⁹ 1.76 eV,⁵ 2.40 eV,⁶ 2.47 eV,⁶ 2.70 eV,¹ and 3.18 eV,⁶⁰ respectively (Fig. 4).

Fig. 4 Bandgap values of T-C₃N₂, H-C₃N₂, and synthesized carbon nitride monolayers and their corresponding detection range as photoelectronic detectors, i.e., ultraviolet (UV), visible light (VIS), near-infrared (NIR), short-wave infrared (SWIR), middle-wave infrared (MWIR), and long-wave infrared (LWIR).

Two-dimensional carbon nitrides are always synthesized in their stacking forms,^5,35 such as t-C₃N₄ in the form of triplets⁶ and C₃N in the inversion symmetric AA′ and AB′ stacking form.⁵⁹ The four different stacking configurations AA, AB, AA′, and AB′ for H-C₃N₂ and T-C₃N₂ are present in Fig. 5a–f. AB is the most favorable configuration with the lowest energy among different malposed bilayers in Fig. S5 (ESI†). For bilayer T-C₃N₂, the AB′, AA′, and AA stacking configurations are all higher in energy than the AB stacking bilayer configuration successively 0.02 eV, 0.55 eV, and 0.71 eV in the unit cell, respectively. Owing to almost equal lattice constants, the AA′ stacking bilayer has the smallest interlayer spacing of 2.71 Å as compared with interlayer spacings of 3.07 Å, 3.08 Å, and 3.40 Å for the AB′, AB, and AA stacking bilayers, respectively (Fig. S10, ESI†). Both AB and AB′ stacking bilayers have larger band gaps (100 meV and 220 meV) than that (11 meV) of the T-C₃N₂ monolayer. The electronic structure transforms from direct to indirect semiconduction (Fig. 5g). For bilayer H-C₃N₂, its AA (AB) stacking bilayer is the same as the AA′ (AB′), and the former is higher in energy than the latter by 0.87 eV in the unit cell. Lattice constants of AA (AA′) and AB (AB′) stacking bilayers are almost equal to that of the H-C₃N₂ monolayer, while the interlayer spacings are distinctly different (3.62 Å and 2.99 Å) as presented in Fig. S10 (ESI†). Band gaps of both AA (AA′) and AB (AB′) stacking bilayers decrease compared with the H-C₃N₂ monolayer by PBE method, as well as they are 0.35 eV and 0.49 eV (Fig. 5h), respectively, retaining the direct band gap feature at the Γ symmetry point. While the interlayer spacings of AA (AA′) stacking bilayers are smaller than AB (AB′), the smaller band gap of the former relative to the latter indicates the stronger interlayer interaction of AA (AA′) stacking bilayers. Beyond all expectations, both AA and AA′ stacking bilayers of T-C₃N₂ are nodal-line semimetals under van der Waals's interaction, forming a closed ring centered at the Γ point. To be more explicit, we calculate band structures of AA and AA′ stacking bilayers of T-C₃N₂ with a large number of k points(30 × 30 × 1) by the PBE method (Fig. 5i and j). As seen in Fig. 5i and j, the AA stacking bilayer has a bigger closed ring than the AA′ stacking bilayer. This is attributed to the weaker van der Waals's interaction with the larger interlayer spacing according to the differential charge density of the AA stacking bilayer (Fig. S11a, ESI†), with weak charge transfer between layers. However, the smaller interlayer spacing of the AA′ stacking bilayer leads to charge accumulation between graphitic N atoms within the TAPA molecules of the upper layer and the lower layer leading to covalent bonds (Fig. S11b, ESI†) similar to those in bilayer g-C₃N₄.⁶¹ Because of the linear band dispersion near the node-line loop, the conductivity in T-C₃N₂ bilayer (AA and AA′) is expected to be relatively high, implying that it can be a promising candidate for transparent conductors in touch screens and solar cells.⁶²

Fig. 5 (a–f) The different stacking bilayers of T-C₃N₂ and H-C₃N₂, based TAPA and HAB building blocks, respectively. (g and h) Band gaps of AA (AA′) and AB (AB′) bilayers for T-C₃N₂ and H-C₃N₂ by the PBE method. (i and j) Band structures of AA and AA′ bilayers with a higher number of K points (30 × 30 × 1) for self-consistent-field calculations of T-C₃N₂ by the PBE method.

3.4 Carrier mobilities and optical properties of T-C₃N₂ and H-C₃N₂ monolayers

The carrier mobilities of semiconductor materials determine the performance of electronic devices. In this connection the carrier mobilities of C₃N₂ monolayers were evaluated based on deformation potential theory,⁶³ using the formula containing the three variables C_2d, m*, m_d, and E_2d, which are the elastic constants, the effective mass, the average effective mass () and the deformation potential constant, respectively. The other constants e, k_B, ℏ, and T respectively stand for electron charge, Boltzmann constant, Planck constant, and room temperature (300 K). According to the formula, the carrier mobility is most affected by the deformation potential constant and the effective mass. In terms of orientation, the effective mass is essentially isotropic in the x and y directions, similar to the elastic constant (Fig. S12a and b, ESI†). This is particularly evident for H-C₃N₂ and can also be seen from the band dispersion near the VBM and CBM at the high symmetry point Γ (Fig. S12d, ESI†). In detail, T-C₃N₂ has smaller effective masses than H-C₃N₂ (Fig. S12c, ESI†), down to 0.11 m₀ in the x-direction of the hole. This low effective mass leads to ultrahigh mobility (27.76 × 10³ and 23.20 × 10³ cm² V⁻¹ s⁻¹) in the x-direction, despite its larger deformation potential constant. The large deformation potential constant relative to the electron indicates the VBM is sensitive to the strain (Fig. S12e, ESI†). The VBM is mainly determined by the pyridinic nitrogen atoms, implying the strain force has a greater influence on the pyridinic nitrogen atoms. For the CBM, the main contribution is from the graphitic nitrogen atoms, and the stronger bond makes the CBM less affected by the strain force, leading to a smaller deformation potential constant compared with the hole (Fig. S12d, ESI†). The H-C₃N₂ monolayer only has pyridinic nitrogen atoms, and thus the strain results in similar deformation potential constants with structural isotropy. The small deformation potential constant of H-C₃N₂ in combination with the relatively small effective mass of its CBM also leads to ultrahigh electron mobility (25.39 × 10³ cm² V⁻¹ s⁻¹ and 22.67 × 10³ cm² V⁻¹ s⁻¹ in Table 2), while the large effective mass results in low hole mobility (0.16 × 10³ and 0.15 × 10³ cm² V⁻¹ s⁻¹ in Table 2), leading to pronounced electron-hole anisotropic mobility. The carrier mobilities of T-C₃N₂ and H-C₃N₂ are comparable to C₃N monolayer/AB bilayer (Table 2), as well as larger than those of the AB′ bilayer (6.22 × 10³ cm² V⁻¹ s⁻¹) and the AA′ bilayer (1.20 ×10³ cm² V⁻¹ s⁻¹) of C₃N,⁵⁹ C₂N-h2D,⁷ and black phosphorus (6.00 × 10³ cm² V⁻¹ s⁻¹).⁶⁴

Table 2 Calculated effective mass (m*/m₀), deformation potential constant (E_2d), 2D elastic modulus C^2D, and mobility (μ) for the electron (e) and the hole (h) along zigzag (a) and armchair (b) directions

2D				C ^2D x (N m^−1)	C ^2D y (N m^−1)	E ^x2d (eV)	E ^y2d (eV)	μ x × 10^3 (cm^2 V^−1 s^−1)	μ y × 10^3 (cm^2 V^−1 s^−1)	Exp.
T-C3N2	e	0.37	0.48	180	180	1.76	1.86	7.94	5.48
	h	0.11	0.13	180	180	3.24	3.26	27.76	23.20
H-C3N2	e	0.27	0.27	94	94	1.04	1.10	25.39	22.67
	h	2.90	3.00	94	94	1.20	1.22	0.16	0.15
C3N^59,65	e	0.76	0.45	371.2	371.2	6.34	6.47	0.226	0.62	0.136
	h	0.12	0.85	371.1	371.1	5.82	9.47	10.8	0.08	1.108
C3N(AB)^65	e	0.75	0.43	742.6	742.6	6.21	6.38	0.48	1.39
	h	0.11	0.83	742.3	742.3	5.25	10.05	31.5	0.15

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Besides carrier mobility, the absorption coefficient is also crucial for optoelectronic devices. The absorption properties of C₃N₂ monolayers are calculated based on the dielectric function ε(ω) = ε₁(ω) + iε₂(ω), where ω is the frequency. The absorption coefficient α(ω) was calculated from

where ε₁ is the real part of the complex dielectric function, which could be obtained from ε₂ using the Kramer–Kronig relationship. The ε₂ is defined as:^5,6
where α and β refer to the x and y directions, and Ω is the volume of the unit cell. The indices c and v refer to the conduction and valence band states, respectively. μ_ck are the corresponds to an eigenstate with wave vector k. T-C₃N₂, a direct semiconductor with a narrow band gap of 0.35 eV, has the highest 2.25 × 10⁵ cm⁻¹ absorption coefficient in the visible-light region, almost equal to H-C₃N₂ (Fig. 6a). The absorption coefficients of the synthesized C₃N₅, g-C₃N₄, and C₂N-h₂D were also computed at the HSE06 level (Fig. 6b). The absorption coefficient of T-C₃N₂ is smaller than that of C₂N-h2D in the visible-light region but significantly larger than that C₃N₅ and g-C₃N₄. More importantly, T-C₃N₂ is a good candidate for an infrared photodetector. In addition, T-C₃N₂ has the potential to be superior to other PCGNs for near-infrared solar harvesting/utilizing techniques because of absorption coefficients of up to 2.25 × 10⁵ cm⁻¹.

Fig. 6 Calculated in-plane absorption coefficients of (a) T-C₃N₂ and H-C₃N₂ monolayers in comparison with synthesized (b) C₃N₅, g-C₃N₄, and C₂N-h2D at the HSE06 level.

4. Conclusion

In summary, we have designed low-energy structures (i.e., the T-C₃N₂ and TH-C₃N₂) in combination with the PSO algorithm approach, proposed theoretically their logical synthesis paths related to the experimental realization of other carbon nitride monolayers (C₂N-h2D, C₃N₅, g-C₃N₄, C₃N, and so on), and systematically investigated T-C₃N₂ and H-C₃N₂ monolayers based on ab initio calculations. Based on the convex hull of T-C₃N₂, C₃N₅, and g-C₃N₄, we proposed that highly stable PGCNs tend to consist of graphitic and pyridinic nitrogen atoms with higher graphitic nitrogen concentration with an increasing x/y ratio in C_xN_y. The calculations also confirmed that the T-C₃N₂ monolayer is thermodynamically most favorable among the three C₃N₂ monolayers. Mechanically, the presence of graphitic nitrogen atoms symmetrically bonded to three C atoms leads to considerable rigidity of T-C₃N₂, while hinges formed by pyridinic nitrogen atoms bonded to only two carbon atoms make H-C₃N₂ more flexible. Moreover, T-C₃N₂ and H-C₃N₂ are direct semiconductors with band gaps of 0.35 eV and 1.97 eV, respectively. Furthermore, their bilayers exhibit a different band gap reduction than the corresponding monolayer. Especially for T-C₃N₂, the AA and AA′ stacking bilayers lead to a transition from a semiconductor to a semimetal. Both T-C₃N₂ and H-C₃N₂ have high carrier mobilities, anisotropic character, and excellent visible-light absorption. In addition, T-C₃N₂ exhibits a strong absorption coefficient in the near-infrared region. These appealing properties suggest that the T-C₃N₂ and H-C₃N₂ monolayers are promising candidates for use in electronic and photovoltaic devices.

Author contributions

X. C. conceived the idea, performed the DFT calculations, and wrote the original draft, J. C., Y. N. analyzed the data, H. W., Y. C., R. B. K. reviewed and edited the paper.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the Sichuan Science and Technology program (2022ZYD0024; 2021YFG0228) and the China Postdoctoral Science Foundation (2021M690325).

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Footnote

† Electronic supplementary information (ESI) available: Design scheme of T-C₃N₂, H-C₃N₂, and TH-C₃N₂; the computational details; atomic configurations for C₃N, C₂N-h2D, and T-C₃N₂; the graphitic N concentration in CNs; ELF, phonon spectrum and MD simulations of the T-C₃N₂ monolayer; electronic structures and the DOS of C₂N-h2D and H-C₃N₂ monolayers; the band structure of H-C₃N₂ relative to the vacuum level; the different stacking bilayers of H-C₃N₂ and T-C₃N₂; the differential charge density of AA and AA′ stacking bilayers T-C₃N₂; carrier effective masses, in-plane stiffness, and the deformation potential constant. See DOI: https://doi.org/10.1039/d2nh00440b

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