Design of two-dimensional carbon-nitride structures by tuning the nitrogen concentration

Graphene possesses exceptional carrier mobility but lacks a bandgap, limiting its utility in switchable electronics. Heteroatom (e.g., nitrogen) doping can tune graphene’s electronic properties, enabling n-type behavior and higher carrier density. Experimentally, NG typically exhibits low nitrogen concentrations (<~0.2) and mixed dopant configurations (graphitic, pyridinic, pyrrolic), which hampers control over carrier concentration and mobility. Prior theoretical and experimental studies suggest strong repulsion between neighboring N atoms, constraints on graphitic N solubility, and possible stability of higher-N 2D carbon nitride phases. The research question is to identify, across the full range of compositions C1−xNx (0 < x < 1), which 2D carbon-nitride structures are thermodynamically favorable, how nitrogen configuration (graphitic vs pyridinic vs pyrrolic) depends on concentration, and how synthesis parameters (feedstock, temperature, pressure) can be used to control stoichiometry and bonding motif. The purpose is to provide a thermodynamic and structural basis for understanding observed low N-doping and mixed configurations in NG and to offer guidelines for synthesizing carbon-nitride sheets with targeted nitrogen content and electronic properties.

Multiple synthesis routes (CVD, annealing, pyrolysis, arc discharge, hydrothermal, plasma) generally yield low N concentrations and mixed N species in NG. Xiang et al. showed nearest-neighbor N dopants are electrostatically repulsive, inhibiting phase separation. Shi et al. estimated a maximum graphitic N content of ~0.333–0.375. Feng et al. suggested higher-N 2D NG structures can be stabilized but lower N content is energetically favored. Experiments frequently report coexistence of graphitic and pyridinic N at low doping, and stability of g-C3N4 containing both configurations. These works motivate a systematic, composition-wide search and thermodynamic analysis of 2D C1−xNx.

• Structure search: A local particle-swarm optimization (PSO) algorithm was used to predict stable 2D C1−xNx structures (0 < x < 1), with fixed cells containing ≤30 atoms and a population size of 30. In each generation, 80% of structures were carried forward and 20% randomly generated; searches ran ~35 generations (~1050 structures). Ten to fifteen low-energy candidates per composition were further relaxed. For very low-concentration pyridinic configurations requiring large cells, structures were constructed manually and optimized by DFT.
• DFT calculations: VASP with PAW pseudopotentials and GGA-PBE exchange-correlation was used. Plane-wave cutoff: 400 eV; vacuum spacing ≥15 Å; geometry relaxation to forces <0.01 eV Å−1 and energy convergence 1×10−5 eV. Monkhorst–Pack k-point meshes were used (details in Supplementary). Bandgaps were refined using the HSE06 hybrid functional.
• Formation energies: Defined relative to μC in graphene and μN in N2 at 0 K. Formation energies per atom (or per N atom, as indicated) were computed for structures across x, including graphitic, pyridinic (hexagonal pore edges of varying sizes and densities), and pyrrolic configurations. N–N pair interaction energies were computed in a 12×12 graphene supercell as a function of dopant separation to identify favorable pairings (e.g., OA–3B, OA–7B).
• Thermodynamic regulation: General expressions for free energies include temperature and pressure dependence via chemical potentials of C and N in gas-phase feedstocks. ΔμC and ΔμN were calculated for representative carbon (CH4, C2H4, C2H2) and nitrogen (N2, NH3, N2H4) feedstocks at typical experimental conditions (e.g., T=1300 K, PH2= Pfeedstock=10−6 MPa). Effects of varying temperature (500–1300 K) and pressure ratios PC/PH2 and PN/PH2 were analyzed.
• Electronic properties: Band structures and bandgaps were computed (PBE, HSE06). Carrier mobilities were estimated via deformation potential theory (using effective masses, deformation potentials, and 2D elastic moduli).

• Stability vs N configuration at low doping: At very low N concentrations (x < ~0.08), graphitic and pyridinic N have similar formation energies (difference ~0.1 eV/atom), explaining their frequent coexistence in experiments. Pyrrolic N is significantly less favorable energetically.
• N–N repulsion and favored pairings: Graphitic N–N interactions are repulsive, intensifying at separations <3 Å. Two local minima in pair-interaction energies were identified (OA–3B and OA–7B), and most stable low-x graphitic structures are composed of these pairs.
• Stability vs nitrogen concentration: Formation energies of graphitic C1−xNx increase with x. For x > 0.25, formation energies rise sharply due to close N–N repulsion. For pyridinic porous structures, formation energy increases with pore size and with pore density (thus with x); small, uniformly spaced hexagonal pores are favored.
• Crossover to pyridinic dominance: As x increases (Region II in the study), pyridinic NG becomes more favorable than graphitic. For x > 0.25 (Region III), pyridinic configurations strongly dominate (energy differences >0.1 eV/atom), favoring porous, pyridinic-only frameworks at higher N content.
• Co-doping benefit: Combining pyridinic and graphitic N can lower formation energies further than pyridinic-only networks. Notably, g-C3N4 (x=0.57; mixed N types) has lower formation energy than CN (x=0.50; pyridinic-only).
• Special stability at C3N: Graphitic C3N (x=0.25) exhibits a local minimum in formation energy due to favorable OA–3B pairings and high symmetry; this phase has been experimentally synthesized.
• Pyrrolic defects: Introducing pyrrolic N increases formation energy in both C2N and g-C3N4; larger defect separations reduce the penalty. At high pyrrolic concentrations in g-C3N4, large strain can break C–N bonds during relaxation.
• Feedstock tuning (ΔμN and ΔμC): Increasing μN by ~0.5 eV (e.g., via N2H4 vs N2) stabilizes higher-N structures; increasing μC stabilizes lower-N, graphitic-rich structures. Using CH4 with N2 favors low x; CH4 with N2H4 favors high x. Using NH3 as N feedstock, C2H2 as C feedstock flattens the energy–x curve, promoting higher-N, pyridinic-rich structures.
• Temperature and pressure effects: Higher growth temperatures favor lower N concentrations and more graphitic N; lower temperatures favor higher N and pyridinic N. Decreasing PC/PH2 or increasing PN/PH2 promotes higher-N pyridinic structures; increasing PC/PH2 or decreasing PN/PH2 favors lower-N graphitic structures.
• Electronic structure: Most graphitic C1−xNx are metallic, with exceptions C12N and C3N (semiconducting). Several pyridinic frameworks (C12N, C2N, C4N, C10N3) show graphene-like Dirac cones; others are direct semiconductors. HSE06 bandgaps: C12N (x=0.08) 0.99 eV; C3N (x=0.25) 1.22 eV; C2N (x=0.33) 2.46 eV; CN (x=0.50) 3.46 eV. Reported experimental bandgaps for C3N and C2N quantum dots fall within similar ranges depending on size.
• Carrier transport: Calculated carrier mobilities are higher for graphitic-N structures (e.g., C3N shows µ2D up to ~2205 cm2 V−1 s−1 along one direction) than for pyridinic-N structures (e.g., C2N shows lower mobilities, tens to hundreds cm2 V−1 s−1 in some directions), indicating configuration-dependent transport performance.

The results rationalize two pervasive experimental observations: (i) NG typically exhibits low nitrogen content because C1−xNx with small x have lower formation energies; and (ii) at low x, graphitic and pyridinic N coexist due to their comparable thermodynamic stabilities. As x increases, repulsive N–N interactions in graphitic doping drive a transition toward porous, pyridinic-dominated carbon nitrides, aligning with reports of pyridinic-rich materials at higher N loadings. The identification of favorable N–N pair arrangements explains the enhanced stability of specific stoichiometries (e.g., graphitic C3N). The thermodynamic framework linking formation energies to chemical potentials of feedstocks, temperature, and pressure provides actionable levers to steer synthesis: lower temperatures, higher PN/PH2, lower PC/PH2, and nitrogen-rich feedstocks (e.g., N2H4) promote higher N content and pyridinic structures; conversely, higher temperatures and carbon-rich conditions favor lower N content and graphitic configurations. Electronic-structure calculations show how nitrogen configuration and concentration tune bandgaps and mobilities, suggesting pathways to engineer semiconducting or metallic behavior, Dirac cones, and high-mobility channels for device applications.

This work maps the stability landscape of 2D C1−xNx across nitrogen concentrations and bonding motifs. It shows: (i) at low x, graphitic and pyridinic N are similarly favorable and often coexist; (ii) at higher x (>0.25), pyridinic structures dominate; (iii) mixed pyridinic–graphitic networks can be more stable than pyridinic-only ones (e.g., g-C3N4 vs CN); and (iv) growth parameters (feedstock chemistry, temperature, pressure) can thermodynamically bias formation toward low-N graphitic or high-N pyridinic materials. These insights reconcile experimental trends of low N content and mixed configurations in NG and provide guidance to synthesize carbon-nitride sheets with targeted stoichiometry and electronic properties. Potential future directions include experimental validation across broader feedstock/condition spaces, kinetic modeling of dopant incorporation and pore formation, exploration of compositions beyond x≈0.5 with mixed motifs, and device-level studies leveraging the predicted tunable bandgaps and mobilities.

• Initial formation-energy analyses reference μC(Gr) and μN(N2) at 0 K; finite-temperature effects are incorporated via chemical potentials with assumptions (e.g., equal thermal contributions for C in graphene and in C1−xNx), which may introduce approximations.
• PSO searches used cells with ≤30 atoms and ~35 generations; very low-concentration pyridinic structures requiring large supercells were constructed manually, potentially biasing the explored configurational space.
• N–N interaction studies used a 12×12 graphene supercell; while larger cells gave similar trends, residual finite-size effects may persist.
• Formation energies address thermodynamic stability but do not capture kinetic barriers and pathways during synthesis.
• Most analyses focus on x ≤ 0.5 for pure pyridinic/graphitic comparisons; higher-x regimes involve mixed motifs and were only partially explored (e.g., g-C3N4).