Graphene's exceptional carrier mobility makes it promising for high-speed transistors. However, its lack of a bandgap hinders effective transistor switching. Heteroatom doping, particularly with nitrogen, offers a solution. Nitrogen atoms, similar in size and electronegativity to carbon, act as electron donors, transforming graphene into an n-type semiconductor and increasing carrier density. Nitrogen-doped graphene (NG) therefore holds significant potential in electronic devices. However, controlled nitrogen doping in graphene is challenging. Current methods typically result in low nitrogen concentrations (generally below 0.2) and a mixture of graphitic, pyridinic, and pyrrolic nitrogen configurations. This mixed doping and low concentration limit control over carrier concentration and reduce carrier mobility due to increased scattering. Previous studies have explored the reasons for these limitations, citing repulsive interactions between nitrogen dopants and limitations on graphitic nitrogen doping concentrations. This work aims to systematically investigate the stable structures of carbon nitride (C1-xNx) with varying C/N ratios to understand the factors governing nitrogen concentration and configuration in NG, paving the way for controlled synthesis of NG with desirable properties.

Several studies have investigated the challenges and limitations of nitrogen doping in graphene. Xiang et al. found strong electrostatic repulsion between neighboring nitrogen atoms hindering complete nitrogen-carbon phase separation. Shi et al. determined the maximum achievable graphitic nitrogen doping concentration to be between 0.333 and 0.375. Feng et al. explored the stable structures of 2D NG at higher nitrogen concentrations, showing that while structures with lower nitrogen concentration are energetically more favorable, higher concentrations can be stabilized. However, a comprehensive understanding of the relationship between nitrogen concentration, configuration, and the thermodynamic stability of the resulting structures remained unclear.

This study employed first-principles calculations combined with a particle-swarm optimization (PSO) algorithm to identify stable structures of 2D carbon nitrides (C1-xNx) with different C/N ratios (0 < x < 1). Density functional theory (DFT) calculations, using the projector-augmented-wave method with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and a plane-wave cutoff energy of 400 eV, were used for structural relaxation and energy calculations. The local PSO algorithm, implemented in the crystal structure analysis by particle swarm optimization software, was used for structure prediction. For DFT calculations, a Monkhorst-Pack k-point mesh was used, and the geometries were optimized until the force on each atom was less than 0.01 eV Å−1 and energy convergence was 1 × 10−5 eV. To obtain more precise band gaps, HSE06 hybrid functional calculations were performed for selected structures. Formation energies were calculated relative to the chemical potentials of carbon in graphene and nitrogen in N2. The influence of varying chemical potentials of carbon and nitrogen, achieved by altering feedstock materials (e.g., CH4, C2H4, C2H2, N2, NH3, N2H4) and growth temperature and pressure, on the formation free energies of C1-xNx structures was also investigated. The effect of these parameters on the relative stability of graphitic, pyridinic, and pyrrolic nitrogen configurations was analyzed.

The calculations revealed that at low nitrogen doping concentrations (x < 0.08), both graphitic and pyridinic nitrogen configurations have comparable formation energies. This explains the experimental observation of the coexistence of both types of nitrogen in low-concentration NG. As the nitrogen concentration increases (x > 0.25), pyridinic nitrogen becomes significantly more favorable due to the strong repulsive interactions between graphitic nitrogen atoms. The formation energies of C1-xNx structures generally increase with nitrogen concentration, indicating that low nitrogen doping concentrations are thermodynamically more favorable. The study found that the interaction energy between graphitic nitrogen atoms increases as their distance decreases, particularly below 3 Å. This interaction plays a crucial role in determining the structure of C1-xNx at low nitrogen concentrations. The most stable structures at low nitrogen concentrations (x < 0.25) are primarily composed of low-interaction N-N pairs (OA-3B and OA-7B). For high nitrogen concentrations (x > 0.25), the formation energies increase sharply due to strong repulsion between closely spaced nitrogen atoms, favoring the formation of porous structures with pyridinic nitrogen. The introduction of pyrrolic nitrogen defects significantly increases the formation energy of the structures, regardless of the presence of pyridinic or graphitic nitrogen, suggesting that pyrrolic nitrogen is not energetically favorable and might be formed primarily at the edges. The formation energies were further analyzed to assess the effect of feedstock materials, temperature, and pressure on nitrogen concentration. Changing the chemical potentials of C and N atoms by altering the feedstock materials was shown to affect the relative stability of different nitrogen concentrations. Lowering the growth temperature was found to favor higher nitrogen concentrations, leading to the formation of pyridinic N. Finally, calculations of electronic properties showed that the band gaps of C1-xNx structures depend strongly on both nitrogen concentration and configuration, with structures containing pyridinic nitrogen often exhibiting larger band gaps. Furthermore, carrier mobilities were significantly higher in structures with graphitic nitrogen compared to those with pyridinic nitrogen.

This study provides a comprehensive understanding of the factors controlling the structure and properties of two-dimensional carbon nitrides. The findings successfully explain the experimentally observed limitations on nitrogen doping concentration and the coexistence of graphitic and pyridinic nitrogen in NG. The ability to tune the nitrogen concentration and configuration by manipulating the synthesis parameters (feedstock choice, temperature, and pressure) opens new avenues for tailoring the electronic properties of NG for diverse applications. The observed higher carrier mobilities in graphitic nitrogen-doped structures compared to pyridinic nitrogen-doped ones highlight the importance of controlling nitrogen configuration in achieving optimal electronic properties. The study's findings are in agreement with numerous experimental observations regarding nitrogen doping in graphene, validating the theoretical approach used. The results strongly suggest that the development of new strategies for controlled synthesis of NG with desired electronic properties should focus on precisely controlling the nitrogen chemical potential, growth temperature, and pressure.

This research successfully elucidates the relationship between nitrogen concentration, configuration, and thermodynamic stability in 2D carbon nitrides. The findings explain experimentally observed limitations in nitrogen doping of graphene and provide insights into tuning material properties through feedstock selection, temperature, and pressure control. Future work could focus on exploring other dopants, investigating the effects of defects beyond pyrrolic nitrogen, and developing advanced synthesis methods based on the insights gained to fabricate high-quality NG materials with precisely controlled nitrogen concentration and configuration for advanced applications.

The study primarily focuses on theoretical calculations and does not directly address experimental challenges in synthesizing the predicted structures. The accuracy of the calculations relies on the accuracy of the DFT functionals and approximations used. While HSE06 offers improved band gap predictions compared to PBE, further experimental validation would be needed to confirm the accuracy of the predicted electronic properties. The consideration of only graphitic, pyridinic, and pyrrolic nitrogen configurations might neglect other possible nitrogen incorporation mechanisms.