
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39237527
67393
10.1038/s41598-024-67393-z
Article
First principles study of BN triphenylene-graphdiyne monolayer and bilayer structures with varying C-chain lengths: insights into optical behavior
Majidi Roya r.majidi@sru.ac.ir
royamajidi@gmail.com

1
Ayesh Ahmad I. ayesh@qu.edu.qa

2
1 https://ror.org/02nkz4493 grid.440791.f 0000 0004 0385 049X Department of Physics, Shahid Rajaee Teacher Training University, Lavizan, Tehran, 16788-15811 Iran
2 https://ror.org/00yhnba62 grid.412603.2 0000 0004 0634 1084 Department of Physics and Materials Sciences, College of Arts and Sciences, Qatar University, P. O. Box 2713, Doha, Qatar
5 9 2024
5 9 2024
2024
14 2072410 6 2024
10 7 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
First-principles calculations engaging density functional theory (DFT) are employed to systematically study the optical characteristics of monolayer and bilayer boron nitride (BN) triphenylene-graphdiyne (Tp-BNyne) structures featuring varying lengths of C-chains. The thermal stability of Tp-BNyne structures at temperatures up to 1000 K is verified. The weak van der Waals interactions due to the small binding energies and significant interlayer distances maintain the cohesion between the layers. The investigation revealed that all Tp-BNyne structures under examination exhibit semiconductor behavior with a band gap in the range of 0.97–2.74 eV. The bilayer configurations demonstrated a narrower energy band gap in comparison to the monolayer ones. Increasing the length of C-chains leads to a reduction in the energy band gap. Delving into the optical behavior of Tp-BNyne structures under photon incidence with parallel and perpendicular polarizations, a distinct anisotropy in the optical characteristics of Tp-BNyne is revealed. The static dielectric constant increases and the optical band gap decreases with increasing C-chain length. The absorption coefficients of monolayer and bilayer Tp-BNyne structures, on the order of 107/m, demonstrate that these sheets can effectively absorb light in the visible and ultraviolet regions. These findings present Tp-BNyne sheets as promising candidates for use in photovoltaic devices to convert sunlight into electrical current, as well as for designing optical devices for ultraviolet protection. Additionally, Tp-BNyne structures are transparent materials, especially in the high-energy range.

Keywords

Graphdiyne
Triphenylene
BNC structure
Two-dimensional materials, band gap
DFT
Optical properties
Subject terms

Graphene
Nanoscale materials
issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

Carbon, renowned for its versatility, manifests in a myriad of structures spanning from zero to three dimensions, including fullerene, graphene, carbon nanotubes, diamond, etc.1 In particular, the discovery of graphene in 2004, catalyzed a surge in interest towards two-dimensional (2D) materials2. Graphene comprises a single monolayer of carbon atoms organized in a hexagonal lattice, offering exceptional electronic behavior, mechanical strength, and thermal conductivity3–5. The two dimensional (2D) feature of graphene and its unique electronic structure allow for its exploitation in the development of electronic devices including sensors and even biomedical fields6–9. The exceptional thermal conductivity of graphene has sparked interest in thermal management applications, while its extraordinary mechanical strength makes it an ideal component for reinforcing composite materials10,11. Furthermore, researchers are exploring graphene-based different materials for innovative energy storage solutions due to their exceptional electrical and electrochemical properties and high surface area12–14. Despite the remarkable properties of graphene, the lack of band gap confines its use in certain electronic devices such as the field effect transistors exhibit a high on–off ratio, in addition to serving as switching for logic and high speed devices. Hence, many solutions have been proposed such as doping impurity, applying external fields and strains, or exploring other 2D materials with intrinsic semiconducting properties to address the band gap limitation of graphene and expand its potential applications in various fields of research and technology15–20. Among the number of detailed investigations, a great deal of attention has been focused mainly on 2D binary and trinary compounds. The obtained results demonstrate that the configurations such as C5N, SiX (X = Te, H), BC2X (x = N, P, As), PbX (X = S, Se, Te) structures are semiconductors with interesting features21–24.

Over the past decade, significant experimental and theoretical work has focused on creating and forecasting novel 2D carbon-containing materials. This category of materials combines a wide variety of members such as graphyne and graphdiyne, each possessing unique structures and properties25. Graphyne, a derivative of graphene, features acetylenic linkages connecting the hexagonal rings in graphene. Various graphyne configurations exist, each showcasing sp and sp2 hybridized of carbon atoms in slightly different arrangements26. These materials exhibit intriguing electronic and optical properties dependent on their atomic arrangement27–31. Graphdiyne is a 2D carbon-based material having sp and sp2 hybridized of carbon atoms, diacetylene linkages, a framework of triangular holes, and an adjustable band gap32,33. Therefore, graphyne and graphdiyne have garnered remarkable attention because of their ability to provide a non-zero band gap for electronic devices34,35.

In a recent experimental study, a novel graphdiyne monolayer structure, known as triphenylene graphdiyne (TpG), is successfully designed and fabricated36. In comparison to graphdiyne, TpG features a substitution of the benzene ring by a triphenyl ring. The electronic states within the triphenyl rings exhibit greater localization than those in benzene, resulting in an enlarged band gap for TpG. This sheet exhibits a band gap of 1.94 eV and band edge positions useful for the photocatalytic process of overall water splitting37,38. Furthermore, researchers have explored the potential of N-, P-, as well as As-TpG sheets38. These nanosheets exhibit remarkable thermal stability and linear elasticity with significant tensile strengths. Importantly, monolayer N-, P-, and As-TpG are predicted to possess semiconducting electronic properties along with highly appealing optical characteristics. The findings from this study highlight the nanosheets based on TpG as promising candidates for use in optoelectronics, nanoelectronics, and energy storage devices38. After the successful synthesis of TpG and the possibility of hybridizing C- as well as BN-units, the stability of the BN analog of TpG sheet is investigated39. This innovative structure, named Tp-BNyne, is created by replacing the carbon atoms in four hexagonal rings of TpG with alternate boron and nitrogen atoms. These four BN hexagonal rings are interconnected by C-chains. The Tp-BNyne proves to be stable and displays semiconducting behavior with a direct band gap of 3.78 eV39. As the length of the C-chain increases, the band gap of Tp-BNyne sheets decreases, contrasting with the minimal change observed in TpG. In addition, the band gap can be effectively adjusted by stacking to multilayer with distinct patterns. These significant discoveries, particularly the ability to engineer the band gap set Tp-BNyne apart, offering advantages over TPG39. Building upon these findings, the current study delves into the optical characteristics of Tp-BNyne in hopes of stimulating further theoretical and experimental inquiries for the prospective utilization of this material in the realms of nanoelectronics and optoelectronics.

Computational details

In this study, the optical properties of different Tp-BNyne sheets are calculated using DFT method, which is implemented in the openMX3.9 code40. The Perdew-Burke-Ernzerhof (PBE) approximation type of the generalized gradient (GGA) is adopted for exchange–correlation functional41,42. The cutoff energy is set to 250 Ry based on the convergence of the total energy, the band gap, and dielectric constant. The atomic sites are optimized with a force criterion of 0.005 eV/Å. A vacuum layer having a specific thickness of 25 Å is included based on convergence testing to prevent interactions among images along the perpendicular direction of the sheets. Additionally, Grimme DFT-D3 correction is applied for van der Waals corrections43.

The binding energy, Eb, utilized to estimate the structural stability of the bilayer Tp-BNyne is calculated as follows:1 Eb=(Ebilayer-2Emonolayer)/∑ini

In the above equation, Emonolayer and Ebilayer represent the total energy of monolayer and bilayer Tp-BNyne, respectively. Here, ni refers to the number of boron, nitrogen, and carbon atoms (i = B, N, C). To examine the thermal stability of the sheets, ab-initio molecular dynamics (AIMD) simulations are carried out in an NVT ensemble with a time step of 2 fs over 10 ps at 1000 K. The temperature is set using the Nose–Hoover method44. The temperature is adjusted by the Nose–Hoover method The optical characteristics is determined by the Kubo-Greenwood formula45. The optical calculations are performed using a 14 × 14 × 5 k-mesh to discretize the Brillouin zone.

Results and discussion

To enhance our understanding of the proposed sheets, we initially introduce the structural geometry of monolayer Tp-BNyne. The configurations of monolayer Tp-BNyne with nC = 4, 6, and 8 are plotted in Fig. 1. Here, nC is the count of carbon atoms in each C-chains, a value that is twice the number of –C≡C– bonds. The primitive unit cell of monolayer Tp-BNyne sheet consists of 9 boron and 9 nitrogen atoms, arranged to form four interconnected BN hexagonal rings. The C-chains link the BN hexagonal rings. The optimized lattice parameters for monolayer Tp-BNyne with nC = 4, 6, and 8 are 13.97, 16.54, and 19.12 Å, respectively. The bond length of C–C and C≡C within the C-chains are found to be 1.23 and 1.34 Å, respectively, aligning with previously reported values for graphdiyne and Tp-BNyne38. The calculated bond lengths of B–N in the BN hexagonal rings fall within the range of 1.43—1.48 Å, akin to those in the pure BN-sheet46. The C–B and C–N bond lengths are 1.50 and 1.35 Å, respectively, showing good agreement with prior research38 (Atomic coordinates for the sheets are presented in Supplementary File.).Figure 1 Top and side views of a 2 × 2 × 1 supercell of monolayer Tp-BNyne with nC = (a) 4, (b) 6, and (c) 8.

The bilayer Tp-BNyne structures, comprising two layers of Tp-BNyne, are also investigated. The binding energies are computed for configurations with various stackings. As anticipated from earlier research, the AB-stacking for bilayer structure, analogous to the AB-stacked bilayer graphene47, emerges as the most energetically favorable configuration. For instance, atomic structure of bilayer Tp-BNyne with nC = 4 is shown in Fig. 2. In bilayer structures, the distance between two layers is found to be 3.5 Å. The magnitude of binding energies for bilayer Tp-BNyne with nC = 4, 6, and 8 are 17, 16, and 7 meV/atom, respectively. The significant interlayer distance and low binding energies indicate that the connection between the two layers primarily relies on the vdW interactions.Figure 2 Top and side views of a 2 × 2 × 1 supercell of bilayer Tp-BNyne with nC = 4.

The thermal stability of the sheets is examined through AIMD simulations, showcasing the total energy fluctuations over time at 1000 K in Fig. 3. The findings demonstrate a steady energy profile with minimal deviation. Moreover, both the initial and concluding atomic arrangements of the sheets are detected, indicating sustained atomic structures throughout the simulation, with no significant changes or bond breakages. For instance, the final structures for monolayer Tp-BNyne with nC = 4 and bilayer Tp-BNyne with nC = 6 are depicted in Fig. 3.Figure 3 (a) The fluctuations of total energy via simulation time at 1000 K, final atomic configurations of (b) monolayer Tp-BNyne with nC = 4 and (c) bilayer Tp-BNyne with nC = 6.

The electronic band structure along with the density of states (DOS) of monolayer and bilayer Tp-BNyne structures are calculated to explore their electronic properties (Fig. 4). The analysis reveals that both valence and conduction bands in these structures do not intersect at the Fermi level. The lack of states at the Fermi level further confirms the semiconducting characteristics of these materials. The band gaps for monolayer Tp-BNyne with nC = 4, 6, and 8 are calculated to be 2.74, 2.16, and 1.95 eV, respectively. It means that increasing the length of C-chains results in a clear reduction of the energy band gap of monolayer Tp-BNyne sheets. This trend and values of band gaps are in good agreement with previous studies showing band gap changes of monolayer Tp-BNyne and TpG structures with C chain length39. Due to the underestimation of band-gap values by the PBE functional, band gaps of Tp-BNyne sheets are additionally calculated using the HSE06 hybrid functional. The band gap values obtained through the HSE06 functional for monolayer Tp-BNyne with nC = 4, 6, and 8 are 3.74, 3.04, and 2.79 eV, respectively, demonstrating a good agreement with a previous study39. In addition, it is observed that the band gap of monolayer Tp-BNyne with nC = 4 is much larger than the gap of 1.26 at the PBE level and 1.94 eV at the HSE06 level for monolayer TpG with nC = 4, and 1.68 at the HSE06 level for monolayer TpG with nC = 838,39.Figure 4 Electronic band structure along with the density of states (DOS) of monolayer and bilayer Tp-BNyne nC = (a) 4, (b) 6, and (c) 8.

The bilayer Tp-BNyne configurations exhibit semiconducting behavior similar to their monolayer counterparts. Using the PBE approach, the band gap values are 2.48 eV, 1.97 eV, and 0.97 eV for nC = 4, 6, and 8, respectively. When analyzed with the HSE06 functional, the estimated band-gap values are 3.49, 2.87, and 1.87 eV for bilayer Tp-BNyne sheets with nC = 4, 6, and 8, respectively. Moreover, the band gap of bilayer Tp-BNyne sheets with nC = 4 is consistent with a previous study, reported to be 2.54 and 3.54 eV when employing the PBE and HSE06 functionals, respectively39. Increasing the number of layers results in a decrease in the energy band gap of Tp-BNyne sheets. This decreasing trend of the band gap from a monolayer to a bilayer in Tp-BNyne mirrors observations in TpG, other graphdiyne, and BN layered systems39,48.

The optical characteristics of a substance can be deduced from its response to incident photons, often determined through the dielectric function. As a result, the initial phase involves computing the dielectric constants associated with monolayer and bilayer Tp-BNyne. The real component assigned the dielectric function, ε1, via the incident photon energy, are depicted in Fig. 5. Both in-plane (parallel) and out-of-plane (perpendicular) light polarizations are taken into account. The presence of anisotropy is clearly evident for these two distinct polarizations, particularly noticeable in the low-energy range.Figure 5 Real part of dielectric constant, ε1, for monolayer and bilayer Tp-BNyne sheets via the energy of the incident photon with (a) parallel (||) and (b) perpendicular (⊥) polarization.

The static dielectric constant, ε1(0), is the dielectric function at zero energy. However, for parallel polarization, monolayer Tp-BNyne with nC = 4, 6, and 8 have static dielectric constants of 1.87, 2.09, and 2.30, respectively. The inverse relationship among the band gap and the real component of the dielectric constant is a widely recognized fact.49,50 In Tp-BNyne sheets, it is observed that an increase in nC causes a decrease in their energy band gap and consequently an increase in the static dielectric constant. For the case of bilayer Tp-BNyne, the static dielectric constants are 2.56, 3.04, and 3.40 for Tp-BNyne with nC = 4, 6, and 8, respectively. As anticipated, the bilayer Tp-BNyne structures, which exhibit energy band gaps smaller than monolayer ones, display higher static dielectric constants. Just like in the monolayer configuration, extending the length of the C-chains of the bilayer structure results in a reduction of the static dielectric constant. Herein, the static dielectric constants of both monolayer and bilayer Tp-BNyne structures are close to that of graphene (2.67) and TpG (2.99), while smaller than γ-graphyne (8.42)28,38,51. For parallel polarization, the dielectric function shows consistency in the infrared range but exhibits a prominent peak in the visible range (Fig. 5a). The peak intensity elevates and the peak position moves towards the lower energy with the extension of C-chain length. This red-shift phenomenon in Tp-BNyne is similar to graphdiyne sheets, which occurs with the increase of the number of acetylenic linkages27,52. In the high-energy range, the dielectric function approaches a value of 1.0, indicating limited optical reactivity at high energies. For perpendicular light polarization, the real component of the dielectric function of Tp-BNyne remains stable, displaying minimal fluctuations at 10–16 eV as illustrated in Fig. 5b. The static dielectric constants are 1.14, 1.11, and 1.09 for monolayer Tp-BNyne with nC values of 4, 6, and 8, respectively. In the case of bilayer Tp-BNyne with the same nC values of 4, 6, and 8, the static dielectric constants are 1.21, 1.19, and 1.16, respectively. These values closely correspond to those reported for graphyne (1.1) and graphene (1.24)28,51. The constant value of the dielectric function suggests a lack of optical reactivity in Tp-BNyne structures when exposed to light with perpendicular polarization.

Figure 6 depicts the relationship between the energy of the incoming photon and the imaginary component of the dielectric function, ε2. The initial peak in the imaginary dielectric function represents the optical band gap. For parallel polarization, the imaginary component of the dielectric constant is zero in the infrared region. Notably, two primary peaks are observed in the visible and near visible ranges (1–5 eV). Previous studies have shown that the first peak of the imaginary dielectric function for TpG with nC = 4 also occurs at 1.75 eV within the visible range38. Thus, Tp-BNyne sheets as well as TpG demonstrate well-defined optical band gaps, making them highly suitable for practical applications in optoelectronic devices that operate within the visible spectral range. As the length of C-chain increases, both the intensity of the peaks in the imaginary component of the dielectric function as well as the real part is increased. The position of the peaks is also moved to the lower energies. These observations suggest that the length of C-chains leads to a decrease in the optical band gap. The initial peak of the imaginary part of the dielectric constant in Tp-BNyne as well as TpG38 falls within the visible range, making them highly suitable for use in optoelectronic devices that operate within this spectral range. For perpendicular polarization, the imaginary component of the dielectric function is zero within the infrared and visible, and wide part of the ultraviolet range. A minor peak is detected at 13 eV.Figure 6 Imaginary part of dielectric constant, ε2, for monolayer and bilayer Tp-BNyne sheets via the energy of the incident photon with (a) parallel (||) and (b) perpendicular (⊥) polarization.

In Fig. 5a, the real component of the dielectric function undergoes a change in sign for parallel polarization. This indicates the existence of collective electron oscillations and the presence of a plasma frequency within Tp-BNyne structures. Notably, for monolayer Tp-BNyne structures with nC = 6 and 8, the real component of the dielectric function changes its sign from negative to positive at 3.8 and 3.3 eV, respectively. For bilayer Tp-BNyne structures with nC = 4, 6, and 8, this transition occurs at energies of 5.1, 4.4, and 4.0 eV, respectively. The electron loss function, L = ε2/(ε12 + ε22), is illustrated in Fig. 7. The prominent peaks at 3.8 and 3.4 eV are observed for monolayer Tp-BNyne structures with nC = 6 and 8, respectively. In bilayer Tp-BNyne structures with nC = 4, 6, and 8, a main peak at 5.2, 4.4, and 4.0 eV is observed. These energies (Fig. 7) correspond to the point at which the real component of the dielectric constant changes its sign (Fig. 5a), indicating the lack of collective electron oscillation and plasma frequency in Tp-BNyne.Figure 7 Electron loss function of monolayer and bilayer Tp-BNyne sheets via the energy of the incident photon with parallel (||) polarization.

The optical conductivity is used to estimate the density of the free carrier. Based on our findings, the optical conductivity of Tp-BNyne structures in the visible light and ultraviolet region is on the order of 105. It drops to zero in the high-energy region (energy exceeding 30 eV).

The absorption coefficient, α, of Tp-BNyne structures is illustrated in Fig. 8. The results demonstrate significant absorption (107/m) in the visible and ultraviolet regions when light is polarized along the sheets. The high ability of monolayer and bilayer Tp-BNyne structures, as well as structures such as TpG, Janus C2h-Al2XY, Si2Pas, silicene, and germanene monolayers38,53–56, to absorb light in the visible and ultraviolet regions emphasizes their suitability for use in photovoltaic devices and applications requiring protection against ultraviolet radiation. For parallel polarization, the edge of absorption for Tp-BNyne with nC = 4, 6, and 8 occurs at around 2.5, 2.0, and 1.6 eV, respectively. These values relate to the energy band gap, indicating energies of 2.74, 2.16, and 1.95 eV in Tp-BNyne with nC = 4, 6, and 8. The first absorption peak for Tp-BNyne occurs in the visible range, similar to the findings of a previous study on the first absorption peak of TpG with nC = 4 in the visible range at 1.88 eV38. In the case of bilayer Tp-BNyne, the absorption edge moves slightly towards lower energies (2.4, 2.0, and 1.65 eV for nC = 4, 6, and 8) due to the narrower band gap (2.48, 1.97, 0.97 eV) of bilayer structures compared to monolayers. The position of the optical absorption peaks shifts towards lower energies due to the decrease appears in the band gap along with increasing length of C-chains. However, the impact of C-chain length on the intensity for the absorption peak, especially in the visible range, is not significant. Light absorption takes place by exciting electrons from the valence towards the conduction band57. This process is slightly more efficient in bilayer Tp-BNyne structures compared to monolayer ones. For perpendicular polarization, Tp-BNyne structures exhibit almost negligible absorption in both infrared as well as visible ranges, but strong optical absorption in the ultraviolet region, with notable absorption peaks at 13.5 eV. The peaks in bilayer structures surpass those in monolayer structures, owing to interactions between the two layers.Figure 8 Optical absorption constant, α, of monolayer and bilayer Tp-BNyne sheets via the energy of the incident photon with (a) parallel (||) and (b) perpendicular (⊥) polarization.

The reflection coefficient as well as transmission coefficient (R and T, respectively) are determined for monolayer and bilayer Tp-BNyne structures (Figs. 9 and 10). For the case of parallel light polarization, the reflection coefficients at zero energy are 2.4%, 3.3%, and 4.2% for monolayer Tp-BNyne with nC = 4, 6, and 8, respectively. These values increase to 5.3%, 7.3%, and 8.8% for bilayer Tp-BNyne. The primary reflection coefficients (11%, 25%, and 34%) for photons with parallel polarization are observed at 4.6, 3.6, and 3.0 eV in monolayer Tp-BNyne with nC = 4, 6, and 8, respectively. For bilayer Tp-BNyne structures with nC = 4, 6, and 8, the maximum reflections are approximately 29%, 46%, and 52% at 4.7, 3.8, and 3.1 eV, respectively. Beyond 6 eV, the reflection coefficients diminish to zero. The transmission coefficient exhibits an inverse pattern compared to the reflection constant. At zero energy, the transmission coefficients are 97.6%, 96.7%, and 95.8% for monolayer Tp-BNyne and 94.7%, 92.7%, and 91.2% for bilayer Tp-BNyne, with nC = 4, 6, and 8, respectively. The transmission coefficients are nonzero and decline to approximately 48% in bilayer Tp-BNyne with nC = 8 for photons with energy below 6 eV. They are near 100% at the high energies. The high transmission coefficients of Tp-BNyne at the high-energy range indicate the capability of these sheets to transmit photons within this energy range. For the case of perpendicular light polarization, a modest peak is observed at around 13.5 eV. The intensity of the peaks increases in bilayer structures and decreases by elongating the C-chain. The findings indicate that enhancing the thickness results in a slight decrease in the transparency of the structures, whereas elongating the C-chain increases their transparency. A maximum reflection of 3% and 6% and a minimum transmission of 97% and 94% are detected for monolayer and bilayer Tp-BNy with nC = 4, respectively. These signify the presence of a small hindrance to the transmission of light with perpendicular polarization; however, the sheets remain transparent to photons with this polarization.Figure 9 Reflection, R, constant of monolayer and bilayer Tp-BNyne sheets via the energy of the incident photon with (a) parallel (||) and (b) perpendicular (⊥) polarization.

Figure 10 Transmission, T, constant of monolayer and bilayer Tp-BNyne sheets via the energy of the incident photon with (a) parallel (||) and (b) perpendicular (⊥) polarization.

Conclusion

Inspired by the successful creation of graphdiyne sheets and the potential for hybridizing C-BN structures, a new two-dimensional material called BN analog of triphenylene graphdiyne (Tp-BNyne) has been designed39. A single layer of Tp-BNyne comprises C-chains and the BN counterpart of triphenylene. The thermal stability of Tp-BNyne structures at temperature upto 1000 K was confirmed. The small binding energies and large interlayer distances are due to the weak vdW interactions that hold the layers together. This study focuses on a first-principles investigation of the electronic and optical properties of Tp-BNyne. The electronic and optical characteristics of single and bilayer Tp-BNyne structures with varying lengths of C-chains were investigated. The C-chains consisting of 4, 6, and 8 carbon atoms with sp hybridization, were analyzed. Both the monolayer and bilayer Tp-BNyne configurations display semiconducting behavior. These sheets demonstrate an anisotropy response to the incident photon with different polarizations. The way the sheets behave in terms of light can be influenced by the number of layers and the length of the C-chain. The dielectric constants of Tp-BNyne sheets closely resemble graphene. Their high optical absorption indicates the potential for utilizing the sheets in energy storage and absorption systems. The transparency of Tp-BNyne sheets is evident from both their reflection and transmission coefficients, mostly in high-energy region. Therefore, the structural and physical properties of Tp-BNyne sheets make them ideal for optoelectronic applications.

Supplementary Information

Supplementary Information.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-67393-z.

Acknowledgements

The first author was supported by Grant 5038 from Shahid Rajaee Teacher Training University.

Author contributions

R. M.: Writing—original draft, Investigation, Software, analysis, Conceptualization. A.I. A.: Writing—review & editing, Verification, Investigation.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Zhang RS Jiang JW The art of designing carbon allotropes Front. Phys. 2019 14 1 17 10.1007/s11467-018-0836-5
Zhang, R. S. & Jiang, J. W. The art of designing carbon allotropes. Front. Phys. 14, 1–17 (2019).10.1007/s11467-018-0836-5
2. Novoselov KS Electric field in atomically thin carbon films Science 2004 1979 306 666 669 10.1126/science.1102896
Novoselov, K. S. et al. Electric field in atomically thin carbon films. Science 1979(306), 666–669 (2004).10.1126/science.1102896
3. Abergel DSL Apalkov V Berashevich J Ziegler K Chakraborty T Properties of graphene: A theoretical perspective Adv. Phys. 2010 59 261 482 10.1080/00018732.2010.487978
Abergel, D. S. L., Apalkov, V., Berashevich, J., Ziegler, K. & Chakraborty, T. Properties of graphene: A theoretical perspective. Adv. Phys. 59, 261–482 (2010).10.1080/00018732.2010.487978
4. Zhen Z Zhu H Structure and properties of graphene Graphene 2018 10.1016/B978-0-12-812651-6.00001-X
Zhen, Z. & Zhu, H. Structure and properties of graphene. Graphene10.1016/B978-0-12-812651-6.00001-X (2018).10.1016/B978-0-12-812651-6.00001-X
5. Novoselov KS Electronic properties of graphene Phys. Status Solidi 2007 244 4106 4111 10.1002/pssb.200776208
Novoselov, K. S. et al. Electronic properties of graphene. Phys. Status Solidi 244, 4106–4111 (2007).10.1002/pssb.200776208
6. Liu J Bao S Wang X Applications of graphene-based materials in sensors: A review Micromachines 2022 13 184 10.3390/mi13020184 35208308
Liu, J., Bao, S. & Wang, X. Applications of graphene-based materials in sensors: A review. Micromachines 13, 184 (2022).35208308 10.3390/mi13020184
7. Sood AK Review of graphene technology and its applications for electronic devices Graphene 2015 10.5772/61316
Sood, A. K. et al. Review of graphene technology and its applications for electronic devices. Graphene10.5772/61316 (2015).10.5772/61316
8. Dubey A Dave S Lakhani M Sharma A Applications of graphene for communication, electronics and medical fields: A review ICEEOT 2016 2016 2435 2439 10.1109/ICEEOT.2016.7755131
Dubey, A., Dave, S., Lakhani, M. & Sharma, A. Applications of graphene for communication, electronics and medical fields: A review. ICEEOT 2016, 2435–2439. 10.1109/ICEEOT.2016.7755131 (2016).10.1109/ICEEOT.2016.7755131
9. Bai RG Husseini GA Graphene-based drug delivery systems Biomimetic Nanoengineered Materials for Advanced Drug Delivery 2019 Elsevier 149 168
Bai, R. G. & Husseini, G. A. Graphene-based drug delivery systems. In Biomimetic Nanoengineered Materials for Advanced Drug Delivery 149–168 (Elsevier, 2019).
10. Mohan VB Lau KT Hui D Bhattacharyya D Graphene-based materials and their composites: A review on production, applications and product limitations Composites B 2018 142 200 220 10.1016/j.compositesb.2018.01.013
Mohan, V. B., Lau, K. T., Hui, D. & Bhattacharyya, D. Graphene-based materials and their composites: A review on production, applications and product limitations. Composites B 142, 200–220 (2018).10.1016/j.compositesb.2018.01.013
11. Kumar A Sharma K Dixit AR A review of the mechanical and thermal properties of graphene and its hybrid polymer nanocomposites for structural applications J. Mater. Sci. 2019 54 5992 6026 10.1007/s10853-018-03244-3
Kumar, A., Sharma, K. & Dixit, A. R. A review of the mechanical and thermal properties of graphene and its hybrid polymer nanocomposites for structural applications. J. Mater. Sci. 54, 5992–6026 (2019).10.1007/s10853-018-03244-3
12. Bonaccorso F Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage Science 2015 10.1126/science.1246501 25554791
Bonaccorso, F. et al. Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage. Science10.1126/science.1246501 (2015).25554791 10.1126/science.1246501
13. Olabi AG Abdelkareem MA Wilberforce T Sayed ET Application of graphene in energy storage device: A review Renew. Sustain. Energy Rev. 2021 135 110026 10.1016/j.rser.2020.110026
Olabi, A. G., Abdelkareem, M. A., Wilberforce, T. & Sayed, E. T. Application of graphene in energy storage device: A review. Renew. Sustain. Energy Rev. 135, 110026 (2021).10.1016/j.rser.2020.110026
14. Chen X Tian Y Review of graphene in cathode materials for lithium-ion batteries Energy Fuels 2021 35 3572 3580 10.1021/acs.energyfuels.0c04191
Chen, X. & Tian, Y. Review of graphene in cathode materials for lithium-ion batteries. Energy Fuels 35, 3572–3580 (2021).10.1021/acs.energyfuels.0c04191
15. Sahu S Rout GC Band gap opening in graphene: A short theoretical study Int. Nano Lett. 2017 7 81 89 10.1007/s40089-017-0203-5
Sahu, S. & Rout, G. C. Band gap opening in graphene: A short theoretical study. Int. Nano Lett. 7, 81–89 (2017).10.1007/s40089-017-0203-5
16. Nandee R Chowdhury MA Shahid A Hossain N Rana M Band gap formation of 2D materialin graphene: Future prospect and challenges Results Eng. 2022 15 100474 10.1016/j.rineng.2022.100474
Nandee, R., Chowdhury, M. A., Shahid, A., Hossain, N. & Rana, M. Band gap formation of 2D materialin graphene: Future prospect and challenges. Results Eng. 15, 100474 (2022).10.1016/j.rineng.2022.100474
17. Si C Sun Z Liu F Strain engineering of graphene: A review Nanoscale 2016 8 3207 3217 10.1039/C5NR07755A 26796960
Si, C., Sun, Z. & Liu, F. Strain engineering of graphene: A review. Nanoscale 8, 3207–3217 (2016).26796960 10.1039/C5NR07755A
18. Majidi R Ghafoori Tabrizi K Electronic properties of defect-free and defective bilayer graphene in an electric field Fullerenes Nanotubes Carbon Nanostruct. 2011 19 532 539 10.1080/1536383X.2010.494780
Majidi, R. & Ghafoori Tabrizi, K. Electronic properties of defect-free and defective bilayer graphene in an electric field. Fullerenes Nanotubes Carbon Nanostruct. 19, 532–539 (2011).10.1080/1536383X.2010.494780
19. Majidi R Karami AR Caffeine and nicotine adsorption on perfect, defective and porous graphene sheets Diam. Relat. Mater. 2016 66 47 51 10.1016/j.diamond.2016.03.014
Majidi, R. & Karami, A. R. Caffeine and nicotine adsorption on perfect, defective and porous graphene sheets. Diam. Relat. Mater. 66, 47–51 (2016).10.1016/j.diamond.2016.03.014
20. Behzad S Chegel R A hybrid density functional study of tensile-induced changes in phonon dispersion, electronic structure and optical absorption of bilayer BN for optoelectronic applications Results Phys. 2024 59 107609 10.1016/j.rinp.2024.107609
Behzad, S. & Chegel, R. A hybrid density functional study of tensile-induced changes in phonon dispersion, electronic structure and optical absorption of bilayer BN for optoelectronic applications. Results Phys. 59, 107609 (2024).10.1016/j.rinp.2024.107609
21. Essaa SA Jappor HR Tunable photocatalytic and optoelectronic properties of SiTe/SiH heterostructure as a photocatalytic water splitting with high hydrogen production J. Phys. Chem. Solids 2024 193 112125 10.1016/j.jpcs.2024.112125
Essaa, S. A. & Jappor, H. R. Tunable photocatalytic and optoelectronic properties of SiTe/SiH heterostructure as a photocatalytic water splitting with high hydrogen production. J. Phys. Chem. Solids 193, 112125 (2024).10.1016/j.jpcs.2024.112125
22. Almayyali AOM Jappor HR PbBi2Se4 monolayer: A new 2D material with outstanding electronic, photocatalytic, and optical properties Solid State Sci. 2024 150 107483 10.1016/j.solidstatesciences.2024.107483
Almayyali, A. O. M. & Jappor, H. R. PbBi2Se4 monolayer: A new 2D material with outstanding electronic, photocatalytic, and optical properties. Solid State Sci. 150, 107483 (2024).10.1016/j.solidstatesciences.2024.107483
23. Bafekry A Layered conjugated porous fused aromatic network structures of two-dimensional carbon nitride: A first-principles calculation of optoelectronic properties Appl. Phys. A 2024 130 1 7 10.1007/s00339-024-07675-5
Bafekry, A. et al. Layered conjugated porous fused aromatic network structures of two-dimensional carbon nitride: A first-principles calculation of optoelectronic properties. Appl. Phys. A 130, 1–7 (2024).10.1007/s00339-024-07675-5
24. Bafekry A Theoretical prediction of two-dimensional BC2X (X = N, P, As) monolayers: Ab initio investigations Sci. Rep. 2022 12 1 10 10.1038/s41598-022-26805-8 34992227
Bafekry, A. et al. Theoretical prediction of two-dimensional BC2X (X = N, P, As) monolayers: Ab initio investigations. Sci. Rep. 12, 1–10 (2022).34992227 10.1038/s41598-022-26805-8
25. Baughman RH Eckhardt H Kertesz M Structure-property predictions for new planar forms of carbon: Layered phases containing sp2 and sp atoms J. Chem. Phys. 1987 87 6687 6699 10.1063/1.453405
Baughman, R. H., Eckhardt, H. & Kertesz, M. Structure-property predictions for new planar forms of carbon: Layered phases containing sp2 and sp atoms. J. Chem. Phys. 87, 6687–6699 (1987).10.1063/1.453405
26. Ivanovskii AL Progress in solid state chemistry graphynes and graphdyines Progr. Solid State Chem. 2013 41 1 19 10.1016/j.progsolidstchem.2012.12.001
Ivanovskii, A. L. Progress in solid state chemistry graphynes and graphdyines. Progr. Solid State Chem. 41, 1–19 (2013).10.1016/j.progsolidstchem.2012.12.001
27. Li Y Wu J Li C Wang Q Shen L Effect of acetylene links on electronic and optical properties of semiconducting graphynes ACS Omega 2021 6 10997 11004 10.1021/acsomega.1c00840 34056253
Li, Y., Wu, J., Li, C., Wang, Q. & Shen, L. Effect of acetylene links on electronic and optical properties of semiconducting graphynes. ACS Omega 6, 10997–11004 (2021).34056253 10.1021/acsomega.1c00840
28. Shao ZG Sun ZL Optical properties of α-, β-, γ-, and 6,6,12-graphyne structures: First-principle calculations Physica E 2015 74 438 442 10.1016/j.physe.2015.07.011
Shao, Z. G. & Sun, Z. L. Optical properties of α-, β-, γ-, and 6,6,12-graphyne structures: First-principle calculations. Physica E 74, 438–442 (2015).10.1016/j.physe.2015.07.011
29. Malko D Neiss C Viñes F Görling A Competition for graphene: Graphynes with direction-dependent Dirac cones Phys. Rev. Lett. 2012 108 086804 10.1103/PhysRevLett.108.086804 22463556
Malko, D., Neiss, C., Viñes, F. & Görling, A. Competition for graphene: Graphynes with direction-dependent Dirac cones. Phys. Rev. Lett. 108, 086804 (2012).22463556 10.1103/PhysRevLett.108.086804
30. Kim BG Choi HJ Graphyne: Hexagonal network of carbon with versatile Dirac cones Phys. Rev. B 2012 86 115435 10.1103/PhysRevB.86.115435
Kim, B. G. & Choi, H. J. Graphyne: Hexagonal network of carbon with versatile Dirac cones. Phys. Rev. B 86, 115435 (2012).10.1103/PhysRevB.86.115435
31. Liu Q Feng N Zou Y Fan C Wang J Exploring the impact of stress on the electronic structure and optical properties of graphdiyne nanoribbons for advanced optoelectronic applications Sci. Rep. 2024 14 1 13 38167627
Liu, Q., Feng, N., Zou, Y., Fan, C. & Wang, J. Exploring the impact of stress on the electronic structure and optical properties of graphdiyne nanoribbons for advanced optoelectronic applications. Sci. Rep. 14, 1–13 (2024).38167627
32. Bao H Wang L Li C Luo J Structural characterization and identification of graphdiyne and graphdiyne-based materials ACS Appl. Mater. Interfaces 2019 11 2717 2729 10.1021/acsami.8b05051 29845862
Bao, H., Wang, L., Li, C. & Luo, J. Structural characterization and identification of graphdiyne and graphdiyne-based materials. ACS Appl. Mater. Interfaces 11, 2717–2729 (2019).29845862 10.1021/acsami.8b05051
33. Gao X Liu H Wang D Zhang J Graphdiyne: Synthesis, properties, and applications Chem. Soc. Rev. 2019 48 908 936 10.1039/C8CS00773J 30608070
Gao, X., Liu, H., Wang, D. & Zhang, J. Graphdiyne: Synthesis, properties, and applications. Chem. Soc. Rev. 48, 908–936 (2019).30608070 10.1039/C8CS00773J
34. Srinivasu K Ghosh SK Graphyne and graphdiyne: Promising materials for nanoelectronics and energy storage applications J. Phys. Chem. C 2012 116 5951 5956 10.1021/jp212181h
Srinivasu, K. & Ghosh, S. K. Graphyne and graphdiyne: Promising materials for nanoelectronics and energy storage applications. J. Phys. Chem. C 116, 5951–5956 (2012).10.1021/jp212181h
35. Long M Tang L Wang D Li Y Shuai Z Electronic structure and carrier mobility in graphdiyne sheet and nanoribbons: Theoretical predictions ACS Nano 2011 5 2593 2600 10.1021/nn102472s 21443198
Long, M., Tang, L., Wang, D., Li, Y. & Shuai, Z. Electronic structure and carrier mobility in graphdiyne sheet and nanoribbons: Theoretical predictions. ACS Nano 5, 2593–2600 (2011).21443198 10.1021/nn102472s
36. Matsuoka R Expansion of the graphdiyne family: A triphenylene-cored analogue ACS Appl. Mater. Interfaces 2019 11 2730 2733 10.1021/acsami.8b00743 29508605
Matsuoka, R. et al. Expansion of the graphdiyne family: A triphenylene-cored analogue. ACS Appl. Mater. Interfaces 11, 2730–2733 (2019).29508605 10.1021/acsami.8b00743
37. Qi S Fan Y Li W Zhao M Computational studies on triphenyldiyne as a two-dimensional visible-light-driven photocatalyst for overall water splitting Phys. Chem. Chem. Phys. 2020 22 20061 20068 10.1039/D0CP03641B 32936175
Qi, S., Fan, Y., Li, W. & Zhao, M. Computational studies on triphenyldiyne as a two-dimensional visible-light-driven photocatalyst for overall water splitting. Phys. Chem. Chem. Phys. 22, 20061–20068 (2020).32936175 10.1039/D0CP03641B
38. Mortazavi B N-, P-, As-triphenylene-graphdiyne: Strong and stable 2D semiconductors with outstanding capacities as anodes for Li-ion batteries Carbon N Y 2019 141 291 303 10.1016/j.carbon.2018.09.070
Mortazavi, B. et al. N-, P-, As-triphenylene-graphdiyne: Strong and stable 2D semiconductors with outstanding capacities as anodes for Li-ion batteries. Carbon N Y 141, 291–303 (2019).10.1016/j.carbon.2018.09.070
39. Muhammad I A BN analog of two-dimensional triphenylene-graphdiyne: Stability and properties Nanoscale 2019 11 9000 9007 10.1039/C9NR02334H 31020293
Muhammad, I. et al. A BN analog of two-dimensional triphenylene-graphdiyne: Stability and properties. Nanoscale 11, 9000–9007 (2019).31020293 10.1039/C9NR02334H
40. User’s manual of OpenMX Ver. 3.9. http://www.openmx-square.org/openmx_man3.9/index.html.
41. Perdew JP Burke K Ernzerhof M Generalized gradient approximation made simple Phys. Rev. Lett. 1996 77 3865 3868 10.1103/PhysRevLett.77.3865 10062328
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10062328 10.1103/PhysRevLett.77.3865
42. Perdew JP Zunger A Self-interaction correction to density-functional approximations for many-electron systems Phys. Rev. B 1981 23 5048 10.1103/PhysRevB.23.5048
Perdew, J. P. & Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048 (1981).10.1103/PhysRevB.23.5048
43. Grimme S Antony J Ehrlich S Krieg H A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu J. Chem. Phys. 2010 132 154104 10.1063/1.3382344 20423165
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).20423165 10.1063/1.3382344
44. Evans DJ Holian BL The Nose-Hoover thermostat J. Chem. Phys. 1985 83 4069 4074 10.1063/1.449071
Evans, D. J. & Holian, B. L. The Nose-Hoover thermostat. J. Chem. Phys. 83, 4069–4074 (1985).10.1063/1.449071
45. Lee, Y. T. Dielectric Function and Optical Conductivity (2019).
46. Beiranvand R Valedbagi S Electronic and optical properties of h-BN nanosheet: A first principles calculation Diam. Relat. Mater. 2015 58 190 195 10.1016/j.diamond.2015.07.008
Beiranvand, R. & Valedbagi, S. Electronic and optical properties of h-BN nanosheet: A first principles calculation. Diam. Relat. Mater. 58, 190–195 (2015).10.1016/j.diamond.2015.07.008
47. Zheng Q Structural and electronic properties of bilayer and trilayer graphdiyne Nanoscale 2012 4 3990 3996 10.1039/c2nr12026g 22677896
Zheng, Q. et al. Structural and electronic properties of bilayer and trilayer graphdiyne. Nanoscale 4, 3990–3996 (2012).22677896 10.1039/c2nr12026g
48. Luo G Zheng Q Mei WN Lu J Nagase S Structural, electronic, and optical properties of bulk graphdiyne J. Phys. Chem. C 2013 117 13072 13079 10.1021/jp402218k
Luo, G., Zheng, Q., Mei, W. N., Lu, J. & Nagase, S. Structural, electronic, and optical properties of bulk graphdiyne. J. Phys. Chem. C 117, 13072–13079 (2013).10.1021/jp402218k
49. Penn DR Wave-number-dependent dielectric function of semiconductors Phys. Rev. 1962 128 2093 10.1103/PhysRev.128.2093
Penn, D. R. Wave-number-dependent dielectric function of semiconductors. Phys. Rev. 128, 2093 (1962).10.1103/PhysRev.128.2093
50. Guo L Zhang S Feng W Hu G Li W A first-principles study on the structural, elastic, electronic, optical, lattice dynamical, and thermodynamic properties of zinc-blende CdX (X = S, Se, and Te) J. Alloys Compd. 2013 579 583 593 10.1016/j.jallcom.2013.07.096
Guo, L., Zhang, S., Feng, W., Hu, G. & Li, W. A first-principles study on the structural, elastic, electronic, optical, lattice dynamical, and thermodynamic properties of zinc-blende CdX (X = S, Se, and Te). J. Alloys Compd. 579, 583–593 (2013).10.1016/j.jallcom.2013.07.096
51. John R Merlin B Optical properties of graphene, silicene, germanene, and stanene from IR to far UV: A first principles study J. Phys. Chem. Solids 2017 110 307 315 10.1016/j.jpcs.2017.06.026
John, R. & Merlin, B. Optical properties of graphene, silicene, germanene, and stanene from IR to far UV: A first principles study. J. Phys. Chem. Solids 110, 307–315 (2017).10.1016/j.jpcs.2017.06.026
52. Majidi R Ayesh AI Comparative study of δ-graphdiyne and δ-graphyne: Insights into structural stability and electronic and optical properties J. Phys. Chem. C 2023 127 22234 22240 10.1021/acs.jpcc.3c05931
Majidi, R. & Ayesh, A. I. Comparative study of δ-graphdiyne and δ-graphyne: Insights into structural stability and electronic and optical properties. J. Phys. Chem. C 127, 22234–22240 (2023).10.1021/acs.jpcc.3c05931
53. Guo G Tan S Guo G Xie Z Strain-enhanced properties of Janus Si2PAs monolayer as a promising photocatalyst for the splitting of water: Insights from first-principles calculations Colloids Surf. A 2023 659 130782 10.1016/j.colsurfa.2022.130782
Guo, G., Tan, S., Guo, G. & Xie, Z. Strain-enhanced properties of Janus Si2PAs monolayer as a promising photocatalyst for the splitting of water: Insights from first-principles calculations. Colloids Surf. A 659, 130782 (2023).10.1016/j.colsurfa.2022.130782
54. Guo G Xu Y Guo G Janus-functionalization induced magnetism and improved optoelectronic properties in two-dimension silicene and germanene: Insights from first-principles calculations J. Phys. 2023 35 335501
Guo, G., Xu, Y. & Guo, G. Janus-functionalization induced magnetism and improved optoelectronic properties in two-dimension silicene and germanene: Insights from first-principles calculations. J. Phys. 35, 335501 (2023).
55. Guo G Liu J Xu Y Guo G Tan S Chemical functionalization induced photocatalytic performance for water splitting of silicene: A first-principles investigation Colloids Surf. A 2023 667 131379 10.1016/j.colsurfa.2023.131379
Guo, G., Liu, J., Xu, Y., Guo, G. & Tan, S. Chemical functionalization induced photocatalytic performance for water splitting of silicene: A first-principles investigation. Colloids Surf. A 667, 131379 (2023).10.1016/j.colsurfa.2023.131379
56. Guo G Zhou Y Guo G Xie Z First-principles study on the optoelectronic and photocatalytic properties of the C2h-Janus Al2XY(X/YS, Se and Te) monolayers Mater. Today Chem. 2024 35 101913 10.1016/j.mtchem.2024.101913
Guo, G., Zhou, Y., Guo, G. & Xie, Z. First-principles study on the optoelectronic and photocatalytic properties of the C2h-Janus Al2XY(X/YS, Se and Te) monolayers. Mater. Today Chem. 35, 101913 (2024).10.1016/j.mtchem.2024.101913
57. Behzad S Chegel R Investigation of effects of interlayer interaction and biaxial strain on the phonon dispersion and dielectric response of hexagonal boron arsenide Sci. Rep. 2023 13 1 11 10.1038/s41598-023-48654-9 36593249
Behzad, S. & Chegel, R. Investigation of effects of interlayer interaction and biaxial strain on the phonon dispersion and dielectric response of hexagonal boron arsenide. Sci. Rep. 13, 1–11 (2023).36593249 10.1038/s41598-023-48654-9
