Introduction

Research on 2D materials has gained much attention since the discovery of graphene1,2. This carbon allotrope that is composed of a hexagonal lattice was demonstrated to possess several exciting features, such as high electrical and thermal conductivity and large mechanical resistance that are aimed at developing the next generation of organic optoelectronic devices3,4. However, when it comes to optoelectronic applications, graphene has a zero bandgap, which precludes its use, for instance, as active material in solar cells. To overcome this issue, gap opening strategies have been developed5,6,7 including the cutting of graphene sheets into graphene nanoribbons8, the adsorption of H-adatoms9 and the use of dopants10,11,12. Recently, the effects of such techniques have also been studied in similar 2D materials such as arsenene13,14, by means of first principle calculations.

When it comes to doping strategies, these are often divided into wet and dry doping methods15. The former makes use of the spin coating of dopant containing solutions so that charge transfer between graphene and dopant may take place. Dry doping strategies, on the other had, include the electrostatic field doping method, which consists on the application of an electric field perpendicular to the graphene sample. This method, however, cannot be applied to single layers of graphene. A more appropriate strategy in the context of this work is the atom substitution method, which can be performed by means of thermal treatment or plasma doping, for instance.

There are a few nature-occurring carbon allotropes, including graphite, fullerenes16, and carbon nanotubes17. Recently, another allotrope was proposed named penta-graphene18 (see Fig. 1), which has a lattice composed of pentagons that resemble the Cairo pentagonal tiling. It is supposed to present ultrahigh ideal strength even above that of graphene and to be able to withstand temperatures of up to 1000 K19. Penta-graphene was not synthesized yet, and it is believed that it can be at least a metastable material19,20,21,22. Furthermore, recent studies have suggested that chemical functionalization employing hydrogenation or fluorination could even increase its structural stability23,24. Electronic structure calculations indicate that penta-graphene is a semiconductor presenting bandgap values about 2.24–4.3 eV19,21,23. Such large bandgap suggests the need for gap tuning strategies to be developed in order to tailor this material for optoelectronic applications. In this sense, the particular topology of penta-graphene, which presents both sp2 and sp3-like carbon hybridizations in its lattice, raises the question of how its structural and electronic properties will behave by targeting a particular hybridization in the doping processes.

Figure 1
figure 1

(Top) Schematic representation for the sp3-like carbons doping strategy. The red color represents the doping atoms (N or Si). Bond length variations for penta-graphene lattices with Nitrogen (Middle) and Silicon (Bottom) doping schemes. In the color palette on the right, the equilibrium distance is 1.575 Å. The maximum deviations are 0.5 Å for Nitrogen and 1.5 Å for Silicon doping schemes.

Full size image

Herein, we carried out density functional theory (DFT) calculations to address the effects of the systematic substitutional doping of either sp2 or sp3-like carbons by nitrogen and silicon atoms in a penta-graphene lattice. Mainly, we investigate the effect of the different number of engineered line defects on their electronic and structural properties (see Fig. 1). As to the choice of dopants, size limitations require us to choose among atoms adjacent to carbon such as nitrogen, boron or silicon. In the particular case of nitrogen, it has been shown that nitrogen doping in graphene is responsible for regulating the electronic properties due to the ease with which nitrogen is able to control the local electronic structure, resulting in improvement of device performance25. Likewise, large area silicon doped graphene has been produced and has shown interesting properties26. Our findings show that, in terms of morphology, nitrogen doping is responsible for increasing the stiffness of the lattice in comparison to pristine penta-graphene, whereas silicon doping results in the simultaneous stretching and compression of Si–C and C–C bonds, respectively, concerning undoped C–C bonds. The two doping schemes investigated here (Si or N) produce significantly different results in terms of electronic behavior. Silicon doping allows us to tune the bandgap when replacing sp3-like carbons and produces metallic behavior when replacing sp2-like ones. Nitrogen doping replacing sp3-like carbons results in a transition from semiconductor to semimetallic to a metallic character. Nitrogen doping replacing sp2-like carbons produces an alternating behavior between semimetallic and semiconductor depending on the number of dopants. These results indicate that engineered line defects can be a very effective way to tune penta-graphene electronic behavior.

Results

In the present work, we investigated the electronic and structural features of penta-graphene lattices with substitutional doping (N or Si) either at sp3 or sp2-like carbons forming engineered line defects. The cases of 1 up to 7 line defects were considered. In this sense, Fig. 1 (top panels) shows a schematic representation of these defective structures for the sp3 case, which is similar to the sp2 one. Figure 1 presents seven scenarios, which are identified by N–XL, with N corresponding the number of line defects in the horizontal/vertical directions, and X refers to either nitrogen or silicon dopant atoms.

Significant structural differences take place in the morphology of the resulting doped structures. For the nitrogen cases, an overall decrease in bond length values was observed, as presented in Fig. 1 (middle panels), where the blue color represents bond length compression when compared to the original non-doped ones. As expected, these effects are more pronounced around the defect lines, but they extend to the other bonds as the number of doping atoms increases. Such a reduction in bond length values can reach 0.5 Å, which corresponds to a roughly 30% decrease concerning the 1.575 Å equilibrium distance found in pristine penta-graphene. In contrast, for the silicon atoms, the newly formed C-Si bonds undergo a substantial expansion of up to 1.5 Å, which would amount to 100% increase in bond length values when compared to pristine penta-graphene C–C bonds, as shown in Fig. 1-bottom. For the remaining C–C bonds, this effect is less pronounced.

It is well-known that structural modifications lead to changes in electronic properties. As such, useful information about these changes can be gained by contrasting the band structures of the doped and undoped penta-graphene sheets. Reports in the literature for penta-graphene indicate a semiconductor material with a bandgap of about 2.4 eV18,21. We have obtained a similar value, as shown in Fig. 2. In this figure, we also present the band results for the sp3 cases for nitrogen (Fig. 2a) and silicon doping (Fig. 2b) as a function of the number of line defects. As we can see from Fig. 2, for the nitrogen with 1 line defect, the bandgap becomes indirect and decreases from 2.4 eV to just 1.5 eV. The Fermi level lies near the conduction band, making this doped penta-graphene structure an n-type semiconductor. As the number of line defects increases, the material no longer presents a bandgap. We can see that for 2 and 3 defect lines, the partial density of states (PDOS) near the Fermi level, presented in Fig. S1a in the Electronic Supporting Information (SI), almost disappears. As the number of defect lines increases, the PDOS around the Fermi levels increases, and the doped penta-graphene becomes fully metallic.

Figure 2
figure 2

Band structures for undoped and doped penta-graphene lattices, as a function of the number of line defects for the sp3 case. (a,b) correspond to the results for Nitrogen and Silicon doping schemes, respectively. Here, X-NL and X-SiL denote the number (X) of dopant lines systematically inserted into the penta-graphene structure.

Full size image

The silicon doping of sp3-like carbons, on the other hand, does not result in metallic materials. As seen in Figs. 2b and S2a of the SI, doped penta-graphene lattices preserve their semiconductor nature. For the 1 line defect case, the only observed effect was the decrease in bandgap to 1.3 eV, with further doping making the bandgap indirect. Interestingly, the bandgap dependence on the number of defect lines has a convex nature, with a minimum bandgap of 0.8 eV observed for the case of 4 defect lines. After this point, the bandgap increases again, reaching 1.76 eV for the lattice with seven defect lines. The decreases in bandgap values are associated with the appearance of states in the valence band closer to the Fermi level.

The second doping strategy considered here consists of the doping of sp2-like carbons. One main difference is the possibility of having N–N and Si–Si bonds, not present for sp3 case. The seven analyzed scenarios are presented in Fig. 3 (top panels). Again, nitrogen doping results in overall contraction of the bond length values up to 0.5 Å concerning undoped penta-graphene ones. These deviations in the bond lengths are represented in Fig. 3 (middle panels) by the blue bonds. Silicon doping, in contrast, produces different patterns. These are mostly characterized by the simultaneous expansion of Si–C bonds, by Si–Si bonds that preserve the original 1.575 Å bond length of pristine penta-graphene and by C–C bonds that slightly contract. The combination of these effects results in the pattern characterized by blue hexagons diagonally sliced by red Si–C bonds, as depicted in Fig. 3-bottom, especially for the six defect lines case. However, two particular cases, 5 and 7 defect lines, break the pattern producing much more disordered configurations likely induced by symmetry breaking. The Si–C distances in the doped penta-graphene lattices can reach 3.8 Å, considerably larger than Si–C bonds found, for instance, in disilicon carbide, which can be as large as 2.2 Å27. This is suggestive that the atoms are no longer bonded and the structures undergo structural rearrangements.

Figure 3
figure 3

(Top) Schematic representation for penta-graphene lattices with sp2-like carbons doping strategy. The red color represents the doping atoms (N or Si). Bond length variations for penta-graphene lattices resulting from Nitrogen doping (Middle) and Similar Silicon doping scheme (Bottom). In the color palette on the right, the equilibrium distance is 1.575 Å. The maximum deviations are 0.5 Å for Nitrogen and 1.5 Å for Silicon doping schemes.

Full size image

In terms of electronic structure, nitrogen and silicon doping produce completely different results. Interestingly, for the sp2 nitrogen doping cases, the bandgap values exhibit a bandgap modulation (alternating increasing/decreasing) behavior, as can be seen in Fig. 4a. For even values of N, semiconducting properties are obtained with almost direct bandgaps that decrease as N grows larger from 2.4 eV for N = 0 to 0.6 eV for N = 6. In contrast, for odd values of N, the valence band maximum (VBM) touches or surpasses the Fermi levels. However, the DOS near the Fermi level is very small, increasing progressively with N. This behavior can be better visualized in the PDOS plots of Fig. S1b in the SI. The even N nitrogen-doped penta-graphene lattices display a semimetallic character, with carbon p orbitals being mostly responsible for the DOS in the vicinity of the Fermi level.

Figure 4
figure 4

Band structures for undoped and doped penta-graphene, as a function of the number of line defects for the sp2 case. (a,b) correspond to the results for Nitrogen and Silicon doping schemes, respectively. Here, X-NL and X-SiL denote the number (X) of dopant lines systematically inserted into the penta-graphene structure.

Full size image

Silicon doped penta-graphene structures, on the other hand, possess semiconductor properties only for N = 1 or N = 2, with a fast transition to bandgap closing. For larger N values, the structures become fully metallic, as shown in Fig. 4b (see also Fig. 2-ESI in SI). It is also worth noting that the effect of the disordered morphology observed for the 5-SiL and 7-SiL cases is to make energy levels practically independent of momentum when compared to the other cases, as evidenced by the almost flat (dispersionless) bands. In this sense, silicon doping of sp2-like carbons is not as effective as in cases of nitrogen doping regarding decreasing the bandgap value.

An important advantage concerning the sp2 doping instead of sp3 one is the effects on the structural stability of the doped structures. In Fig. 5, we present the cohesive energy (Ecoh) values for all doping scenarios. The cohesive energy is the difference per atom between the entire system energy and the sum of the individual energies of its constituents. It is, therefore, associated with the stability of the system. Such a quantity is evaluated by the following expression:

$${E}_{coh}=\frac{({E}_{total}-{N}_{D}{E}_{D}-{N}_{c}{E}_{C})}{{N}_{total}},$$
(1)

where Etotal is the total energy of the system. ND and NC are the number of dopant and carbon atoms of the system, respectively, and Ntotal = ND + NC. ED and EC are the energies of isolated dopant and and carbon atoms, respectively.

Figure 5
figure 5

Cohesive energy for all cases of Nitrogen and Silicon doping schemes of (top) sp3 carbons and (bottom) sp2 carbons.

Full size image

Figure 5-top) and Fig. 5-bottom) refer to sp3 and sp2 results, respectively. It can be seen from this figure that for both sp3 and sp2-like carbon doping, the effects on cohesive energy are similar for N and Si dopants. However, whereas sp3-like carbon doping increases the cohesive energy from −8.0 eV/atom to −6.5 eV/atom, the corresponding increase in the case of sp2-like carbon in less than 1.0 eV/atom.

Finally, we present the charge transfer analysis for all the modeled systems studied here. Figure 6 illustrates the charge density profiles for all the cases of engineered line defects considering silicon (Fig. 6(a)) and nitrogen (Fig. 6(b)) dopants. For silicon-doped lattices, one can note that the charge density profile has an anti-bonding character in the doping regions for both sp2 and sp3 doping channels. As a consequence, charge density states have greater overlap in the regions that have only carbon atoms, as depicted in Fig. 6(a). Conversely, a metallic signature of the nitrogen-doped lattices can be inferred from the predominance of bonding states presented by the charge density localization, as shown in Fig. 6(b). Importantly, no substantial difference in the charge density profile is realized in nitrogen-doped lattices considering both sp2 and sp3 doping channels. In their electronic configuration, nitrogen possesses three electrons in the p orbital (last level 2p) whereas silicon has only two electrons in the last level (3p). The extra electron in the electronic arrangement of nitrogen leads to the greater overlap in the charge density profile and the formation of bonding states. The even (and smaller) number of electrons in the last level for silicon, when contrasted with nitrogen, is responsible for the smaller electronic correlation among the lattice sites, which considerably reduces the charge density overlap in the silicon-doped regions, as can be seen in Fig. 6(b).

Figure 6
figure 6

Charge density configuration for all the cases of engineered line defects presented here considering (a) silicon and (b) nitrogen dopants.

Full size image

Methods

DFT calculations were carried out within the Generalized Gradient Approximation (GGA) scheme as proposed for Perdew, Burke, and Ernzerhof (GGA/PBE)28 along with the DZP29,30, basis set. Relativistic pseudopotentials parameterized within the Troullier-Martins formalism were also considered31. These combined approximations can accurately describe the magnetic and electronic properties of materials composed of atoms with many electrons. All the calculations were performed considering spin polarization. For the bands and density of states calculations, Monkhorst pack grid of 21 × 21 × 3 was used32. A mesh cutoff of 200 Ry was chosen as a parameter for our calculations33. The force criteria convergence was 0.001 eV/Å. In order to establish a good compromise between the accuracy of our results and computational costs, the tolerance in the matrix density and total energy was set to 0.0001 and 0.00001 eV, respectively. All calculations were performed with the SIESTA software suite34,35.

Conclusions

In summary, we have carried out DFT calculations to assess the changes in the structural and electronic properties of penta-graphene lattices resulting from selective N and Si doping (engineered line defects) of either sp3 or sp2-like carbons. Regardless of the type doping, for the nitrogen cases, we observed an overall stiffening of the penta-graphene structures. On the other hand, for the silicon doping cases, we observed only the stretching of Si-C bonds and compression of the remaining C–C bonds.

From an electronic structure perspective, both the doping type and doping atom selection produce significantly different results. Silicon doping of the sp3-like carbons preserves the penta-graphene semiconductor character. The smallest observed bandgap value was 0.8 eV (2.4 eV for pristine penta-graphene) for the 4 line defect case. For a larger number of line defects, the bandgaps increase again. On the other hand, for Si doping sp2-like carbons, the result is a fast transition to metallic behavior.

Nitrogen doping produces more interesting results. For the sp3-like carbons, the doping results in a progressive changes from semiconductor to metallic behavior. For the case of 1 line defects, the doped penta-graphene structure becomes an n-type semiconductor with a 1.5 eV bandgap. For 2 and 3 line defects, the bandgap closes, but the density of states near the Fermi level goes to zero, giving the material a semi-metallic character. From this point on, further doping leads to true metallic behavior.

For the nitrogen doping of sp2-like carbons, we observed a bandgap modulation behavior (alternating increase/decrease). For even numbers of line defects, the bandgap decreases with the number of line defects. In contrast, for odd numbers of line defects, a semi-metallic behavior is observed, combining zero bandgap with near-zero density of states at the vicinity of the Fermi level. Finally, the cohesive energy values indicate that doping the sp2-like carbon affects less the structural stability of the resulting doped structures than sp3-like carbon ones.

These results indicate that selective doping of penta-graphene structures through engineered line defects can be an effective tool to tune their electronic behavior, being possible to create structures that vary from large bandgaps through semiconductors and even metallic or semimetallic ones. Importantly, Liu and coworkers36 have demonstrated the creation of graphene and hexagonal boron nitride (h-BN) in-plane heterostructures with controlled domain sizes by using lithography patterning and sequential CVD growth steps. By employing this approach, the shapes of the graphene and h-BN domains were precisely controlled, and sharp graphene/h-BN interfaces were created. In this way, we believe that such an approach can be employed to yield our proposed model lattices. We hope the present work can stimulate further studies along these lines.