Tuning Penta-Graphene Electronic Properties Through Engineered Line Defects

Penta-graphene is a quasi-two-dimensional carbon allotrope consisting of a pentagonal lattice in which both sp2 and sp3-like carbons are present. Unlike graphene, penta-graphene exhibits a non-zero bandgap, which opens the possibility of its use in optoelectronic applications. However, as the observed bandgap is large, gap tuning strategies such as doping are required. In this work, density functional theory calculations are used to determine the effects of the different number of line defects of substitutional nitrogen or silicon atoms on the penta-graphene electronic behavior. Our results show that this doping can induce semiconductor, semimetallic, or metallic behavior depending on the doping atom and targeted hybridization (sp2 or sp3-like carbons). In particular, we observed that nitrogen doping of sp2-like carbons atoms can produce a bandgap modulation between semimetallic and semiconductor behavior. These results show that engineering line defects can be an effective way to tune penta-graphene electronic behavior.

Herein, we carried out density functional theory (DFT) calculations to address the effects of the systematic substitutional doping of either sp 2 or sp 3 -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 performance 25 . Likewise, large area silicon doped graphene has been produced and has shown interesting properties 26 . 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 sp 3 -like carbons and produces metallic behavior when replacing sp 2 -like ones. Nitrogen doping replacing sp 3 -like carbons results in a transition from semiconductor to semimetallic to a metallic character. Nitrogen doping replacing sp 2 -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 sp 3 or sp 2 -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 sp 3 case, which is similar to the sp 2 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 eV 18,21 . We have obtained a similar value, as shown in Fig. 2. In this figure, we also present the band results for the sp 3 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.
The silicon doping of sp 3 -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 The second doping strategy considered here consists of the doping of sp 2 -like carbons. One main difference is the possibility of having N-N and Si-Si bonds, not present for sp 3 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 Å 27 . This is suggestive that the atoms are no longer bonded and the structures undergo structural rearrangements.
In terms of electronic structure, nitrogen and silicon doping produce completely different results. Interestingly, for the sp 2 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.
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   www.nature.com/scientificreports www.nature.com/scientificreports/ 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: where E total is the total energy of the system. N D and N C are the number of dopant and carbon atoms of the system, respectively, and N total = N D + N C . E D and E C are the energies of isolated dopant and and carbon atoms, respectively. 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).

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 DZP 29,30 , basis set. Relativistic pseudopotentials parameterized within the Troullier-Martins formalism were also considered 31 . 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 used 32 . A mesh cutoff of 200 Ry was chosen as a parameter for our calculations 33 . 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 suite 34,35 . 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 sp 3 or sp 2 -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 sp 3 -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 sp 2 -like carbons, the result is a fast transition to metallic behavior.
Nitrogen doping produces more interesting results. For the sp 3 -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 sp 2 -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 sp 2 -like carbon affects less the structural stability of the resulting doped structures than sp 3 -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 coworkers 36 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.