#
Two−Dimensional Planar Penta−NiPN with Ultrahigh Carrier Mobility and Its Potential Application in NO and NO_{2} Gas Sensing

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{2}(ACS Nano, 2021, 15, 13539–13546), we propose for the first time a novel ternary penta−NiPN monolayer with high stability by partial element substitution. Our predicted penta−NiPN monolayer is a quasi−direct bandgap (1.237 eV) semiconductor with ultrahigh carrier mobilities (10

^{3}–10

^{5}cm

^{2}V

^{−1}s

^{−1}). Furthermore, we systematically studied the adsorption properties of common gas molecules (CO, CO

_{2}, CH

_{4}, H

_{2}, H

_{2}O, H

_{2}S, N

_{2}, NO, NO

_{2}, NH

_{3}, and SO

_{2}) on the penta−NiPN monolayer and its effects on electronic properties. According to the energetic, geometric, and electronic analyses, the penta−NiPN monolayer is predicted to be a promising candidate for NO and NO

_{2}molecules. The excellent electronic properties of and the unique selectivity of the penta−NiPN monolayer for NO and NO

_{2}adsorption suggest that it has high potential in advanced electronics and gas sensing applications.

## 1. Introduction

_{2}is a potential material for selective and reversible NO

_{2}detection at low operating temperatures [8], while Qin et al. developed a flexible paper substrate sensor based on 2D WS

_{2−x}for NH

_{3}detection at room temperature [9]. So far, many types of gas detection have been realized experimentally or theoretically based on various 2D materials, such as NO, CO, SO

_{2}, NH

_{3,}H

_{2}O, and others [10,11,12,13]. However, developing a high−sensitivity, fast−response, and completely desorbed gas sensor based on 2D materials under harsh working conditions remains a challenge. Nonetheless, the search for new 2D materials with excellent electronic properties that can be used in gas sensors remains a major research focus.

_{2}with an ideal Cairo tessellation via a high−pressure route. Notably, this penta−NiN

_{2}has a typical layered structure and is stable at room temperature, suggesting that a penta−NiN

_{2}monolayer can be obtained by mechanical exfoliation, similar to that with graphene or black phosphorene [15,16]. Theoretical studies have shown that the penta−NiN

_{2}monolayer is a direct bandgap semiconductor with moderate thermal conductivity and outstanding mechanical properties, and it can be applied to bifunctional oxygen electrocatalysts and gas sensors [17,18,19,20,21]. In fact, before the experimental synthesis of penta−NiN

_{2}, similar structures had been studied extensively, such as penta−MX

_{2}(M = Ni, Pd, Pt; X = N, P, As, Sb) [17,22,23,24,25,26,27]. This family of 2D materials demonstrated excellent properties, such as a suitable bandgap, a high optical absorption coefficient, ultrahigh carrier mobility, and so on [22,23,24,25]. However, most research on this family of 2D materials focused on binary systems, and previous studies showed that the properties of systems can be effectively improved by introducing homologous elements, such as α−P

_{1−x}As

_{x}[28]. Therefore, the successful experimental realization of penta−NiN

_{2}provides a material basis for further study of relevant ternary systems.

_{2}monolayer using first−principles calculations. After careful stability analysis, we focused on electronic structures and adsorption properties for 12 kinds of common gases. Electronic property analysis showed that the penta−NiPN monolayer is a quasi−direct bandgap semiconductor (1.237 eV) with ultrahigh carrier mobility (up to 10

^{5}cm

^{2}V

^{−1}s

^{−1}). The results of gas adsorption revealed that the penta−NiPN monolayer exhibits good selectivity for NO and NO

_{2}, indicating its potential as a gas−sensitive material for NO and NO

_{2}.

## 2. Methods

^{−7}eV and 0.005 eV/Å per atom, respectively. For geometry optimization, a 12 × 12 × 1 and a 5 × 5 × 1 k−point grid, following the scheme of Monkhorst–Pack [35], was used to sample the Brillouin zones for unit cells of the penta−NiPN monolayer and the gas adsorption supercell model, respectively. Denser k−point grids were used for self−consistent and electronic property calculations. Grimme’s DFT–D2 [36] was adopted to describe the van der Waals (vdW) corrections in gas adsorption. A vacuum layer of 20 Å length was introduced into all models to avoid interactions between adjacent layers. Phonon dispersion for the new predicted penta−NiPN monolayer was performed using VASP and Phonopy code [37], based on density functional perturbation theory (DFPT). Additionally, ab initio molecular dynamics (AIMD) simulations lasting for 5 ps at room temperature were employed to evaluate the thermal stability of the penta−NiPN monolayer using a 4 × 4 × 1 supercell.

## 3. Results and Discussion

#### 3.1. Structure and Stability

_{2}P

_{2}N pentagons and Ni

_{2}PN

_{2}pentagons with a calculated lattice constant a/b of 4.995/5.011 Å (see Table 1). This value is larger than that of the penta−NiN

_{2}monolayer (4.53 Å) [17] and smaller than that of the penta−NiP

_{2}monolayer (5.55 Å) [22]. The penta−NiPN monolayer has lower symmetry (space group: Pb2

_{1}m, No.26) than a single element system (space group: P4/mbm, No.127) due to the existence of two non−metallic elements (N and P). As a result, two kinds of unequal Ni−N bonds and Ni−P bonds with bond lengths of 1.929/1.910 Å and 2.125/2.107 Å, respectively, exist in the penta−NiPN monolayer. The bond lengths in the penta−NiPN monolayer are between the lengths of the Ni−N and Ni−P bonds in the penta−NiN

_{2}monolayer (1.88 Å) and the penta−NiP

_{2}monolayer (2.16 Å). The N−P bond length in the penta−NiPN monolayer is 1.605 Å, while the N−N bond length and P−P bond length in penta−NiN

_{2}monolayer and penta−NiP

_{2}monolayer are 1.24 Å and 2.11 Å, respectively.

_{2}and −NiP

_{2}) or three elements cannot form a perfect pentagonal Cairo tile. Figure 1b shows the corresponding bond lengths and bond angles of Ni

_{2}N

_{3}, Ni

_{2}P

_{2}N/Ni

_{2}PN

_{2}, and Ni

_{2}P

_{3}pentagons in the penta−NiN

_{2}, NiPN, and NiP

_{2}monolayers. For the Ni

_{2}N

_{3}and Ni

_{2}P

_{3}pentagons, the corresponding bond angles of N−Ni−N (90°) and P−Ni−P (90.01°) coincide with the ideal pentagonal Cairo tile. However, among other bond angles, such as Ni−N(P)−N(P) and Ni−N(P)−Ni, the results largely deviate from the ideal pentagonal Cairo tile. Among pentagonal monolayers, the penta−NiPN monolayer is notably more complex than the penta−NiN

_{2}and −NiP

_{2}monolayers. Due to the introduction of two non−equivalent non−metallic elements, there exist non−equivalent pentagons (Ni

_{2}P

_{2}N and Ni

_{2}PN

_{2}) in the lattice (as seen in Figure 1b). Generally, the Ni

_{2}P

_{2}N and Ni

_{2}PN

_{2}pentagons undergo varying degrees of distortion compared to the ideal pentagonal Cairo tiling. Naturally, this atomic divergence leads to an array of unique characteristics in this predicted monolayer.

_{coh}), as another thermodynamic indicator, can evaluate the predicted system’s relative realizability under experimental conditions. The E

_{coh}of the penta−NiPN monolayer is defined as ${E}_{\mathrm{coh}}=\left(2{E}_{\mathrm{Ni}}+2{E}_{\mathrm{P}}+2{E}_{\mathrm{N}}-{E}_{\mathrm{NiPN}}\right)/6$, where ${E}_{\mathrm{Ni}}$/${E}_{\mathrm{P}}$/${E}_{\mathrm{N}}$ and ${E}_{\mathrm{NiPN}}$ are the energy of a single Ni/P/N atom and the total energy of penta−NiPN monolayer, respectively. According to the definition, a higher E

_{coh}value signifies greater stability. The calculated E

_{coh}of the penta−NiPN monolayer is 4.55 eV, which is higher than that of the NiP

_{2}monolayer (4.09 eV, 3.944 eV) [22,23], silicene (3.94 eV) [24], and phosphorene (3.477 eV) [38] but slightly lower than that of penta−NiN

_{2}(4.98 eV) [17]. As silicene and phosphorene have been obtained successfully in experiments, the high−realization potential of the penta−NiPN monolayer is likewise promising, especially considering that Bykov et al. [14] recently achieved a room−temperature stable penta−NiN

_{2}layer experimentally. Therefore, it is reasonable to anticipate the experimental realization of a penta−NiPN monolayer (such as via element substitution doping) in the near future.

_{11}, C

_{22}, C

_{12}, and C

_{66}are the independent elastic constants of the predicted monolayer. For the penta−NiPN monolayer, the calculated C

_{11}, C

_{22}, C

_{12}, and C

_{66}are 158.25 N m

^{−1}, 154.64 N m

^{−1}, 31.85 N m

^{−1}, and 41.22 N m

^{−1}, respectively. These values confirm that the predicted penta−NiPN monolayer in this work possesses good mechanical stability.

_{11}, C

_{22}, C

_{12}, and C

_{66}) above. The angle dependent in−plane Young’s modulus Y(θ) and Poisson’s ratio υ(θ) can be expressed as follows [40]:

_{2}and −NiP

_{2}monolayer. The maximum Young’s modulus is 151.69 N m

^{−1}along the x direction (Y

_{11}, θ = 0°/180°), while the Y

_{22}(148.23 N m

^{−1}, θ = 90°/270°) is slightly smaller than that of Y

_{11}. The minimum Young’s modulus is 114.66 N m

^{−1}along the diagonal direction (θ = 45°/135°/225°/315°). The Young’s modulus of the penta−NiPN monolayer is lower than that of the penta−NiN

_{2}monolayer (168.8 N m

^{−1}) [17], but higher or comparable to that of the penta−NiP

_{2}monolayer (122.19 N m

^{−1}) [22]. The corresponding Poisson’s ratio of the penta−NiPN monolayer is shown in Figure 2b. In contrast to the Young’s modulus, the minimum value of Poisson’s ratio is obtained in the axial direction υ

_{22}(θ = 90°/270°), where the value is 0.201, while υ

_{11}(0.206, θ = 0°/180°) is slightly higher than υ

_{22}. In addition, the penta−NiPN monolayer has a maximum Poisson’s ratio value of 0.391 in the diagonal direction (θ = 45°/135°/225°/315°). The minimum Poisson’s ratio of the penta−NiPN monolayer is much higher than that of the penta−NiN

_{2}monolayer (0.130) [17] but comparable to that of the penta−NiP

_{2}monolayer (0.22). Therefore, in general, the penta−NiPN monolayer is less stiff and more flexible than the penta−NiN

_{2}and −NiP

_{2}monolayers. With the intrinsic anisotropy of the penta−NiPN monolayer considered, it can be anticipated that penta−NiPN has a more diverse and adjustable set of mechanical properties than the penta−NiN

_{2}and −NiP

_{2}monolayers.

#### 3.2. Electronic Structure

_{2}and −NiP

_{2}monolayers, which exhibit direct bandgap features, the penta−NiPN monolayer is an indirect bandgap semiconductor with a bandgap value of 0.518/1.237 eV at the PBE/HSE06 level. As summarized in Table 1, the bandgap of the penta−NiPN monolayer is larger than that of the penta−NiN

_{2}(1.10 eV) and −NiP

_{2}(0.81 eV) monolayers. The valence band maximum (VBM) and conduction band minimum (CBM) of the penta−NiPN monolayer are both located near the S−point along the S−X direction, whereas for the penta−NiN

_{2}and −NiP

_{2}monolayers, the VBM and CBM are both located at the S−point. It should be noted that, although the penta−NiPN monolayer is an indirect bandgap semiconductor, the energy difference (ΔE) between its direct and indirect bandgaps is only 0.0013/0.0449 eV at the PBE/HSE06 level, making it a quasi−direct bandgap semiconductor. The combination of a suitable bandgap and quasi−direct band features in the penta−NiPN monolayer may have potential applications in optoelectronic devices.

^{*}, the deformation potential constant |E

_{il}|, and the elastic modulus C

_{2D}of the penta−NiPN monolayer, as summarized in Table 2. In addition, Figure 4 shows more details for the calculation of C

_{2D}and E

_{il}. Our calculations show that the effective masses m

^{*}of electrons and holes in the penta−NiPN monolayer along the a/b−direction are 0.38/0.36 m

_{e}and 0.22/0.24 m

_{e}, respectively, which are higher than those in the penta−NiP

_{2}monolayer (0.106/0.140 m

_{e}and 0.119/0.170 m

_{e}along the a/b−direction, respectively) [22]. Meanwhile, the deformation potential constant of the penta−NiPN monolayer is much smaller than that of penta−NiP

_{2}(2.10/0.85 eV vs. 5.23/5.23 eV; 0.74/0.99 eV vs. 1.53/1.53 eV), whereas the elastic constant of the penta−NiPN monolayer is larger than that of the penta−NiP

_{2}monolayer (147.68/146.24 N m

^{−1}vs. 118.19/118.19 N m

^{−1}). By combining the effective mass, deformation potential constant, and elastic constant, we calculated the carrier mobility of penta−NiPN monolayer. The obtained electron mobilities are 0.51 and 3.24 × 10

^{4}cm

^{2}V

^{−1}s

^{−1}along the a− and b−directions, respectively, whereas the hole mobility is even higher, reaching up to 11.36 and 5.76 × 10

^{4}cm

^{2}V

^{−1}s

^{−1}along a− and b−directions, respectively. These values are much higher than those of some typical 2D materials, such as MoS

_{2}(~49 to 200 cm

^{2}V

^{−1}s

^{−1}) [47], GaPS

_{4}(~14 to 1306 cm

^{2}V

^{−1}s

^{−1}) [40], and GeP

_{3}(~14 to 190 cm

^{2}V

^{−1}s

^{−1}) [48], and comparable to that of phosphorene (~10

^{4}cm

^{2}V

^{−1}s

^{−1}) [49] and penta−MX

_{2}(M = Ni, Pd, Pt; X = N, P, As, Sb; 10

^{3}~10

^{5}cm

^{2}V

^{−1}s

^{−1}) [22,23,24]. The suitable bandgap and ultra−high carrier mobility in the penta−NiPN monolayer make it promising for nanoelectronics and microelectronics.

#### 3.3. Gas Adsorption

_{2}[52]. On the other hand, penta−NiN

_{2}[21] and penta−PdAs

_{2}[27], which belong to the same family as the penta−NiPN proposed in this work, have proved to be very good gas−sensitive materials as well. Therefore, we believe that the gas−sensitive properties of the penta−NiPN monolayer are worth exploring. In this section, we focus on evaluating the potential applications of the penta−NiPN monolayer in gas sensors by exploring its gas adsorption properties. First, there are eight unequal adsorption sites in the penta−NiPN monolayer, as labeled in Figure 1f. These eight adsorption sites comprise the top site of the Ni/P/N atom (site 1/2/3), a bridge site located along the Ni−P/Ni−N/N−P bond (site 4/5/6), and a hollow site present in the Ni

_{2}P

_{2}N/Ni

_{2}PN

_{2}pentagon (site 7/8). For gases, we selected 12 typical gas molecules as the study objects, i.e., CO, CO

_{2}, CH

_{4}, H

_{2}, H

_{2}O, H

_{2}S, N

_{2}, NO, NO

_{2}, NH

_{3}, SO

_{2}, and O

_{2}. Our main reason for choosing H

_{2}O and O

_{2}was to evaluate the moisture sensitivity and oxidation resistance of the penta−NiPN monolayer, respectively. The remaining gases included greenhouse gases, toxic gases, or gases commonly found in the air.

_{2}, H

_{2}S, NO, NO

_{2}, NH

_{3}, and SO

_{2}. For CO

_{2}and N

_{2}, the top site of the N atom was more favorable. CH

_{4}tended to be adsorbed at the bridge site along the Ni−N bond, while H

_{2}O was adsorbed at the hollow site of the Ni

_{2}PN

_{2}pentagon. The most unusual case was during the adsorption of O

_{2}on the penta−NiPN monolayer, whereby it reacted directly with the substrate, leading to the dissociation of O

_{2}molecules into O atoms and ultimately forming a new material. However, for a reusable gas−sensitive material, it is necessary to have the ability to both adsorb and release gases. According to the results of O

_{2}adsorption on the penta−NiPN monolayer, this process is irreversible. Therefore, our findings indicate that the penta−NiPN monolayer may require an oxygen−free environment if used as a medium material for a gas sensor. We do not discuss the case of O

_{2}in the subsequent studies, considering the strong reactivity during the adsorption of oxygen and the penta−NiPN monolayer.

_{a}) and adsorption distance (d). The E

_{a}of gas adsorption on the penta−NiPN monolayer is defined as follows: ${E}_{\mathrm{a}}={E}_{\mathrm{NiPN}-\mathrm{gas}}-{E}_{\mathrm{NiPN}}-{E}_{\mathrm{gas}}$, where ${E}_{\mathrm{NiPN}-\mathrm{gas}}$, ${E}_{\mathrm{NiPN}}$, and ${E}_{\mathrm{gas}}$ are the total energy of the NiPN monolayer with gas adsorption, a pristine NiPN monolayer, and a single gas molecule, respectively. By definition, a negative E

_{a}implies that gas adsorption is an exothermic process and can be spontaneous. Conversely, if the E

_{a}value is positive, the process is endothermic and non−spontaneous. The magnitude of the absolute value determines the likelihood of the reaction. The adsorption distance d refers to the minimum distance between the gas molecule and the substrate at the optimal adsorption site. We conducted a statistical analysis of E

_{a}and d for 11 gases adsorbed on the penta−NiPN monolayer, as shown in Figure 6 and Table 3. For the 11 gases studied, the adsorption energy on the NiPN monolayer is negative (−1.011 to −0.072 eV), indicating that all adsorption could be spontaneous. Furthermore, the absolute values of adsorption energy are in the order of $\left|{E}_{a}^{{\mathrm{NO}}_{2}}\right|>\left|{E}_{a}^{\mathrm{NO}}\right|>\left|{E}_{a}^{\mathrm{CO}}\right|>\left|{E}_{a}^{{\mathrm{NH}}_{3}}\right|>\left|{E}_{a}^{{\mathrm{SO}}_{2}}\right|>\left|{E}_{a}^{{\mathrm{H}}_{2}\mathrm{S}}\right|>\left|{E}_{a}^{{\mathrm{H}}_{2}\mathrm{O}}\right|>\left|{E}_{a}^{{\mathrm{CO}}_{2}}\right|>\left|{E}_{a}^{{\mathrm{CH}}_{4}}\right|>\left|{E}_{a}^{{\mathrm{N}}_{2}}\right|>\left|{E}_{a}^{{\mathrm{H}}_{2}}\right|$. The largest was $\left|{E}_{a}^{{\mathrm{NO}}_{2}}\right|$ (1.011 eV), followed by $\left|{E}_{a}^{\mathrm{NO}}\right|$= 0.751 eV, indicating that the penta−NiPN monolayer is an excellent trapping material for these two gases. On the other hand, H

_{2}and N

_{2}exhibited very small adsorption energy values (0.072 eV and 0.100 eV), suggesting that they are challenging to capture in normal environments. Regarding the adsorption distances, the values ranged from 1.834 Å (CO) to 3.117 Å (N

_{2}). The adsorption distances for NO and NO

_{2}are 1.862 Å and 2.065 Å, respectively, which are shorter than the values observed for NO and NO

_{2}absorption on the penta−NiN

_{2}monolayer (2.190 Å and 2.124 Å) [21]. Adsorption energy and distance can characterize the strength or weakness of interactions between gas molecules and host materials. Our results show that six gas molecules, including CO, H

_{2}S, NO, NO

_{2}, NH

_{3}, and SO

_{2}, had relatively strong interactions with the penta−NiPN monolayer.

_{2}, CH

_{4}, H

_{2}, H

_{2}O, N

_{2}, and the host material showed very little charge transfer (< 0.1 e), indicating weak interactions that can be neglected. The remaining six gas molecules can be categorized into two classes, depending on the direction of charge transfer between them and the penta−NiPN monolayer. The first class comprised electron donors, such as H

_{2}S and NH

_{3}, which donated electrons (−0.100 e and −0.103 e, respectively) to the penta−NiPN monolayer, with the corresponding Q < 0. In contrast, the second class comprised electron acceptors, such as CO, NO, NO

_{2}, and SO

_{2}. For these four gas molecules, the electrons transferred from the host material to the gas molecules during the absorption process. CO and SO

_{2}both obtained 0.100 e and 0.187 e, respectively, which were lower than NO (0.216 e) and NO

_{2}(0.553 e). Therefore, in comparison with other gas molecules, NO and NO

_{2}exhibited higher adsorption energy and larger charge transfer during adsorption, suggesting that these gases are more easily adsorbed on the penta−NiPN monolayer, with stronger coupling between them and the host material. Taken together, these results indicate that penta−NiPN monolayer may be a promising material for sensing NO and NO

_{2}gases.

_{2}adsorbed penta−NiPN monolayers with residual magnetic moments (M), all the other adsorbed systems were nonmagnetic. Therefore, we present only the results of NO and NO

_{2}, considering spin polarization in the latter electronic structures. When nonmagnetic molecules, such as CO, CO

_{2}, CH

_{4}, H

_{2}, H

_{2}O, H

_{2}S, N

_{2}, NH

_{3}, and SO

_{2}, were adsorbed, the system remained a nonmagnetic semiconductor with various bandgaps (see Figure 8). The results of PDOS indicated that the orbital hybridization between the gas molecules and the host material was weak or almost non−existent after the adsorption of nine nonmagnetic molecules. Most significantly, the orbital energy levels of gas molecules were primarily in the deep valence band and were distant from the Fermi level (see Figure 8).

_{2}molecules (1.00 µB) could transform the penta−NiPN monolayer into a magnetic semiconductor. After the adsorption of NO and NO

_{2}on the penta−NiPN monolayer, the magnetic moment of NO and NO

_{2}was reduced to 0.604 µB and 0.242 µB, respectively. At the same time, the magnetic moment of 0.091 µB and 0.636 µB was introduced into the host material penta−NiPN monolayer, resulting in a total magnetic moment of 0.695 µB and 0.878 µB, respectively, in each system (see Table 3). Therefore, the penta−NiPN monolayer can be electrically and magnetically sensitive to both NO and NO

_{2}molecules. In Figure 9, we have plotted the spin−dependent PDOS for the NO and NO

_{2}adsorbed systems with various energy ranges, respectively. For the NO adsorbed system, there were electronic states (spin−up DOS) just below the Fermi energy, which contributed to the orbital hybridization between the penta−NiPN monolayer and the NO molecule. Similarly, electron states were introduced into the NO

_{2}adsorbed system, but unlike the NO condition, the electron state in NO

_{2}was mainly below the conduction band. Clearly, the adsorption of NO and NO

_{2}on the surface of the penta−NiPN monolayer induced strong coupling between the gas molecules and the host material. Due to the strong orbital coupling between them, a significant charge transfer occurred. Moreover, the strong adsorption interaction also provided a large magnitude of adsorption energy.

_{2}by the penta−NiPN monolayer introduced electronic states or impurity levels near the Fermi level or the bottom of the conduction band, directly affecting the electronic transmission properties of the system. This change in electron transport characteristics is manifested as resistance drift in the system. Therefore, gas sensing can be achieved by measuring resistance changes with and without gas adsorption. Figure 10 shows a schematic diagram of a gas sensor based on the penta−NiPN monolayer. When a bias voltage is introduced at the right/left electrode, specific recognition is achieved through the current−voltage curve, reflecting the difference in electronic transmission properties after the adsorption of different gas molecules [21]. However, as the penta−NiPN monolayer serves as the host material for gas sensing, it must be used in an oxygen−free environment. Otherwise, there may be irreversible reactions between the penta−NiPN monolayer and atmospheric oxygen.

## 4. Conclusions

^{5}cm

^{2}V

^{−1}s

^{−1}in the penta−NiPN monolayer based on deformation potential theory. Moreover, we systematically studied the adsorption properties of 12 common gas molecules (CO, CO

_{2}, CH

_{4}, H

_{2}, H

_{2}O, H

_{2}S, N

_{2}, NO, NO

_{2}, NH

_{3}, O

_{2}, and SO

_{2}) on the surface of the penta−NiPN monolayer. Our results show that the penta−NiPN monolayer exhibits good selectivity for NO and NO

_{2}, and has the potential to be used as a sensor for these two gases. Overall, our findings suggest that the penta−NiPN monolayer is a desirable candidate for high−performance electronic devices, as well as NO and NO

_{2}gas sensors.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Feng, S.; Farha, F.; Li, Q.; Wan, Y.; Xu, Y.; Zhang, T.; Ning, H. Review on Smart Gas Sensing Technology. Sensors
**2019**, 19, 3760. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mamom, J.; Ratanadecho, P.; Mingmalairak, C.; Rungroungdouyboon, B. Humidity−Sensing Mattress for Long−Term Bedridden Patients with Incontinence−Associated Dermatitis. Micromachines
**2023**, 14, 1178. [Google Scholar] [CrossRef] [PubMed] - Marti, E.; De Miguel, M.A.; Garcia, F.; Perez, J. A Review of Sensor Technologies for Perception in Automated Driving. IEEE Intell. Transp. Syst. Mag.
**2019**, 11, 94–108. [Google Scholar] [CrossRef] [Green Version] - Tyagi, D.; Wang, H.; Huang, W.; Hu, L.; Tang, Y.; Guo, Z.; Ouyang, Z.; Zhang, H. Recent Advances in Two−Dimensional−Material−Based Sensing Technology toward Health and Environmental Monitoring Applications. Nanoscale
**2020**, 12, 3535–3559. [Google Scholar] [CrossRef] - Zhang, L.; Khan, K.; Zou, J.; Zhang, H.; Li, Y. Recent Advances in Emerging 2D Material-Based Gas Sensors: Potential in Disease Diagnosis. Adv. Mater. Interfaces
**2019**, 6, 1901329. [Google Scholar] [CrossRef] - Buckley, D.J.; Black, N.C.G.; Castanon, E.G.; Melios, C.; Hardman, M.; Kazakova, O. Frontiers of Graphene and 2D Material−Based Gas Sensors for Environmental Monitoring. 2D Mater.
**2020**, 7, 032002. [Google Scholar] [CrossRef] - Yang, S.; Jiang, C.; Wei, S. Gas Sensing in 2D Materials. Appl. Phys. Rev.
**2017**, 4, 021304. [Google Scholar] [CrossRef] - Ou, J.Z.; Ge, W.; Carey, B.; Daeneke, T.; Rotbart, A.; Shan, W.; Wang, Y.; Fu, Z.; Chrimes, A.F.; Wlodarski, W.; et al. Physisorption−Based Charge Transfer in Two−Dimensional SnS
_{2}for Selective and Reversible NO_{2}Gas Sensing. ACS Nano**2015**, 9, 10313–10323. [Google Scholar] [CrossRef] - Qin, Z.; Song, X.; Wang, J.; Li, X.; Wu, C.; Wang, X.; Yin, X.; Zeng, D. Development of Flexible Paper Substrate Sensor Based on 2D WS
_{2}with S Defects for Room−Temperature NH_{3}Gas Sensing. Appl. Surf. Sci.**2022**, 573, 151535. [Google Scholar] [CrossRef] - Liu, X.; Ma, T.; Pinna, N.; Zhang, J. Two−Dimensional Nanostructured Materials for Gas Sensing. Adv. Funct. Mater.
**2017**, 27, 1702168. [Google Scholar] [CrossRef] - Thomas, S.; Asle Zaeem, M. Superior Sensing Performance of Two−Dimensional Ruthenium Carbide (2D−RuC) in Detection of NO, NO
_{2}and NH_{3}Gas Molecules. Appl. Surf. Sci.**2021**, 563, 150232. [Google Scholar] [CrossRef] - Hakimi Raad, N.; Manavizadeh, N.; Frank, I.; Nadimi, E. Gas Sensing Properties of a Two−Dimensional Graphene/h−BN Multi−Heterostructure toward H
_{2}O, NH_{3}and NO_{2}: A First Principles Study. Appl. Surf. Sci.**2021**, 565, 150454. [Google Scholar] [CrossRef] - Aasi, A.; Mortazavi, B.; Panchapakesan, B. Two−Dimensional PdPS and PdPSe Nanosheets: Novel Promising Sensing Platforms for Harmful Gas Molecules. Appl. Surf. Sci.
**2022**, 579, 152115. [Google Scholar] [CrossRef] - Bykov, M.; Bykova, E.; Ponomareva, A.V.; Tasnádi, F.; Chariton, S.; Prakapenka, V.B.; Glazyrin, K.; Smith, J.S.; Mahmood, M.F.; Abrikosov, I.A.; et al. Realization of an Ideal Cairo Tessellation in Nickel Diazenide NiN
_{2}: High−Pressure Route to Pentagonal 2D Materials. ACS Nano**2021**, 15, 13539–13546. [Google Scholar] [CrossRef] - Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Zhang, Y.; Dubonos, S.V.; Grigorieva, I.V.; Firsov, A.A. Electric Field Effect in Atomically Thin Carbon Films. Science
**2004**, 306, 666–669. [Google Scholar] [CrossRef] [Green Version] - Li, L.; Yu, Y.; Ye, G.J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X.H.; Zhang, Y. Black Phosphorus Field−Effect Transistors. Nat. Nanotechnol.
**2014**, 9, 372–377. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yuan, J.-H.; Song, Y.-Q.; Chen, Q.; Xue, K.-H.; Miao, X.-S. Single−Layer Planar Penta−X
_{2}N_{4}(X = Ni, Pd and Pt) as Direct−Bandgap Semiconductors from First Principle Calculations. Appl. Surf. Sci.**2019**, 469, 456–462. [Google Scholar] [CrossRef] - Mortazavi, B.; Zhuang, X.; Rabczuk, T.; Shapeev, A.V. Outstanding Thermal Conductivity and Mechanical Properties in the Direct Gap Semiconducting Penta−NiN
_{2}Monolayer Confirmed by First−Principles. Phys. E Low−Dimens. Syst. Nanostructures**2022**, 140, 115221. [Google Scholar] [CrossRef] - Hu, Y.; Zhao, X.; Yang, Y.; Xiao, W.; Zhou, X.; Wang, D.; Wang, G.; Bi, J.; Luo, Z.; Liu, X. Coordination Engineering on Novel 2D Pentagonal NiN
_{2}for Bifunctional Oxygen Electrocatalysts. Appl. Surf. Sci.**2023**, 614, 156256. [Google Scholar] [CrossRef] - Zhang, C.; Sun, J.; Shen, Y.; Kang, W.; Wang, Q. Effect of High Order Phonon Scattering on the Thermal Conductivity and Its Response to Strain of a Penta−NiN
_{2}Sheet. J. Phys. Chem. Lett.**2022**, 13, 5734–5741. [Google Scholar] [CrossRef] [PubMed] - Li, M.; Wang, X.-F. Adsorption Behaviors of Small Molecules on Two−Dimensional Penta−NiN
_{2}Layers: Implications for NO and NO_{2}Gas Sensors. ACS Appl. Nano Mater.**2023**, 6, 6151–6160. [Google Scholar] [CrossRef] - Yuan, J.-H.; Zhang, B.; Song, Y.-Q.; Wang, J.-F.; Xue, K.-H.; Miao, X.-S. Planar Penta−Transition Metal Phosphide and Arsenide as Narrow−Gap Semiconductors with Ultrahigh Carrier Mobility. J. Mater. Sci.
**2019**, 54, 7035–7047. [Google Scholar] [CrossRef] [Green Version] - Qian, S.; Sheng, X.; Xu, X.; Wu, Y.; Lu, N.; Qin, Z.; Wang, J.; Zhang, C.; Feng, E.; Huang, W.; et al. Penta−MX
_{2}(M = Ni, Pd and Pt; X = P and As) Monolayers: Direct Band−Gap Semiconductors with High Carrier Mobility. J. Mater. Chem. C**2019**, 7, 3569–3575. [Google Scholar] [CrossRef] - Liu, Z.; Wang, H.; Sun, J.; Sun, R.; Wang, Z.F.; Yang, J. Penta−Pt
_{2}N_{4}: An Ideal Two−Dimensional Material for Nanoelectronics. Nanoscale**2018**, 10, 16169–16177. [Google Scholar] [CrossRef] [PubMed] - Shao, X.; Liu, X.; Zhao, X.; Wang, J.; Zhang, X.; Zhao, M. Electronic Properties of a π−Conjugated Cairo Pentagonal Lattice: Direct Band Gap, Ultrahigh Carrier Mobility, and Slanted Dirac Cones. Phys. Rev. B
**2018**, 98, 085437. [Google Scholar] [CrossRef] [Green Version] - Shao, X.; Sun, L.; Ma, X.; Feng, X.; Gao, H.; Ding, C.; Zhao, M. Multiple Dirac Cones and Lifshitz Transition in a Two−Dimensional Cairo Lattice as a Hawking Evaporation Analogue. J. Phys. Condens. Matter
**2021**, 33, 365001. [Google Scholar] [CrossRef] - Raval, D.; Gupta, S.K.; Gajjar, P.N. Detection of H
_{2}S, HF and H_{2}Pollutant Gases on the Surface of Penta−PdAs_{2}Monolayer Using DFT Approach. Sci. Rep.**2023**, 13, 699. [Google Scholar] [CrossRef] [PubMed] - He, Y.; Xiong, S.; Xia, F.; Shao, Z.; Zhao, J.; Zhang, X.; Jie, J.; Zhang, X. Tuning the Electronic Transport Anisotropy in α−Phase Phosphorene through Superlattice Design. Phys. Rev. B
**2018**, 97, 085119. [Google Scholar] [CrossRef] - Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total−Energy Calculations Using a Plane−Wave Basis Set. Phys. Rev. B
**1996**, 54, 11169–11186. [Google Scholar] [CrossRef] - Kresse, G.; Furthmüller, J. Efficiency of Ab−Initio Total Energy Calculations for Metals and Semiconductors Using a Plane−Wave Basis Set. Comput. Mater. Sci.
**1996**, 6, 15–50. [Google Scholar] [CrossRef] - Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev.
**1964**, 136, B864–B871. [Google Scholar] [CrossRef] [Green Version] - Kohn, W.; Sham, L.J. Self−Consistent Equations Including Exchange and Correlation Effects. Phys. Rev.
**1965**, 140, A1133–A1138. [Google Scholar] [CrossRef] [Green Version] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett.
**1996**, 77, 3865–3868. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Krukau, A.V.; Vydrov, O.A.; Izmaylov, A.F.; Scuseria, G.E. Influence of the Exchange Screening Parameter on the Performance of Screened Hybrid Functionals. J. Chem. Phys.
**2006**, 125, 224106. [Google Scholar] [CrossRef] [PubMed] - Monkhorst, H.J.; Pack, J.D. Special Points for Brillouin−Zone Integrations. Phys. Rev. B
**1976**, 13, 5188–5192. [Google Scholar] [CrossRef] - Grimme, S. Semiempirical GGA−Type Density Functional Constructed with a Long−Range Dispersion Correction. J. Comput. Chem.
**2006**, 27, 1787–1799. [Google Scholar] [CrossRef] - Togo, A.; Oba, F.; Tanaka, I. First−Principles Calculations of the Ferroelastic Transition between Rutile−Type and CaCl
_{2}−Type SiO_{2}at High Pressures. Phys. Rev. B**2008**, 78, 134106. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Wu, Z.-F.; Gao, P.-F.; Fang, D.-Q.; Zhang, E.-H.; Zhang, S.-L. Structural, Elastic, Electronic, and Optical Properties of the Tricycle−like Phosphorene. Phys. Chem. Chem. Phys.
**2017**, 19, 2245–2251. [Google Scholar] [CrossRef] - Born, M.; Huang, K. Dynamical Theory of Crystal Lattices; Clarendon Press: Oxford, UK, 1954. [Google Scholar]
- Yuan, J.-H.; Xue, K.-H.; Wang, J.-F.; Miao, X.-S. Gallium Thiophosphate: An Emerging Bidirectional Auxetic Two−Dimensional Crystal with Wide Direct Band Gap. J. Phys. Chem. Lett.
**2019**, 10, 4455–4462. [Google Scholar] [CrossRef] - Becke, A.D.; Edgecombe, K.E. A Simple Measure of Electron Localization in Atomic and Molecular Systems. J. Chem. Phys.
**1990**, 92, 5397–5403. [Google Scholar] [CrossRef] - Savin, A.; Jepsen, O.; Flad, J.; Andersen, O.K.; Preuss, H.; von Schnering, H.G. Electron Localization in Solid−State Structures of the Elements: The Diamond Structure. Angew. Chem. Int. Ed. Engl.
**1992**, 31, 187–188. [Google Scholar] [CrossRef] - Tang, W.; Sanville, E.; Henkelman, G. A Grid−Based Bader Analysis Algorithm without Lattice Bias. J. Phys. Condens. Matter
**2009**, 21, 084204. [Google Scholar] [CrossRef] - Bardeen, J.; Shockley, W. Deformation Potentials and Mobilities in Non−Polar Crystals. Phys. Rev.
**1950**, 80, 72–80. [Google Scholar] [CrossRef] - Yuan, J.-H.; Xue, K.-H.; Miao, X. Two−Dimensional ABC
_{3}(A = Sc, Y; B = Al, Ga, In; C = S, Se, Te) with Intrinsic Electric Field for Photocatalytic Water Splitting. Int. J. Hydrog. Energy**2023**, 48, 5929–5939. [Google Scholar] [CrossRef] - Yuan, J.-H.; Xue, K.-H.; Wang, J.; Miao, X. Designing Stable 2D Materials Solely from VIA Elements. Appl. Phys. Lett.
**2021**, 119, 223101. [Google Scholar] [CrossRef] - Cai, Y.; Zhang, G.; Zhang, Y.-W. Polarity−Reversed Robust Carrier Mobility in Monolayer MoS
_{2}Nanoribbons. J. Am. Chem. Soc.**2014**, 136, 6269–6275. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jing, Y.; Ma, Y.; Li, Y.; Heine, T. GeP
_{3}: A Small Indirect Band Gap 2D Crystal with High Carrier Mobility and Strong Interlayer Quantum Confinement. Nano Lett.**2017**, 17, 1833–1838. [Google Scholar] [CrossRef] [Green Version] - Jiang, J.-W.; Park, H.S. Negative Poisson’s Ratio in Single−Layer Black Phosphorus. Nat. Commun.
**2014**, 5, 4727. [Google Scholar] [CrossRef] [Green Version] - Cheng, M.-Q.; Chen, Q.; Yang, K.; Huang, W.-Q.; Hu, W.-Y.; Huang, G.-F. Penta−Graphene as a Potential Gas Sensor for NO
_{x}Detection. Nanoscale Res. Lett.**2019**, 14, 306. [Google Scholar] [CrossRef] [Green Version] - Wei, M.; Dou, X.; Zhao, L.; Du, J.; Jiang, G. Monolayer Penta−BCN: A Promising Candidate for Harmful Gases Detection. Sens. Actuators Phys.
**2022**, 334, 113326. [Google Scholar] [CrossRef] - Jiang, X.; Zhang, G.; Yi, W.; Yang, T.; Liu, X. Penta−BeP
_{2}Monolayer: A Superior Sensor for Detecting Toxic Gases in the Air with Excellent Sensitivity, Selectivity, and Reversibility. ACS Appl. Mater. Interfaces**2022**, 14, 35229–35236. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**a**) Top and side views of the penta−NiPN monolayer; the unit cell is marked by a red border. (

**b**) Geometry of single ideal (pentagonal Cairo tiling) Ni

_{2}N

_{3}, Ni

_{2}P

_{2}N, Ni

_{2}PN

_{2}, and Ni

_{2}P

_{3}pentagons. Numbers indicate interatomic distances (Å) and bond angles (deg). (

**c**) The Brillouin zone of the penta−NiPN monolayer. (

**d**) The phonon dispersion and corresponding phonon DOS of the penta−NiPN monolayer. (

**e**) The AIMD simulation results of the penta−NiPN monolayer at 300 K; the insert is the initial and final structure of the penta−NiPN monolayer. (

**f**) The eight adsorption sites have been labeled in the diagram.

**Figure 3.**Calculated (

**a**) electronic band structures and (

**b**) DOS, as well as PDOS, of the penta−NiPN monolayer at the HSE06 level. (

**c**) Spatial distributions of the wave functions corresponding to the VBM and CBM of the penta−NiPN monolayer at the GGA–PBE level. The charge contour density is 0.01 e/Å

^{3}. (

**d**) Calculated ELF of the penta−NiPN monolayer.

**Figure 4.**(

**a**) The relationship between the total energy and the applied strain (Δl/l

_{0}) along the a/b direction of the penta−NiPN monolayer. (

**b**) The shift of VBMs and CBMs for the penta−NiPN monolayer with respect to the vacuum energy under the applied strain along the a/b direction. All the calculations are at the GGA–PBE level.

**Figure 5.**Top and side views of the most favorable adsorption configurations for (

**a**) CO, (

**b**) CO

_{2}, (

**c**) CH

_{4}, (

**d**) H

_{2}, (

**e**) H

_{2}O, (

**f**) H

_{2}S, (

**g**) N

_{2}, (

**h**) NO, (

**i**) NO

_{2}, (

**j**) NH

_{3}, (

**k**) SO

_{2}, and (

**l**) O

_{2}on the penta−NiPN monolayer.

**Figure 6.**The calculated adsorption energy and adsorption distance for CO, CO

_{2}, CH

_{4}, H

_{2}, H

_{2}O, H

_{2}S, N

_{2}, NO, NO

_{2}, NH

_{3}, and SO

_{2}on the penta−NiPN monolayer.

**Figure 7.**The charge density differences between (

**a**) CO, (

**b**) CO

_{2}, (

**c**) CH

_{4}, (

**d**) H

_{2}, (

**e**) H

_{2}O, (

**f**) H

_{2}S, (

**g**) N

_{2}, (

**h**) NO, (

**i**) NO

_{2}, (

**j**) NH

_{3}, and (

**k**) SO

_{2}gas molecules and the penta−NiPN monolayer. The equivalent surface was 0.012 e/Å

^{3}, and the electron accumulation (loss) is represented by yellow (blue). In addition, the direction of charge transfer (represented by arrows) and the amount of charge transfer are marked.

**Figure 8.**The PDOS (based on HSE06 functional) from the gas molecules are plotted together for the penta−NiPN monolayer with the adsorbed molecules (

**a**) CO, (

**b**) CO

_{2}, (

**c**) CH

_{4}, (

**d**) H

_{2}, (

**e**) H

_{2}O, (

**f**) H

_{2}S, (

**g**) N

_{2}, (

**h**) NH

_{3}, and (

**i**) SO

_{2}. Only the spin−up DOS is shown in spin–degenerate systems. The X represents nitrogen atoms.

**Figure 9.**The PDOS (based on HSE06 functional) from the gas molecules are plotted for the penta−NiPN monolayer with the adsorbed molecules (

**a**) NO and (

**b**) NO

_{2}. The corresponding enlarged PDOS results of (

**c**) NO and (

**d**) NO

_{2}are given as well. The spin−up and spin−down DOS are shown as positive and negative, respectively. The X represents nitrogen atoms.

**Table 1.**Calculated lattice constant a/b, bond length l, cohesive energy E

_{coh}, and bandgap E

_{g}(based on HSE06 functional) of the penta−NiPN monolayer.

Materials | a (Å) | b (Å) | l_{Ni−N} (Å) | l_{Ni−P} (Å) | l_{N−N}/l_{N−P}/l_{P−P} (Å) | E_{coh} (eV) | E_{g} (eV) |
---|---|---|---|---|---|---|---|

NiPN NiN _{2} [17]NiP _{2} [22] | 4.995 4.53 5.55 | 5.011 4.53 5.55 | 1.929, 1.910 1.88 −− | 2.125, 2.107 −− 2.16 | 1.605 1.24 2.11 | 4.55 4.98 4.09 | 1.237 1.10 0.81 |

**Table 2.**Calculated m

^{*}(unit: m

_{e}), |E

_{il}| (unit: eV), C

_{2D}(unit: N m

^{−1}), and μ

_{2D}(unit: 10

^{4}cm

^{2}V

^{−1}s

^{−1}) for the penta−NiPN monolayer along the a and b directions.

Materials | Carrier Type | m_{a}^{*} | m_{b}^{*} | |E_{la}| | |E_{lb}| | C_{a}^{2D} | C_{b}^{2D} | μ_{a}^{2D} | μ_{b}^{2D} |
---|---|---|---|---|---|---|---|---|---|

NiPN | Electron | 0.38 | 0.36 | 2.10 | 0.85 | 147.68 | 146.24 | 0.51 | 3.24 |

Hole | 0.22 | 0.24 | 0.74 | 0.99 | 147.68 | 146.24 | 11.36 | 5.76 | |

NiP_{2} [22] | Electron | 0.106 | 0.140 | 5.23 | 5.23 | 118.19 | 118.19 | 0.71 | 0.54 |

Hole | 0.119 | 0.170 | 1.53 | 1.53 | 118.19 | 118.19 | 6.35 | 4.45 |

**Table 3.**Calculated adsorption energy (E

_{a}), adsorption distance (d), magnetic moment (M), and charge transfer (Q) between the gas molecules and the penta−NiPN monolayer. Here, “+” and “−” represent gained and lost electrons, respectively.

Gas Molecules | E_{a} (eV) | d (Å) | $\mathit{M}({\mathit{\mu}}_{\mathit{B}}$ | Q (e) |
---|---|---|---|---|

CO CO _{2}CH _{4}H _{2}H _{2}OH _{2}SN _{2}NO NO _{2}NH _{3}SO _{2} | −0.640 −0.184 −0.162 −0.072 −0.272 −0.316 −0.100 −0.751 −1.011 −0.545 −0.445 | 1.834 3.054 2.661 2.613 2.248 2.210 3.117 1.862 2.065 2.119 2.573 | 0 0 0 0 0 0 0 0.695 0.878 0 0 | +0.100 +0.026 +0.010 +0.011 +0.025 −0.100 +0.015 +0.216 +0.553 −0.103 +0.187 |

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**MDPI and ACS Style**

Wang, H.; Li, G.; Yuan, J.-H.; Wang, J.; Zhang, P.; Shan, Y.
Two−Dimensional Planar Penta−NiPN with Ultrahigh Carrier Mobility and Its Potential Application in NO and NO_{2} Gas Sensing. *Micromachines* **2023**, *14*, 1407.
https://doi.org/10.3390/mi14071407

**AMA Style**

Wang H, Li G, Yuan J-H, Wang J, Zhang P, Shan Y.
Two−Dimensional Planar Penta−NiPN with Ultrahigh Carrier Mobility and Its Potential Application in NO and NO_{2} Gas Sensing. *Micromachines*. 2023; 14(7):1407.
https://doi.org/10.3390/mi14071407

**Chicago/Turabian Style**

Wang, Hao, Gang Li, Jun-Hui Yuan, Jiafu Wang, Pan Zhang, and Yahui Shan.
2023. "Two−Dimensional Planar Penta−NiPN with Ultrahigh Carrier Mobility and Its Potential Application in NO and NO_{2} Gas Sensing" *Micromachines* 14, no. 7: 1407.
https://doi.org/10.3390/mi14071407