Germanene: a new electronic gas sensing material

Abstract

The structural stability and electronic properties of the adsorption characteristics of several toxic gas molecules (NH₃, SO₂ and NO₂) on a hexagonal armchair of a germanene monolayer were investigated using density functional theory (DFT) based on an ab initio method. The sensitivity of the germanene monolayer has been investigated by considering the most stable adsorption configurations, adsorption energies, projected density of states and charge transfer between the monolayer and gas molecules. The adsorption energy of NO₂ gas molecules on the germanene monolayer was the lowest energy (273.72 meV: B-type configuration) compared to all other possible configurations and also higher than that of NH₃ and SO₂. The charge transfer between the NO₂ gas molecules and the germanene is the same order of magnitude, but larger than compared to that of NH₃ and SO₂ gas molecules. The higher charge transfer between the monolayer and gas molecules shows that this configuration can be utilized in germanene based field effect transistor (FET) sensors due to its greater stability and sensitivity.

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1. Introduction

In general, toxic gases such as oxynitrides (NO_x), sulfur dioxide (SO₂), ammonia (NH₃), and carbon monoxide (CO) are the origin of acid rains and cause serious diseases so it is important to invigilate gas molecules for both industrial and civilian purposes.¹ In present times, gas sensing has become a necessary field of continuous research and the detection of toxic gases is extremely important since the lives of living beings are at stake.^2,3 In industries, power plants, domestic homes, and in the environment, a very small amount of toxic gas leakage can cause hazardous effects, which could finally lead to death. Due to these effects, the detection of toxic gas is of significant importance. For the detection of different types of toxic gases, some researchers have worked on solid state gas sensing materials due to their good sensitivity and low power consumption. More recently, the transition metal dichalcogenide (TMDs) nanomaterials offer unique advantages as potential sensing materials^4,5 because of their very high surface-to-bulk ratios. In particular, the semiconducting material MoS₂ shows extraordinarily physicochemical property as it has been confirmed that it is capable of detecting gases.^6,7 Furthermore, improvements and modifications in the capacity of gas sensors have deep implications. A significant stem of materials can be changed due to different adopted configurations. According to those changes, similar to the introduction of the dopant,⁸ defect,^9,10 and changes in curvature,¹⁰ we can change the sensitivity or stability of several sensors.

In the recent years have rapid progress in the synthesis, characterization, electronics industries and applications, the research community has to spend much more effort on investigating new materials with specific properties, which render application in electronic devices. Among the new advanced materials, 2D monolayer nanomaterial structures are considered as a breakthrough because of their ultrathin size and amazing electronic characteristics, which have vast applications in electronic and spintronic devices, nanomagnetic devices, and gas sensors. Since the discovery of two-dimensional (2D) monolayer graphene, there has been considerable interest in two-dimensional (2D) materials because of potential applications in nanoelectronics and electrochemical devices.^11,12 For example, graphene has been suggested for applications in energy storage and conversion, electrochemistry, bio-sensing, environmental remediation, flame retardation and membrane separation.^13,14 In addition to graphene, other 2D materials yielded numerous graphene-like layered materials, such as BN, silicene and transition metal dichalcogenides, with fascinating properties complementary to graphene.¹⁵ Confined to a small space, quasi-particles, such as electrons, holes, excitons and phonons in atomically thin 2D materials, can give rise to novel electronic and photonic behaviors and phenomena distinctively different compared to bulk.¹⁶

Furthermore, in addition to studies on the group-IV monolayer nanomaterials composed of carbon (C),¹⁷ silicon (Si)¹⁸ and germanium (Ge),¹⁹ researchers have also studied their corresponding hydride analogues such as graphane (CH),²⁰ silicane (SiH)²¹ and germanane (GeH).²² Luo et al.²³ determined the structural and electronic properties of single-layer, few-layer, and multilayer GeH and the chair GeH structure is the most stable structure among all uncovered single layer GeH structures, which is similar to what has been obtained for CH and SiH. There are some theoretical investigations that describe the influence of various gas molecules on several surfaces such as MoS₂ by S. Zhao et al.,²⁴ boron nitride by Srivastava et al.,²⁵ WS₂ monolayer by Bui et al.,²⁶ and silicene by Chandiramouli et al.²⁷ for applications in gas sensors.

To fully reveal the possibilities of germanene based sensors, it is important and necessary to understand the interaction between the germanene monolayer and the adsorbate gas molecules. We performed first-principles calculations based on density functional theory (DFT) for NH₃, NO₂, and SO₂ molecules adsorbed on the armchair structure of the germanene monolayer. We obtained their exact orientation and arrangement on the surface and their most preferred binding site by investigating their adsorption energy. Their charge transfer to the germanene monolayer was investigated in order to determine the donor or acceptor character of the molecular dopant. We have also investigated the effects of the presence of the NH₃, SO₂ and NO₂ molecules near germanene (GeH) and optimized the quality of the interactions. According to this, we carried out a theoretical investigation to obtain the effects of gas molecules (NH₃, SO₂ and NO₂) interacting on the germanene and investigated the pictorial insights of the electronic structures based on the data obtained.

2. Computational details

As mentioned above, the mechanisms of the common toxic gas molecules (NH₃, SO₂ and NO₂) adsorbed onto a GeH monolayer have been investigated by employing the Quantum Espresso (QE) package²⁸ performed within the DFT framework. The effects of the correlation and exchange of the electrons were handled using the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE).²⁹ The electron-ion interactions were conducted using the pseudopotentials method.^30,31 van der Waals (vdW) interactions were confirmed by including a rectification to the GGA functionals, when connected, with the vdW-DF2 functionals.³² These exchange-correlation functionals were utilized for expanded precision as a part of assessing the harmonic partitions, strengths of the gas molecules, and van der Waals' interactions at intermediate separation longer than balance ones .³² Up to the kinetic energy cutoff of 60 Ry, the electron wave functions were expanded into planar waves. A 12 × 12 × 1 Monkhorst–Pack mesh³³ was used to generate the k-points in the unit cell. To calculate the structural, electronic, and charge transfer properties of chair structure monolayer of germanene with different molecules, our theoretical gas appurtenant model consisted of the gas of interest in a (3 × 3 × 1) hexagonal supercell. We investigated the electronic properties of a germanene monolayer under the influence of the absorbed gas (NH₃, SO₂ or NO₂). In a lattice circulation, to secure good boundary conditions in all models, the c-axis amplitude is selected as 15 Å, which is sufficiently large to deny interlayer interactions. Herein, an entire structure optimization was performed using a conjugate gradient algorithm, and the relaxation of atoms was terminated until all the forces on each atom converged within less than 0.03 eV Å⁻¹. According to our calculation, the configurations with different gas molecules such as NH₃, SO₂ and NO₂ adsorbed onto the surface of the monolayer of GeH have been considered. These gas molecules were adsorbed onto the monolayer of GeH during the process of structure relaxation. Here, the unit cell volume was kept fixed and the monolayer and gas molecules on the monolayer were allowed to change. When relaxing the adsorption configurations of the germanene monolayer, all the positions of the atoms tended to change. To investigate the interactions between the armchair structure of the germanene monolayer and the gas molecules, the adsorption energy is defined as

E_ad = E_(GeH+gas) − E_GeH − E_gas, (1)

where E_(GeH+gas) represents the total energy of the optimized adsorption configuration. E_gas and E_GeH are the energies of the hexagonal germanene monolayer sheet and the isolated gas molecules (NH₃, SO₂ and NO₂), respectively. According to this definition, a negative value for the adsorption energy demonstrated that the adsorption was exothermic and energetically favorable, and the opposite situation was implied by a positive value for the adsorption energy. The charge transfer between the adsorbate and adsorbent was obtained using Bader analysis.³⁴

3. Results and discussion

3.1 Stability of the structure

The chair structure of the GeH monolayer was the most stable phase, which was reported by Luo et al.,²³ wherein Ge atoms have two coordinates and its top view shows six atomic rings. The bond length of Ge–H is 1.56 Å. The study of the chair structure of the GeH monolayer showed that a H–H repulsion existed because of the arrangement in the directions of the Ge and H. The directions of the Ge–H bonds in the chair layer were perpendicular to the surface. The bond length of Ge–Ge is 2.46 Å for the same structure. As shown in Fig. 1, the utilized buckling distance for the GeH chair was 0.74 Å.

Fig. 1 Top view and side view of the optimized structure of the hexagonal armchair 3 × 3 × 1 germanene monolayer.

The Ge atoms existed out of the plane, which gave rise to a buckling distance of the GeH chair larger than that in germanene. Moreover, the GeH chair has a 4.08 Å lattice constant, which is larger compared to germanene's lattice constant. The structural properties of the GeH monolayer chair were similar to the ones previously reported for CH,³⁵ SiH,³⁶ and GeH.²³ In addition, the structures have negative binding energies, indicating that the structures are thermodynamically stable.

Furthermore, the 2D monolayer GeH armchair (3 × 3 × 1) was chosen as per the calculation configuration due to their symmetry. For the determination of the interaction behavior between the gas molecules of NH₃, NO₂ and SO₂ and the monolayer, we placed the gas molecules on the surface of the GeH monolayer at a distance of approximately 1.4 Å. In these calculations, the bond lengths of the gas molecules were 1.017 Å for NH₃, 1.197 Å for NO₂ and 1.426 Å for SO₂, whereas the bond angles for the nonlinear gas molecules were 107.74° for NH₃, 134.30° for NO₂ and 119.319° for SO₂.

In order to obtain the stability of the structure of the GeH monolayer, we performed a phonon dispersion calculation for the chair structure of the GeH monolayer. Phonon dispersion curves with high symmetry k-points in the Brillouin zone are shown in Fig. 2. According to these results, we are able to compare the stability and structural rigidity of other phases of the germanene (GeH) monolayer.²³ The phonon dispersion curves showed that all the phonon modes had positive frequencies throughout the Brillouin zone and that around the Γ point, the acoustic modes showed linearity, proving that the structure was dynamically stable.

Fig. 2 Full phonon dispersion curve of the monolayer chair form of the germanene monolayer using GGA-PBE.

3.2 Electronic properties

The electronic band structure and projected density of states (PDOS) of the chair structure of the GeH monolayer showed semiconducting behavior with a 0.96 eV direct bandgap at the Γ point (Fig. 3). It is in a good agreement with the results from Lue et al.,²³ which reported the bandgap value of 0.97 eV obtained using GGA-PBE and 1.66 eV using a hybrid HSE06 functional.

Fig. 3 The electronic band structure and projected density of state (PDOS) for the chair structure of the germanene monolayer.

3.3 Effect of toxic gas molecules

The adsorption behavior of the NH₃, NO₂ and SO₂ gases on the monolayer (3 × 3 × 1) of the GeH chair structure was investigated. All the following results have been computed from the most stable adsorption configurations. There are mainly two types of gas molecule configurations (most stable), which are represented as E-type and F-type configurations and shown in Fig. 7. In Fig. 4, we computed the electronic band structure and projected density of state (PDOS) of the E-type configuration of NH₃, NO₂ and SO₂, respectively, adsorbed on the germanene monolayer. As the interaction took place between the GeH monolayer and the gas molecules, it caused a change in the structure and behavior of both the gas molecules and monolayer. According to these changes, we summarized the calculated values of the adsorption energy (E_ad), the band gaps of complex systems (monolayer and gas molecules) after interaction with the gas molecules, the bond lengths (b) between N–H, N–O and S–O of the gas molecules (NH₃, NO₂ and SO₂), angles (θ) H–N–H, O–N–O, O–S–O between the gas molecules, the charge transfer between the gas molecules and monolayer of GeH (ΔQ), the changes of parameter such as bond angle between the H–N–H, O–N–O, O–S–O of the gas molecules (Δθ), and the changes in the bond lengths of N–H, N–O and S–O of the gas molecules (NH₃, NO₂ and SO₂) (Δb, in Å) and of the gas molecules (NH₃, NO₂ and SO₂) before and after the interaction with the GeH monolayer and the band gaps in the Table 1. It was observed that the inclusion of vdW interactions into the DFT within the GGA-PBE functionals induces a large increase in binding energy, heights, the tilt angles, the bending and buckling and also influences on the adsorption process. Therefore, in our case (Table 1), the adsorption energies changed from 6.22 meV to 144.51 meV for NH₃, 195.58 meV to 260.96 meV for NO₂ and 10.23 meV to 122.18 meV for SO₂, which is consistent with other reports such as Yildirim et al.,³⁷ including vdW interaction, the binding energy of the system varies from 1.29 to 1.32 eV and Fajín et al.,³⁸ the adsorption energy through GGA-PBE-D2 is 0.42 eV but this increase to 0.69 eV due to the vdW interactions. Furthermore, according to the interpretation of Bedolla et al.,³⁹ the adsorption energy values changed from 48 meV to 436 meV corresponding to the PBE and vdW-DF functionals, respectively.

Fig. 4 The electronic band structure and projected density of state (PDOS) of the lowest energy (E-type) configuration for (a) NH₃ (b) NO₂ and (c) SO₂ gas molecules on the hexagonal armchair (3 × 3 × 1) germanene monolayer.

Table 1 Parameters of different gas molecules before and after adsorption onto the chair structure of the GeH monolayer. The comparison of all the parameters with and without van der Waals' (vdW) interactions of the gas molecules on the monolayer of GeH for an E-type

Gas molecule	Free molecules		Adsorption onto the monolayer with/without vdW				Bandgap Eg (eV) with/without vdW
	b (Å)	θ	Δb (Å)	Δθ	ΔQ (e)	Ead (meV)
NH3	1.017	107.74	0.0004/0.0001	1.385/1.389	0.0824/0.0440	−144.51/−6.22	1.01/1.01
NO2	1.197	134.30	0.0006/−0.0196	5.874/5.800	0.0915/0.092	−260.96/−195.58	1.01/1.03
SO2	1.426	119.32	−0.0010/−0.0254	0.000/0.206	0.0756/0.017	−122.18/−10.23	0.35/0.34

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Furthermore, we have discuss the electronic properties of the relaxed structure of the GeH monolayer for the E-type and shown in Fig. 4(a)–(c) of the NH₃, NO₂ and SO₂ gas molecules on it. These properties were computed by band structure and projected density of states (PDOS) analyses for each gas molecule depicted in Fig. 4. Furthermore, we also calculated the electronic band structures of the F-type configuration for comparison of the band gaps with the E-type. In the case of the F-type, we changed the orientation of gas molecules on the GeH monolayer.

According to our calculations, it was seen that after the interaction between an ammonia (NH₃) gas molecule and the surface of the GeH monolayer, the band gap increased to that of the pure GeH monolayer. It can be seen from the band structures of Fig. 4(a) and 6 that the bandgap is 1.01 eV and 1.00 eV for the E-type and F-type, respectively. While in the case of the NO₂ gas molecule, the behavior of the electronic band structure was like a semiconductor and the band gaps were 1.01 eV for the E-type and 1.06 eV for the F-type (Fig. 4(b) and 6). The valence bands were near the Fermi level, which is defined as p-type behavior. In the case of the SO₂ gas molecule, it shows semiconducting behavior with a bandgap of 0.35 eV for the E-type (0.78 eV for the F-type), which indicates the decrease in the bandgap to the GeH monolayer, as shown in Fig. 4(c) and 6.

Furthermore, to analyze the electronic properties of the GeH monolayer, the projected density of states (PDOS) have also been computed (Fig. 4) for the E-type configuration for all three molecules (e.g., NH₃, NO₂ and SO₂). We have also discussed the orbital contributions of each atom of the gas molecules (e.g., NH₃, NO₂ and SO₂) and pure GeH monolayer. The PDOS shows the number of electronic states available for occupancy per energy interval. In the case of the NH₃ gas molecule, it was observed that there are no electronic bands present at the Fermi level, revealing the semiconducting behavior of the GeH monolayer with NH₃ gas molecules. The PDOS observation of the chair structure of the GeH monolayer indicates that in the valence band, the p-orbital of the N atom is dominant. Herein, few electronic bands are present near the Fermi level. On the other hand, in the conduction band, the p-orbital of the Ge atom is dominant. However, no states are present at the Fermi level and the p-orbital of the N atom of NH₃ gas indicates their presence in the valence band. In the valence band, the s-orbital of the Ge atom and the s-orbital of the NH₃ atom are partially overlapped. Comparing this PDOS with the pure substrate, it shows the decreasing behavior of the orbitals of the GeH substrate in the conduction band wherein the valence band orbitals shows same characteristics, which are indicated into Fig. 4(a). There is no significant interaction between the Π-bonding orbital of the GeH monolayer substrate and the p-orbital of the N atom of the NH₃ gas molecule. In the case of NO₂ gas molecules on the surface of the GeH monolayer, a small portion of the bands are shifted towards the Fermi level and therefore, it shifted towards the valence band and behaves like a p-type dopant with a band gap of 1.03 eV. This energy could be used to excite an electron from the valence band maxima (VBM) to the conduction band minima (CBM). Therefore, the NO₂ gas molecule shows p-type doping on the GeH monolayer.⁴⁰ It was recently observed in another study by Mahabal et al.⁴¹ that the electronic density of states (DOS) showed a small portion of the electronic states crossing the Fermi level. The orbital contribution in the PDOS of the GeH monolayer with the NO₂ gas molecule indicated that near the Fermi level, the p-orbital of the O atom was dominant compared to the orbital of another atom and clearly defined a p-type behavior with the band gaps of 1.01 eV and 1.03 eV with and without a vdW interaction, respectively. Moreover, the p-orbital of the Ge atom crossed the Fermi level, whereas in the pure substrate, it just touched the Fermi level because of the strong hybridization at the Fermi level between the Ge 4p, N 2s, N 2p and O 2p orbitals (Fig. 4(b)). Herein, there is a significant interaction between the Π-bonding orbital of the GeH monolayer sheet and the p-orbital of the O atoms of the NO₂ gas molecule. For the SO₂ gas molecule (Fig. 4(c)), according to the PDOS, the band lines are present at the Fermi level. The PDOS graph shows that the p-orbital of the O atom is more dominant. The valence bands primarily consist of O 2p states, Ge 4p states and H 1s states, showing the strong hybridization below the Fermi level, whereas in the conduction band, the strong hybridization between the O 2p states and S 2p states takes place slightly above the Fermi level. In this case, the interaction is less significant between the Π-bonding orbitals of the GeH monolayer sheet and the p-orbital of the SO₂ gas molecules.

3.4 Adsorption energy

As revealed in Fig. 5 and 8, we were able to distinguish among the three gas molecules with different positions and orientations (optimized structure in Fig. 7) of the gas molecules (e.g., NH₃, NO₂ and SO₂) on the GeH monolayer wherein NO₂ had the highest adsorption energy (273.72 meV for the B-type, Table 2), which indicates the existence of a stronger interaction between NO₂ and the GeH monolayer. In addition, the maximum adsorption energies (E_ad) for all of the different positions and different configurations for NH₃, NO₂ and SO₂ are −185.97 meV (D-type), 273.72 meV (B-type) and 170.83 meV (F-type), respectively (Table 2).

Fig. 5 Adsorption energies (meV) of NH₃, SO₂, and NO₂ gas molecules on the hexagonal armchair (3 × 3 × 1) germanene monolayer of lowest energy (E-type) configuration.

Fig. 6 The electronic band structure of F-type configurations (a) NH₃ (b) NO₂ and (c) SO₂ gas molecules on the hexagonal armchair (3 × 3 × 1) germanene monolayer.

Fig. 7 Top view and side view of the optimized structure of the hexagonal armchair 3 × 3 × 1 GeH monolayer with gas molecules of NH₃, NO₂ and SO₂, respectively. The complete relaxed structures of the complex system (GeH monolayer and gas molecules) with different positions and orientations of gas molecules on the GeH monolayer and A, B, C, D, E and F have different types of configurations of the gas molecules on the GeH-monolayer. Each type of configuration is represented with NH₃, NO₂ and SO₂ gas molecules.

Table 2 Comparisons of the adsorption energies of the gas molecules on the top of the GeH monolayer in different positions: A (gas molecule on top of the H-atom), B (gas molecule on top between the Ge–H bond atom), C (gas molecule on top of the Ge-atom), D (gas molecule on top between the hexagonal monolayer of GeH), E (gas molecule placed vertically on the GeH monolayer) and F (same as the position of the E-type but the orientation of gas molecules is different)

Adsorption energy of gas molecules at different positions and orientations of the gas molecule	A (meV)	B (meV)	C (meV)	D (meV)	E (meV)	F (meV)
GeH_NH3	−162.11	−105.22	−87.77	−185.97	−144.51	−111.04
GeH_NO2	−255.18	−273.72	−249.25	−248.00	−260.96	−223.56
GeH_SO2	−121.84	−110.28	−104.16	−132.80	−122.18	−170.83

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Furthermore, we relaxed gas molecules on the GeH monolayer with different orientations and positions, as depicted in Fig. 6. The calculated adsorption energies corresponding to the possible orientations and different positions of the gas molecules on the GeH (armchair 3 × 3 × 1) monolayer are presented in Fig. 8 and in Table 2. For each orientation and different position, the maximum adsorption energy was found for NO₂ gas molecules and the maximum adsorption energy, 273.72 meV (B-type configuration), was obtained for the top position of the Ge–H bond. In past theoretical studies of the adsorption of different gas molecules on multi-diameter single wall MoS₂ nanotubes, the investigations defined that the NO molecules have a higher adsorption energy (129.3 meV) due to their higher sensitivity as a gas sensor.^42–46 Therefore, a higher adsorption energy shows a strong binding between the monolayer and the gas molecules and predict that the GeH monolayer is most preferable for NO₂ gas sensors.

Fig. 8 Adsorption energies (meV) of NH₃, SO₂, and NO₂ gas molecules on the chair structure of a 3 × 3 × 1 supercell monolayer of germanene. The adsorption energy of gas molecules on the surface of the germanene monolayer is shown with different orientations and different positions. The adsorption energies of A, B, C and D have the same orientation but different positions on the substrate of GeH (A – top of Ge-atom, B – mid of Ge–H bond, C – top of H-atom, D – mid of hexagonal structure) and F is in a different orientation.

3.5 Charge density analysis

Charge transfer between gas molecules (e.g., NH₃, NO₂ and SO₂) and the germanene monolayer for the E-type configuration acts as an important background for sensing devices based on nanomaterials. Fig. 9 shows the charge contours of different gas molecules on the GeH monolayer. From the charge density plots, we were able to distinguish between the charge transfers according to their color. Violet color indicates the charge depletion and the yellow-green color shows the charge accumulation. The isolines show the equipotential surface. To estimate the charge transfer value in the gas–GeH system, we utilized a Bader analysis.⁴⁷ The obtained results for charge transfer (ΔQ) of different gas–GeH systems are presented in Table 1. The Bader charge analysis shows that NH₃, NO₂ and SO₂ act as electron acceptors, which accept 0.0824e, 0.0915e and 0.0746e, respectively. The higher charge transfer in NO₂ indicates a higher adsorption energy (260.96 meV).

Fig. 9 The charge density difference plots for (a) NH₃ (b) NO₂ and (c) SO₂ gas molecules interacting with the top surface of the hexagonal armchair 3 × 3 × 1 GeH monolayers of E-type configurations.

The charge transfer value between the gas molecules and the GeH monolayer sheet material has an important impact on the sensitivity of field-effect transistor (FET) sensors, which was described by Cao et al.⁴² As the value of the charge transfer increased, the variation in the conductivity of the sensing material also increased and it provided for a greater sensitivity of the sensors. The most charge transfer occurred in the NO₂ gas molecule adsorption on the GeH (3 × 3 × 1) monolayer, indicating that the GeH monolayer showed higher sensitivity for NO₂ gas sensor.

4. Conclusion

In summary, using the first principles DFT calculations, we exploited the possibilities of the GeH monolayer to detect common toxic gas molecules (NH₃, NO₂ and SO₂). Our theoretical results demonstrate that all the molecules are physisorbed on it. In all of these configurations, the electronic band structure shows semiconducting behavior with band gaps of 1.01, 1.01 and 0.35 eV with the vdW interaction included, corresponding to NH₃, NO₂ and SO₂, wherein NO₂ gas molecule behaves like p-type dopant. The maximum adsorption energy for all different position and different configuration E_ad values for NH₃, NO₂ and SO₂ are −185.97 meV (D-type), 273.72 meV (B-type) and 170.83 meV (F-type), respectively. Among these gas molecules, the NO₂ molecule has the strongest interaction with the GeH monolayer (273.72 meV). In addition, the charge transfer mechanisms of gas molecules on the surface of GeH monolayer are studied. The charge transfer values for NO₂ is much higher than the other two gas molecules (NH₃ and SO₂). Our theoretical results indicate that the hexagonal armchair monolayer GeH monolayer has a highest stability and sensitivity for the detecting NO₂ gas. Miniaturized devices utilized as a gas sensor have great potential application in sensors areas from industrial processes to environmental issues. The results show that the germanene monolayer has strong potential for use as an electronic sensor in the field of detecting NO₂ gas.

Acknowledgements

S. K. G. acknowledges the use of high performance computing clusters at IUAC, New Delhi to obtain the partial results presented in this study. SKG also thanks the Science and Engineering Research Board (SERB), India for financial support (Grant no. YSS/2015/001269). Helpful discussion with Dr Igor Lukacevic is gratefully acknowledged to improve the scientific content of the article.

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