Adsorption performance of M-doped (M = Ti and Cr) gallium nitride nanosheets towards SO₂ and NO₂: a DFT-D calculation

Abstract

The structure, adsorption characteristics, electronic properties, and charge transfer of SO₂ and NO₂ molecules on metal-doped gallium nitride nanosheets (M-GaNNSs; M = Ti and Cr) were scrutinized at the Grimme-corrected PBE/double numerical plus polarization (DNP) level of theory. Two types, M_Ga-GaNNSs and M_N-GaNNSs, of doped nanostructures were found. The M_Ga sites are more stable than the M_N sites. The results showed that adsorption of SO₂ and NO₂ molecules on Ti_Ga,N-GaNNSs is energetically more favorable than the corresponding Cr_Ga,N-GaNNSs. The stability order of complexes is energetically predicted to be as NO₂–Ti_Ga-GaNNS > NO₂–Ti_N-GaNNS > SO₂–Ti_Ga-GaNNS > NO₂–Cr_N-GaNNS > SO₂–Ti_N-GaNNS > NO₂–Cr_Ga-GaNNS > SO₂–Cr_N-GaNNS > SO₂–Cr_Ga-GaNNS. The electron population analysis shows that charge is transferred from M_Ga,N-GaNNSs to the adsorbed gases. The Ti_Ga-GaNNS is more sensitive than the other doped nanostructures to NO₂ and SO₂ gases. It is estimated that the sensitivity of Ti_Ga-GaNNS to NO₂ gas is more than to SO₂ gas.

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1. Introduction

At present, air pollution is a significant factor limiting economic progression.¹ The emission of toxicant gases into the air is a serious matter due to the dangers of these air pollutants.² The source of air pollutants might be extensive in the Earth’s environment.³ Sulfur dioxide (SO₂) and nitrogen dioxide (NO₂) are noteworthy gaseous pollutants, discharged from natural and industrial procedures which have major environmental effects.^4–6 Thus, specific harmful gas detecting will be a major advantage to daily life for all people.^7–9

For the first time in 2005, boron nitride (BN) nanosheets were forecast.¹⁰ The honeycomb samples of BN sheets have analogies similar to graphene with equal numbers of alternating boron and nitrogen atoms that exhibit remarkable properties.¹¹ The electronic properties of BN sheets can be modified by B or N vacancies, Stone–Wales defects and doping heteroatoms.^12–16 In recent years, different studies have been done via surface quantum engineering of BN nanosheets.^17,18 For BN modification, the doped BN nanosheets were explored for developing a sensor for detecting harmful gases.^19–21

Recently, III–V nanostructures have attracted great attention for their potential applications in novel electronic,^22–24 optical,^25–27 and electrochemical devices.^28–30 One of the III–V nanostructures were gallium nitride nanosheets (GaNNSs) which have been theoretically predicted^31–33 and then experimentally discovered.^34,35 It was found that the GaNNSs have many remarkable properties such as a high surface area to volume ratio, high thermal stability and a tunable band gap indicating that GaNNSs have advantages in electronic usage such as effective gas sensor applications and so on.³⁶ There are some experimental studies focusing on the GaN based NO₂ and SO₂ sensors.^37–40 Bishop et al.⁴¹ suggested a double Schottky junction NO₂ gas sensor based on BGaN/GaN. Triet et al. synthesized Al_0.27Ga_0.73N/GaN-based Schottky diode sensors for SO₂ gas detection.⁴² For example, the adsorption capabilities of gallium nitride nanosheets towards noxious gases (such as HCN, NH₃, H₂S, H₂, CO₂ and H₂O) have been described.⁴³ Therefore, most of the research studies have focused on nanomaterials for increasing the adsorption of adsorbates on GaNNSs. For this purpose, the electronic properties of GaNNS can be modified by doping which generates more reactive adsorption sites.^44,45 Transition metals such as Ti, Cr, Fe, Ni and Zn have been theoretically explored as dopants in GaNNSs to increase the adsorption properties towards CO harmful gases.⁴⁶ The adsorption of H₂S, NH₃ and SO₂ molecules on pure and doped GaNNSs has been considered using first-principles calculations. The results show that the metal doped GaNNSs are more suitable for gas molecules detection compared with the pure ones.⁴⁷ The doping effect of metal atoms on the electronic properties of GaNNSs was studied for tuning the optoelectronic properties, gas adsorption, hydrogen storage and catalytic reaction.^48–51 The electronic and optical properties of GaNNSs as a function of thickness and strain with predictive calculations were scrutinized.⁵² Based on the results reported about the magnetic properties of GaNNSs, the metallic and ferromagnetic properties of GaNNSs can be attained by semi-hydrogenation.⁵³ The chemical oxidation of GaNNSs was explored by using first-principles calculations⁵⁴ that show the oxygen adsorption mechanism can be useful for application in novel semiconducting materials. So, it would be attractive to continue investigating the promising applications of GaNNSs in gas sensors.

To the best of our knowledge, this is the first report on the adsorption of SO₂ and NO₂ molecules on the surface of Ti and Cr doped GaNNSs. The influence of transition metals doping on the adsorption behavior of SO₂ and NO₂ on the metal doped GaNNSs for exploring the possibility of using the doped GaNNSs as candidates for removing and sensing of these molecules was considered herein at the Grimme-corrected PBE/double numerical plus polarization (DNP) level of theory.

2. Computational details

In this theoretical research, the double numerical plus polarization (DNP) basis sets were selected implemented in the DMol³ package.^55,56 The periodic spin-unrestricted DFT calculation is employed using generalized-gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional.⁵⁷ The density functional semi-core pseudopotentials (DSPP) were generated by fitting all-electron relativistic DFT results.⁵⁸

To consider the van der Waals (vdW) interactions, an empirical dispersion-corrected density functional theory (DFT-D) was used in the calculations. The Brillouin zone integration was sampled using a 10 × 10 × 1 Monkhorst–Pack grid. A convergence tolerance of energy of 1.0 × 10⁻⁵ Ha, maximum force of 0.001 Ha per Å and maximum displacement of 0.005 Å were employed in all the geometry optimizations. To get reliable results, the real space global orbital cutoff radius was set as high as 5.2 Å and the smearing of electronic occupations to be 0.005 Ha.

To calculate the adsorption energies (AE) of the SO₂ and NO₂ molecules on the pure and metal doped GaNNSs, the following equation is given:

AE = E_T − [E_S + E_m] (1)

where E_T, E_S and E_m are the energies of gas–M-GaNNSs complexes, M-GaNNSs and SO₂ or NO₂ molecules, respectively.

3. Results and discussion

3.1. Adsorption of SO₂ and NO₂ gas molecules over pure GaNNSs

The optimized geometries of adsorbed molecules and gallium nitride nanosheets are displayed in Fig. 1. As demonstrated in Fig. 1, the calculated bond lengths of X=O (X = N and S) in free SO₂ and NO₂ molecules are 1.482 Å and 1.201 Å, respectively, and that of the Ga–N bond length in the optimized geometry of GaNNS is 1.861 Å.

Fig. 1 The optimized geometries of SO₂, NO₂, pure and most stable adsorption complexes of GaNNSs.

To find the most stable complexes obtained from adsorption of SO₂ and NO₂ gas molecules on the GaNNS, several configurations of SO₂ and NO₂ molecules on top of the GaNNSs are explored. The most stable adsorption complexes are illustrated in Fig. 1. After optimization, the C₂ axis of the SO₂ molecule is parallel to the GaNNS and that of the NO₂ molecule is perpendicular to the nanosheet. As presented in Table 1, the nearest distances between the SO₂ and NO₂ molecules with SO₂–GaNNS and NO₂–GaNNS are 1.782 Å and 2.298 Å, respectively.

Table 1 The calculated adsorption energy (AE), equilibrium distance between molecules and nanosheet (D), charge of Ga and N atoms (Q), charge transfer (CT) and band gaps for the most stable adsorption complexes

Configurations	AE (kcal mol^−1)	D (Å)	Q (e)	CT (e)	Band gap (eV)
Pure GaNNS	—	—	0.39^Ga (−0.39)^N	—	2.52
SO2–GaNNS	−27.22	1.782	0.40 (−0.38)	0.17	2.51
NO2–GaNNS	−11.86	2.298	0.39 (−0.39)	0.09	0.29

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The values of the adsorption energies (AEs) are −27.22 and −11.86 kcal mol⁻¹ for SO₂–GaNNS and NO₂–GaNNS complexes, in good agreement with the smaller SO₂–GaNNS distance obtained. Hence, the SO₂ and NO₂ molecules are chemically adsorbed on the GaNNSs. The adsorption energy for the SO₂ molecule on the GaNNS is comparable with those found for graphene (−6.45 kcal mol⁻¹)⁵⁹ and boron nitride nanosheet (−7.14 kcal mol⁻¹).²¹ For adsorption of NO₂ on graphene, the calculated adsorption energy is −11.06 kcal mol⁻¹.⁴¹

The Hirshfeld charges on the Ga and N atoms in pristine GaNNS are 0.39e and −0.39e, respectively, which change to 0.40e and −0.38e in SO₂–GaNNS, and 0.39e and −0.39e in NO₂–GaNNS. The charges on S and O change from 0.38e and −0.19e in free SO₂ to 0.33 e and −0.25e in SO₂–GaNNS, respectively. Besides, the charges on N and O are 0.17e and −0.09e which change to 0.11e and −0.10e in NO₂-GaNNS. This reveals that oxygen atoms in SO₂–GaNNS and NO₂–GaNNS complexes have the main contribution to charge transfer between the gas and nanosheet. The charge analyses show that the 0.17e and 0.09e charges are shifted from the GaNNSs to the SO₂ and NO₂ molecules, respectively, in good agreement with greater AE found for the SO₂–GaNNS complex.

The negative AEs demonstrate the orbital interactions between the gases and GaNNS. The Mulliken electron populations of the total and each of the s, p and d orbitals before and after interactions are given in Table 2. Inspection of the s, p and d orbital contributions in the free gases and in the SO₂–GaNNS and NO₂–GaNNS complexes indicate that the p orbital of the S atom in SO₂–GaNNS and O atom in NO₂–GaNNS have the most contribution in the interaction of molecules with the d orbital of Ga and p orbital of N atoms in the GaNNS. Comparison of the total electron population of orbitals shows that the population increases by 0.352e for SO₂ and 0.169e for NO₂ after interaction of the gas with the surface. This indicates that the adsorbates will get electrons from the GaNNSs. The change in the electronic population of the orbitals in SO₂–GaNNS is greater than for NO₂–GaNNS, in good agreement with the greater AE and Hirshfeld charge transfer values found for SO₂–GaNNS compared with NO₂–GaNNS.

Table 2 Mulliken electron population of the total and each of the s, p and d orbitals before and after interactions

	Total pop.	Orbital				Total pop.	Orbital
		s	p	d			s	p	d
Free SO2					NO2–CrGa-GaNNS
S	15.558	5.838	8.872	0.848	N	6.72	3.637	2.942	0.14
O	8.22	3.836	4.346	0.04	O	8.346	3.839	4.461	0.047
Free NO2					Cr	13.317	2.592	6.454	4.272
N	6.646	3.449	3.028	0.17	NO2–CrN-GaNNS
O	8.176	3.851	4.272	0.055	N	6.759	3.684	2.951	0.124
SO2–GaNNS					O	8.343	3.852	4.443	0.05
S	15.514	5.674	8.922	0.918	Cr	13.917	2.71	6.441	4.767
O	8.424	3.846	4.546	0.032	SO2–TiGa-GaNNS
NO2–GaNNS					S	15.613	5.802	9.203	0.608
N	6.669	3.541	2.972	0.156	O	8.364	3.834	4.499	0.031
O	8.25	3.841	4.36	0.049	Ti	11.018	2.433	6.304	2.281
TiGa-GaNNS					SO2–TiN-GaNNS
Ti	11.244	2.658	6.202	2.384	S	15.651	5.82	9.29	0.542
TiN-GaNNS					O	8.384	3.832	4.522	0.03
Ti	11.465	2.612	6.347	2.505	Ti	11.322	2.51	6.383	2.43
CrGa-GaNNS					SO2–CrGa-GaNNS
Cr	13.357	2.655	6.345	4.357	S	15.706	5.81	9.364	0.533
CrN-GaNNS					O	8.399	3.837	4.531	0.03
Cr	14.014	2.888	6.232	4.894	Cr	13.286	2.589	6.463	4.234
NO2–TiGa-GaNNS					SO2–CrN-GaNNS
N	6.72	3.644	2.932	0.142	S	15.6	5.802	9.198	0.6
O	8.4	3.838	4.518	0.042	O	8.423	3.856	4.532	0.034
Ti	11.048	2.45	6.3	2.3	Cr	13.842	2.714	6.462	4.667
NO2–TiN-GaNNS
N	6.734	3.666	2.934	0.134
O	8.382	3.86	4.478	0.046
Ti	11.386	2.516	6.44	2.43

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3.2. Ti and Cr doped GaNNSs

In order to investigate the effect of metal doping on the geometrical and electronic properties of the GaNNSs, one of the central atoms in the nanosheet was substituted by Ti and Cr metal atoms. Hereafter, M_Ga-GaNNS and M_N-GaNNS denote that Ga and N atoms in GaNNS have been substituted by M metal atoms, respectively.

The optimized structures of M_N(Ga)-GaNNSs are illustrated in Fig. 2. The average bond distances between the metal atoms and the neighboring atoms are given in Table 3. The results show that the M–Ga bonds in M_N-GaNNS nanostructures are longer than the M–N bonds in M_Ga-GaNNSs. For example, the Ti–Ga and Cr–Ga bonds are longer than the Ti–N and Cr–N bonds by about 0.92 and 0.62 Å, respectively. Accordingly, it is predicted that binding of the metal to the nanosheet is stronger for M_Ga-GaNNS than M_N-GaNNS. Fig. 2 presents the three bond angles A₁, A₂ and A₃ around the M atoms of the NS and their average values are listed in Table 3. The averages of the three bond angles are 120.0°, 119.9°, 83.1° and 87.1° in Ti_Ga-GaNNS, Cr_Ga-GaNNS, Ti_N-GaNNS and Cr_N-GaNNS, respectively.

Fig. 2 Optimized geometries of Ti and Cr doped GaNNSs.

Table 3 The calculated average of M–N and M–Ga bond distances, average of bond angles (A₁, A₂ and A₃), binding energies of pristine and M (M = Ti and Cr) doped GaNNSs and Hirshfeld charge values of M atoms

Configurations	Bond distances (Å)	Bond angle (°)	Binding energies (kcal mol^−1)	Q (e)
GaNNS	1.862	118.2	—	—
TiGa-GaNNS	1.913	120.0	−330.5	0.30
TiN-GaNNS	2.838	83.1	−236.1	0.26
CrGa-GaNNS	1.883	119.9	−246.9	0.43
CrN-GaNNS	2.505	87.1	−61.6	0.28

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The binding energies (BEs) of Ti_Ga-GaNNS, Ti_N-GaNNS, Cr_Ga-GaNNS and Cr_N-GaNNS are −330.5, −236.1, −246.9 and −61.6 kcal mol⁻¹, respectively (Table 3). It is found that the BEs increase in the order M_Ga-GaNNSs > M_N-GaNNSs so that the value for the Ti_Ga-GaNNS structure is greater than other ones. Therefore, the Ga sites for M doping are energetically more appropriate than N sites. The sequence of BEs for the M_Ga-GaNNS series is Ti_Ga > Cr_Ga and that of the M_N-GaNNS series is Ti_N > Cr_N. The more-negative BE indicates that the adatom is easier to be incorporated into the GaNNS and M doped GaNNSs are stable.

The Hirshfeld⁴⁴ charge values of M atoms for M-GaNNSs are shown in Table 3. The results show that the charge of the M atom in all M-doped GaNNSs is positive, indicating that the GaNNS in many cases acts as an electron-withdrawing support. The considerable electron transfer from the metal atom to the GaNNS leads to the strong bonding between the M atom and its neighbor atoms and stabilization of single-metal doped GaNNS. Besides, the positive charge of the M atom in M_Ga-GaNNSs is more than M_N-GaNNSs, in good agreement with their binding energy (BE) and the average value of the M–NS bond length. Thus, because of greater transfer of charge between the nanosheet and M atoms in M_Ga-GaNNSs with respect to the corresponding M_N-GaNNSs, the M_Ga-GaNNSs are predicted to be more stable than M_N-GaNNSs.

3.3. Adsorption of SO₂ and NO₂ gas molecules over Ti-doped GaNNSs

Now, we investigate the adsorption of SO₂ and NO₂ gas molecules on the Ti-doped GaNNSs as displayed in Fig. 3. Our results show that for the SO₂–Ti_Ga-GaNNS and NO₂–Ti_Ga-GaNNS complexes, the averages of the three binding distances (Ti–N) are 1.901 Å and 1.899 Å, respectively. For the SO₂–Ti_N-GaNNS and NO₂–Ti_N-GaNNS complexes, the averages of the three binding distances (Ti–Ga) are 2.983 Å and 2.949 Å, respectively. The calculated averages of the bond lengths of the S–O and N–O bonds in SO₂–Ti_Ga-GaNNS, SO₂–Ti_N-GaNNS, NO₂–Ti_Ga-GaNNS and NO₂–Ti_N-GaNNS have increased from 1.482 and 1.201 Å to 1.576, 1.606, 1.274 and 1.288 Å, respectively. These results show that the change in the SO₂ and NO₂ bond lengths upon adsorption on the Ti_N-GaNNS is greater than those of Ti_Ga-GaNNS.

Fig. 3 The most stable adsorption configurations of SO₂ or NO₂ on Ti-doped GaNNSs.

Table 4 Adsorption energy (AE), the shortest equilibrium distance between molecules and nanosheet (D) and Hirshfeld charge transfer (CT) for the most stable configurations of SO₂ and NO₂ on metal doped GaNNSs

Configurations	AE (kcal mol^−1)	D (Å)	CT^a (e)
a Absolute value of the sum of atomic charges in complexed gases.
NO2			0.00
NO2–TiGa-GaNNS	−76.83	2.025	0.21
NO2–TiN-GaNNS	−70.68	2.048	0.25
NO2–CrGa-GaNNS	−54.79	1.912	0.22
NO2–CrN-GaNNS	−60.81	1.952	0.31
SO2
SO2–TiGa-GaNNS	−61.06	2.000	0.16
SO2–TiN-GaNNS	−58.36	1.896	0.21
SO2–CrGa-GaNNS	−40.46	1.834	0.27
SO2–CrN-GaNNS	−53.28	2.124	0.26

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The modified surface of Ti-doped GaNNSs facilitates the doped region to interact with approaching SO₂ and NO₂ molecules because of the higher chemical reactivity of the doped M atom. The results show that the SO₂⋯Ti distance of SO₂–Ti_Ga-GaNNS complex is larger than SO₂–Ti_N-GaNNS ones. Also, the NO₂⋯Ti distance for the NO₂–Ti_N-GaNNS complex is larger than for NO₂–Ti_Ga-GaNNS, indicating that the interaction in these complexes is stronger than in other ones.

The range of adsorption energies for SO₂ and NO₂ adsorbed on Ti-doped GaNNSs was between −58.36 to −61.06 and −70.68 to −76.83 kcal mol⁻¹, respectively. The negative value of the AE indicates that adsorption of SO₂ and NO₂ on Ti doped GaNNSs is an exothermic process. It is found that SO₂ and NO₂ molecules are adsorbed on Ti_N-GaNNSs in the sequence NO₂–Ti_N-GaNNS > SO₂–Ti_N-GaNNS and on the Ti_Ga-GaNNSs in the order NO₂–Ti_Ga-GaNNS > SO₂–Ti_Ga-GaNNS. Besides, it is found that the SO₂ and NO₂ adsorption energy values on Ti_Ga-GaNNSs are greater than on Ti_N-GaNNSs. The obtained results indicate that the adsorption capability of Ti_Ga-GaNNSs is greater than that of Ti_N-GaNNSs. Our results show that SO₂ and NO₂ molecules are chemically adsorbed on all Ti_Ga,N-GaNNSs.

The Hirshfeld population analysis presents that the charges are transferred from the Ti_Ga,N-GaNNSs complexes to the SO₂ and NO₂ molecules. In other words, SO₂ and NO₂ act as electron acceptors. There is a correlation between charge transfer values and adsorption energy in the process of adsorption of SO₂ and NO₂ on the GaNNSs. Comparison of charge transfer values between M-doped GaNNSs and SO₂ and NO₂ molecules demonstrate that the value for adsorption of NO₂ is greater than that of the corresponding SO₂ one, with the exception of that obtained for Cr_Ga-GaNNS. This indicates that other parameters than charge transfer are responsible for the stability of the complexes.

The electron populations of orbitals given in Table 2 show that population of d-orbitals as well as total population of the M metals decrease upon the interaction of gases with Ti_Ga,N-GaNNSs. Besides, total electron population of orbitals in gases increases after adsorption of gases on the surface. This finding reveals that gases will take the electrons from Ti_Ga,N-GaNNSs. After adsorption of gases, total electron populations of orbitals of NO₂ (0.522e for NO₂–Ti_Ga-GaNNS and 0.500e for NO₂–Ti_N-GaNNS) are greater than those of SO₂ (0.343e for SO₂–Ti_Ga-GaNNS and 0.421e for SO₂–Ti_N-GaNNS), in good agreement with the greater AEs found for NO₂–Ti_Ga,N-GaNNS complexes. The decrease in total electron population of Ti before and after interaction is −0.196e and −0.079e in NO₂–Ti_Ga-GaNNS and NO₂–Ti_N-GaNNS, respectively, in good agreement with the greater AE found for NO₂–Ti_Ga-GaNNS. Besides, the total electron population of Ti after interaction with SO₂ decreases by −0.226e and −0.143e in SO₂–Ti_Ga-GaNNS and SO₂–Ti_N-GaNNS, respectively, in good agreement with the greater AE found for SO₂–Ti_Ga-GaNNS.

3.4. Adsorption of SO₂ and NO₂ gas molecules over Cr-doped GaNNSs

For the SO₂–Cr_Ga-GaNNS and NO₂–Cr_Ga-GaNNS complexes, the averages of three binding distances (Ti–N) are 1.834 Å and 1.912 Å, respectively. The calculated averages of bond lengths of S–O and N–O bonds in SO₂–Cr_Ga-GaNNS, SO₂–Cr_N-GaNNS, NO₂–Cr_Ga-GaNNS and NO₂–Cr_N-GaNNS have increased from 1.482 Å to 1.527, 1.574, 1.277 and 1.307 Å, respectively. For the SO₂–Cr_N-GaNNS and NO₂–Cr_N-GaNNS complexes, the averages of the three binding distances (Ti–Ga) are 2.124 Å and 1.952 Å, respectively. These results show that the change in the SO₂ and NO₂ bond lengths upon adsorption on the Cr_N-GaNNS is greater than that for Cr_Ga-GaNNS. The optimized structures of the NO₂ and SO₂ adsorbed on Cr-doped GaNNSs are illustrated in Fig. 4. The modified surface of the Cr-doped GaNNSs facilitates the doped region to interact with approaching SO₂ and NO₂ molecules because of the higher chemical reactivity of the doped M atom. The results show that the SO₂⋯Cr distance for the SO₂–Cr_N-GaNNS complex is larger than that for the SO₂–Cr_Ga-GaNNS one. Also, the NO₂⋯Cr distance for the NO₂–Cr_N-GaNNS complex is larger than that for NO₂–Cr_Ga-GaNNS, indicating that interaction in these complexes is stronger than for other ones.

Fig. 4 The most stable adsorption configurations of SO₂ or NO₂ on Cr-doped GaNNSs.

The adsorption energies for SO₂ adsorbed on Cr_Ga-GaNNS and Cr_N-GaNNS are −40.46 and −53.28 kcal mol⁻¹ and those for NO₂ are −54.79 and −60.81 kcal mol⁻¹, respectively. The negative value of the AE indicates that adsorption of SO₂ and NO₂ on Cr doped GaNNSs is an exothermic process. It is found that the ability of Cr_N-GaNNS towards adsorption of SO₂ and NO₂ molecules is in the sequence NO₂–Cr_N-GaNNS > SO₂–Cr_N-GaNNS and that of Cr_Ga-GaNNS is in the order NO₂–Cr_Ga-GaNNS > SO₂–Cr_Ga-GaNNS. In addition, it is found that SO₂ and NO₂ adsorption energies on Cr_N-GaNNS are greater than on Cr_Ga-GaNNS. The obtained results indicate that the adsorption capability of Cr_N-GaNNS is greater than Cr_Ga-GaNNS. Our results show that SO₂ and NO₂ molecules are chemically adsorbed on all M-doped GaNNSs.

The Hirshfeld population analysis shows that the charges are transferred from the Cr_Ga,N-GaNNS complexes to the SO₂ and NO₂ molecules. As can be seen in Table 4, the CT values are 0.22e, 0.31e, 0.27e and 0.26e in NO₂–Cr_Ga-GaNNS, NO₂–Cr_N-GaNNS, SO₂–Cr_Ga-GaNNS and SO₂–Cr_N-GaNNS, respectively. This finding reveals that the charge transferred from the nanosheet to the gas in NO₂–Cr_N-GaNNS is greater than in other complexes, in good agreement with the greater AE obtained for these complexes. It should be noted that other parameters than charge transfer can affect the adsorption of gases.

Analysis of the electron population of orbitals involved in the interaction between gases and nanosheets given in Table 2 reveals that the total electron population of Cr decreases by −0.040e, −0.097e, −0.071e and −0.172e in NO₂–Cr_Ga-GaNNS, NO₂–Cr_N-GaNNS, SO₂–Cr_Ga-GaNNS, SO₂–Cr_N-GaNNS, respectively, in good agreement with the greater AE found for NO₂(SO₂)–Cr_N-GaNNSs compared with NO₂(SO₂)–Cr_Ga-GaNNSs. In addition, the results show that the population of d-orbitals of Cr decreases and those of the NO₂ and SO₂ gases increase upon interaction with Cr_Ga,N-GaNNSs. This finding demonstrates that gases will get electrons from Cr_Ga,N-GaNNSs, in good agreement with the computed Hirshfeld charge transfer from the surface to adsorbed gases.

3.5. HOMO and LUMO based electronic properties

There is an obvious difference between the electronic properties of doped and un-doped GaNNSs. As can be seen in Table 5, compared to pristine GaNNS, the energy of the highest occupied molecule orbital (HOMO) increases and that of the lowest un-occupied molecular orbital (LUMO) decreases in doped GaNNS so that the amount of increase in HOMO is greater than decrease in LUMO. After adsorption of NO₂, the energies of the HOMO and LUMO decrease, but the LUMO energy shows a further decrease. In the case of SO₂, adsorption of gas on the Ti-doped GaNNS decreases both the HOMO and LUMO, but its adsorption on the Cr-doped GaNNS increases them. These changes in HOMO and LUMO energy levels lead to a change in the HOMO–LUMO gap and, in turn, in the electronic properties of GaNNS.

Table 5 The E_HOMO, E_LUMO, the HOMO–LUMO gap and gap change of pure and NO₂ or SO₂ on M doped GaNNSs

Configurations	EHOMO (eV)	ELUMO (eV)	Eg (eV)	ΔEg (eV)
GaNNS	−5.75	−3.23	2.52	—
TiGa-GaNNS	−3.76	−3.28	0.47	2.05
TiN-GaNNS	−4.50	−3.60	0.90	1.62
CrGa-GaNNS	−4.28	−3.64	0.64	1.88
CrN-GaNNS	−4.26	−3.78	0.47	2.05
NO2–GaNNS	−5.83	−5.53	0.29	2.23
NO2–TiGa-GaNNS	−5.90	−3.62	2.28	1.81
NO2–TiN-GaNNS	−4.96	−4.01	0.95	0.05
NO2–CrGa-GaNNS	−4.52	−3.87	0.65	0.01
NO2–CrN-GaNNS	−5.08	−4.18	0.91	0.44
SO2–GaNNS	−5.90	−3.37	2.11	0.41
SO2–TiGa-GaNNS	−4.69	−3.29	1.39	0.92
SO2–TiN-GaNNS	−4.59	−3.47	1.11	0.21
SO2–CrGa-GaNNS	−3.45	−2.91	0.53	0.11
SO2–CrN-GaNNS	−3.82	−3.53	0.28	0.19

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The results indicate that the band gap energies in both M_Ga,N doped GaNNSs are smaller than the pure GaNNS, making it more conductive. The results given in Table 5 demonstrate that the band gap value of pristine GaNNS is 2.52 eV that changes to 2.11 eV in SO₂–GaNNS and 0.29 eV in NO₂–GaNNS. Because of the greater decrease in the LUMO level in NO₂–GaNNS with respect to that of SO₂–GaNNS, the change in the band gap for SO₂–GaNNS is lesser than for NO₂–GaNNS. Therefore, it is predicted that GaNNS is more sensitive to NO₂ gas than SO₂ gas. So, the large changes in band gap value for GaNNS (2.52 to 0.29 eV) with NO₂ gas molecule adsorption can lead to a significant change in electrical conductivity.

The electronic properties of doped GaNNSs are affected by the adsorption of SO₂ and NO₂ molecules. Upon adsorption of SO₂ and NO₂ molecules on the Ti_Ga,N-GaNNS complexes the energy gap decreases in comparison with the pristine GaNNS. The energy gap values are in the sequences SO₂–Ti_N-GaNNS (1.11 eV) > NO₂–Ti_N-GaNNS (0.95 eV) and NO₂–Ti_Ga-GaNNS (2.28 eV) > SO₂–Ti_Ga-GaNNS (1.39 eV). Reduction of the band gap for SO₂–Ti_N-GaNNS is more than for NO₂–Ti_N-GaNNS and that for NO₂–Ti_Ga-GaNNS is more than for SO₂–Ti_Ga-GaNNS. Therefore, it can be concluded that the sensitivity of Ti_N-GaNNS to SO₂ gas is greater than to NO₂ gas. Besides, for Ti_Ga-GaNNS, it is predicted that the sensitivity to NO₂ gas is more than to SO₂ gas. It is a well-known issue that reduction of the energy gap enhances the electrical conductivity. Thus, the electrical conductivities are predicted to be in the order SO₂–Ti_N-GaNNS > NO₂–Ti_N-GaNNS and NO₂–Ti_Ga-GaNNS > SO₂–Ti_Ga-GaNNS.

Also, after adsorption of SO₂ and NO₂ molecules on the Cr_Ga,N-GaNNS complexes the band gap decreases in comparison with the pristine GaNNS. The band gap values are in sequence NO₂–Cr_N-GaNNS (0.91 eV) > SO₂–Cr_N-GaNNS (0.28 eV) and NO₂–Cr_Ga-GaNNS (0.65 eV) > SO₂–Cr_Ga-GaNNS (0.53 eV). The reduction in band gap for SO₂–Cr_Ga-GaNNS is more than for NO₂–Cr_Ga-GaNNS and that for NO₂–Cr_N-GaNNS is more than for SO₂–Cr_N-GaNNS. In consequence, the conductivities of SO₂–Cr_Ga-GaNNS and NO₂–Cr_N-GaNNS are greater than NO₂–Cr_Ga-GaNNS and SO₂–Cr_N-GaNNS, respectively. Also, from the changes in band gap energy values, it is forecast that the sensitivity of Cr_N-GaNNS to NO₂ gas is more than to SO₂ gas.

The top and side view plots of the electron density are illustrated in Fig. 5. An orbital overlap can be observed between the NO₂ (SO₂) gas molecules and the GaN sheets, revealing the occurrence of a strong chemisorption. It is clearly displayed that the electrons dominantly accumulate in the region between gases and M-GaNNSs. These results are in accordance with the obtained adsorption energies and binding distances. The orbital mixing and the charge transfer are expected to bring significant changes to the electronic structure of the GaN nanosheets which is beneficial for sensing applications. The isovalue for adsorption of gas molecules on GaNNS is 0.2e Å⁻³.

Fig. 5 The electron density schema (top and side views) of SO₂ or NO₂ adsorbed on doped GaNNSs with isovalue = 0.2e Å⁻³.

To obtain a better understanding about the electronic properties of the complexes, densities of states (DOSs) of the nanostructures are calculated and visualized in Fig. 6 and 7. As can be observed, the GaNNS, NO₂–GaNNS, SO₂–GaNNS, NO₂–Ti_Ga-GaNNS, NO₂–Ti_N-GaNNS and NO₂–Cr_N-GaNNS nanostructures are nonmagnetic systems because the spin-up and spin-down in the DOS plots are the same as each other. From this figure, it can be found that new states appear in the band gap regions of NO₂–Cr_Ga-GaNNS, SO₂–Ti_Ga-GaNNS, SO₂–Ti_N-GaNNS, SO₂–Cr_Ga-GaNNS and SO₂–CrN-GaNNS. Since the spin-up and spin-down DOSs are different, NO₂–Cr_Ga-GaNNS, SO₂–Ti_Ga-GaNNS, SO₂–Ti_N-GaNNS, SO₂–Cr_Ga-GaNNS and SO₂–Cr_N-GaNNS have magnetic properties.

Fig. 6 The densities of states (DOSs) of GaNNS and SO₂ (NO₂) adsorbed on pristine GaNNSs.

Fig. 7 The densities of states (DOSs) of SO₂ or NO₂ adsorbed on doped GaNNSs.

4. Conclusions

DFT calculations are performed to consider the adsorption of sulfur dioxide and nitrogen dioxide molecules on metal-doped gallium nitride nanosheets. The results present that adsorption of NO₂ on M_N-GaNNS and M_Ga-GaNNS is energetically more favorable than that of SO₂ on corresponding NSs. A brief comparison of AEs of SO₂ and NO₂ molecules on Ti and Cr doped GaNNSs indicates that the AEs of NO₂ and SO₂ on Ti_Ga,N-GaNNSs are greater than on Cr_Ga,N-GaNNSs. The electron populations of orbitals were calculated before and after interaction. There is a correlation between the change in electron population of orbitals of adsorbate and adsorbent and the AE obtained for complexes. The electron population analysis shows that charge is transferred from M_Ga,N-GaNNSs to the adsorbed gases. After the adsorption of SO₂ and NO₂ molecules, the electronic properties of the pure and doped GaNNSs indicate the considerable changes in the conductivity of the nanosheets. Furthermore, the sensitivity of Ti_Ga-GaNNS is predicted to be more than for other NSs toward SO₂ gas. It is estimated that the sensitivity of Ti_Ga-GaNNS to NO₂ gas is more than to SO₂ gas. Therefore, these results show that GaNNS-based materials can be used as noxious gas sensors.

Conflicts of interest

The all authors declare that they have no conflict of interest.

Acknowledgements

This work was supported by the University of Guilan and Iran National Science Foundation through research facilities and financial grants.

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