A Study Based on the First-Principle Study of the Adsorption and Sensing Properties of Mo-Doped WSe₂ for N₂O, CO₂, and CH₄

Abstract

As industry continues to develop rapidly, the greenhouse effect is becoming increasingly severe. CO₂, CH₄, and N₂O are the three primary greenhouse gases, making their effective monitoring a crucial step in reducing emissions. This paper investigates the gas sensing performance of Mo-doped WSe₂ for these three gases, through a theoretical study. First, using first-principles calculations, the doping behavior of Mo in WSe₂ is examined. Subsequently, the adsorption properties of Mo-WSe₂ for CO₂, CH₄, and N₂O are analyzed by calculating adsorption energy, charge transfer, the electron localization function (ELF), Hirshfeld partition (IGMH), and the density of states (DOSs), culminating in an analysis of its sensing properties. The results indicate that when Mo is positioned above the upper Se atom, the structure is most stable. Therefore, this position is selected as the optimal adsorption site for studying the adsorption of the three gases. The adsorption energies for CO₂, CH₄, and N₂O are 1.349 eV, −1.194 eV, and −0.528 eV, respectively, with corresponding charge transfers of 0.418, 0.450, and 0.115. In the N₂O and CO₂ adsorption systems, significant adsorption energy and charge transfer are observed, leading to relatively better adsorption compared to the CH₄ system. Additionally, considering the adsorption performance, Mo-WSe₂ demonstrates good sensor response and desorption times for N₂O and CO₂ at temperatures above 298 K. The findings of this research provide theoretical guidance for the application of Mo-WSe₂ as a gas sensing material for detecting greenhouse gases.

1. Introduction

With the rapid development of industry, the detrimental effects of greenhouse gas emissions on ecosystems and socio-economies are becoming increasingly apparent, presenting a serious challenge for the 21st century [1,2,3]. Additionally, as economic growth and population numbers continue to rise, anthropogenic greenhouse gas emissions are also steadily increasing. CO₂, CH₄, and N₂O are the primary greenhouse gases contributing to global warming, collectively accounting for nearly 80% of the greenhouse effect [4]. Therefore, effective sensing and monitoring of these gases are essential for mitigating greenhouse gas emissions.

Currently, sensors for monitoring greenhouse gases include electrochemical gas sensors [5], semiconductor gas sensors [6], infrared gas sensors [7], and emerging nano-gas sensors. Compared to traditional gas sensors, new nano-gas sensors offer advantages such as high sensor response, low operating temperature, and compact size, significantly expanding their application fields [8,9,10,11,12]. Gas-sensitive materials are at the core of these nano-gas sensors, and primarily include metal oxide semiconductors [13], carbon nanotubes [14], graphene [15], and transition metal dichalcogenides (TMDs) [16,17,18]. TMDs, a novel class of two-dimensional layered nanomaterials with the general formula MX₂ (where M is a transition metal element like Mo or W, and X is a chalcogen element such as S, Se, or Te), have a unique structure, with two layers of X atoms sandwiching a single layer of M atoms [19]. Unlike graphene, TMDs possess a band gap, which enhances their potential for gas adsorption and sensing [20]. Among TMD materials, WSe₂ shows considerable promise for gas sensing applications [21]. Ni et al. studied the adsorption of small gas molecules on single-layer WSe₂ doped with Pt, Au, Ag, and Pd, finding that these transition metals improve the adsorption of CO₂, NO₂, and SO₂ [22]. Mi et al. [23] investigated the adsorption of Cl₂, SO₂, and N₂O on WSe₂ doped with three Ag atoms, while Chen et al. [24] examined the adsorption of HCN on WSe₂ doped with Fe, Ag, Au, As, and Mo. These studies confirm that doping with transition metals can enhance gas molecule adsorption performance. However, the feasibility of using transition metal-doped WSe₂ for greenhouse gas adsorption still requires further investigation. Currently, Mo-doped WSe₂ shows promising adsorption effects for some small gas molecules. To expand the options for greenhouse gas sensing materials, further in-depth research on the adsorption and sensing properties of greenhouse gases with Mo-doped WSe₂ is necessary.

Therefore, the Mo-doped WSe₂ model based on first principles is established, to obtain the most stable structure of Mo-WSe₂. Furthermore, the adsorption properties of Mo-WSe₂ for CO₂, CH₄, and N₂O are analyzed by calculating the adsorption energy, charge transfer, electron localization function (ELF), Hirshfeld partition (IGMH), and density of states (DOSs). Meanwhile, the sensor response and desorption time of the three gases by Mo-WSe₂ are also calculated, to evaluate the feasibility of Mo-WSe₂ as a gas-sensitive material. This study provides theoretical support for the application of Mo-doped WSe₂ gas sensors in various environments.

2. Computational Method

Density Functional Theory (DFT) is a method used to study multi-electron systems [25]. It is also highly effective in the field of gas sensing [26]. In this paper, calculations are performed using the DMol3 module in Materials Studio [27]. A monolayer WSe₂ superlattice, consisting of 16 W atoms and 32 Se atoms, is constructed. A vacuum layer with a thickness of 15 Å is introduced to prevent interactions between the periodic WSe₂ crystals. The Perdew–Burke–Ernzerhof (PBE) functional, within the framework of the generalized gradient approximation (GGA), is used to handle the exchange–correlation interactions between electrons, while the Tkatchenko–Scheffler (TS) method describes van der Waals interactions. Double numerical polarized (DNP) atomic orbital basis sets are employed, with a global orbital cutoff radius of 5 Å [28]. To simplify the process, a DFT semi-core pseudopotential (DSPP) with relativistic effects is used. The structure is geometrically optimized using a 5 × 5 × 1 Monkhorst Pack k-point grid, with the following convergence criteria: tolerance precision, maximum force, and maximum displacement are set to 10⁻⁵ Ha, 0.002 Ha/Å, and 0.005 Å, respectively. The bonding between molecules is further analyzed in Multiwfn, using the ELF and IGMH [29,30].

3. Results

The molecular structure of the gas molecules is first geometrically optimized, and the optimized gas molecules are shown in Figure 1, where both CO₂ and N₂O with linear structures, with C-O, N-N, and N-O bond lengths of 1.178 Å, 1.141 Å, and 1.197 Å, respectively, are shown. CH₄, on the other hand, exhibits high symmetry, forming a regular tetrahedron with C-H bond lengths of 1.097 Å.

3.1. Analysis of Monolayer Mo-WSe₂

In this paper, geometric optimization of the WSe₂ unit cell is carried out, resulting in lattice constants of a = b = 13.308 Å and C = 18.363 Å. As shown in Figure 2, doping modification of the WSe₂ surface is performed to improve the adsorption and sensing properties of the material [31,32]. Three surface positions of WSe₂ are considered as possible doping sites for Mo atoms, namely, above the Se atom, at the center of the six-membered ring formed by three Se atoms, and above the upper-layer W atom. The initial distance of the doping atom from the doping site is set to 2 Å.

The adsorption energy (E_bind) of the doping atom on the adsorbent material is calculated according to Equation (1).

E_bind = E_Mo-WSe2 − E_Mo − E_WSe2

(1)

Here, E_Mo-WSe2 represents the total energy of Mo-WSe₂, E_Mo is the energy of the Mo atom, and E_WSe2 is the total energy of the monolayer WSe₂.

Lower adsorption energies clearly correspond to more stable adsorption structures.

Table 1. Different parameters of Mo at three doping positions on the WSe₂.

Dope Position	Ebind/eV
Above the upper Se atom	−0.830
Center of the three Se atoms	0.526
Above the W atom	−0.693

displays the adsorption results of Mo atoms at three different doping sites. Comparing these results reveals that the adsorption energy is lowest when the Mo atom is positioned directly above the Se atom, at −0.830 eV. As illustrated in Figure 3, this position is relatively stable. Figure 4 shows the difference charge density map of Mo-WSe₂ at the optimal adsorption site, where green indicates charge accumulation and blue indicates charge depletion. Charge depletion is predominantly concentrated near the adsorbed Mo atom, with the lost charge mainly involved in forming the Mo-Se bond. This suggests that the incorporation of Mo atoms modifies the electronic structure of WSe₂, reducing the surface chemical reaction potential energy. Consequently, these factors establish this position as the optimal adsorption site for gas molecules.

The DOS and partial density of states (PDOSs) for Mo-doped WSe₂ are presented in Figure 5. From Figure 5a, it is evident that Mo doping leads to a decrease in the overall energy of the WSe₂ material and induces changes in its shape. A new peak appears at 0 eV following Mo doping. Additionally, the DOS above the Fermi level is significantly affected by the Mo atom, resulting in peaks in Mo-WSe₂ at 0 eV to 1.6 eV, higher than those observed in pristine WSe₂. Figure 5b illustrates the PDOS of the adsorbent material, where the Mo 4p orbital strongly hybridizes with the Se 4s, 4p, and 4d orbitals, as well as the W 5p orbital within the range of −8 eV to 2 eV. This hybridization contributes to the formation of a stable adsorption system of Mo atoms on WSe₂, aligning with the previous analysis.

3.2. Adsorption Performance Analysis of Mo-WSe₂

3.2.1. Adsorption Configuration Analysis

The gas molecules N₂O, CO₂, and CH₄ were positioned at the optimal adsorption sites of Mo-WSe₂, as previously identified. By varying the position and orientation of these gas molecules and performing geometric optimizations, the most stable adsorption configurations were determined. For the N₂O molecule, three adsorption configurations were evaluated: the O-atom end oriented perpendicularly, the N-atom end oriented perpendicularly, and the N₂O molecule oriented parallel to the surface. For the CO₂ molecule, only perpendicular and parallel orientations were considered, due to its symmetry. Similarly, for CH₄, two orientations were assessed: one with the H-atom end oriented perpendicularly, and the other with the central C atom directed toward the surface. Based on the simulation results, the adsorption system structures with the lowest adsorption energies are illustrated in Figure 6.

In order to further analyze the adsorption properties of gases on Mo-WSe₂, this study takes the energy change of gas molecules during the adsorption process on the Mo-WSe₂ surface as the adsorption energy. The adsorption energy Ead of the gas adsorption process is shown in Equation (2).

E_ad = E_gas/Mo-WSe2 − E_Mo-WSe2 − E_gas

(2)

where E_gas/Mo-WSe2, E_Mo-WSe2 and E_gas represent the total energy of the system after gas adsorption, the energy of the adsorbent material Mo-WSe₂, and the energy of the gas molecule, respectively.

Table 2. Parameters before and after adsorption of gas molecules on Mo-doped WSe₂.

Gas	Ead/eV	dgas’/Å	dgas/Å	dMo-Se’/Å	dMo-Se/Å	D/Å
N2O	−1.349	1.141	1.251	2.219	2.580	2.079
CO2	−1.194	1.178	1.315	2.214	2.552	2.084
CH4	−0.528	1.097	1.116	2.702	2.475	2.223

shows parameters such as the bond length of the gas molecule before adsorption (dgas’), the bond length of the gas molecule after adsorption (dgas), the bond length of Mo-Se before adsorption (dMo-Se’), and the bond length of Mo-Se after adsorption (dMo-Se), as well as the adsorption distance and adsorption energy for the three systems.

As shown in Figure 6a,b, the N₂O adsorption system reveals significant changes in the bond lengths of the N₂O molecule before and after adsorption compared to the undoped state. The N-N bond length increases from 1.141 Å to 1.251 Å. Additionally, the Mo-Se bond length extends from 2.219 Å to 2.580 Å, and the distance between the Mo atom and the central N atom increases notably, to 2.079 Å. With an adsorption energy of −1.349 eV, Mo-WSe₂ demonstrates a strong adsorption effect on N₂O. In the CO₂ adsorption system, as shown in Figure 6c,d, the distance between the C atom and the Mo atom increases significantly, to 2.084 Å. Furthermore, the C=O bond length, particularly between the O atom closest to the Mo atom and the C atom, increases from 1.178 Å to 1.315 Å. The Mo-Se bond length also extends from 2.214 Å to 2.552 Å, with an adsorption energy of −1.194 eV, indicating that Mo-doped WSe₂ has a good adsorption effect on CO₂. In contrast, the CH₄ adsorption system, depicted in Figure 6e,f, shows a much weaker adsorption effect compared to CO₂ and N₂O. The C-H bond length closest to the Mo atom only increases slightly, to 1.116 Å, and the change in the Mo-Se bond length is relatively minimal. With an adsorption energy of −0.528 eV, the adsorption effect of CH4 on Mo-doped WSe₂ is relatively poor, compared to the other two gases.

To further analyze the electronic distribution of certain chemical bonds in the doped adsorption system after bonding, the charge density difference of these systems is studied, as shown in Equation (3):

Δρ = ρ_gas/Mo-WSe2 − ρ_gas − ρ_Mo-WSe2

(3)

Here, ρ_gas/Mo-WSe2, ρ_gas and ρ_Mo-WSe2 represent the charge density difference of the gas molecule adsorption system, the charge density difference of a single gas molecule, and the charge density difference of Mo-WSe₂. The calculation results are shown in Figure 7, where the green region indicates charge accumulation and the blue region indicates charge loss.

As shown in Figure 7, there is a significant charge transfer in the N₂O, CO₂, and CH₄ adsorption systems, and the number of transferred electrons can be obtained through calculations. Firstly, for the N₂O adsorption system, 0.418 electrons are transferred from the Mo/WSe₂ adsorbent material to N₂O, and the electrons primarily accumulate between the Mo and N atoms for the formation of Mo-N bonds. Secondly, for the CO₂ adsorption system, Mo atoms transferred 0.332 electrons to the nearest C and O atoms, which are used to form Mo-C and Mo-O bonds. Moreover, Mo/WSe₂ transferred 0.450 electrons to CO₂. However, for the CH₄ adsorption system, a difference from the previous two cases is that CH₄ transferred 0.115 electrons to Mo/WSe₂. Mo atoms also only lost 0.157 electrons, with more electrons transferred to the C-H bonds. Therefore, no chemical bond is formed between the Mo and C atoms. Combining the analysis of bond lengths and adsorption energies mentioned above, it can be further concluded that Mo/WSe₂ has a better adsorption effect on N₂O and CO₂.

3.2.2. Analysis of the Interaction Force

In order to further investigate the direct interaction force between gas molecules and Mo-WSe₂, the three N₂O, CO₂ and CH₄ gas systems are analyzed, based on IGMH. The IGMH isosurfaces and scatter plots of the three adsorption systems are shown in Figure 8. Blue, green and red colors indicate regions where sign (λ₂) ρ > 0, sign (λ₂) ρ < 0 and sign (λ₂) ρ ≈ 0, respectively. The isovalue is 0.05 a.u. As can be seen in Figure 8a, there is a section of blue color between N₂O and Mo, which indicates an obvious gathering of electrons between the N atom and Mo atom, leading to the formation of a N-Mo. In addition, the peak at the symbol (λ₂) ρ = −0.1 a.u. corresponds to the attraction of this position, and the δ g_inter at the peak is as high as 0.19 a.u., which indicates that there is a strong adsorption between Mo-WSe₂ and N₂O. In the CO₂ adsorption system shown in Figure 8b, there is a significant electron aggregation between C and O and Mo, resulting in the formation of C-Mo and O-Mo; the peak corresponding to this position reaches 0.18 a.u., suggesting that there is also a strong adsorption between Mo-WSe₂ and CO₂. For Figure 8c, the region between CH₄ and Mo is repulsive, due to the spatial site resistance effect. However, due to the presence of attractive forces between H and Mo, there is, in turn, a partial region of mutual attraction, corresponding to the peak at the symbol (λ₂) ρ = −0.035 a.u. The value of δ g_inter at the peak is 0.058 a.u., which indicates that the adsorption between CH₄ and Mo-WSe₂ is weak, mainly due to van der Waals forces. The results are all in agreement with the analysis before and after this paper.

3.2.3. Analysis of ELF

To further investigate the adsorption properties of Mo-WSe₂ on the three gas molecules, the Electron Localization Function (ELF) was analyzed, and the results are presented in Figure 9. As shown in Figure 9a, a distinct green region forms between the N and Mo atoms, with the ELF value between them close to 0.55. This indicates a strong charge accumulation between the N and Mo atoms, suggesting a good bonding tendency and confirming the effective adsorption of N₂O by Mo-WSe₂. In Figure 9b, the electrons are primarily concentrated between the C and Mo atoms, with an ELF value close to 0.6. This also indicates a strong adsorption effect of Mo-WSe₂ on CO₂. In contrast, Figure 9c shows that the electrons are uniformly distributed around the CH₄ molecule, with almost no charge accumulation between it and the Mo atoms. The ELF value is close to 0, confirming the poor adsorption effect of Mo-WSe₂ on CH₄.

3.2.4. Analysis of the DOS of the Adsorption Systems

To further analyze the interaction between gas molecules and the adsorbent material surface, this section investigates the DOS and PDOS of the three gas adsorption systems. The results are shown in Figure 10.

From Figure 10, it can be observed that the DOS and PDOS of Mo-WSe₂ change, to varying degrees, after gas adsorption. In the N₂O adsorption system, as shown in Figure 10a, after adsorption, two new peaks appear at −19.5 eV and −9 eV for N₂O/Mo-WSe₂. Additionally, in the range from −1.4 eV to 0.6 eV, the Mo 4d orbitals strongly hybridize with the N 2p and O 2p orbitals. This also confirms that Mo-WSe₂ exhibits a good adsorption effect on N₂O, leading to structural changes in the N₂O gas molecule. In the CO₂ adsorption system, as shown in Figure 10b, the adsorption behavior causes three new peaks to appear for CO₂/Mo-WSe₂, located at −21.5 eV, −20 eV, and −8 eV. The Mo 4d orbital strongly hybridizes with the C 2p and O 2p orbitals in the range from −4 eV to 0.6 eV, indicating a strong adsorption effect of Mo-WSe₂ on CO₂ and leading to changes in the CO₂ structure. From Figure 10c, it can be seen that the CH₄ adsorption system is different from the above two gas adsorption systems, in that the peak changes are not significant; the Mo-4d orbital only shows a slight hybridization with the C-2p and H-1s orbitals in the range from −9 eV to −7 eV, which indicates weak adsorption of CH₄ by Mo-WSe₂.

3.3. Analysis of the Sensing Performance of Mo-WSe₂

To evaluate the potential of Mo-WSe₂ as a resistive gas sensor, the sensor response and desorption time after adsorption of each gas are studied. Sensor response can be obtained by detecting the change in conductivity of the material before and after adsorption of the gas, and the bandgap is the main factor determining the conductivity of the material.

Additionally, there is a quantitative relationship between the conductivity (σ) and the bandgap (Bg), given by Equation (4) [33,34]:

σ = A × e^(−Bg/2kT)

(4)

in which A is the attempt frequency, typically around 10⁻¹², k is the Boltzmann constant, and T represents the thermodynamic temperature.

The relationship between sensor response (S) and conductivity (σ) is given by Equation (5) [35]:

$$S=\left|{\displaystyle \frac{\frac{1}{{\sigma }_{\mathrm{gas}}}-\frac{1}{{\sigma }_{\mathrm{pure}}}}{\frac{1}{{\sigma }_{\mathrm{pure}}}}}\right|$$

(5)

where σ_gas and σ_pure represent the conductivity of the gas adsorption system and the Mo-WSe₂ pristine, respectively.

The band structures of N₂O, CO₂, and CH₄ after adsorption are shown in Figure 11. The calculated sensitivities of Mo-WSe₂ to N₂O, CO₂, and CH₄ at room temperature are 31781.96, 789.44, and 0.99, respectively, using Equations (4) and (5). This indicates that Mo-WSe₂ has a high sensor response to N₂O and CO₂, with significant changes in conductivity before and after adsorption. In contrast, the sensor response of Mo-WSe₂ to CH₄ is much lower than the response to the other two gases mentioned above. Therefore, Mo-WSe₂ is more suitable for detecting N₂O and CO₂.

Additionally, desorption time (τ) is an important indicator for evaluating gas sensors, representing the time it takes for a gas to desorb from the material surface, as shown in Equation (6) [36,37]:

τ = A⁻¹ × e^(−Eg/kT)

(6)

where A is the attempt frequency, typically around 10⁻¹², k is the Boltzmann constant, T represents the thermodynamic temperature, and Eg represents the energy barrier; the value of the energy barrier for the desorption process can be considered as the absolute value of the adsorption energy.

If the desorption time is prolonged, it can significantly impact the sensor response and accuracy of the adsorbent material. Ideally, desorption should occur within a few seconds to a few dozen seconds. If the desorption time is not optimal, adjusting the temperature is necessary to achieve a suitable desorption time.

Table 3. Desorption times of different gases at different temperatures.

Gas	τ/s
	298 K	398 K	498 K	598 K
N2O	6.52 × 1011	1.21 × 105	44.86	0.233
CO2	1.55 × 108	1.316 × 103	1.21	0.011
CH4	1.25 × 10−3	6.48 × 10−6	2.78 × 10−7	3.42 × 10−8

presents the desorption times of different gases at varying temperatures. In the case of the N₂O adsorption system, the optimal desorption time is observed between 498 K and 598 K. Similarly, for the CO₂ adsorption system, the optimal desorption time ranges from 398 K to 498 K. However, due to the weaker adsorption effect in the CH₄ system, achieving the desired desorption time necessitates a significantly lower temperature. Consequently, Mo-doped WSe₂ is suitable for the adsorption and sensing of N₂O and CO₂ in various environments.

4. Discussion

This paper investigates the adsorption properties of three typical greenhouse gases (N₂O, CO₂, and CH₄) on Mo-doped WSe₂ models. Through a comprehensive analysis involving adsorption energy, charge transfer, adsorption geometry, density of states, charge density difference, band structure, conductivity, and desorption time, the study explores the adsorption and sensing performance of these gases on monolayer Mo-WSe₂. The findings indicate that the lowest adsorption energy occurs when Mo is doped above the Se atom in WSe₂, identifying it as the optimal adsorption site. Mo-WSe₂ demonstrates superior adsorption performance for CO₂ and N₂O, compared to CH₄. In terms of conductivity sensor response, Mo-WSe₂ is more responsive to N₂O and CO₂ detection. The desorption time for different gases on Mo-WSe₂ is temperature-dependent, highlighting the importance of optimizing sensing conditions based on temperature. When compared with Ti-HfSe₂, as reported in the literature study [35], Mo-WSe₂ is shown to be more effective as a sensor for N₂O. These results contribute to the exploration of monolayer WSe₂ doped with metals for potentil gas sensing applications.