DFT study of MoSe₂ monolayers for cohesive adsorption of harmful gases CO, CO₂, SO₂, and NF₃

Abstract

According to the World Health Organization, contact with atmospheric airborne pollutants (CO, CO₂, SO₂, and NF₃) causes 4.2 million deaths annually. Globally, there is a well-established demand for highly sensitive, inexpensive, tiny, and energy-efficient gas sensors that are able to recognize and steer clear of high pollution hotspots. Density functional theory (DFT) is utilized to analyze the electronic properties of CO, CO₂, SO₂, and NF₃ gases in the MoSe₂ monolayer for gas sensing mechanism. On MoSe₂, calculations and discussions are made on the adsorption energies and configurations that are most stable. A detailed analysis is conducted on the adsorption distance (d (Å)), charge transfer (Q_T), adsorption energy (E_ads), band gap (E_g), density of states (DOS), electron difference density (EDD), and Recovery time $\left( \tau \right)$. The outcomes attained demonstrate that the adsorption of CO, CO₂, SO₂, and NF₃ gases significantly alters the electrical characteristics as well as the adsorption of MoSe₂ monolayer. However, in comparison to CO, CO₂, and SO₂, the MoSe₂ monolayer system shows larger adsorption energy towards NF₃ and a higher sensitivity. The transport characteristics employing the non-equilibrium Green's function (NEGF) method validate the efficiency of the MoSe₂ monolayer in terms of considerable current–voltage (I–V) response for enhanced CO, CO₂, SO_2, and NF₃ gas sensing. Compared to CO, CO₂, and SO₂, MoSe₂ has a much higher sensitivity to NF₃.

1 Introduction

Among the greatest dangers to human health in contemporary times is environmental air pollution. The World Health Organization (WHO) claimed in 2019 that 91% of people worldwide live in areas where air pollution levels are higher than recommended. Because fossil fuels are so economical, developing nations are still hesitant to limit their usage of them. Gases including nitrogen trifluoride (NF₃), carbon monoxide (CO), carbon dioxide (CO₂), and sulfur dioxide (SO₂) are examples of harmful gases, that have emerged as a troubling problem. For example, the poisonous, odorless, tasteless, and colorless CO gas is produced when fuels like natural gas and oil burn partially (Yogi and Jaiswal 2019). The ability of CO to bind with hemoglobin is now known to be essential to its toxicity mechanism, which results in a hypoxic environment inside cells (Gorman et al. 2003). The principal greenhouse gas responsible for the phenomenon of global warming is carbon dioxide (CO₂) (Yamakasi 2003). Moreover, one of the primary air pollutants created largely by industrial processes as well as the burning of coal and oil is SO₂, a colorless, corrosive, and powerful excitant odor (Yang et al. 2016). When SO₂ is dissolved in water, it generates sulfuric acid, which has a major negative impact on human skin and the mucous membranes of the eyes and nose (Yang et al. 2016). Global warming might be triggered 16,600 times more often by nitrogen trifluoride (NF₃) than by carbon dioxide (CO₂). Its atmospheric lifespan is 740 years (Tsai 2008; Lu et al. 2017). It's important to note that NF₃ is one of the fluorine sources that the electronics sector uses extensively (Flamm 1993). Each of these pollutants has suggested exposure limits, and when they are surpassed, they can have a negative effect on the environment in a few ways, including eutrophication (the disturbance of ecosystems owing to an abundance of nutrients), acidification (acid rain), and global warming. Since its start, the study of gas sensing has been primarily concerned with contaminated or poisonous gas sensing, industrial monitoring, agricultural output, and health diagnostics (Chen et al. 2013). The ability to detect hazardous gases is crucial because it supports both the protection of human health and the monitoring and management of environmental pollution (Tit et al. 2017; Zhao et al. 2020).

2-D nanomaterials have attracted a lot of attention for potential new gas sensing applications since the successful experiment synthesis of graphene (Geim 2007; Zhang et al. 2016). The primary benefits of nanostructures for detecting gases are their larger surface-active site, large surface-to-volume ratio, small size and dimensions, and large specific surface area. The use of nanoparticles for gas removal and monitoring is becoming more and more necessary. The use of resistive sensors is important in environmental monitoring because they use surface coatings to increase surface contact-mediated electron transit among the gases and the substrate (Pearton et al. 2010) and to use electrical resistance adjustment to measure gas concentrations (Zhang et al. 2021). Growing gas-sensitive materials that work at room temperature is crucial. It is essential to growing gas-sensitive materials that can function at ambient temperature. However, due to the advantages of low cost, micro miniaturization, superior physicochemical stability, and remarkable detecting characteristics, sensors for gases made from nanosized semiconductors are becoming increasingly common. The study thus focused on contemporary nanoscale semiconductor-based gas detectors (Zhang et al. 2017). Despite graphene-based chemical sensors receiving much attention due to their superior gas-sensing capabilities, poor switching characteristics are caused by graphene's zero-band gap (Geim 2007). A variety of materials in two dimensions, including III–IV compounds, V group monolayers, and transition metal dichalcogenides (TMDs), have recently been shown to have strong interactions with gas molecules and should possess strong electron mobility and good chemical reactivity (Cui et al. 2019a; Zhang et al. 2018).

The novelty lies in the specific combination of material (MoSe₂), the theoretical approach (DFT), and the focus on multiple harmful gases, all of which contribute to advancing knowledge in the field of 2-D materials and their applications in environmental technology (Zhao et al. 2017; Shen et al. , 2022; Kadioglu et al. 2017). The study focuses on the unique properties of molybdenum diselenide (MoSe₂) monolayers, which are a less explored material compared to more common 2-D materials like graphene or MoS₂, WS₂, WSe₂ etc. (Zhao et al. 2017; Shen et al. , 2022; Kadioglu et al. 2017). The paper examines the adsorption behavior of multiple harmful gases (CO, CO₂, SO₂, and NF₃), providing a broad spectrum of data. This comprehensive analysis could reveal differential adsorption capacities and mechanisms for each gas, contributing to a deeper understanding of the material's selectivity and efficiency. By exploring the adsorption of environmentally harmful gases, the research has significant implications for pollution control and environmental protection. The findings could lead to the development of effective gas sensors or filters based on MoSe2 monolayers. Based on the first principal simulations, it was determined that the BN bilayer is a potential optical sensor for SO₂, CO₂, and NO₂. Its adsorption properties for CO₂, SO₂, and NO₂ were calculated (Hussein et al. 2023). By using the first principles to analyze the electrical behavior of (CO, CO₂, SO₂) gases adsorbed on the armchair graphene nanoribbon monolayer (Salih and Ayes 2020). By applying the first principles to the electrical behavior of SO₂, CO₂ gases adsorbed on the Cu-doped WSe₂ monolayer found that CO₂ and H₂S adsorption performed better (Cui et al. 2022).

We describe the design and theoretical discussion of a 2-D MoSe₂ monolayer-based ecologically harmful gas sensor, applying the first-principles density functional theory (DFT). High chemical stability, quick reaction times, and sensitivity are necessary for an outstanding gas sensor (Sajjad and Feng 2014). A novel approach to creating a new gas sensor could be offered by the 2-D MoSe₂ monolayer. The Band structure, density of states (DOS), recovery time, and charge transfer (Q_T) were also computed in order to determine the differences between the pure 2-D MoSe₂ monolayer and the gas molecules adsorbed MoSe₂ nanosheet, wherein the environmentally hazardous CO, CO₂, SO₂, and NF₃ molecules are taken into account. The Non-Equilibrium Green's Function (NEGF) technique was utilized to determine the current–voltage (I–V) characteristic to validate the sensing application in a realistic scenario.

2 Theory and method of simulations

A MoSe₂ supercell $6 \times 6$ with ambient gas molecules adsorbed onto it served as the basis for the system. Exchange–correlation factions were generated in DMol³'s (Diederich et al. 1992) calculation process using the PBE i.e., Perdew–Burke–Ernzerhof (Delley 1990; Cui et al. 2019b) algorithm within a general gradient approximation i.e., GGA. The grid-mesh cutoff is set to 500 eV for MoSe₂ nanosheet structural optimization. Using a Methfessel-Paxton smearing of 0.01 Ry and a $1 \times 4 \times 4$ Monkhorst–Pack k-point grid, the Brillouin zone was sampled. All atomic structures were relaxed until the Hellmann–Feynman force as well as total energy reached $1.0 \times 10^{ - 5}$ eV and 0.06 eV/Å, respectively (Becke 1993). MoSe₂ nanosheets were optimized using the double-zeta polarization (DZP) and conjugated gradient (CG) algorithms. The weak van der Waal contact has been considered between the 2-D single-layer nanoribbon and gas molecule and is done using Grimme's DFT-D2 method (Grimme 2006; Sarkar et al. 2022). To estimate the numerous qualities that the GGA-PBE functional is unable to estimate, the Grimme dispersion term is utilized to account for extended interactions. We determined the adsorption energy $\left( {E_{ads} } \right)$ of adsorbed systems, which was specified as follows, to evaluate the gas-molecule interaction with the surface of the adsorption sheet.

The capacity for adsorption was determined by putting a molecule of gas on top of a 2-D MoSe₂ monolayer and letting it move in three dimensions while the structure was optimized. In order to evaluate the interactions among gas molecules and the adsorption 2-D single layer (Sarkar et al. 2023), we computed the energy needed for the adsorption of the adsorbed configuration, which was given as follows.

We determined the adsorption energy $\left({E}_{ads}\right)$ of adsorbed systems, which was specified as follows, to assess the interplay between gas molecules as well as the adsorption sheet surface (Sarkar et al. 2023).

$$ E_{ads} = E_{MoSe_2 @GAS} - \left( {E_{MoSe_2 } + E_{GAS} } \right) $$

(1)

where $E_{MoSe_2 }$ is the MoSe₂ energy, $E_{GAS}$ is the CO, CO₂, SO₂, and NF₃ gases energy, and $E_{MoSe_2 @GAS}$ represents the overall energy of the system that has been adsorbed with MoSe₂. The calculations for all energies used optimized atomic structures. Adsorption energy plays a crucial role in determining whether adsorption is exothermic or endothermic. The negative value of adsorption energy indicates favorable adsorption i.e., exothermic, and the positive value of adsorption energy indicates unfavorable adsorption i.e., endothermic.

The difference between the highest conduction band and the bottom valence band can be used to compute the band gap.

$$ E_g = V_{\left( {V.B} \right)} - V_{\left( {C.B} \right)} $$

(2)

The Mulliken population equation was utilized to compute the amount of the transferred charges of the above-mentioned gases (Bo et al. 2019; Mulliken 1955):

$$ Q_T = Q_{ads} - Q_{iso} $$

(3)

where the gas's charge transfer is denoted by $Q_T$, $Q_{ads}$, and $Q_{iso}$, and the Mulliken charges of the gas before and after adsorption, respectively. $Q_T$ < 0 indicates gas electron loss.

The NEGF technique was used to do the electrical transport calculations (30). The basis sets that are double-ζ polarized (DZP) and have an energy cut-off of 250 Ry were employed in the computations. Regarding the electrode and transportation computations, Monkhorst–Pack k-point grids of 1 × 1 × 80 were utilized. The Landauer-Buttiker formulation defines the connection between current and voltage throughout the system of atoms scale (Sarkar et al. 2023).

$$ I\left( {V_{bias} } \right) = G_0 \int {\mathfrak{I}\left( {E,V_{bias} } \right)\left[ {f\left( {E - \mu_L } \right) - f\left( {E - \mu_R } \right)} \right]} dE $$

(4)

where $V_{bias}$ and $f_{L / R} \left( E \right)$ stand for the applied bias voltage and the left/right electrode's Fermi–Dirac distribution functions, respectively, and L/R represents the electrodes' chemical potential $\mu_{L/R}$. The probability of electrons incidental at energy (E) under potential bias $\left( {V_{bias} } \right)$ is represented by $\mathfrak{I}\left( {E,V_{bias} } \right)$. $G_0 = {{2e^2 } / h}$ represents the quantum conductance (Fig. 1).

Fig.1

Flow chart of the simulation framework

3 Result and discussion

3.1 The properties of structure

Figure 2a depicts the MoSe₂ unit cell, which has three atoms total (Se: 2 and Mo: 1) arranged in the regular hexagonal lattice, representing the equilibrium structure of the monolayer MoSe₂. Mo–Se and Se–Se bond lengths were determined to be 2.31 Å and 3.288 Å. The layered hexagonal unit cell of MoSe₂ has a lattice constant of $\left| \alpha \right| = 3.319$ Å. As a result, the monolayer of MoSe₂ has a significantly bigger atomic structure than WS₂ and MoS₂-TMDs due to Se's high atomic radius. The lattice constant and length of bond found for the 2-D MoSe₂ monolayer in the present investigation agree with recently published studies (Kang et al. 2013) and experimental work (Nagarajan and Chandiramouli 2017). MoSe₂ monolayer is made up of three layers of atoms, with Se atoms in the upper and lower layers and Mo atoms in the middle layer. Before analyzing the adsorption behavior on the surface of a single-layer MoSe₂, we computed the optimized geometry of the MoSe₂ monolayer $1 \times 4 \times 4$ supercell, as illustrated in Fig. 2a.

Fig. 2

The geometry of a pristine MoSe₂ monolayer, b CO, c NF₃, d SO₂, e CO₂

4 CO molecules adsorption on MoSe₂ nanosheet

The adsorption of CO has also been shown in Fig. 3a, c. The CO molecule has a linear structure with a 1.13Å C–O bond. Additionally, oxygen in the carbon monoxide molecule hybridizes its orbitals to create three sp hybrid orbitals. O atom of CO molecule adsorbed on Se of MoSe₂ monolayer. The bond length between Se of MoSe₂ and O of CO molecules is found 2.05 Å. The adsorption energy of the system is found − 0.93 eV. The calculated charge transfer (Q_T) is − 0.03e, as shown in Table 1. The negative sign of the transfer of charges signifies that CO transfers the charge to the MoSe₂. The electron difference density (EDD) plot is shown in Fig. 4a, c.

$$ Mo_{24} Se_{48} + CO \to Mo_{24} Se_{48} @CO + E_{ad} ,\;\left( {E_{ad} = - 0.93\;{\text{eV}}} \right) $$

(5)

Fig. 3

The geometry of a top view of CO adsorbed MoSe₂ monolayer, b top view of CO₂ adsorbed MoSe₂ monolayer, c front view of CO adsorbed MoSe₂ monolayer, d front view of CO₂ adsorbed MoSe₂ monolayer, e top view of SO₂ adsorbed MoSe₂ monolayer, f top view of NF₃ adsorbed MoSe₂ monolayer, g front view of SO₂ adsorbed MoSe₂ monolayer, h front view of NF₃ adsorbed MoSe₂ monolayer

Table 1 Comparison study of adsorption parameters between CO, CO₂, SO₂, and NF₃ molecule and MoSe₂: E_ads for the adsorption energy, d, Q_T, Style, and E_g for distance, charge transfer, Type of the charge transfer, and Energy Band Gap

Fig. 4

The electron difference density (EDD) plot a top view of CO adsorbed MoSe₂ monolayer, b top view of CO₂ adsorbed MoSe₂ monolayer, c front view of CO adsorbed MoSe₂ monolayer, d front view of CO₂ adsorbed MoSe₂ monolayer, e top view of SO₂ adsorbed MoSe₂ monolayer, f Top view of NF₃ adsorbed MoSe₂ monolayer, g front view of SO₂ adsorbed MoSe₂ monolayer, h front view of NF₃ adsorbed MoSe₂ monolayer

5 CO₂ molecules adsorption on MoSe₂ nanosheet

The adsorption of CO₂ has also been illustrated in Fig. 3b, d. The CO₂ molecule has a linear structure with a 1.14 Å C–O bond. Additionally, oxygen in the carbon dioxide molecule hybridizes its orbitals to create three sp² hybrid orbitals. After adsorption of CO₂ on MoSe₂ monolayer it is found that the calculated distance between the C of CO₂ and Se of MoSe₂ is 1.83 Å. The calculated adsorption energies are − 0.8 eV for CO₂. The charge transfer from MoSe₂ to CO₂ gas molecule was 0.017e, the positive sign signifies that 0.017e charge from MoSe₂ to CO₂. The electron difference density (EDD) plot is shown in Fig. 4b, d.

$$ Mo_{24} Se_{48} + CO_2 \to Mo_{24} Se_{48} @CO_2 + E_{ad} ,\;\left( {E_{ad} = - 0.8\;{\text{eV}}} \right) $$

(6)

6 SO₂ molecules adsorption on MoSe₂ nanosheet

The adsorption of SO₂ has also been illustrated in Fig. 3e, g. The SO₂ molecule has a linear structure with a 1.43Å S–O bond. Additionally, oxygen in the Sulfur dioxide molecule hybridizes its orbitals to create three sp² hybrid orbitals. In MoSe₂@SO₂ the bond length between Se of MoSe₂ and S of SO₂ is 1.54 Å. The adsorption energy of the system is − 0.54 eV, and the charge transfer from MoSe₂ to SO₂ gas molecule was 0.21e, the positive sign signifies that 0.21e charge from MoSe₂ to SO₂. The electron difference density (EDD) plot is shown in Fig. 4e, g.

$$ Mo_{24} Se_{48} + SO_2 \to Mo_{24} Se_{48} @SO_2 + E_{ad} , \, (E_{ad} = - 0.54eV) $$

(7)

7 NF₃ molecules adsorption on MoSe₂ nanosheet

The adsorption of NF₃ has also been shown in Fig. 3f, h. The NF₃ molecule has a linear structure with a 1.37 Å N–F bond. Additionally, oxygen in the Nitrogen trifluoride molecule hybridizes its orbitals to create three sp³ hybrid orbitals. In MoSe₂@NF₃ the bond length between Se of MoSe₂ and N of NF₃ is 1.48 Å. The adsorption energy of the system is − 0.5 eV, the charge transfer from MoSe₂ to NF₃ gas molecule was − 0.03e, and the negative sign signifies that 0.21e charge to MoSe₂ from SO₂. The electron difference density (EDD) plot is shown in Fig. 4f, h.

$$ Mo_{24} Se_{48} + NF_3 \to Mo_{24} Se_{48} @NF_3 + E_{ad} , \, (E_{ad} = - 0.5eV) $$

(8)

8 Electronic properties of CO, CO₂, SO₂, and NF₃ adsorbed on MoSe₂ surface

Figure 5a, e illustrates how gas adsorption (CO, CO₂, SO₂, and NF₃) affects the band structure of pristine MoSe₂ systems. Notable changes in the band structure due to adsorption for both gases are shown in Fig. 5. Table 1 shows the observed changes for both pure MoSe₂ crystals. Our study shows that the band structure of MoSe₂ monolayer 1.43 eV which is very close to 1.55 eV reported in previous studies (Geim 2007) as mentioned in Table 1. After adsorption of CO on the MoSe₂ monolayer, the band gap is lowered to 1.39 eV, shown in Fig. 5b i.e., a fall of 5.6% can be noticed as compared to MoSe₂. After adsorption CO₂ on MoSe₂ monolayer addition of bands can be observed near the conduction and valance band close to Fermi level as illustrated in Fig. 5c. The reduced band gap is 1.25 eV, which is 12.6% lower as compared to MoSe₂. Hybridization and orbital overlaps are likely to blame for the bandgap's reduction. SO₂ adsorption causes the band gap of the MoSe₂ monolayer to drop to 0.86 eV, i.e., a 39.9% drop as compared to Pure MoSe₂ can be observed. Moreover, because both gases adsorb on virgin structures, new subbands form within the valence bands as well as conduction bands. Furthermore, MoSe₂ exhibits a significantly less band gap difference following NF₃ adsorption than other gases. The determined band gap is 0.64 eV which is 56% less as compared pristine MoSe₂ monolayer. The band gap's modifications after the adsorption of CO, CO₂, SO₂, and NF₃ gas molecules, as well as all the newly formed bands both above and below the Fermi level, indicate that the band structure analysis's conclusions may also be used to validate the sensing of CO, CO₂, SO₂, and NF₃ gas molecules. The changes observed in the density of states (DOS) after the adsorption of all the gases are explained by the formation of new subbands, as can be seen below.

Fig. 5

Band structures of a 2-D pristine MoSe₂ monolayer, b CO adsorbed MoSe₂ monolayer, c CO₂ adsorbed MoSe₂ single layer, d SO₂ adsorbed MoSe₂ monolayer, e NF₃ adsorbed MoSe₂ single layer

The adsorption of both gases on pure MoSe₂ structures causes the DOS to be analyzed to study the electronic energy levels in the valance and conduction bands, as seen in Fig. 6a–e. The energy range of the systems taken from − 2 to 2 eV is displayed in Fig. 6. As seen in Fig. 6a, the DOS plot of the MoSe₂ monolayer. The DOS plot consists of the Total DOS of MoSe₂ monolayer, Mo, d orbital, and Se, p-orbital with similar peck position. The available energy states can be observed from − 0.72 to − 2 eV on the right side and 0.71–2 eV on the Fermi level's left side in the DOS plot. On the left side of the Fermi level, several peaks can be observed. The highest peak is present at 1 eV. Figure 6b shows that the adsorption on MoSe₂ monolayer introduces new energy levels at − 0.67 eV to − 0.72 eV and 0.68 eV to 0.71 eV within the conduction as well as valance bands, respectively, indicating a decrease in band gap energy. After adsorption peak present in the conduction band is also reduced. P-orbital of the O and C atoms present in the CO is responsible for the addition of new energy levels. The peaks of both sides of the Fermi level are influenced by the d-orbital of Mo. It's interesting to note that CO₂ will be adsorbed in a manner akin to CO adsorption when interacting with the MoSe₂ monolayer. The electronic structure presented in Fig. 6c indicates that the strong bonding between C–Se is correlated with the Mo d-, Se p-, C p- and O p-orbitals, respectively. As a result of CO₂ adsorption on the MoSe₂ monolayer new energy bands were added to both sides of the conduction from 0.58 to 0.71 eV and a valance band from − 0.62 to − 0.72 eV. Figure 6d represents the DOS plot of SO₂ adsorbed MoSe₂ monolayer. The primary cause of the alteration of the occupied states of DOS for pristine MoSe₂ systems is the newly occupied electronic states that come from SO₂ adsorption. d—Orbital of Mo in MoSe₂ and p—orbital O in SO₂ are responsible for additional energy states in valance and conduction band. At around 0.4 eV and − 0.4 eV an addition of energy states can be observed on both sides of the fermi level. DOS plot MoSe₂@NF₃ shown in Fig. 6e, the addition of a significant amount of energy states introduced because of the adsorption of NF₃ on MoSe₂. The energy states were observed near − 0.27 eV in the valance band and at 0.32 eV in the conduction band. P-orbital of N in NF₃ and d-orbital of Mo in MoSe₂ monolayer. Because it contains "chemisorption" occurrence, when it comes to identifying CO gas molecules, the MoSe₂ system is incredibly sensitive and selective. The chemisorption process has a significant impact on both bandgap narrowing and electrical structure.

Fig. 6

DOS plot of a pristine 2-D MoSe₂ monolayer, b CO adsorbed MoSe₂ monolayer, c CO₂ adsorbed MoSe₂ monolayer, d SO₂ adsorbed MoSe₂ monolayer, e NF₃ adsorbed MoSe₂ monolayer

9 Recovery property

A shorter span of recovery time might be advantageous for a gas sensor's reversibility. The sensor is heated to extreme temperatures to experimentally evaluate the recovery time; however, in principle, it is computed using the transition state theory, which establishes the connection between the recovery period and the adsorption energy. Thus, it is important to remember that in sensing applications, the recovery time is crucial. The Van't Hoff-Arrhenius expression (Demir and Fellah 2020) for the rate constant may be used to estimate the recovery time $\left( \tau \right)$. This can be done by using the definition that follows.

$$ \tau = \frac{1}{{\omega \exp \left( {{\raise0.7ex\hbox{${E_{ads} }$} \!\mathord{\left/ {\vphantom {{E_{ads} } {K_B T}}}\right.\kern-0pt}\!\lower0.7ex\hbox{${K_B T}$}}} \right)}} $$

(8)

where it is typically believed that the attempt frequency $\left( \omega \right)$ is "a typical value" in the range of 10¹²–10¹³ s⁻¹ according to transition state theory, it is assumed to be 10¹² s⁻¹, where T represents temperature, the Boltzmann constant is denoted by $K_B$ (8.318 × 10⁻³ kJ/(mol K)) (Peng et al. 2004; Hoa et al. 2009). We take the value of E_ads to represent the potential barrier (E_a) of the process of desorption since desorption is thought of as the opposite of adsorption (Cui et al. 2019c; Sarkar et al. 2021). To completely comprehend the 2-D MoSe₂ monolayer desorption property, we considered the temperatures of 300 K, 400 K, and 500 K. The computed recovery time is presented in Fig. 5. Which illustrates how the recovery period may magnify an adsorption energy differential of less than 1 eV by many orders of magnitude. MoSe₂@CO has the longest recovery time i.e., 3422.8 s at the temperature of 300 K. The MoSe₂@NF₃ system has the quickest recovery time i.e., 0.23 ms. The recovery time of the adsorbed system can be arranged as follows MoSe₂@NF₃ < MoSe₂@SO₂ < MoSe₂@CO₂ < MoSe₂@CO. Recovery time also depends on temperature as illustrated in Fig. 5. As the temperature rises the recovery time decreases. Thus, the candidate materials with the right gas adsorption energy and quick response time should be chosen when other requirements are satisfied (Fig. 7).

Fig. 7

Recovery time of different sensing systems

10 Current–voltage

To evaluate the true implications of 2-D MoSe₂ monolayer for CO, CO₂, SO₂, and NF₃ gas sensor, it has to be investigated as a gas resistive sensor or field effect transistor (FET), where the main variable reacts to the resistance or threshold voltage. To test the 2-D MoSe₂ monolayer output with and without CO, CO₂, SO₂, and NF₃ gas molecules, we thus employed the NEGF technique to compute the transport properties for a wide spectrum of (voltage). A scattering zone was placed between the left as well as right electrodes, which were modeled using identical material. The hazardous gasses CO, CO₂, SO₂, and NF₃ are adsorbed in the scattering region, and the electrode is thought to be semi-infinite (Fig. 8).

Fig. 8

a Circuit diagram of 2-D MoSe₂ monolayer, b MoSe₂@CO₂, c MoSe₂@CO, d MoSe₂@SO₂, e MoSe₂@NF₃

In all critical computations, relaxed upper cell structures are used to analyze electronic transport characteristics. To draw similarities, the current (I)–voltage (V) characteristics without the gases were examined. A monolayer is used to adsorb the gas molecules CO, CO₂, SO₂, and NF₃. The induced current for NF₃ is more than that of any other molecule used here such as CO, CO₂, and SO₂ when different bias voltages are applied. As opposed to the pure MoSe₂ monolayer, gas molecules adsorbed on the MoSe₂ monolayer, such as CO, CO₂, SO₂, and NF₃, showed the greatest current fluctuation with voltage. It was found that the pristine current is zero from 0 to 1 V bias and increases to 1.2 µA at 2 V. The I–V properties of the MoSe₂ monolayer before as well as after adsorption with the gases are shown in Fig. 9. From 0 to 1 V bias voltage, the device is in turned off condition. At 2 V bias voltage, the observed currents are 1.2 µA for pristine MoSe₂, 2.14 µA for CO absorbed, 2.96 µA for CO₂ absorbed, 4.06 µA for SO₂ and 5.50 µA for NF₃ absorbed. Because of the high surface-to-volume ratio in nano devices such as 2-D MoSe₂ monolayer devices, surface states and interface traps play a more significant role in causing current nonlinearity. Moreover, defects and variability introduced by nanoscale manufacturing can result in varying electric fields and carrier transport, which further exacerbates nonlinear behavior.

Fig. 9

IV characteristics

Sensitivity is explicitly defined as the relative change in current (conductance) caused by the adsorption of gas molecules in the context of a 2-D material-based sensor that detects gas molecules. This is frequently stated as a change in percentage or fraction. The formula below is used to determine the sensitivity (S) of the gases to assess how a monolayer MoSe₂ sensor reacts to harmful gases like CO, CO₂, SO₂, and NF₃ molecules.

$$ S = \frac{{\left| {G - G_0 } \right|}}{G_0 } = \frac{{\left| {I - I_0 } \right|}}{I_0 } $$

(9)

where, the conductance and electric current, respectively, in the presence and absence of gas molecules are denoted by $\left( {G,G_0 } \right)$ and $\left( {I,I_0 } \right)$. Figure 10 illustrates the MoSe₂ monolayer sensitivity to harmful gases like CO, CO₂, SO₂, and NF₃ molecules. The MoSe₂ monolayer-based gas sensor for harmful gases like CO, CO₂, SO₂, and NF₃ molecules exhibits an increment in sensitivity at 1.6 V but after that sensitivity decreases. It is observed that at voltages (e.g., V = 1.6 V), the MoSe₂ gas sensor shows improved sensing capability.

Fig. 10

Sensitivity plot of the gas sensors

11 Conclusion

Van der Waals corrected DFT simulations were accustomed to analyzing the adsorption behavior as well as electronic characteristics of the molecules adsorbed by the MoSe₂ monolayer in order to investigate its potential as a high-performance ambient temperature CO, CO₂, SO₂, and NF₃ sensor. The adsorption of these molecules on the MoSe₂ monolayer has been thoroughly investigated theoretically, and the modifications in the band structure (E_g), DOS, adsorption energy (E_ads), and recovery time have all been examined. All of the gases adsorb on the MoSe₂ single layer by the physisorption process, according to our data, which also suggests the adsorption energy follows the sequence NF₃ > SO₂ > CO₂ > CO. Additionally, all three gases had fast recovery times, which is a crucial result as it establishes whether or not a sensing material is worth recycling. The CO (3422.8 s) molecule has a very significant recovery time, whereas the CO₂ (23.06 s), SO₂ (1 ms), and NF₃ (0.22 ms) molecules have very low values of recovery durations. Since MoSe₂ has a very low recovery time, it can be used as a reusable and recyclable sensor for detecting NF₃ and SO₂. The very sensitive nature of the MoSe₂ monolayer is confirmed by the considerable fluctuation in its I–V properties following exposure to gas molecules. Our findings suggest that 2-D MoSe₂ monolayers may be employed as gas sensor materials with multi-time reusability and recyclability for several gases (CO, CO₂, SO₂, and NF₃).