Superior Gas Sensing Properties of $\beta$-In$_2$Se$_3$: A First-Principles Investigation

Using first-principles calculations, we report structural and electronic properties of CO, NO$_2$, and NO molecular adsorption on $\beta$-In$_2$Se$_3$ in comparison to a previous study on alpha-phase. Analysis and comparison of adsorption energies and extent of charge transfer indicates $\beta$-In$_2$Se$_3$ to be selective in detecting gas molecules. We found NO molecules acting as charge donor whereas CO and NO2 molecules as charge acceptors, respectively, experiencing physisorption in all cases. Owing to enhanced adsorption, faster desorption and improved selectivity of the gas molecules discussed in detail, we conclude $\beta$-In$_2$Se$_3$ to be a superior gas sensing material ideal for chemoresistive-type gas sensing applications.


Introduction
The need to identify gas leakage, toxic gases, and organic vapours for human and environmental safety is fundamental to develop next-generation sensing technologies. Gases that are by-products of our day-to-day activities (e.g., CO, NO2, and NO etc.) and toxic even at lower concentrations demand great attention. Different materials are thus employed in a bid to identify toxic gases which includes conducting polymers, 1-3 carbon nanotubes (CNTs), 4,5 and semiconducting metal oxides 6,7 to list a few. Conducting polymers are easily processed, but effects of humidity and degradation hamper their applicability. [8][9][10] On the other hand, metal oxides show prospects in sensing molecules, however, high operating temperature, large power consumption, and low selectivity have been a major issue in their commercial usage. [11][12][13] Owing to these obvious drawbacks, researchers have intensified efforts in exploring potential new materials that can efficiently detect gases at room temperature and standard environmental conditions while retaining high selectivity and sensibilities.
The successful synthesis of graphene 14 earlier this century has birthed an extensive and increasing research attention on two dimensional (2D) materials. Since then, 2D materials have been explored for countless applications (such as Li-ion batteries, 15 electrocatalysis, 16 photon-emitting 17 devices to name a few). Their inimitable geometry, 18 large surface-tovolume ratio 19 with strong surface reactivity 20 and possibility to achieve thickness-modulated sensing characteristics 21 make 2D materials highly suitable for gas sensing applications.
These remarkable features have led to an increased use of 2D materials for gas-sensing applications and there exist several theoretical and experimental reports showing good sensing abilities with high response. [22][23][24] Indium selenide (In 2 Se 3 ) is a promising 2D semiconductor belonging to the III 2 -VI 3 chalcogenides covering a broad range of light absorption, 25 having tunable bandgap, 26,27 and phase change properties. 27,28 It is a polymorphic non-transition metal chalcogenide that crystallizes in five distinct polymorphs namely α, β, γ, δ and κ depending on growth temperature and pressure. [29][30][31][32][33][34] The α-and β-phases experience van der Waals interactions 29,35 making them suitable for several applications including phase-change memory, 36 e-skin applications, 37 optoelectronics, 26,38 and photodetection 39 to list a few. While both phases possess similar geometries, they exhibit significant difference in electronic properties. 34 The electronic band structure of β-In 2 Se 3 is reported to have stronger sensitivity to externally applied electric fields compared to the α-phase. 30,34 However, while the gas sensing applications of α-In 2 Se 3 have been reported in literature, 40 the gas sensing abilities of atomically thin β-In 2 Se 3 have so far remain lacking. In addition, the existing report on α-In 2 Se 3 does not take into account the van der Waals dispersion corrections for the molecular adsorptions.
It is therefore in this study we investigate gas sensing properties of β-In 2 Se 3 for CO, NO 2 , and NO molecules by using first-principles calculations incorporating van der Waals dispersion corrections. Various atomic sites were carefully inspected for molecular absorption to reveal the most favourable structural configurations, for which electronic band structures and density-of-states are calculated. We found the NO molecule to have the highest binding energy whereas Bader charge analysis shows significant charge transfer for NO 2 molecule compared to others. Similarly, we observed that the NO 2 physisorption gave rise to mid-gap states whereas NO molecules strongly perturb region close to the conduction band minimum.
Our analysis and comparison to the α-phase shows that β-In 2 Se 3 is a promising material for chemoresistive based gas sensing applications.

Computational Method
We have performed first-principles calculations based on density functional theory (DFT) 41,42 as implemented in the Quantum Espresso package. 43,44 To describe exchange and correlation effects, we used generalized gradient approximations (GGA) in the Perdew-Burke-Ernzerhof parameterization (PBE). 45 The projected augmented wave (PAW) method of DFT with plane-wave cut-off energy truncated at 45 Ry was used. 46 For structural relaxation (selfconsistent calculations), we used 2 × 2 × 1 (4 × 4 × 1) k-mesh, respectively, whereas a dense 8 × 8 × 1 k-mesh was used for density-of-states (DOS) calculations. To avoid spurious interactions between the periodic images and efficiently model the adsorbents, a 3 × 3 × 1 supercell of β-In 2 Se 3 with 15Å vacuum was constructed. In the iterative solution of the Kohn-Sham equations, an energy convergence of 10 −4 Ry and a force convergence of 10 −3 Ry/Bohr was achieved. We used Grimme's DFT-D3 approach to describe the interlayer vdW interactions. 47,48 Bader charge transfer was performed using the method described in Ref. 49

Results and Discussion
The optimized lattice constant of β-In 2 Se 3 turns out to be 4.03Å which is in good agreement to the experimental value of 4.025. 50 It consists of five covalently bonded atomic sheets known as quintuple layers (QL) that are vertically stacked in the sequence Se-In-Se-In-Se atoms. Each stratum in the QL takes the form of a well-aligned triangular lattice which is also characterized by a surface projected hexagonal void. As a precondition to investigate gas sensing, we first identify the energetically favourable adsorption sites for CO, NO   The adsorption energy was calculated using equation (1), where E In 2 Se 3 +M , E In 2 Se 3 , and E M corresponds to the total energies of β-In 2 Se 3 with the adsorbed molecule, the pristine β-In 2 Se 3 detached molecule, respectively. It follows from the above formula that a negative value of -0.109 eV is obtained implying an exothermic reaction, resembling the case of CO adsorption on graphene. 52 Table 1: Favourable atomic sites, interlayer distance between α-or β-In 2 Se 3 and molecule, adsorption energies E ads , and magnitude of charge transfer (∆Q). Data for the α-In 2 Se 3 was obtained from Ref. 40 Molecule It is also pertinent to mention that when compared with the adsorption behaviour on α-In 2 Se 3 40 our obtained adsorption energies are adequately large to inhibit room-temperature thermal fluctuations (see Table 1) especially in the case of NO 2 on α-In 2 Se 3 where a weak physisorption energy of -0.058 eV was reported. In addition, our adsorption energy for NO and NO 2 molecules is indicative of a better adsorption/desorption recovery process on β-  NO has an enhanced electron transfer with the monolayer when compared to the case of CO molecule. We also plot the electronic band structure in Figure 2b for the pristine and molecular adsorbed β-In 2 Se 3 . Evidently, no visible change is observed for the CO adsorption, whereas, for NO 2 , a localized state is manifested above the VBM. On the other hand, for NO molecular adsorption, the band structure shows a downward shift in the CBM when compared to the pristine case.
To better understand charge transfer between β-In 2 Se 3 and adsorbents, we next plot the charge density difference (CDD) in Figure 3 using equation ∆ρ = ρ In 2 Se 3 +M − ρ In 2 Se 3 − ρ M , whereas ρ In 2 Se 3 +M , ρ In 2 Se 3 , and ρ M represent charge densities for the monolayer with the adsorbed molecule, the pristine monolayer, and detached molecules, respectively. As shown in Figure 3a, adsorption of CO results in charge redistribution within the molecule. Looking at the charge depletion from C atom that is accumulated on the O atom, we notice charge depletion from the Se atom tending towards the CO molecule. Using the Bader charge analysis, we found that the CO molecule accepts 0.02 e from the monolayer underneath confirming CO molecule to be a weak acceptor of electrons on β-In 2 Se 3 as it were on InSe. 51 The CDD for the adsorption of NO 2 on monolayer is shown in Figure 3b. Evidently, NO 2 induces charge redistribution in the region between the molecule and the monolayer surface.
The charge accumulation can be found around the molecule while the depletion is occurring mainly on the Se atom in the vicinity of the molecule, thereby indicating that NO 2 obtains charge from the monolayer. According to Bader charge analysis, NO 2 molecule accepts 0.14 e from β-In 2 Se 3 .
However, the converse was observed for the NO molecule adsorption on β-In 2 Se 3 (see

Conclusion
Using first-principles calculations, we investigate structural and electronic properties of β-In 2 Se 3 with the adsorption of CO, NO 2 , and NO molecules. Experiencing physisorption in all cases, we found that β-In 2 Se 3 would be selective in gas detection as CO and NO 2 acts as electron acceptors with 0.02 e and 0.14 e obtained respectively from the monolayer while NO acts as an electron donor by donating 0.02 e to the monolayer. In addition, we observed that CO had no significant effect on the electronic properties of the monolayer while NO 2 and NO introduced interstitial impurity states. It follows straight forwardly from the foregoing that β-In 2 Se 3 from amongst the tested gases would sense best the NO molecules compared to other studied cases. In addition, our results suggest enhanced adsorption, faster desorption and improved selectivity of the gas molecules thereby making β-In 2 Se 3 a superior gas sensing material compared to its α-phase. Hence, our first-principles findings suggest that β-In 2 Se 3 is a promising material in the fabrication of gas sensors built on the charge transfer mechanisms.

Acknowledgement
The computational resource for this calculation was provided by the High Performance Computing Centre at King Abdulaziz University (Aziz Supercomputer).

Competing Interests
The Authors declare no competing financial or non-financial interests.

Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.