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Charge Transfer and Functionalization of Monolayer InSe by Physisorption of Small Molecules for Gas Sensing

First-principles calculations are performed to investigate the effects of the adsorption of gas molecules (CO, NO, NO2, H2S, N2, H2O, O2, NH3 and H2) on the electronic properties of atomically thin indium selenium (InSe). Our study shows that the lone-pair states of Se are located at the top of the valence band of InSe and close to the Fermi energy level, implying its high sensitivity to external adsorbates. Among these gas molecules, H2 and H2S are strong donors, NO, NO2, H2O and NH3 are effective acceptors, while CO and N2 exhibit negligible charge transfer. The O2 molecule has very limited oxidizing ability and a relatively weak interaction with InSe which is comparable to the N2 adsorption. A clear band gap narrowing is found for the H2S, NO2, and NH3 adsorbed systems whereas a Fermi level shifting to the conduction band is observed upon a moderate uptake of H2 molecules. Our analysis suggests several interesting applications of InSe: 1) Due to the different interaction behaviors with these external molecules, InSe can be used for gas sensing applications; 2) By monitoring the adsorption/desorption behavior of these gas molecules, the population of hole states in InSe due to photon stimulation or defect production can be quantitatively estimated; and 3) It is promising for novel electronic and optoelectronic applications since the adsorption-induced in-gap states and strong charge transfer are able to change the content and polarity of charged carriers and lead to different optical properties.


INTRODUCTION
Two-dimensional (2D) materials have received a great deal of attention in recent years due to their intriguing electronic properties originated from quantum confinement and high surface-volume ratio [1][2][3][4][5][6] . In particular, layered 2D materials with van der Waals (vdW) interaction between atomically thin layers allow for high-quality exfoliation/transfer and ultrahigh flexibility, and thus are highly promising for flexible nanoelectronics applications [7][8][9][10] . For 2D semiconducting materials with a finite band gap like MoS 2 and phosphorene, their electronic band gaps and work functions are generally layer number-dependent 11 , which allows for more efficient solar utilization and carrier injection at the 2D materials-electrodes interfaces. In addition, their electronic properties and structural stability are sensitive to environmental molecules due to the high surface-volume ratio and weak electronic screening [12][13][14][15][16] . As a result, 2D materials are highly suitable for gas sensing via modulating the carrier density and shifting the Fermi level 12,13 . Last but not least, 2D materials can be easily functionalized by molecular doping, which can be used to modify their electronic, optical, and thermoelectric properties [17][18][19][20][21][22][23] , in addition to strain engineering and heterogeneous construction 24,25 .
More recently, indium selenides (InSe), a layered material with each InSe layer being composed of a Se-In-In-Se structure, gains increasing attention  . Many 3 studies have been performed to understand its charge carrier dynamics 26,27,38 , structure stability 28 , electronic structure 29,32-37, 39,40 , photoluminescence and surface photovoltaic effect 41 . In addition, the growth 42,43 and chemical functionalization 44 of ultrathin InSe nanosheets have been explored, and potential applications based on InSe in nanoelectronics 45 , sensors 46 , optoelectronics and photodetectors [47][48][49][50][51] have been sought. These studies have revealed many fascinating behaviors of InSe. For example, it possesses a high carrier mobility (up to 10 3 cm 2 V −1 s −1 and 10 4 cm 2 V −1 s −1 at room and liquid-helium temperatures, respectively) and a high thermal stability up to 660°C 26,27 . Importantly, InSe sheets are stable under ambient conditions and no decomposition in air is observed 28 . A band gap narrowing of around 0.5 eV was observed from bulk InSe (1.35 eV 29 ) to bilayer InSe according to photoluminescence spectroscopy measurement 30,31 . Density functional theory (DFT) calculations revealed that bulk InSe has a direct band gap at Z point 32 and few-layer InSe shows an indirect band gap [33][34][35][36][37] . Despite the presence of heavy atoms of In and Se, the effect of spin-orbital coupling on the states at the top of the valence band and the bottom of the conduction band is negligible, and thus the band gap is less affected by this coupling 32 . Similar to black phosphorus, much lighter carriers are found for transport along the out-of-plane direction than the in-plane direction 32,34 .
For many applications, examining the effects of external factors, such as environment molecules and dopants [52][53][54] , contacting electrodes 55 , and supporting substrates on 2D materials 56 is highly important to achieve improved stability, robust performance, and tunable functionality. For instance, water and oxygen molecules 4 were found to affect the stability of phosphorene 57,58

A. Features in the electronic structure of pristine monolayer (1L) InSe
The band structure of the 4×4 supercell structure of monolayer InSe is shown in The local density of states (LDOS) and band structure are shown in Fig. 2c and d, respectively. It can be seen that there is no additional CO induced states within the band gap. Concerning the frontier orbitals like the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the adsorbed CO molecule, its 4σ (HOMO-2), 1π (HOMO-1), 5σ (HOMO) and 2π*(LUMO) states are located at -8.50, -6.23, -3.58 and 3.40 eV relative to the E f . According to the LDOS plot, the 5σ peak, which coincides well with the valence states of the InSe host, is slightly more broadened than 4σ, 1π and 2π* levels. As the 5σ state mainly distributes on the C atom and there are enhanced bonding charges between C and Se atoms as shown in Fig. 2a, it is highly likely that the CO-InSe interaction mainly occurs via the 9 hybridization between the 5σ state and the lone pair electrons on the Se atoms.
H 2 adsorption: Similar to the case of CO molecule, the lowest energy configuration of H 2 above InSe also adopts a parallel alignment with the basal plane (Fig. 3a). The H 2 is located at about 3.01 Å above the terminated Se lattice plane with the length of H-Se bonds ranges from 3.60 to 3.77 Å. The corresponding E ad is -0.05 eV, comparable to that of H 2 above graphene with E ad of -0.04 eV/H 2 64 . It is well known that graphene is a potential material for hydrogen storage due to its appropriate H 2 binding energy for simultaneously stable hybrogen storage and facile release 65 .
Herein the predicted comparable adsorption energy of H 2 above InSe suggests that it may be a promising material for hydrogen storage despite its smaller gravimetric value due to its larger density than graphite.
Charge transfer analysis shows that there is a strong depletion of electrons in the H 2 molecule upon adsorption. The isosurface plot of the DCD shown in Fig. 3a reveals that diminishing electrons mainly distribute at the two ends of H 2 . An increase of electrons at the nearest Se atoms can be clearly observed. Charge integration analysis is presented in Fig. 3b (Fig. 3c).  (Table 1).

N 2 adsorption:
The most stable configuration of the adsorbed N 2 molecule adopts a nearly parallel configuration relative to the basal plane. It is located at around 2.90 Å above the center of the hexagonal void. The E ad is calculated to be -0.12 eV. Figure   5a shows C. Molecular acceptors NH 3 adsorption: The lowest-energy configuration for the NH 3 adsorbed InSe 12 system is shown in Fig. 6a, where the molecule is located at above the hollow hexagon center with the N atom pointing toward the surface and the three H atoms pointing away from the surface (Fig. 6a). The NH 3 molecule is about 2.49 Å above the Se basal plane and the length of the three N-Se bonds ranges from 3.60 to 3.70 Å.
The E ad is found to be -0.20 eV. Figure 6b shows that there is a significant charge redistribution between the NH 3  It should be noted that the way of charge transfer in the case of NH 3 is slightly different from the cases of preceding donor molecules. While clear lobes and nodal planes appear in the vdW gap of the DCD plots in the donor molecules like CO, H 2 , H 2 S and N 2 , no such characteristics appears in the DCD plot of NH3 in Fig. 6a. It seems that the charges are redistributed via forming slight hybridized states between the NH 3 and InSe. The DOS plot (Fig. 6c) shows that the nonbonding HOMO orbital (3a 1 ), which consists of the lone electron pair at the N atom, is located at around -0.97 eV below the E f . The large broadening of this level could be an indicator of its hybridization with valence states of InSe. Instead, the doubly degenerated NH 3 1e 13 level, which consists of the s-p hybridized molecular orbitals, is located separately with respect to the valence bands of InSe, indicating a relatively weak interaction.
Similar to other molecular dopants, there are negligible changes in the curves of the band structure (Fig. 6d) due to NH 3 adsorption. However, the band gap reduces from 1.50 eV of pure InSe to 1.45 eV upon adsorbing NH 3 (Table 1).

NO adsorption:
For the NO molecule, its adsorbing geometry and energetics are similar to those of CO adsorption. The most stable adsorbing configuration shows the NO lying parallel to the surface with 3.10 Å above the center of the hexagon and the E ad of -0.13 eV, comparable to that of CO (see Table 1). However, the NO molecule is an open-shell molecule and shows a very different charge transfer and electronic modification of InSe than that of CO adsorption. According to the DCD plot shown in 14 Free NO gas molecule has a singly occupied electron in a doubly degenerated antibonding 1π* orbital, followed by a lower-energy doubly degenerated 1π orbital and a 2σ orbital. As can been from the DOS and band structure shown in Fig. 7c  The state alignment and hybridization between NO 2 and InSe can be reflected in the plots of the DOS and band structure ( Fig. 8c and d)

IV. DISCUSSION
The recent experiments demonstrated a high mobility of InSe 26,27 . Understanding the effects of environmental molecules on its electronic and chemical properties should be highly important for its potential applications. Figure 9 shows the relationship of the dipole moment and E ad for the adsorbed molecules on the InSe surface. For comparison, we also plot the data for the molecular adsorption on the phosphorene with the same computational method 14 . For both cases, the curve adopts a "V" shape. Starting from the zero dipole molecules, the adsorption enhances with increasing the dipole moment of the adsorbates, reaches maximum for the NO 2 molecule and then weakens afterward with further increasing the dipole moment. Two mechanisms are responsible for the interaction of the molecules with the surface: chemical hybridization and the dipole-dipole interaction. It is expected that the former mechanism is dominated for adsorptions of molecules with a small dipole moment. As shown in Fig. 9, the E ad for the adsorption of the small-moment molecules (H 2 , CO, NO, NO 2 ) on InSe is around a half of those for adsorption on phosphorene. This suggests that the chemical interaction between the molecule and InSe is weaker than that between the molecule and phosphorene, which is well-known for its sensitivity to environmental molecules and low structural degradation. The overall much weaker E ad for molecules on the InSe surface suggests that InSe in air should be more stable than phosphorene in air.
Our calculations have shown that the carrier density and polarity of the InSe sheet can be easily modulated upon selective adsorption of gas molecules. It should be noted that in our current study, we only consider the dilute doping of molecular adsorbates. In high doping condition, the strength of interaction and the degree of charge transfer per molecule should be smaller than our predicted values due to the increasingly important role of the intermolecular interaction. While our current work only investigates the gas adsorption on monolayer InSe, it is expected that the predicted oxidation states of these molecules should remain true for few-layer InSe since the surface chemistry is similar and the interlayer interaction is through weak vdW interaction.
In addition, the charge transfer induced by the molecular adsorption may allow the modulation of optical properties of InSe. Due to the atomically thin structure of InSe, the electronic screening effect is expected to be weak and its optical properties may exhibit a high sensitivity to environment. Previous studies show that the amount of charge transfer induced by chemical molecules can greatly suppress the non-radiative recombination in 2D transition metal dichalcogenides [72][73][74][75] and in some cases, it may even lead to near-unity photoluminescence 76 . The photoluminescence can also be modulated by controlling the charge transfer by selecting different substrates 77    on phosphorene is adapted from Ref. [14] with the same computational method.