1. Introduction

Graphene and similar ‘‘two-dimensional’’ materials have attracted increasing technological and scientific interests because of their special mechanical and electronic features ^{[1, 2, 3]}. Molecu- lar interaction at their surfaces is a subfield of considerable interest due to potential applications such as electronic devices and chemical sensors ^{[4, 5]}. Their high surface area to volume ratio is ideal for gas sensors. The reactivity of graphene is often adjusted by doping with other elements or topological defects ^[6]. Hexagonal BN,a layered material,so-called ‘‘white graphene’’,has been isolated from bulk BN and could be useful as a complementary two-dimensional dielectric substrate for graphene electronics ^[7]. In contrast to the half-metal behavior of graphene,BN sheets possess polar B-N bonds and a wide band gap ^[8]. Zhang et al. ^[9] have investigated adsorption mechanisms of carbon monoxide on BN sheets with various modifications,including Al doping,mono- vacancies,and Stone-Wales defects via density functional theory (DFT). It was found that the modified sheet is more sensitive than the pristine sheet for detecting CO molecules. In this work,by means of DFT calculations,we investigate the adsorption of N₂O molecules on pristine and Al-doped BN sheets to verify whether or not the sheets can be used as gas sensors in environmental monitoring. Besides the interest in N₂O as a greenhouse gas,there is also a need tomonitor N₂O gas inmedical,dental,and veterinary environments,where N₂O is routinely used as an anesthetic. Long- term exposure to N₂O gas has been linked to DNA damage, suppression of immune defenses,and reduced fertility ^[10].

2. Theory and computational method

We selected a BN sheet,consisting of 33 B and 33 N atoms (Fig. 1) in which the end atoms were saturated with hydrogen atoms to reduce the boundary effects.We also replaced a B atomof the sheet with an Al atom and studied the N₂O adsorption on this surface according to the full geometries shown in Figs. 2 and 3. Geometry optimizations were performed using the B3LYP func- tional augmented with an empirical dispersion term (B3LYP-D), with the 6-31G (d) basis set as implemented in the GAMESS suite of programs ^[11]. The optimization was performed using default convergence criteria in GAMESS with no restrictions.

Energy calculations,natural bond orbital analysis (NBO),and density of states (DOS) analysis were performed at the same level of theory. GaussSum program^[12] was used to obtain DOS results. The B3LYP density functional has been previously shown to reproduce experimental properties and has been commonly used in nanostructure studies ^{[13, 14, 15, 16]}. It has been also demonstrated that the B3LYP provides an efficient and robust basis for calculations of III-V semiconductors by Tomic et al. ^[17],capable of reliably predicting both the ground state energies and the electronic structure. We used the definition of N₂O adsorption energy Ead as follows:

where E(N₂O/sheet) corresponds to the energy of the sheet in which the N₂O has been adsorbed on the surface,E(sheet) is the energy of the isolated sheet,E(N₂O) is the energy of a single N₂O molecule,and EBSSE is the energy of the basis set superposition error. The BSSE is calculated based on the Boys and Bernardi counterpoise method ^[18]. HOMO-LUMO energy gap is defined as where ELUMO and EHOMO are the energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO),respectively.

3. Results and discussion

The optimized geometry of the pristine BN sheet is shown in Fig. 1,in which B-N bond length is in the range 1.460-1.471 ,in good accordance with previous results ^[19]. The NBO charge analysis indicates that some electron charges (about 0.49-0.53 e) are transferred from the B atom to its adjacent N atom within the sheet,indicating the partially ionic character of the B-N bonds. It has been previously shown that N₂O molecules are weakly adsorbed on the pristine and Stone-Wales defected BN nanosheets,indicating that the electronic properties of the sheets is not sensitive to N₂O ^[20]. Herein,several possible initial adsorption mechanisms were provided including single (nitrogen or oxygen),double (N-N or N-O),and triple N-N-O bonded atoms on the B and N atoms of the sheet. After relaxation,one stable structure was obtained as shown in Fig. 1,in which the closet distance between N₂O and the sheet is about 3.734 . Our calculations show that the Ead of N₂O is about -5.12 kJ/mol, indicating a weak adsorption. The calculated energy gaps of the pristine and N₂O adsorbed sheet are about 5.93 and 5.87 eV, respectively. A chemical sensor works based on the electrical conductivity change upon the adsorption of an adsorbate. The electrical conductivity can be related to the energy gap according to the following equation ^[21]:

where C,T,and s are constant,temperature,and the electric conductivity,respectively,qe,me,mh,and k are the charge of an electron,mobility of electrons and holes,and the Boltzmann constant,respectively. It should be noted that this equation works only for semiconductors in which by increasing the temperature the electrical conductivity will be increased. According to the equation,smaller values of the energy gap at a given temperature lead to larger electric conductivity. As the energy gap of the pristine sheet is only slightly changed during the adsorption process,the pristine nanosheet will not be sensitive to N₂O molecules.

In order to improve the electrical sensitivity of the nanosheet, we decided to replace a B atomof the sheet with a larger andmore polarizable Al atom. Experimentally,Hjiri et al. ^[22] have shown that Al-doping makes the ZnO nanostructures sensitive to CO molecules. Inserting an Al atom dramatically changes the geometric structure of the sheet (Fig. 2). The Al atom is projected out of the sheet surface in order to reduce stress due to its larger size compared to a B atom. The formed Al-N bond length is about 1.743 ,which is much longer than the corresponding B-N bond. Subsequently,we explored N₂O adsorption on the Al-doped BN sheet (ABN) by locating themolecule above the Al atomfromits N- or O-head. After relax optimization,two stable complexes were predicted (Fig. 3).

The most stable complex (O) is that in which the N₂O molecule is attached from its oxygen atom to the dopant Al atom. The predicted Ead for this adsorption process is about -40.86 kJ/mol,indicating that the interaction of N₂O molecule with the ABN is much stronger than thatwith the pristine sheet. The newly formed Al-O bond length is about 2.172 . The bond lengths of N-Nand N-O of N₂O in the complex are about 1.142 and 1.210 ,compared to 1.151 and 1.221 for the freemolecule,respectively. Shortening of these bonds may be because of an NBO charge transfer of about 0.213 e from the molecule to the nanosheet. In the second most stable configuration (N,Fig. 3),the N₂O is attached fromits N atom to the Al atom with an interaction distance of about 2.209 . The Ead is about -33.96 kJ/mol,and the charge transfer from the N₂O molecule to the nanosheet is about 0.206 e.

The stronger interaction of the N₂O molecule fromits O atomin comparison to the N atom can be rationalized based on the higher NBO negative charge (-0.323 e) which is located on the O atom in comparison to the N head (-0.057 e). It emphasizes that the O- head is a stronger Lewis base in comparison to the N-head. The NBO analysis shows that the hybridization of Al atom is about sp2.94 (nearly sp³ ),in comparison to sp^2.01 of the B atom. Thus,the Al atomis projected out and is favorable for nucleophilic attacks. In the other words,unlike boron atoms,the Al atom can have a coordination number of 4 because of its approximately sp³ hybridization. This may be a reason that the interaction of N₂O molecule with the ABN is much stronger than the pristine sheet.Also,to determine the nature of this stronger interaction,we analyzed the frontier molecular orbitals. Fig. 4 shows that in the pristine sheet the HOMO and LUMO are localized on the N and B atoms,respectively. After the Al doping,the LUMO is mainly located on the Al atom,but the HOMO is still on the N atoms. Therefore,it is expected that the interaction of the HOMO of the N₂O molecule with the LUMO of ABN is stronger than thatwith the LUMO of the pristine sheet.

Calculated DOS of ABN is shown in Fig. 3,indicating that its energy gap value is reduced to 5.50 eV compared to the pristine sheet (5.93 eV). The DOS plot shows that the ABN is still a large-gap semiconductor. DOS plot of the O and N complexes shows a considerable change. New states have appeared at -2.26 and -2.35 eV energy levels in the DOS of O and N complexes in comparison to the bare ABN. This indicates that the electronic properties of the ABN are sensitive to the N₂O adsorption. It is revealed from DOS plot of this configuration that its conduction level shifts to lower energies significantly,but the valence level remains constant compared to the bare ABN. The energy gap value of the ABN decreased from 5.50 eV to 3.93 eV and 3.80 eV in the O and N complexes,respectively. These changes would result in an electrical conductivity change of the defected sheet according to Eq. (3). The ABN becomes a p-type semiconductor due to the appearance of an acceptor state within the energy gap after N₂O adsorption. Compared with the pristine BN sheet,the ABN would have excellent N₂O detection ability. So,we believe that Al doping process may be a good strategy for improving the sensitivity and reactivity of the sheet to N₂O,which cannot be trapped and detected by the pristine BN graphene (Table 1).

We think that the adsorption of N₂O on the surface of ABN may be reversible because of themoderate Ead. Very strong interactions are not favorable in gas detection because these imply that desorption could be difficult and the device may suffer from long recovery times. If the Ead significantly becomes more negative, much longer recovery time is expected based on the conventional transition state theory ^[21]:

where t is recovery time,T is the temperature,k is Boltzmann’s constant,and n0 is the attempt frequency. According to this equation,more negative Ead values will prolong the recovery time in an exponential manner. However,the calculated Ead of N₂O in the ABN systemis not so large as hinder the recovery of the sensor, and the recovery time may be short.

4. Conclusion

The geometric structures and electronic properties of the pristine and Al-doped BN sheets in the presence and absence of an adsorbed N₂O moleculewere explored using DFT. Itwas found that the N₂O molecule interacts with the pristine BN sheet via van der Waals forces,but it presents much higher reactivity toward the ABN. Based on DOS analysis,it was suggested that ABN may be used in a gas sensor to detect and monitor N₂O. The detection mechanism is by an adsorption process which induces a change in conductance of the ABN,providing an electrical signal.