The efficiency of n- and p-type doping silicon carbide nanocage toward (NO₂, SO₂, and NH₃) gases

Abstract

The sensitivity of pristine silicon carbide nanocage Si₁₂C₁₂ and their doping with n-type (Si_P–Si₁₁C₁₂) and p-type (C_B–Si₁₂C₁₁) were investigated for NO₂, SO₂, and NH₃ gases using density functional theory (DFT). The reactivity of nanocages was examined through adsorption energy, charge transfer, the density of states (DOS), thermodynamic parameters, frontier molecular orbitals, molecular electrostatic potential, and nonlinear optical properties. The results revealed that doping with p-type has excellent sensitivity for SO₂, NO₂, and NH₃ gases compared with pristine and n-type doped nanocages.

Introduction

Air pollution with solid materials such as car exhaust and smoke or toxic gaseous materials such as combustion gases (CO, SO₂, NO₂) resulting from industrial development are important matters as they negatively affect both the environment and human health (Chen et al. 2021; Shi et al. 2021; Dai et al. 2021; Xu et al. 2022). The release of a large amount of nitrogen dioxide and sulfur into the air causes smog and acid rain, which have adverse effects on fresh water and soil. Toxic ammonia gas with a pungent odor is used in many industries such as water purification, a refrigerant gas, fertilizer, and in the removal of sulfur oxides and nitrogen oxides from smokestacks (Timmer et al. 2005; Soleimanpour et al. 2013; Srivastava et al. 2015). To reduce the number of toxic gases in the air, there is a promising challenge to search for materials that are used as sensitive materials for these gases.

Researchers conducted their study using three-dimensional (3D) such as MnO₂ (Ye et al. 2020), two-dimensional (2D) such as graphene (Ali and Tit 2019; Ardehjani and Farmanzadeh 2019; Kumar et al. 2017; Chen et al. 2018; Zhou et al. 2017), GeS monolayer (Ma et al. 2018), MoS₂ monolayer (Zhang et al. 2019; Abbasi and Sardroodi 2019; Wei et al. 2018), and g-C₃N₄ (Zhang et al. 2018), one-dimensional (1D) such as polypyrrole (Hernandez et al. 2007) and zero-dimensional materials (0D) such as fullerenes and fullerenes-like structure (Salimifard et al. 2017; Li et al. 2020) for the sensitivity of harmful gases. Fullerenes-like structure and fullerenes as novel materials based on physical and chemical properties. Several nanoclusters (XY)₁₂ (X: B, Al, Ga,…)(Y: N, P, …, etc.) were investigated that have inherent special stability. Noei (2017) studied the sensitivity of B₁₂N₁₂ and Al₁₂N₁₂ nanoclusters for SO₂ gas. He reported that Al₁₂N₁₂ nanocage displays a higher sensitivity toward SO₂ molecule and adsorbs on the tetragonal ring of the Al₁₂N₁₂. Rad and Ayub (2017) investigated B₁₂N₁₂ nanocage functionalized by nickel for sensing SO₂ and O₃ molecules and the study reveals high adsorption for both SO₂ and O₃ molecules.

Silicon carbide (SiC) compound that is composed of silicon and carbon belongs to the same group (IV) of the periodic table. After diamond and boron nitride, SiC is the third hardest material, which provides it exceptional features including high-temperature stability, chemical resistance, and biological compatibility (Locke et al. 2012). Silicon carbide nanomaterials are one of the most promising semiconductors due to their superior properties. They are used in electronic industrial (Cho et al. 2000; Bhatnagar and Baliga 1993) and biophysics fields (Zhou et al. 2006; Zhang et al. 2003). Hence, silicon carbide nanostructures have attracted wide and great interest. Mpourmpakis et al. (2006) reported the potential of the SiC nanotubes for hydrogen storage. They found that SiC nanotubes show 20% in comparison with carbon nanotubes for the binding energy of the H2 molecules. Silicon carbide Si₁₂C₁₂ nanocage consists of hexagons and tetragons. Wang et al. (2005) have studied the structure of (SiC)_n cages (n = 6–36) showing that (SiC)₁₂ nanocage is the most stable cage in this family. Solimannejad et al. (2017) investigated the Si₁₂C₁₂ nanocage by Cu decoration toward cyanogen gas using DFT calculations and the result reveals that the interaction of cyanogen gas with nanocage is chemisorption which is a good sensor for detecting NCCN molecules. To our knowledge, no research article studied the interaction of NO₂, SO₂, and NH₃ toxic gases with the Si₁₂C₁₂ nanocage. It is known that atom doping improves the electronic properties of semiconductor materials. Therefore, we also studied the n- and p-type doped for the sensitivity of NO₂, SO₂, and NH₃ toxic gases.

Computational details

In this work, we have carried out a computational study based on the density functional theory by performing full optimization of both the pristine and the doped nanocages in the absence and presence of gas molecules. All DFT calculations were implemented in the Gaussian 09 code (Frisch et al. 2009) using B3LYP functional and 6–31 g(d,p) basis set for NH₃ system and 6–31 g(d) for SO₂ and NO₂ systems. The density functional B3LYP has been widely employed in nanostructures research (Arab and Habibzadeh 2016; Tabtimsai et al. 2013; Ghorbaninezhad and Ghorbaninezhad 2013; Beheshtian et al. 2013). The adsorption energy (E_ads) of gas molecules on nanocage can be calculated using the following equations:

$$E_{{{\text{ads}}}} = E_{{{\text{G}}@{\text{nanocage}}}} - E_{{\text{G}}} - E_{{{\text{nanocage}}}}$$

(1)

$$E_{{{\text{ads}}}} = E_{{{\text{G}}@{\text{doped}}\,{\text{nanocage}}}} - E_{{\text{G}}} - E_{{{\text{doped}}\,{\text{nanocage}}}}$$

(2)

The counterpoise method (Beheshtian et al. 2013) was used to compute the adsorption energy (E_ads) of gas molecules on nanocage, which was corrected with basis set superposition error (BSSE).

$$E_{{{\text{ads}}}}^{{{\text{corr}}}} = E_{{{\text{ads}}}} - E_{{{\text{BSSE}}}}$$

(3)

where E_G@nanocage, E_{G@doped nanocage}, E_nanocage, E_{doped nanocage}, E_G are the total energies of gas molecules on pristine nanocage(Si₁₂C₁₂), gas molecules on doped nanocage (PSi₁₁C₁₂ and Si₁₂BC₁₁), nanocage, doped nanocages, and gas molecules, respectively.

We have calculated thermodynamic parameters at T = 298 K and P = 1 atm as follow:

$$\Delta H = H_{{{\text{G}}@{\text{nanocage}}}} {-}H_{{\text{G}}} - H_{{{\text{nanocage}}}}$$

(4)

$$\Delta H = H_{{{\text{G}}@{\text{doped}}\,{\text{nanocage}}}} {-}H_{{\text{G}}} - H_{{\text{doped nanocage}}}$$

(5)

where H_G@nanocage, H_{G@doped nanocage}, H_nanocage, H_{doped nanocage}, H_G are sum of electronic and thermal enthalpies of gas molecules on pristine nanocage(Si12C12), gas molecules on doped nanocage (PSi₁₁C₁₂ and Si₁₂BC₁₁), nanocage, doped nanocages, and gas molecules, respectively. The Gibbs free energy and entropy were calculated by a similar method. The figures were plotted with the Gauss View software. The partial density of state (PDOS) for the selected systems was carried out by the GaussSum program (O'Boyle et al. 2008) (Fig. 1).

Fig. 1

Structural model of a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; (C) C_B–Si₁₂C₁₁

Results and discussion

The adsorptions configurations and energetic of SO₂ on Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ nanocages

To investigate the reactivity of silicon carbide nanocage that doping with phosphorus (n-type) and boron atoms (p-type) toward various toxic gases, the adsorption of these gases at the pure Si₁₂C₁₂ was initially calculated as a reference. Next, the adsorption configuration and corresponding adsorption energies were examined to clarify how the n-type and p-type of doped silicon carbide nanocage affect the SO₂, NO₂, and NH₃ adsorption using DFT with the B3LYP methods. Three non-equivalent adsorption orientations including monodentate and cycloaddition orientations, named a, b and c, were considered for the adsorption of SO₂ on the pristine Si₁₂C₁₂, Si_P–Si₁₁C₁₂ (n-type), and C_B–Si₁₂C₁₁ (p-type) surfaces, Figs. 2, 3 and 4. To form a monodentate configuration (structure a), the oxygen atom of SO₂ is bonded with a silicon atom of Si₁₂C₁₂, Fig. 2. The two O atoms of gas bind to two adjacent surface Si atoms to form structure b, whereas the S atom of SO₂ binds to a surface C atom, and the two O atoms of gas bind to two adjacent surface Si atoms to form structure c. The comparative adsorption energy of SO₂ on various sites is summarized in Tables 1, 2 and 3. As demonstrated in Tables 1, 2 and 3, the negative values of binding energy correspond to the exothermic reaction consequently the adsorption of SO₂, NO_2, and NH₃ on the surface of Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ are energetically favorable. The results elucidated that SO₂ molecules are chemically adsorbed on structures 1b (− 2.36 eV), all Si_P–Si₁₁C₁₂ (− 1.315 to − 1.530 eV), and C_B–Si₁₂C₁₁ (− 2.20 and − 2.63 eV) whereas physically adsorbed on (structures 1a and 1c). The sequence of adsorption energy for the SO₂ gas is C_B–Si₁₂C₁₁ > Si₁₂C₁₂ > Si_P–Si₁₁C₁₂, suggesting that, the C_B–Si₁₂C₁₁ (p-type) is energetically more appropriate than Si_P–Si₁₁C₁₂ (n-type).

Fig. 2

The optimized structure of a SO₂; b NO₂; c NH₃ at the pristine Si₁₂C₁₂

Fig. 3

The optimized structure of a SO₂; b NO₂; c NH₃ at Si_P–Si₁₁C₁₂

Fig. 4

The optimized structure of a SO₂; b NO₂; c NH₃ at C_B–Si₁₂C₁₁

Table 1 Geometrical parameters (Å), binding energy (E_ads), charges (q) of SO₂, NO₂ and NH₃ on Si₁₂C₁₂ nanocage

Table 2 Geometrical parameters (Å), binding energy (E_ads), charges (q) of SO₂, NO₂ and NH₃ on Si_P-i₁₁C₁₂ nanocage

Table 3 Geometrical parameters (Å), binding energy (E_ads), charges (q) of SO₂, NO₂ and NH₃ on C_B-Si₁₂C₁₁ nanocage in gas phase and two different solvent phases

The variation in the bond lengths of the SO₂ molecule at the Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ showed that the calculated bond lengths Si–C, P–C, and Si–B increased from 1.834 Å to 1.977 Å, 1.844 Å to 1.860 Å and 1.974 Å to 2.080 Å, respectively, demonstrating that adsorbed gases weakened the interaction between Si–C, P–C, and Si–B of Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁. Meanwhile, the nearest distances between the SO₂ molecules with the carbon atom of Si₁₂C₁₂ (1b), and Si_P–Si₁₁C₁₂ (2b) were 1.765, 1.808 Å, respectively, implying the possible strong interaction between the C atom of nanocage and the S atom of SO₂. Moreover, the oxygen atoms of SO₂ interact with Si atoms of Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁ at distances of 1.837, 1.833, and 1.812 Å, respectively. The calculated averages bond lengths of the S–O bonds in SO₂@Si₁₂C₁₂ (1b), SO₂@ Si_P–i₁₁C₁₂ (2b), and SO₂@ C_B–Si₁₂C₁₁ (3a) is significantly enlarged from 1.462 Å in free SO₂ molecule with a close agreement with Chen et al. (2016) to 1.636, 1.655 and 1.669 Å in the most stable configuration of adsorbed gas molecules on Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ (structure 1b, 2b and 3a) that are depicted in Tables 1, 2 and 3. According to the provided results, the change in the SO₂ bond lengths upon adsorption at C_B–Si₁₂C₁₁ is greater than those of Si_P–i₁₁C₁₂ and Si₁₂C₁₂.

To examine the effect of solvent on the interaction of the most stable configuration of SO₂ molecule at the C_B–Si₁₂C₁₁ (3a), full geometry optimizations were performed for gas molecule on C_B–Si₁₂C₁₁ in aqueous solution and acetonitrile as polar solvents, using the conductor-like polarizable continuum model (CPCM) and the self-consistency reaction field (SCRF) approach (Barone and Cossi 1998). According to the provided results in Table 3, all the adsorption energies of SO₂ molecule at the C_B–Si₁₂C₁₁ (3a) are lower in polar solvents than in the gas phase, indicating that the molecular polarities of SO₂ molecule at the C_B–Si₁₂C₁₁ (3a) in the solvent phases are lower than in the gas phase. Although the calculated averages bond lengths of the most stable configuration of adsorbed SO₂ molecule at the C_B–Si₁₂C_{11 1} (3a) in the two solvents show a similar trend, the length elongation of S–O in the solvent phase is greater than corresponding bond lengths in the gas phase. According to NBO analysis, a significant charge transfer of − 0.617e and − 0.611 e from C_B–Si₁₂C₁₁ to the sensitive SO₂ is greater than that of gas phase (− 0.595 e), while the corresponding energy gaps exhibit a negligible change (~ 0.003 eV).

The effect of diffuse basis set (6–31 g + (d)) on the interaction of the most stable configuration of SO₂ molecule at the C_B–Si₁₂C₁₁ (3a) is examined Table 3. Although the results indicate a significant decrease in adsorption energy when compared to the 6–31 g(d) basis set, the bond lengths and charge transfers of the SO₂/C_B–Si₁₂C₁₁ (3a) system are almost the same in both basis sets.

The adsorptions configurations and energetic of NO₂ on Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁ nanocage

The geometrical, electronic properties, and the binding energies of NO₂ on the various adsorption sites of the Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ nanocages were examined and compared. To find the most stable complexes due to the adsorption of NO₂ on the Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁, several configurations of NO₂ molecules are explored. Then, molecular configurations were systematically estimated to examine the most active and stable surface that was energetically more favorable, Figs. 2, 3 and 4. Our results showed that NO₂ molecules are chemically adsorbed on all Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ surfaces. From Tables 1, 2 and 3, the adsorption energies of the most stable configurations of NO₂ (structure 4a, 5a, and 6a) at Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ are − 1.80, − 2.15, and − 3.58 eV, respectively, indicating the adsorption capability of C_B–Si₁₂C₁₁ is greater than that of Si_P–Si₁₁C₁₂ and Si₁₂C₁₂.

The greater adsorption energies values corresponded to Si–O, P–O, and B–O bond lengths are 1.723, 1.669, and 1.490 Å for Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁, respectively; suggesting the strongest adsorption at C_B–Si₁₂C₁₁ with the lowest bond length. On the other hand, the shorter length of the O–Si bond at 1.76 Å compared with 1.79 Å for O–Si (Pekka and Michiko 2009; Lina et al. 2020) elucidates the nature of exothermic chemisorptions confirming the large interaction energy and charge transfer, Tables 1, 2 and 3. The length elongation of N–O (1.508 Å) at Si_P–Si₁₁C₁₂ is greater than corresponding bond lengths at the Si₁₂C₁₂ (1.41 Å) nanocage. The elongated N–O bond is due to the strong adsorption of NO₂ with Si_P–Si₁₁C₁₂ (structure 5a). According to the provided results in Table 3, the length elongation of N–O bond lengths upon adsorption on the C_B–Si₁₂C₁₁ is greater than that for Si_P–Si₁₁C₁₂ and Si₁₂C₁₂ nanocages. From the comparison of NO₂ and SO₂ binding energies, it is also worth noting that NO₂ in the most stable configurations binds significantly more strongly than SO₂ at the same sites, in accordance with (Artuc et al. 2014).

The adsorptions configurations and energetic of NH₃ on Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁ nanocages

The variation in interaction energies of the most stable orientations of supplementary materials, NH₃ on Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁ nanocages is represented in Figs. 2, 3 and 4. The corresponding adsorption energies, charge transfers, the nearest distance between the NH₃ molecule and the nanocage are listed in Tables 1, 2 and 3. The NH₃ molecule has the highest interaction at Si₁₂C₁₂ and C_B–Si₁₂C₁₁ with the binding energy of − 1.53 eV (structure 7a) and − 1.34 eV (structure 9b), which is categorized in the region of chemisorptions. The E_ads of NH₃ at Si_P–Si₁₁C₁₂ structures (8a–8c) are − 0.24, 0.09, and − 0.11, which revealed that the adsorption of NH₃ is weak physical adsorption or weak van der Waals forces of attraction even if the reaction is spontaneous. The overall increase in the binding energies for NH₃ on the C_B–Si₁₂C₁₁ with respect to the Si₁₂C₁₂ and Si_P–Si₁₁C₁₂ clearly suggests that the C_B–Si₁₂C₁₁ (P-type) surface mediated mechanism is active. Interestingly, the C–N bond length with 4.172, 3.957 Å shows that there is only a faint interaction between NH₃ and both Si₁₂C₁₂ and Si_P–Si₁₁C₁₂ (structures 7c and 8c). Meanwhile, as shown in Tables 1, 2, the physisorption N–H bond length demonstrated a negligible change.

The BSSE calculations were examined using the counterpoise approach as described by Boys and Bernardi (1970) for the most stable adsorption system configurations. The BSSE corrected stabilization energy values are significantly lower than the uncorrected values (Table 1). The stabilization energies of SO₂, NO_2, and NH₃ on C_B–Si₁₂C₁₁ nanocage were determined to be 0.014, 0.008 and 0.008 eV, suggesting that BSSE does not play an important role in the studied systems.

Natural bond orbital (NBO) analysis

Natural bond orbital (NBO) analysis of adsorbed SO₂, NO_2, and NH₃ molecules was investigated as shown in Tables 1, 2 and 3. It should be noted that the strong SO₂ and NO₂ adsorption induces a significant electronic redistribution at the surface of nanocages. The negative values of SO₂ and NO₂ refer to electron transfer from nanocages to gas molecules (acceptor character), whereas the positive value of the NH₃ (donor character) represents charge transfer from NH₃ molecule to the Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁. The P and B atoms in the Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ molecules supply the majority of the charges to the molecule to stabilize the binding between adsorbed gas and the surface. This means that the charge of doped P atoms can easily transfer to their nearby C atom of the silicon carbide to stabilize the entire system. Consequently, a better charge transfer takes place from the phosphorus-doped silicon carbide nanocages to the neighboring carbon atom of Si_P–Si₁₁C₁₂ accepted by SO₂ and NO₂. Therefore, the presence of carbon adjacent to P at the Si_P–Si₁₁C₁₂ increases the charge depletion at the P atoms to 0.620 e and 0.715 e, due to the greater electronegativity of O and S compared to that of the P atom. These results can be explained by the electronegativity variation among S, O, and N atoms, where the most electronegative O atom withdraws more electrons at Si_P–Si₁₁C₁₂, resulting in more d-states available for greater binding energies of NO₂ and SO₂ gases. Meanwhile, phosphorus-doped silicon carbide acts as a bridge for interacting with adsorbed gases (SO₂, NO₂)_, and the carbon atoms of Si_P–Si₁₁C₁₂ subsequently, it plays an important role as a great potential application as NO₂ and SO₂ gas sensor. According to NBO analysis, a significant charge transfer of − 0.477 and − 0.323 e from Si_P–Si₁₁C₁₂ to the sensitive SO₂ and NO₂ was mainly accumulated over the oxygen atom of SO₂ and NO₂. The charge transfer from Si_P–Si₁₁C₁₂ to the NO₂ and SO₂ gases results in a reduction in Si_P–Si₁₁C₁₂ carrier density. Therefore, the resistance of n-type Si_P–Si₁₁C₁₂ enhances, while the corresponding energy gaps exhibit a negligible change, Table 2. As a result, the phosphorus-doped silicon carbide with a positive charge and negatively charged at SO₂, NO₂ creates an electrical field on the surface that enhances the dipole moment. Even though the B atom of C_B–Si₁₂C₁₁has a negative charge that increases from − 1.146 to − 1.588 in the SO₂@ C_B–Si₁₂C₁₁ (3a), it decreases to − 0.931 in NO₂@ C_B–Si₁₂C₁₁ (6a) complex. As a result, the resistance of the p-type of NO₂@ C_B–Si₁₂C₁₁ (6a) structure reduces and the corresponding energy gaps exhibit a negligible change, Table 3.

According to the provided results (Tables 1, 2 and 3), the more negative E_ads suggests a higher charge transfer and a significant molecular orbital overlap matrix between Si₁₂C₁₂ and C_B–Si₁₂C₁₁ and the NH₃ adsorbed gases. In contrast, the low E_ads, low transfer charge, and larger bond length have demonstrated that Si_P–Si₁₁C₁₂ has weak adsorption of NH₃ molecule. Moreover, the slightly positive charge accumulated on the most stable configurations of NH₃ (structure 7a and 9b) where the adsorbed gas donates 0.231 and 0.394 e toward the Si₁₂C₁₂ and C_B–Si₁₂C₁₁, respectively. Overall, when the NH₃ molecule is adsorbed at C position on the Si₁₂C₁₂ nanocage, there is a minimum charge transfer (0.032e) compared to others, whereas the NH₃@ C_B–Si₁₂C₁₁ (9b) complex has the maximum charge transfer (0.480e). Consequently, the reducing (NH₃) gas molecules adsorbed on C_B–Si₁₂C₁₁ act as charge donors, transferring electrons to the C_B-Si₁₂C₁₁ monolayer, reducing the charge carrier density of the p-type C_B–Si₁₂C₁₁ surface and enhancing its resistance.

Frontier molecular orbital analysis

The kinetic stability and chemical reactivity of phosphorus and boron silicon carbide nanocages as molecular gas sensors is fundamentally attributed to the FMOs, HOMO, LUMO, and energy gap of the most stable adsorption configurations of SO₂, NO_2, and NH₃ at Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁ nanostructure were investigated in Tables 1, 2 and 3 and Figs. 5, 6, 7 and 8. It was shown that the energy gap of isolated pristine Si₁₂C₁₂ is essentially reduced from 3.23 to 2.858 eV and 2.933 eV by doping P and B atoms at the Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ surfaces, respectively, causing improvement of the conduction properties of the doping nanocage. It can be displayed in Fig. 5 that the HOMO and LUMO mainly distribute on Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁ fragments. The adsorption of the NO₂ at Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ systems reduced the energy gap notably up to 0.024 and 0.838 eV especially at C_B–Si₁₂C₁₁ surface is noteworthy with the smallest band gap, suggesting an enhancement in the reactivity of the complexes.

Fig. 5

HOMO and LUMO states of a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁

Fig. 6

HOMO and LUMO states of SO₂ at a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁

Fig. 7

HOMO and LUMO states of NO₂ at a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁

Fig. 8

HOMO and LUMO states of NH₃ at a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁

Although the strong localization of HOMO occurs essentially on the Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ nanocages, strong delocalization of the LUMOs occurs on the SO₂ and NO₂ and the P- and B-doped sites (Figs. 6 and 7). These results show a significant flow of electron cloud toward the interface between the adsorbed gas (SO₂ and NO₂) and the Si_P–Si₁₁C₁₂, C_B–Si₁₂C₁₁, suggesting the enhanced chemisorption adsorption of SO₂ and NO₂. The oxygen atom in SO2 and NO2 have more electrons than sulfur and nitrogen atoms, they prefer to bond with the Si atom in Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁. The contribution to the HOMO of NO₂@ C_B–Si₁₂C₁₁ (6a) is fundamentally centered on the C-2p while N-2p, O-2p, B-2p, and their close vicinity Si-3p orbitals mostly contribute to the LUMO, however, the contributions of the other atoms are insignificant. Furthermore, the band gaps of NH₃@Si₁₂C₁₂ (7a) and NH₃@ C_B–Si₁₂C₁₁ (9b) complexes are 3.23 and 2.938 eV remains almost the same as Si₁₂C₁₂ and C_B–Si₁₂C₁₁, respectively.

Because the oxygen atoms in SO₂ and NO₂ have more electrons than sulfur and nitrogen atoms, they prefer to bond with the Si atom in Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁.

Molecular electrostatic potential (MEP) analysis

To investigate the charge transfer mechanism during physisorption and chemisorptions of the SO₂, NO_2, and NH₃ on Si₁₂C₁₂, Si_P–Si₁₁C₁₂, and C_B–Si₁₂C₁₁, molecular electrostatic potential maps (MEP) of the most stable configuration of adsorbed gases are plotted in Figs. 9, 10 and 11. The red color denotes that electron-rich “negative” regions will react with electrophilic molecules. The blue color, on the other hand, denotes a “positive” personality that favors chemical reactions with nucleophilic molecules.

Fig. 9

Molecular electrostatic potential of a Si₁₂C₁₂, b SO₂; c NO₂; d NH₃ at the pristine Si₁₂C₁₂

Fig. 10

Molecular electrostatic potential of a Si_P–Si₁₁C₁₂, b SO₂; c NO₂; d NH₃ at the Si_P–Si₁₁C₁₂

Fig. 11

Molecular electrostatic potential of a C_B–Si₁₂C₁₁, b SO₂; c NO₂; d NH₃ at the C_B–Si₁₂C₁₁

The pictures of electrostatic potential for Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ show nonuniformity when contrast with that of the pure Si₁₂C₁₂ (Fig. 9). The phosphorus- and boron-doped silicon carbide changes the local electron density and surface polarity, as shown in the electrostatic potential analysis above. For Si_P–Si₁₁C₁₂, as shown in Fig. 9b, the electrons transfer from the P atom to the C atom takes place. Due to the color between the P atom and the C atom in Si_P–Si₁₁C₁₂ being darker than the color between the P atom and the Si atom, the electron transfer between the P and C atoms is greater than the electron transfer between the P and Si atoms in Si_P–Si₁₁C₁₂. These modifications have a significant effect in the interaction between hazardous gases (SO₂, NO₂, and NH₃) with the Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ nanocages.

It can be displayed in Figs. 9, 10 and 11 that the electrostatic potential of oxygen atoms in SO₂ and NO₂ indicates electron accumulation. However, in the areas of P and Si, which are marked as positive zones, phosphorus-doped silicon carbide has a higher positive electrostatic potential, whereas C is marked as negative zones. Furthermore, the plotted MEP visualizes that the red color represents negative zones, which are mainly at the C and B atoms of the C_B–Si₁₂C₁₁ site, while the blue color represents electron-deficient sites at the Si atom. However, no significant color variation in MEP maps is observed during NH₃ adsorption, confirming the lower Eads and charge transfer.

Thermodynamic parameters and nature of the binding forces

To investigate the influence of doping silicon carbide with phosphorus and boron atoms on the thermodynamic stability of the complex formation process, the Gibbs free energy change (ΔG), enthalpy change (ΔH) and entropy change (ΔS) for the studied systems in the gas phase have been calculated at standard pressure and temperature (STP,1 atm. and 298.15 K), using B3LYP level, Tables 4, 5 and 6. It can be seen that mostly all the Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁ surfaces show spontaneous adsorption behavior for SO₂ and NO₂ at ambient temperature (i.e., negative ΔG values). The high negative free energy change (ΔG) values of the most stable SO₂@Si₁₂C₁₂ (1b), NO₂@Si₁₂C₁₂ (4a), and NH₃@Si₁₂C₁₂ (7a) complexes are − 53.24, − 41.12, and − 32.71 kcal mol⁻¹, respectively), indicating spontaneous adsorption on the surface with strong interaction.

Table 4 Thermodynamic parameters of SO₂, NO_2, and NH₃ on Si₁₂C₁₂ nanocage

Table 5 thermodynamic parameters of SO₂, NO_2, and NH₃ on Si_P-i₁₁C₁₂ nanocage

Table 6 Thermodynamic parameters of SO₂, NO₂ and NH₃ on C_B-Si₁₂C₁₁ nanocage

The enthalpy change values ΔH of the most stable adsorption configurations of SO₂, NO_2, and NH₃ with C_B–Si₁₂C₁₁ nanocage are − 50.06, − 80.78 and − 28.44, Kcal mol⁻¹, and the corresponding ΔG of the same configurations are − 35.99, − 66.72, and − 18.23 kcal mol⁻¹, respectively, demonstrate the process's viability and the interaction between the donors and the acceptors is an exothermic and enthalpy stabilized, consequently electrostatic interactions are present. In contrast, the interaction of NH₃ at C_B–Si₁₂C₁₁ nanocage is less thermally stable than that of SO₂ and NO₂ at the same conditions. The free energies of the interaction of NH₃ for orientation (7b,7c) at Si₁₂C₁₂ are 36.26 (5.01) Kcal mol⁻¹, respectively. Therefore, during the complexation of NH₃ at Si₁₂C₁₂ (orientation b and c) and Si_P–Si₁₁C₁ (all orientations), the ΔG values reveal that the interaction of NH₃ on these nanocages is an unviable process (positive free energy), Tables 4, 5 and 6. Subsequently, the ΔG of NH₃ complexation reflects the less exergonic process, confirming the lowest adsorption energy and weakly bound adsorption for NH₃ at this system.

Finally, a comparison between the ΔG° of SO₂, NO_2, and NH₃ at Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ nanocage results shows that over the entire temperature and pressure range studied, the C_B–Si₁₂C₁₁ (p-type) nanocage is thermodynamically more favorable than both Si₁₂C₁₂, Si_P–Si₁₁C₁₂ (n-type) nanocage. Thermodynamic analysis revealed that the boron atom doped silicon carbide nanocage is energetically stable, increasing the surface capacity of adsorbing NO₂, SO₂, and NH₃.

The projected density of states (PDOS) analysis

To further study the interaction and electronic properties between SO₂, NO₂, NH₃ and Si₁₂C₁₂, Si_P–Si₁₁C₁₂, C_B–Si₁₂C₁₁ nanocages, the most thermodynamically favorable phosphorus and boron functionalities on the electronic properties of pristine Si₁₂C₁₂ nanocages toward SO₂, NO₂, and NH₃ were analyzed by calculating the projected density of states (PDOS). After fully optimization, the most stable configuration of SO₂@Si₁₂C₁₂ (1b), SO₂@Si_P–i₁₁C₁₂ (2b), SO₂@C_B–Si₁₂C₁₁ (3a), NO₂@Si₁₂C₁₂ (4a), NO₂@Si_P–i₁₁C₁₂ (5a), NO₂@ C_B–Si₁₂C₁₁ (6a), NH₃@Si₁₂C₁₂ (7a) and NH₃@ C_B–Si₁₂C₁₁ (9b) complexes were selected for further study of projected density of states. The calculated PDOS of C-2p, B-2p, N-2p, O-2p, P-3p, P-3d, S-3p, S-3d Si-3p, and Si-3d states were shown to detect the contribution of outermost atomic orbital to PDOS, Figs. 12, 13, 14 and 15.

Fig. 12

The projected density of states (PDOS) of a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁. The Fermi level is set to be 0 eV

Fig. 13

The projected density of states (PDOS) of SO₂ at a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁. The Fermi level is set to be 0 eV

Fig. 14

The projected density of states (PDOS) of NO₂ at a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁. The Fermi level is set to be 0 eV

Fig. 15

The projected density of states (PDOS) of NH₃ at a pristine Si₁₂C₁₂; b Si_P–Si₁₁C₁₂; c C_B–Si₁₂C₁₁. The Fermi level is set to be 0 eV

For SO₂@Si₁₂C₁₂ (1b) and NO₂@Si₁₂C₁₂ (4a) complexes, it can also be clarified that the orbital of O-2p and Si-3p overlaps from − 15.3 to − 6.1 eV below the Fermi level, which indicates the possible bonding between Si and O. The O-2p and S-2p orbitals also overlap from − 15.3 to − 6.1 and from − 4.2 to 4.5 above the Fermi level, showing strong hybridization between S and O. In addition, for SO₂ and NO₂ at Si_P–Si₁₁C₁₂, obvious strong hybridizations are between P-3p, P-3d orbitals and O-2p orbitals from − 16.7 eV to − 10.3 eV. It can be observed that the intensity of phosphorus states reduces when compared with phosphorus states before adsorption of SO₂ and NO₂, indicating charge transfer from P to O atom of the adsorbed gas (Figs. 12, 13, 14 and 15).

Furthermore, it can be deduced that S-3p, O-2p orbitals (HOMO) are mainly contributed by B-2p and Si-3p states that vicinity the C_B site excessively from ~ − 9.4 eV to − 6.5 eV below the Fermi level. However, the LUMO is dominated by B-2p orbitals of B atoms neighboring the Si contributed over a wide range from ~ − 0.5 eV to 6.5 eV above Fermi level, Fig. 9. The intensity of sulfur states reduces when compared with sulfur states of SO₂@Si₁₂C₁₂ (1b) complex, suggesting charge transfer from S to O atom (Figs. 12 and 14). The slightly higher energy shifts of Si-3p and B-2p orbitals are due to charge transfer from the Si, and S atoms toward the B-2p and O-2p states, increasing Eg of SO₂@ C_B–Si₁₂C₁₁ (3a) (3.006 eV) compared with C_B–Si₁₂C₁₁ before adsorption of SO₂ (2.933 eV), therefore SO₂ adsorption on C_B–Si₁₂C₁₁ is more stable than that of Si_P–Si₁₁C₁₂ (Figs. 13 and 14).

The intensity of B-2p and O-2p states increased at − 6.9 and 10.8 eV when compared with B-2p and O-2p states before adsorption of NO₂ due to the electron transfer from Si and N, Table 3. Furthermore, there are obvious overlapping peaks at − 8.9 eV and − 5.8 eV between the B-2p and O-2p orbital, indicating that there is strong hybridization and combination between the orbital, which may be due to the formation of strengthening the bond between B and O. These differences suggested that the interaction of NO₂ with Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ is stronger than that between SO₂ and the same surfaces. Furthermore, the B-2p, Si-3p, and Si-3d orbitals were upshifted toward the Fermi level, from − 4.5 eV to − 2.4 eV, indicating the band gap after the adsorption of NO₂ on C_B–Si₁₂C₁₁ decreased from 2.933 to 2.095 eV. The intensity of B-2p and Si-3p orbitals decreased at − 6.9 and 10.8 eV when compared with B-2p and Si-3p orbitals before adsorption of NO₂, indicating the charge transfer from B to O atom of NO₂ molecule, Table 3.

As shown in these figures, the partially filled N-2p, O-2p, orbitals of NO₂ adsorbed on Si_P–i₁₁C₁₂ and C_B–Si₁₂C₁₁ elucidated a stronger hybridization than on pure Si₁₂C₁₂, due to the wide distribution of P-3p and B-2p states below the Fermi level, ranging from − 16.8 to − 6.5 eV, instead of the more localized behavior observed on pristine Si₁₂C₁₂. In contrast, the orbital hybridization between NH₃ and Si_P–Si₁₁C₁₂ is not obvious (Fig. 15), indicating that Si_P–Si₁₁C₁₂ was not sensitive to NH₃ molecule, but only weak physical adsorption (− 0.24 eV). However, hybridization is not as strong for NH₃ and does not occur near the Fermi level, increasing the energy band gap in those systems, which is consistent with the lower binding energies listed in Tables 1, 2 and 3. The great orbital hybridization further indicates that the powerful capability of C_B–Si₁₂C₁₁ (P-type) has excellent adsorption performance to sense the poisonous NO₂, SO₂ and NH₃ gases.

Nonlinear optical properties

Polarizabilities and first hyperpolarizabilities characterize the response of a system in an applied electric field. Therefore, theoretical calculations based on quantum mechanics are used to determine the magnitude of polarizability and first hyperpolarizability of the material that is responsible for more active nonlinear optical (NLO) performance (Yaqoob et al. 2022). The significance of the polarizability and the first hyperpolarizability are responsible for the efficiency of electronic communication between SO₂, NO₂, NH₃ and Si₁₂C₁₂, Si_P–Si₁₁C₁₂, C_B–Si₁₂C₁₁ surfaces (substrates) as well as intramolecular charge transfer (Prasad et al. 2010; Cinar et al. 2011).

In this regard, polarizability (α_o) and first hyperpolarizability (β_o) are calculated by using Eq. (2) and (3) and are given in Tables 7 and 8. As given in Table 7, the polarizability of Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ increase to 172.7364 a.u and 584.4089 a.u with respect to 0.0954 a.u that of isolated Si₁₂C₁₂. The first hyperpolarizability of the isolated Si₁₂C₁₂, Si_P–Si₁₁C_12, and C_B–Si₁₂C₁₁ is only 2.217, 280.83, and 1166.027 a.u, confirming the doping of P and B atoms significantly enhances the polarizability and first hyperpolarizability for the Si₁₂C₁₂ nanocage. The largest values of α_o and β₀ are reported for C_B–Si₁₂C₁₁ (P-type) which is much larger than for Si₁₂C₁₂ and Si_P–Si₁₁C₁₂ due to the distortion of symmetry of the nanocage. Because the predominant charge transfer interaction of the studied systems takes place along the longitudinal x-axis, the longitudinal x-components of polarizability (α_xx) and first hyperpolarizability (β_xxx) have been used as longitudinal components. Thus, the polarizabilities of the structure SO₂@Si₁₂C₁₂ (1b), NO₂@Si₁₂C₁₂ (4a), and NH₃@Si₁₂C₁₂ (7a) complexes increase to 86,426.9, 6154.45, and 3988.13, respectively, with respect to 0.0954 that of isolated Si₁₂C₁₂. The sequence of the polarizabilities for the three various toxic gases is SO₂ > NO₂ > NH₃ at the same substrate. It is clear that the first hyperpolarizabilities for the three complexes depend very strongly on the distance and charge transfer between the Si₁₂C₁₂, Si_P–Si₁₁C₁₂, C_B–Si₁₂C_11, and the respective gas.

Table 7 Polarizabilities (α) of the Si₁₂C₁₂, Si_P-i₁₁C₁₂, C_B-Si₁₂C₁₁ and their complexes with the most stable configuration of SO₂, NO₂, NH₃ molecules calculated at the B3LYP level of theory

Table 8 First hyperpolarizabilitie(βo) of the of the Si₁₂C₁₂, Si_P-i₁₁C₁₂, C_B-Si₁₂C₁₁ and their complexes with the most stable configuration of SO₂, NO₂, NH₃ molecules calculated at the B3LYP level of theory

The highest value of polarisability α_o and first hyperpolarizability β_o are assigned to SO₂@ C_B–Si₁₂C₁₁ structure 3a (11,700.77 a.u), whereas NH₃@Si₁₂C₁₂ (7a) has the lowest hyperpolarizability (52.162 a.u.). Such a decreasing trend for β_o can be attributed to the geometric distance and the lowest charge transfer between NH₃ and the surface of nanocage. The greater electron transfer and binding energy between the SO₂ at C_B–Si₁₂C₁₁ surfaces are corresponding to the large hyperpolarizability. Finally, the SO₂@ C_B–Si₁₂C₁₁ (3a) complex is the most candidate for photonic and optical limiting applications because of the enhanced optical nonlinearities, clearly, the new strategy is extremely effective in improving the NLO response.

Conclusions

DFT calculations have been performed to explore the adsorption geometry, adsorption energy, charge transfer, FMOs, PDOS, the polarizabilities, and first hyperpolarizabilities of SO₂, NO_2, and NH₃ with silicon carbide nanocage that doping with phosphorus (n-type) and boron atoms (p-type). Based on the geometric structure and interaction energies, the C_B–Si₁₂C₁₁ nanocage is energetically more effective for the SO₂, NO_2, and NH₃ adsorption, stable and preferred than Si_P–Si₁₁C₁₂. The adsorption of the NO₂ at Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ systems reduces the band gap significantly up to 0.838 eV, especially at C_B–Si₁₂C₁₁ surface is noteworthy with the smallest band gap, confirming an enhancement in the conductivity and reactivity of the complexes. The NO₂ interaction energies are, significantly larger than those for the corresponding geometries of SO₂ at the same sites as well as the Si_P–Si₁₁C₁₂ are not suitable for the detection of NH₃. C_B–Si₁₂C₁₁ (p-type) has excellent adsorption performance to sense the poisonous NO₂, SO_2, and NH₃ gases. Therefore, from a thermodynamic point of view, a comparison between the ΔG° of SO₂, NO_2, and NH₃ at Si_P–Si₁₁C₁₂ and C_B–Si₁₂C₁₁ nanocage results show that over the entire temperature and pressure range studied, the C_B–Si₁₂C₁₁ (p-type) nanocage is thermodynamically more favorable than both Si₁₂C₁₂, Si_P–Si₁₁C₁₂ (n-type) nanocage. The SO₂@C_B–Si₁₂C₁₁ (3a) complex is the most candidate for photonic and optical limiting applications to enhance the NLO response. In summary, C_B–Si₁₂C₁₁ has superior sensing performance to SO₂, NO_2, and NH₃ compared with Si₁₂C₁₂, Si_P–Si₁₁C₁₂.