Lithium Polysulfide Catalytic Mechanism of AlN/InN Heterojunction by First-Principles Calculation

Abstract

To solve the shuttling effect and transformations of LiPSs in lithium–sulfur batteries, heterostructures have been designed to immobilize LiPSs and boost their reversible conversions. In this paper, we have constructed AlN/InN heterojunctions with AlN with a wide band gap and InN with a narrow band gap. The heterojunctions show metallic properties, which are primarily composed of 2s, 2p N atoms and 5s, 5p In atoms. InN has relatively higher adsorptivity for LiPSs than AlN. Reaction profiles show that on the surface of AlN, there is a lower rate-limiting step than on that of InN, from S₈ to Li₂S₆, and a higher rate-limiting step from Li₂S₄ to Li₂S₂, which is more favorable for InN during the reduction from Li₂S₄ to Li₂S₂. The heterojunction can realize the synergistic reaction of trapping–diffusion–conversion for LiPSs, in which AlN traps large Li₂S₈ and Li₂S₆, the heterojunction causes the diffusion of Li₂S₄, and InN completes the conversion of Li₂S₄ to Li₂S.

1. Introduction

Along with high theoretical specific capacity and energy density, lithium–sulfur batteries (Li-S batteries) are considered to be the next generation of high-energy batteries for energy storage equipment and electric vehicles [1]. However, the practical application of Li-S batteries suffers from several bad problems, including poor conductivity of active materials (S₈/Li₂S) and a large volume, which expands upon cycling [2]. The reaction kinetics associated with complex lithium polysulfide (LiPSs) transformations is usually tardy and thus follows serious shuttling effect of LiPSs [3]. Many efforts have been implemented in sulfur positive electrode design, diaphragm modification, electrolyte modification and solid electrolytes [4], such as carbon materials [5], carbon doping [6], transition metal oxide [7], transition metal sulfide [8] and transition metal carbon and nitrides [9]. The design aim has improved the ability to capture sulfur in electrodes, to increase conductivity and to prevent polysulfide dissolution [10]. It has been shown that polar materials can effectively reinforce the immobilization of LiPSs. Heterostructures have been designed to immobilize LiPSs and improve their reversible conversions [11,12]. MoP-MoS₂ [13] or NiCoP/CoP [14] heterojunctions with abundant anchoring sites can accelerate both reduction of LiPSs and oxidation of Li₂S. CoSe/ZnSe heterostructures with a negligible band gap show metallic properties and possess a low sulfur reduction energy, which can accelerate redox reaction kinetics during the charging and discharging process [15]. Calculations have been shown that MoS₂ has a wide band gap semiconductor and Ni₃S₂ has metallic properties in MoS₂-Ni₃S₂ heterojunctions and electrochemical exams have been shown that heterojunction have better conductivity and lower interfacial resistance [16].

Moreover, Ⅲ-nitride semiconductors have attracted extensive attention in ultraviolet light-emitting diodes and high-frequency, high-power transistors [17,18]. AlN is a wide band gap semiconductor with excellent chemical stability and high thermal conductivity [19]. InN is an end-point compound. The optical adsorption edge of sputter-grown InN films has been shown to possess high electron concentration and low electron mobility [20]. Optical synaptic devices based on GaN/AlN periodic structure have shown strong persistent photoconductivity in ultraviolet detection, which is caused by the strong polarization of GaN/AlN heterojunctions [21]. The band gap of AlN/Al₂O₃ heterojunctions has been reduced significantly, making it about 3.9 eV that is owing to the competition between the elongated Al-N and Al-O bonds across the interface. And the incoherent interface can generate a very strong interfacial ultraviolet light emission [22]. In this paper, we have designed a strong polarization AlN/InN heterojunction and studied its ability in terms of LiPS conversion in Li-S batteries in the following sections. We will discuss the adsorption ability of AlN and InN with regard to LiPSs, as well as LiPS conversion capacity at the heterojunction interface.

2. Calculation Method

Calculations are performed based on the DFT method and are executed by VASP [23]. PAW pseudopotentials have been applied to deal with electron–ion interactions [24]. The exchange–correlation interaction between electrons was treated by GGA with the Perdew–Burke–Ernzerfhof (PBE) function [25]. To prevent severe band gap underestimation, the hybrid DFT-HSE06 hybridization generalized function is employed to obtain the band gap [26,27]. The electron wave function is unfolded on the basis of plane waves, and E_cut is 500 eV. The convergence threshold of total energy and ionic force are 1 × 10⁻⁴ eV/Å.

The surface adsorption of LiPSs are constructed on the 3 × 3 × 1 2D surface of AlN and InN, on which a vacuum layer of 20 Å has been installed to avoid the interaction between images caused by periodic boundaries. In order to obtain the adsorption energy between AlN, InN, AlN/InN heterojunction and LiPSs, the following equations are used:

$${\Delta \mathrm{E}}_{\mathrm{a}\mathrm{d}\mathrm{s}}=\mathrm{E}(\mathrm{s}\mathrm{u}\mathrm{f}/\mathrm{L}\mathrm{i}\mathrm{P}\mathrm{S}\mathrm{s})-\mathrm{E}\left(\mathrm{s}\mathrm{u}\mathrm{f}\right)-\mathrm{E}\left(\mathrm{L}\mathrm{i}\mathrm{P}\mathrm{S}\mathrm{s}\right)$$

where $\mathrm{E}\left(\mathrm{s}\mathrm{u}\mathrm{f}\right)$ is the energy of AlN, InN and the heterojunction without adsorbing LiPSs; $\mathrm{E}\left(\mathrm{L}\mathrm{i}\mathrm{P}\mathrm{S}\mathrm{s}\right)$ is the energy of the LiPSs; and $\mathrm{E}$($\mathrm{s}\mathrm{u}\mathrm{f}/\mathrm{L}\mathrm{i}\mathrm{P}\mathrm{S}\mathrm{s}$) is the energy of the surface structure with the LiPS adsorbate. The Van der Waals interactions between the surface and the LiPSs can be described by the empirical correction scheme of the DFT-D2 (D stands for dispersion) method in the Grimme scheme [28]. The Gibbs free energy of the sulfur reduction reaction was calculated by following equation:

$$\Delta \mathrm{G}=\Delta {\mathrm{E}}_{\mathrm{a}\mathrm{d}}+\Delta {\mathrm{E}}_{\mathrm{Z}\mathrm{P}\mathrm{E}}-\mathrm{T}\Delta \mathrm{S}$$

where $\Delta {\mathrm{E}}_{\mathrm{a}\mathrm{d}}$ is the change in reaction energy obtained by calculation, $\Delta {\mathrm{E}}_{\mathrm{Z}\mathrm{P}\mathrm{E}}$ represents the zero-point energy difference, and $\Delta \mathrm{S}$ represents the entropy difference. Charge transfers between different atoms are illustrated by applying Bader’s charge [29].

3. Results and Discussion

3.1. The Band Gap Structure of AlN, InN and AlN/InN Heterojunctions

AlN and InN belong to the triple group of N compounds within the P_m63 space group. The structure of SL has smaller lattice parameters, a and c, and a shorter bond length than that of bulk AlN and InN, which comes from the stronger interactions between atoms in a single layer. The energy band structures of AlN and InN are shown in Figure 1. It can be seen from Figure 1a,b that the band gap of bulk AlN is 5.4099 eV and the band gap of bulk InN is 0.8016 eV, which is in agreement with other calculations [30] and is smaller than the experimental value [31]. The bulk structures all have direct band gaps located at the Γ point. The band gap of SL (as shown Figure 1c,d) is different, in which the band gap of AlN narrows (4.6731 eV) and that of InN broadens (1.0674). SL structures have an indirect band gap, which is in agreement with other research showing that the band gap transition from direct to indirect can occur in the transitional metal dichalcogenides [30]. The bonding states at VBM with lower energy are located at Γ, which is composed of hybridized p_x and p_y orbitals. The anti-bonding states at CBM with higher energy are at M.

The optimization results of constructed monolayer AlN/InN heterojunctions are shown in Figure 2a. The smooth 2D planar configuration of AlN and InN is broken and slightly deformed. Bader charge analysis shows that there are charge transfers before and after the formation of the heterojunction, in which N atoms in the InN obtain more electrons (0.03 e) than 0.01 e for the AlN. The energy band structure of the heterojunction (Figure 2b) shows metallic properties. The calculated density of states has no gap at the Fermi level, as shown in Figure 2c. These states are primarily composed of 2s, 2p N atoms and 5s, 5p In atoms. The contribution of the electronic states of the Al atoms is small. It has been confirmed that the enhancement of the conductivity of a catalyst can promote electron transfer between the components [32].

3.2. Catalytic Mechanism of Li₂S_n for AlN and InN

The optimized structures of five kinds of LiPS adsorbed onto AlN and InN surfaces are obtained; Li₂S, Li₂S₄ and Li₂S₆ are three optimized structures shown in Figure 3. All Li₂S_n (n = 1, 2, 4, 6, 8) was optimized, as also shown in Figure 3. It can be seen that the Li atoms of all types of LiPS molecules are directly connected to N atoms, and the S atoms to the metal atoms of Al or In. Along with LiPS adsorption, the surface of the AlN still remains smooth, and for the InN substrates, roughness can be observed on the surface.

Adsorption energies are calculated to quantitatively evaluate the interaction between Li₂S_n and AlN or InN compounds, as shown in Figure 4. For AlN and InN, the adsorption energies of insoluble Li₂S/Li₂S₂ are lower than those of soluble Li₂S₄, Li₂S₆ and Li₂S₈. Along with the stepwise reduction of Li₂S_n, LiPSs+ molecules will accept electrons when adsorbed on the surface of the material. However, AlN has relatively higher adsorptivity for LiPSs than InN does. For the surface of AlN structures, the adsorption energies of Li₂S, Li₂S₂, Li₂S₄, Li₂S₆ and Li₂S₈ are −3.02 eV, −2.35 eV, −1.41 eV, −1.35 eV and −1.16 eV, respectively. The adsorption ability of AlN is relatively weaker for all LiPSs molecules, especially for the large molecule Li₂S_n (n = 4, 6, 8). The higher adsorption energies of soluble Li₂S₄, Li₂S₆ and Li₂S₈ mean that the opportunities for transfer electrons from AlN are few and thus retard electrochemical kinetics. Hence, the final product is comparatively difficult to deposit owing to the larger surface energy. In addition, along with the end of the discharge, the number of nuclear sites will be less, and the particle size of the final product, Li₂S, will be large. The adsorption energy is stronger for LiPSs adsorbed on the InN material surface, with values of −8.57 eV, −8.09 eV, −7.61 eV, −6.88 eV and −7.15 eV for Li₂S, Li₂S₂, Li₂S₄, Li₂S₆ and Li₂S₈, respectively. This indicates that adsorption energies are relatively low, and along with the molecular volume becoming larger increase only slightly. This effect of LiPSs volume manifests on the surface of materials, which shows that molecular volume is a contributing factor to adsorption energy. Hence, the chemical interaction between LiPSs and different materials is considered to be the most important of all contributing factors. The lower the adsorption energies of LiPSs are, the better the electrochemical reaction rate is. So, rate performance will be enhanced, and the shuttle effect can be inhibited. The stronger adsorption energy of Li₂S illustrates that its nucleation and precipitation can happen easily on an InN surface. This can be also seen from free energy profiles, as shown in the inset in Figure 4. Reaction profiles from S₈ to Li₂S₆ for AlN have lower rate-limiting steps than InN in the discharge process. And then, the reduction process from S₈ to Li₂S₆ is thermodynamically more favorable on an AlN surface than on an InN surface. However, there is a rate-limiting step from Li₂S₄ to Li₂S₂ in AlN surface, and it is more favorable for InN during the reduction from Li₂S₄ to Li₂S₂. Hence, the polarity of semiconducting materials can strengthen the interaction of polar LiPSs with the electrode surface.

To illustrate the interaction between LiPSs and catalytic materials, charge transfers are analyzed using differential charge densities. When LiPSs are adsorbed on the surfaces of materials, the charge densities of the surface around adsorbed Li atoms and S atoms are redistributed, as shown in Figure 5. Li₂S_n, AlN and InN act as electron donors and acceptors, respectively. The electron of AlN and InN will be transfered and the surface structures will be altered during the adsorption process. When LiPS molecules are adsorbed on AlN or InN surfaces, the Li atoms will transfer electrons to thier surrounding N atoms and metal atoms. It can be seen from

Table 1. Transfer charges for LiPSs adsorbed on AlN and InN surfaces.

LiPSs	AlN		InN
	N	Al	N	In
Li2S	−0.0102 e	0.0291 e	−0.1233 e	0.0474 e
Li2S2	−0.0081 e	0.0245 e	−0.1227 e	0.0220 e
Li2S4	0.0029 e	0.0077 e	0.1167 e	0.0234 e
Li2S6	0.0024 e	0.0188 e	0.1304 e	0.0052 e
Li2S8	0.0083 e	0.0071 e	0.1217 e	0.0184 e

that the Al and In will obtain electrons along with Li₂S_n adsorbed on the material surface, and the N atom will lose electrons for small LiPSs (Li₂S and Li₂S₂) and obtain electrons for larger Li₂S₄, Li₂S₆ and Li₂S₈. Harvest electrons mean that the unpaired electrons of atoms tend to be saturated, and the electron transition region between S atoms and Al/In atoms during catalysis have the overlapping part of the symmetry-adapted frontier orbitals and a small electron gain region among atoms. For the InN structure, more charges are transferred between Li atoms and N atoms than for the AlN structure, which indicates that the adsorbed Li₂S_n has stronger interactions with the surface of InN. This means that the binding of Li-N is dominated by charge depletion, indicating a strong covalent interaction between Li of LiPSs and N on the surface of materials. Thus, AlN or InN can be used as a good catalytic agent for Li-S batteries, owing to their good adsorption behavior, and can enhance the key reactions of lithium sulfur battery systems.

3.3. Catalytic Mechanism of Li₂S_n for AlN/InN Hetrojunction

Electrocatalysis techniques have been developed to accelerate the sulfur redox reaction. Catalysts, such as metal [33], metal oxides [7], metal sulfides [8], etc., are able to restrict LiPS shuttling and promote sulfur transformation reactions. A heterojunction constructed by dissimilar couplings and different band gaps can meet the above demands for LiPS transformation. It has been reported that heterostructured catalytic cathodes, such as Mn₃O₄-MnS [34], TiO₂-TiN [35], have synergistic functions that have been revealed active sites and built-in electric fields in heterogeneous interfaces and form a synergistic effect between the strong adsorption of Mn₃O₄ and the fast conversion of MnS to LiPSs [34]. The twinborn TiO₂-TiN heterostructure combines the merits of highly adsorptive TiO₂ with conductive TiN and achieves smooth trapping–diffusion–conversion of LiPSs across the interface [35]. Here, heterojunctions constructed with AlN with a broad band gap and InN with a narrow band gap show metallic properties. The adsorbing energy of Li₂S and Li₂S₆ near the junction is calculated, as shown in Figure 6a,b. It can be seen that on the AlN side of the junction, the adsorption energy of the larger Li₂S₆ molecule is lower than that of the small Li₂S molecule, and on the InN side of the junction, the smaller Li₂S molecule has lower adsorption energy, which is agreement with previous research [35]. TiN, with its better conductivity, is favorable for the reversible electrochemical conversion of LiPSs in the charge/discharge process, and TiO₂, with its relatively poor conductivity, is favorable for the adsorption of LiPSs [35]. This confirms the synergistic effect of AlN and InN. The synergistic process can be illustrated by the reduction process shown in the inset figure of Figure 4. So, AlN traps large Li₂S₈ and Li₂S₆, the junction causes the diffusion of Li₂S₄, and InN completes the conversion of Li₂S₄ to Li₂S, which realizes the synergistic reaction of trapping–diffusion–conversion for LiPSs on the surface and interface of the catalytic agent.

Figure 6c shows the three diffusion paths of Li₂S₄ from AlN to InN in the junction, namely PATH1, PATH2 and PATH3. Free energy from adjacent adsorbing sites (Figure 6d) is obtained, which shows the migration abilities of the Li₂S₄ molecule. Larger mobile energy is needed before or after passing though junctions for PATH1 and PATH2. With PATH3, there is lower resistance for migration of Li₂S₄ molecule before or after passing though the junction, and then there is a suitable migration path. As Li₂S₄ molecule is moving across the junction, larger energy is needed to overcome the built-in electric field originating from the interface of the AlN/InN heterojunction, which is favorable for converting polysulfides [36]. It may be to authenticate that the synergistic reaction of trapping–diffusion–conversion for LiPSs has happened, in which AlN traps large Li₂S₈ and Li₂S₆, the heterojunction causes the diffusion of Li₂S₄, and InN completes the conversion of Li₂S₄ to Li₂S.

4. Conclusions

In summary, the AlN/InN heterojunction constructed by AlN with a wide band gap and InN with a narrow band gap shows better catalytic ability regarding LiPSs in nearby junctions. The energy band structure of the heterojunction shows metallic properties, which are primarily composed of 2s, 2p N atoms and 5s, 5p In atoms and a small contribution of electronic states by Al atoms. AlN has relatively higher adsorptivity for LiPSs than InN. Reaction profiles show that on the surface of AlN S₈, Li₂S₆ has a lower rate-limiting step than on InN, and Li₂S₄ to Li₂S₂ has a higher rate-limiting step, which is more favorable for InN during the reduction from Li₂S₄ to Li₂S₂. The adsorbing energy of Li₂S and Li₂S₆ near the junction also illustrates that the AlN side of the junction has stronger adsorption for larger Li₂S₆ molecules, and small Li₂S molecules are favorable for adsorption on the InN side of the junction. The synergistic effect of AlN and InN occurs near the heterojunction, where AlN traps large Li₂S₈ and Li₂S₆, heterojunction forms diffusion of Li₂S₄, and InN completes the conversion of Li₂S₄ to Li₂S and realizes the synergistic reaction of trapping–diffusion–conversion for LiPSs on the surface and interface of catalytic agent.