Ultrathin insulators as gate dielectric for blue phosphorene field-effect transistors

2D semiconductors with atomic size thickness, no hanging bonds, and excellent electronic properties (such as high carrier mobility and high on/off ratio) have been explored as potential channel materials to suppress short-channel effects of future nanoscale channel field-effect transistors (FETs) to extending Moore’s law.^1–4 To date, there have been extensive experimental and theoretical efforts to research 2D semiconductors as promising candidates for channel materials of short-channel FETs, including black phosphorene, transition metal dichalcogenides (TMDCs), GaAs, InSe, and WSi₂P₂As₂.^5–9 Compared with the above-mentioned 2D semiconductors, monolayer blue phosphorene (BlueP) has attracted great attention and research interest due to its indirect bandgap of about 2 eV and unique anisotropic in-plane properties, since its successful preparation in the laboratory in 2016.¹⁰ Moreover, BlueP has both a higher carrier mobility (over 1000 cm² V⁻¹ s⁻¹) than TMDCs and a higher on/off ratio than crystalline Si, resulting in a better balance between the carrier mobility and on/off ratio of FETs,¹¹ making BlueP a very competitive channel material for short-channel FETs.^12,13

It is well known that the performance of practical FETs strongly depends not only on the properties of channel material but also on the quality of gate dielectric layer and the properties of interface between dielectric and channel. However, one of the main challenges in achieving practical applications of 2D semiconductor-based FETs is to explore suitable gate dielectric materials interfaced with 2D semiconductors to guarantee efficient gate control,^14,15 and to scale the thickness of the gate dielectric layer and to control its quality. An excellent gate dielectric for 2D semiconductors requires a large dielectric constant, which can effectively screen the charge scattering^16,17 and can significantly reduce the device supply gate voltage and power consumption.¹⁸ Moreover, a desirable gate dielectric also demands low equivalent thickness (EOT) and a large bandgap,¹⁹ which can prevent the carrier transport to gate electrodes.²⁰ Typical oxides used as gate dielectrics are SiO₂, Al₂O₃, HfO₂, and ZrO₂ insulators.^21–24 However, it is difficult to achieve high-quality interfaces between these dielectrics and 2D semiconductor channels due to high interface state density,^25,26 which leads to the deterioration of device performance. Therefore, considerable efforts have been made to search for new suitable dielectrics. So far, it has been reported that 2D insulators such as h-BN, CaF₂, and Bi₂SeO₅ layers can achieve high-quality interfaces on 2D TMDC semiconductors by van der Waals interactions^27–31 and are expected to be used as gate dielectrics for future 2D FETs. Unfortunately, many problems and obstacles remain to be solved. For example, recent studies have shown that there exists a large leakage current in 2D devices using h-BN as a dielectric.³² Furthermore, whether these 2D dielectrics are also suitable for other 2D semiconductor-based FETs, such as BlueP-based FETs? In addition, the integration of 2D dielectric into 2D semiconductors at high quality for practical applications remains challenging. Although various efforts have been made, finding satisfied dielectrics and integrating them into the channels at high quality still remain a major obstacle to the further development of next-generation FETs for practical applications.

In particular, when a FET works under a gate voltage for practical applications, the dielectric-channel heterostructure is actually placed under a vertical external electric field. It has been reported that applied electric fields can significantly control the band alignment and Schottky barrier height of a heterojunction.^33,34 Thus, as an excellent dielectric-channel heterostructure in a FET device, it is crucial that the dielectric and channel can exhibit their own good insulation and semiconductor properties in the absence of an electric field and can continue to maintain their respective desired properties under a vertical external electric field. However, until now, the effects of electric field on the electronic properties of dielectric and channel in their dielectric-channel heterostructure have been little studied.

Since HfO₂ has a large dielectric constant (∼25) and excellent thermal stability with Si substrates,³⁵ TiO₂ has a very large dielectric constant (∼80) and easy synthesis and stability;³⁶ BN has a dielectric constant about 5, very high thermal and chemical stability and easy stacking on 2D materials;³⁷ monolayer CaF₂ has a large dielectric constant (∼8.43), a wide bandgap (∼9.49), and dynamic stability;³⁸ HfO₂, TiO₂, BN, and CaF₂ insulator layers are selected as gate dielectrics of BlueP-based FET in the present work. We focus on investigating the structures and electronic properties of BlueP-dielectric heterojunctions, including BlueP-BN, BlueP-HfO₂, BlueP-TiO₂, and BlueP-CaF₂. For the first time, an intensive insight is gained into the electronic properties of the heterojunctions between BlueP and these dielectrics via applying perpendicular external electric fields. The calculated results suggest that HfO₂ and CaF₂ dielectrics are suitable as gate dielectrics for BlueP-based FETs; furthermore, CaF₂ is superior to HfO₂. Then, we investigate the effects of interfacial intrinsic atomic vacancy on the structure and electronic properties of BlueP-HfO₂ and BlueP-CaF₂ heterostructures. In addition, we use hydrogen passivation to the F-vacancy of BlueP-CaF₂ heterostructure to study its effective protection of BlueP channel and CaF₂ dielectric, which will help improve the performance of 2D semiconductor-based nanoelectronic devices with CaF₂ as a gate dielectric.

All calculations for BlueP-dielectric heterojunctions, including BN-BlueP-BN, HfO₂-BlueP-HfO₂, TiO₂-BlueP-TiO₂, and CaF₂-BlueP-CaF₂, were performed by first-principles calculations based on density-functional theory (DFT),³⁹ as implemented in the Vienna Ab initio Simulation Package (VASP). The projector augmented wave (PAW) was used, and the Perdew–Burke–Ernzerhof (PBE) method of generalized gradient approximation (GGA)^40–43 was employed to deal with the exchange–correlation energy. The energy cutoff of the plane wave basis was 520 eV, and the Monkhorst–Pack k-mesh density with ∼0.03 Å⁻¹ was sampled to ensure numerical accuracy. Geometry optimizations were carried out until the Hellmann–Feynman force on each atom was less than 0.02 eV/Å and the total energy converged to 10⁻⁶ eV. In the supercell models for BlueP-dielectric heterojunctions, a vacuum separation of 20 Å was employed to avert the artificial coupling role between layers in two adjacent periodic images. The optimized PBE van der Waals (optB88-vdW) was used to consider the van der Waals interactions between layers in the heterojunctions.

Figures 2(a)–2(e) show that our calculated lattice constants for monolayer BlueP, bilayer BN, monolayer CaF₂, bulk HfO₂, and bulk TiO₂ were 3.28, 2.51, 3.59, 5.06, and 4.66 Å, respectively, which are in agreement with other theoretical calculations.^38,44–47 Figures 1(a)–1(f) show the energy band structures of monolayer BlueP and the dielectric BN, TiO₂, HfO₂, HfO₂, and CaF₂ thin-layers. Monolayer BlueP exhibits an indirect bandgap of 1.93 eV, which is consistent with our preceding reported result and those of other studies.^12,48,49 Bilayer BN exhibits an indirect bandgap of 4.44 eV, which is close to the result of 4.37 eV of other research,⁵⁰ and TiO₂(101) thin-layer has a direct bandgap of 1.89 eV. The bandgaps for HfO₂(111) thin-layers with thicknesses of three Hf-O atomic layers (labeled as HfO₂-3) and four Hf-O atomic layers (labeled as HfO₂-4) are very close, with direct bandgaps of 4.25 and 4.12 eV, respectively. Monolayer CaF₂ exhibits an indirect bandgap of 7.26 eV, which agrees well with the previous result of 7.17 eV.³⁸ 

There is no obvious deformation at the interfaces when five 2D layers are combined to form heterojunctions. The interlayer spacings d₁ and d₂ are the same for BlueP-BN, BlueP-HfO₂-3, BlueP-HfO₂-4, and BlueP-CaF₂ heterojunctions, being 3.53, 3.23, 3.47, and 3.42 Å, respectively, except that the d₁ and d₂ of BlueP-TiO₂ heterojunction are slightly different, which are 2.29 and 2.34 Å, respectively. Here, the marks of d₁ and d₂ are labeled in Fig. 2. Large interlayer spacings between BlueP and dielectric layers suggest weak interactions between the components of heterojunctions. As shown in Figs. 3(a)–3(e), both BlueP and dielectrics basically remain their original semiconductor and dielectric properties. However, the band alignments are different in five heterogeneous structures, as shown in Figs. 3(f)–3(h). In these figures, CBM and VBM are conduction band minimum and valence band maximum, respectively. In particular, for BlueP-HfO₂ (or BlueP-CaF₂) heterojunction, the band alignment is as follows: VBM-HfO₂ (or VBM-CaF₂) < VBM-BlueP < CBM-BlueP < CBM-HfO₂ (or CBM-CaF₂), called type-I. In type-I, the bandgap of HfO₂ (or CaF₂) is greater than that of BlueP. The CBM of HfO₂ (or CaF₂) is higher than that of BlueP, while the VBM of HfO₂ (or CaF₂) is lower than that of BlueP. This type-I enables effective carrier confinement within the BlueP layer, significantly suppressing leakage currents through spatial charge separation.⁵⁹ For BlueP-BN heterojunction, VBM-BlueP < VBM-BN < CBM-BlueP < CBM-BN, called type-II. This type-II promotes efficient electron–hole pair separation across the interface, thereby minimizing recombination losses.⁶⁰ For BlueP-TiO₂, VBM-TiO₂ < VBM-BlueP < CBM-TiO₂ < CBM-BlueP, called type-III. As a result of weak coupling among components and band alignment, the VBM and CBM of entire heterojunctions are significantly changed compared to isolated BlueP and dielectrics. The bandgaps of BlueP-BN, BlueP-TiO₂, BlueP-HfO₂-3, BlueP-HfO₂-4, and BlueP-CaF₂ are 1.73, 1.51, 1.68, 1.73, and 1.99 eV, respectively.

In practical semiconductor nanotransistor applications, to minimize the leakage current through gate electrodes, the conduction band offset (CBO) and valence band offset (VBO) between gate dielectric and semiconductor channel should be larger than 1 eV.¹⁶ Our estimated CBO and VBO for BlueP-BN, BlueP-TiO₂, BlueP-HfO₂-3, BlueP-HfO₂-4, and BlueP-CaF₂ are about 2.4 and 0.3, 0.3 and 0.7, 1.0 and 1.7, 1.0 and 1.6, and 2.4 and 4.0 eV, respectively, which can be obtained from Figs. 3(a)–3(e). Obviously, only BlueP-HfO₂ and BlueP-CaF₂ can match the desired CBO and VBO well. Furthermore, CaF₂ is superior to HfO₂ as a dielectric for BlueP-based FETs.

It is well-known that an excellent gate dielectric layer in 2D semiconductor-based nanoscale FETs requires a high potential barrier for electrons or holes so that the dielectric can perform its main screening role, which could effectively suppress current flow from the gate to the channel.^53,54 When a gate voltage is applied to the FET, a vertical electric field is essentially applied to the dielectric-channel heterojunction. In this case, the dielectric still requires a high barrier for electrons or holes to perform its screening role. However, it is well known that applying an electric field can effectively modulate the electronic structure of 2D materials and allows significant control of band alignment and Schottky barrier height of the heterojunction.^33,34 So, when a gate voltage is applied to the FET, whether the dielectric layer can preserve its good screening role is very important. Next, we mainly explore the electronic properties of heterostructures under applied electric fields and by analyzing the screening role of dielectric by valence and conduction band offsets (VBO and CBO). The electric fields are applied perpendicular to the interface of heterojunction, ranging from 0 to 0.6 V/Å, and the step is 0.1 V/Å. Figures 5(a)–5(t) plot the electronic band structures of BlueP-BN, BlueP-TiO₂, BlueP-HfO₂-3, BlueP-HfO₂-4, and BlueP-CaF₂ heterojunctions under different applied electric fields (E). Figure 6(a) plots the bandgap evolution of BlueP and dielectric in five heterojunctions under the influence of an external electric field (E). For all five heterojunctions, as E increases, the bandgap of BlueP changes little, while the bandgap of dielectric decreases significantly. Careful observation from Figs. 5(a)–5(t) shows that the band alignment for BlueP and dielectric changes greatly. Then, we further analyze the effects of an external electric field on the band structures of dielectric layers located on both sides of BlueP. Figures 7(a)–7(d) show the band structures of layer-I, layer-II, layer-III, and layer-IV dielectric layers (labeled in Fig. 2) in BlueP-HfO₂-4 and BlueP-CaF₂ heterojunctions without and under an external electric field of 0.6 V/Å. Similar behavior can also be observed in BlueP-BN, BlueP-TiO₂, and BlueP-HfO₂-3 heterojunctions. It can be found that under E, the band structures of layer-I and layer-II dielectric layers move downward, and the band structures of layer-III and layer-IV move upward. The conduction bands of the whole dielectric are mainly contributed by layer-I and layer-II, and the valence bands are mainly contributed by layer-III and layer-IV. Consequently, all the bandgaps of the whole dielectric become small, as shown in Fig. 6(a). Observed clearly from the relative movement of valence bands, as shown in Fig. 7, it is found that the response of outer dielectric layers (layer-I and layer-IV) to an external electric field is greater than that of inner layers (layer-II and layer-III). As E increases, the band alignment types for BlueP-BN, BlueP-TiO₂, and BlueP-CaF₂ heterojunctions roughly remain their original types until E = 0.6 V/Å. However, the band alignment types for BlueP-HfO₂-3 and BlueP-HfO₂-4 heterojunctions have changed at about E = 0.4 V/Å.

Next, we explore why the energy bands of heterojunctions vary with external electric fields. When E is exerted, the different junctions (atom layers) of the heterojunction have their own different Fermi energies (E_F), shown in Fig. 6(b), and the E_F of the whole heterojunction is changed with E. As a consequence, the variation of the bandgap of the whole heterojunction under E is attributed to the shifts of E_F for the BlueP layer and two dielectric layers on both sides under E, which promotes the transfer of electrons between BlueP and dielectric layers. Notably, when E reaches 0.6 V/Å, the BlueP-BN heterojunction abruptly becomes metallic due to the breakdown and charge tunneling of dielectric layers. Similar behavior can also be observed in BlueP-TiO₂ and BlueP-HfO₂-3 heterojunctions, as shown in Figs. 5(d), 5(h), and 5(l), resulting in large vertical leakage currents and poor dielectric properties of dielectric layers. If this happens in a FET device, it will cause a large gate leakage current and reduce the performance of the device. Fortunately, the BlueP-HfO₂-4 and BlueP-CaF₂ heterojunctions remain semiconductor, as shown in Figs. 5(p) and 5(t). However, as E increases, only the CaF₂ dielectric layer can still satisfy the requirements that CBO and VBO between CaF₂ and BlueP are larger than 1 eV, which can play a protective role as gate dielectrics. In particular, its bandgap still mainly depends on BlueP, which is less affected by an external electric field, as shown in Figs. 5(q)–5(t). This implies that the resistance of CaF₂ dielectric layer to an external electric field is the strongest among the five dielectric layers. Furthermore, monolayer CaF₂ dielectric is significantly thinner than the BlueP-HfO₂-4 layer, which is an urgent requirement for reducing dielectric layer thickness in nanoscale FETs. These indicate that monolayer CaF₂ may be a good gate dielectric for BlueP-based FETs.

In addition, an ab initio molecular dynamics (AIMD) simulation was performed to further investigate the thermodynamic stabilities of BlueP-HfO₂-4 and BlueP-CaF₂, which are very important in practical applications for FETs. Canonical ensemble (NVT) was used in AIMD simulations, the simulation time was 10 ps, and the time step was 2 fs. As shown in Fig. 9, our AIMD simulations show only minimal variation in the energy and no significant reconstruction in the structure throughout the calculation at 300 K. This reveals the excellent thermal stabilities of BlueP-HfO₂-4 and BlueP-CaF₂ heterojunctions at room temperature.

Atomic vacancy is easy to generate in the preparation process of 2D materials, which can have significant impacts on the structure and electronic properties of materials, especially for monolayer structures. Next, we focus on the effects of interfacial intrinsic atomic vacancies on the structure and electronic properties of BlueP-HfO₂ and BlueP-CaF₂ heterostructures, including O-vacancy in an interfacial HfO₂ layer and F-vacancy in CaF₂. O-vacancy defects are more likely to appear on the HfO₂ surface in the interfacial region,^55–57 which may affect the dielectric properties of HfO₂. Therefore, the performance of HfO₂ as a gate dielectric for 2D BlueP-based FETs with O-vacancy defects in the interfacial region was further investigated in this paper. For simplicity, we consider the case in which O-vacancy defects are only in one side of the interfacial region of BlueP-HfO₂-4, as shown in Fig. 10(a), called BlueP-HfO₂-4 (V_O). The calculated interfacial binding energy E_b is −0.82 eV/Atom. Compared with the E_b of −0.18 eV/Atom for BlueP-HfO₂-4 without O-vacancy defects, O-vacancy defects have resulted in an obvious increase in E_b, which indicates that the O-vacancy is easy to exist at the interface of the BlueP-HfO₂-4 heterojunction. After geometrical optimization, the O-vacancy makes the HfO₂ layer, where the vacancy is located close to the BlueP layer, and the interlayer distance d₁ is 1.26 Å, which is about 2.21 Å shorter than that of BlueP-HfO₂-4. Another interlayer distance d₂ is 2.84 Å, which is 0.63 Å shorter than that of BlueP-HfO₂-4. This indicates that the O-vacancy induces large deformations, leading to the reconstruction of the structure.

Figure 10(b) illustrates that the type-I energy band alignment is preserved in the BlueP-HfO₂-4 (V_O) heterojunction without an external electric field. However, the band offsets vary compared with those of BlueP-HfO₂-4 without O-vacancy. When E is exerted, the different junctions of heterojunction have similar behavior as they do in the BlueP-HfO₂-4 heterojunction without O-vacancy, as shown in Fig. 5. The bandgap of heterojunction is reduced as E increases. The difference is that when E reaches 0.6 V/Å, BlueP-HfO₂-4 (V_O) becomes metallic. It implies that the HfO₂-4 dielectric with O-vacancy is less resistant to an external electric field than HfO₂-4 without O-vacancy, indicating that O-vacancy at the interface will reduce the dielectric properties of the gate dielectric. Moreover, comparing Fig. 8(d) with Fig. 11, when E reaches 0.6 V/Å, the amount of charge accumulation on the left surface layer (the red dashed box on the left of Fig. 11) is slightly smaller than the amount of charge depletion on the right surface layer (the red dashed box on the right of Fig. 11), suggesting that the electrons move to the right side of the dielectric layer and accumulate on this surface to respond to an external electric field. It coincides with the result of the electronic band structure in Fig. 10(e). The interfacial O-vacancy not only has a strong effect on the structure of the BlueP-HfO₂-4 heterostructure but also has a serious effect on its electrical properties, greatly reducing the screening role of the HfO₂ dielectric layer. If such O-vacancy occurs in 2D semiconductor-based FETs with HfO₂ as a gate dielectric, leakage current through gate will greatly increase and the electron transport along channel will be greatly reduced, resulting in the deterioration of device performance.

Figure 12(a) shows the structure of BlueP-CaF₂ with F-vacancy defects only in one side of the interface region, called BlueP-CaF₂ (V_F). Our calculated interfacial binding energy E_b of BlueP-CaF₂ (V_F) is about −0.43 eV/Atom, indicating that F-vacancy defects also have resulted in an obvious increase in E_b compared with that of BlueP-CaF₂ without F-vacancy defects (E_b = −0.11 eV/Atom). It indicates that the F-vacancy can exist at the interface of the BlueP-CaF₂ (V_F) heterojunction. However, F-vacancy causes significant structural deformation, as shown in Fig. 12(a). F-vacancy makes the CaF₂ layer closer to the BlueP layer, and the interlayer distances d₁ and d₂ are 2.74 and 2.69 Å, respectively, which are about 0.68 and 0.72 Å shorter than that of BlueP-CaF₂. Similar to the BlueP-HfO₂-4 (V_O) heterojunction, F-vacancy does not change the type-I band alignment, as shown in Fig. 12(b). However, as E increases, the bandgap of BlueP is almost constant and the CaF₂ bandgap becomes slightly smaller, as can be clearly seen in Figs. 12(c)–12(e). Moreover, BlueP-CaF₂ (V_F) exhibits metallic. It implies that F-vacancy at the interface will seriously damage the dielectric properties of CaF₂. Comparing Fig. 13 with Fig. 8(e), when E is exerted, the charge transfer amount of BlueP-CaF₂ (V_F) at the left interface is distinctly smaller than that at the right interface where F-vacancy is located, which is different from BlueP-CaF₂ without F-vacancy. It indicates that the gain and loss of electrons near the vacancy increase under E. The above-mentioned results show that F-vacancy seriously affects the structure of the BlueP-CaF₂ heterostructure and its electrical properties, leading to great deterioration of the screening role of the CaF₂ dielectric layer. If such F-vacancy occurs in 2D semiconductor-based FETs with CaF₂ as a gate dielectric, the performance of the device will also be greatly reduced. The vacancy both seriously reduces the dielectric properties of BlueP-CaF₂ and BlueP-HfO₂. However, compared with BlueP-HfO₂, the F-vacancy deteriorates the dielectric properties of BlueP-CaF₂ more severely. BlueP-CaF₂ exhibits metallic even without an external electric field, as shown in Fig. 12(b).

Yang et al. have found that hydrogen passivation can effectively terminate the dangling bonds at the surface or interface.⁵⁸ Next, we study the structure and electrical properties of the BlueP-CaF₂ (V_F) heterojunction after hydrogen passivation. Our calculated adsorption energy for BlueP-CaF₂ (V_F) with hydrogen passivation on the F vacancies is −0.11 eV/Atom. The negative adsorption energy suggests that hydrogen adsorption is energetically favorable and easy to achieve. Comparing the structures of heterojunctions with/without hydrogen passivation on the F vacancies, as shown in Figs. 12(a) and 14(a), hydrogen adsorption apparently makes CaF₂ remain its original structure and nearly intact, thus greatly improving the interface quality between BlueP and CaF₂. More importantly, hydrogen adsorption on the F vacancies of CaF₂ can remarkably improve the dielectric properties of CaF₂ and protect the semiconductor properties of BlueP. It can be clearly seen from Figs. 14(b)–14(e) that the bandgap of hydrogen passivated BlueP-CaF₂ (V_F) is nearly identical to that of BlueP-CaF₂ without F-vacancy [Figs. 5(q)–5(t)] except for adding the electron states of hydrogen. Expectedly, the better dielectric properties of CaF₂ are reached after hydrogen passivation. As shown in Fig. 15, hydrogen passivation well suppressed the movement of Fermi level to the conduction band edge of BlueP-CaF₂ (V_F). More excitingly, when the external electric field is exerted, hydrogen passivation well inhibits the electrons from moving from the left to the right of BlueP-CaF₂ (V_F). It implies that the hydrogenation strategy can very effectively protect the CaF₂ dielectric and BlueP semiconductor. These results will help improve the performance of 2D semiconductor-based nanoelectronic devices with CaF₂ as a gate dielectric.

In summary, the binding energies, band structures, and electronic properties of BlueP-dielectric heterojunctions, including BlueP-BN, BlueP-HfO₂, BlueP-TiO₂, and BlueP-CaF₂ were studied by first-principles calculations. Moreover, the electronic properties of all heterojunctions under perpendicular external electric fields were studied. The calculated results show that all heterojunctions are relatively easily available energetically. The results of band structures show that HfO₂ layer and monolayer CaF₂ dielectrics are appropriate as gate dielectrics for BlueP-based FETs, and monolayer CaF₂ is superior to HfO₂ dielectric. AIMD calculations reveal the excellent thermal stability of BlueP-HfO₂-4 and BlueP-CaF₂ heterojunctions at room temperature. In addition, the effects of interfacial intrinsic atomic vacancy on the structure and electronic properties of BlueP-HfO₂ and BlueP-CaF₂ heterostructures with perpendicular external electric fields and hydrogen passivation to the F-vacancy of BlueP-CaF₂ (V_F) were also studied. The results show that the interfacial intrinsic atomic vacancy seriously affects the electrical properties of the whole heterojunction, greatly reducing the screening role of the dielectric layer. Fortunately, we found that hydrogen passivation to the F-vacancy of BlueP-CaF₂ (V_F) can effectively protect the semiconductor properties of BlueP and dielectric properties of CaF₂. It suggests that the hydrogen passivation strategy may help improve the performance of 2D semiconductor-based nanoelectronic devices with CaF₂ as a gate dielectric.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62174032 and 62474041) and the Natural Science Foundation of Fujian Province of China (Grant Nos. 2021J01189 and 2021J01188). This work was carried out at the National Supercomputer Center in Tianjin, and the calculations were performed on Tianhe-1(A).

The authors have no conflicts to disclose.

Xian Lin: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal). Jian-Min Zhang: Data curation (equal); Methodology (equal); Validation (equal). Guigui Xu: Data curation (equal); Methodology (equal); Validation (equal). Kehua Zhong: Funding acquisition (lead); Supervision (equal); Writing – review & editing (equal). Zhigao Huang: Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.