First-Principle Study of Two-Dimensional SiP₂ for Photocatalytic Water Splitting with Ultrahigh Carrier Mobility

Abstract

Two-dimensional materials present abundant novel properties when used in advanced applications, which develops considerable focus. In this investigation, the first-principles calculations are explored to study the structural characteristic of the monolayered SiP₂, which is stable even at 1200 K. The SiP₂ monolayer is a semiconductor with an indirect bandgap of 2.277 eV. The decent band alignment and light absorption capacity imply that the application is a suitable photocatalyst for water splitting. Furthermore, the SiP₂ monolayer possesses an ultrafast electron mobility at 33,153 cm²·V⁻¹·s⁻¹ in the transport direction. The excellent Gibbs free energy of the SiP₂ monolayer is also addressed in an examination of the hydrogen evolution reaction.

1. Introduction

With the discovery of graphene in 2004 [1], two-dimensional (2D) materials gradually have gained considerable research, such as magnetic [2], thermal [3,4] and catalytic performances [5]. Two-dimensional materials have robust chemical bonds in the two-dimensional plane, which can even be prepared from corresponding bulk materials by way of mechanical stripping method [6]. Importantly, 2D materials exhibit excellent mechanical [7], magnetic [8] and optical properties [9]. For example, under external biaxial strain, the bandgap of the arsenene can be transformed from indirect to direct bandgap. Furthermore, as the strain continues to increase, the optical absorption ability of arsenene also can be enhanced, enabling optical absorption energy that ranges in 1.2–2.2 eV [10]. The hardness of GeC is weaker than that of graphene, while the obtained Poisson value (about 0.28) is 1.5 times that of graphene. At the same time, the in-plane stiffness of the GeC is 41%, and the GeC possesses a small limited strain under biaxial strain [11]. All of this reveals the promising applications used by 2D materials [12,13,14,15]. To further develop the advanced functional 2D materials and potential applications, some significant methods are adopted. Contacting two different layered materials as type-II van der Waals can separate photogenerated electrons and holes, which prolongs the lifetime of the charges when used as a photocatalyst for water splitting [16,17,18,19]. The hydrogen evolution reaction (HER) ability of the MoS₂ monolayer in the inert basal planes can be activated by using different intrinsic defects [20]. Furthermore, external strain and electric field engineering are also advantageous for improving the catalytic, electronic and thermal performances [21,22,23].

Since Fujishima and Honda first reported that TiO₂ electrodes can be collectively used as a photocatalyst for water splitting in 1972 [24], developing 2D materials to decompose the water became desirable. When the 2D semiconductor absorbs the photons from the light, the excited electrons can migrate from the valence band (VB) to the conduction band (CB) to induce the HER and oxygen evolution reaction (OER), respectively. For example, the stripped g-C₃N₄ nanosheets can greatly increase the efficiency of its photocatalytic water decomposition by increasing the specific surface area in order to increase the activity [25]. Carrier mobility of the photogenerated electrons and holes is also a critical parameter in water splitting [26], because the higher mobilities can obtain a high utilization of electrons and holes in oxidations and reductions before recombination. A recent study on photocatalytic water splitting reported that the GeSe monolayer even possesses ultrahigh electron mobility at about 32,507 cm²·V⁻¹·s⁻¹ [27]. Recently, 2D SiP₂ has been successfully prepared [28], which presents in an unconventional excitonic state. Subsequently, SiP₂ also can be prepared with h-BN used as a gate-controlled phototransistor, which additionally demonstrates an ultrahigh sensitivit. All of this demonstrates that SiP₂ has excellent electronic and optical properties. Current investigations have revealed a promising application for nanodevices, while the critical parameter of carrier mobility has been rarely explored. Furthermore, the suitable band edge energy of the SiP₂ monolayer has also not been studied, even though it may have a potential application as a photocatalyst. All these things have aroused the exploration of the advanced applications of the SiP₂ monolayer in our work.

In this investigation, the thermal stability and electronic property of the SiP₂ monolayer are addressed by the first-principles method. The semiconductor nature is obtained and the band edge positions are also explored as suitable for redox reaction in water splitting. Additionally, the excellent carrier mobility and the hydrogen evolution reaction performance are first examined for the promising novel photocatalytic activity of the SiP₂ monolayer. The research outline of this investigation is expressed by Figure 1.

2. Computational Methods

In our simulations, the structural optimization, phonon spectrum, band structure, carrier mobility and the Gibbs free energy were calculated by Device Studio [Hongzhiwei Technology, Device Studio, Version 2021A, China, 2021. Available online: https://iresearch.net.cn/cloudSoftware, accessed on 2 June 2023] program, which provides a number of functions for performing visualization, modeling and simulation. And all that simulations using DS-PAW software are integrated in Device Studio program [29]. Based on density functional theory (DFT), the Vienna ab initio simulation package (VASP) was explored to develop the other first-principles calculations [30]. The generalized gradient approximation (GGA) method was used with the projector augmented wave potentials (PAW) to employ the Perdew–Burke–Ernzerhof (PBE) functional, which also explains the exchange-correlation functional [31,32]. The energy cut-off used was 550 eV. In the first Brillouin zone (BZ), the Monkhorst–Pack k-point grid was set to 17 × 17 × 1. In addition, the Heyd–Scuseria–Ernzerhof hybrid method was adopted to calculated the projected band structure [33]. The vacuum space was set at 25 Å, which can prevent the interaction between nearby layers. The convergence for the energy is 0.01 meV, while the force is controlled at 0.01 eV·Å⁻¹. The PHONOPY code was used to calculated phonon spectra based on the density functional perturbation theory [34,35].

3. Results and Discussion

3.1. Structural and Stability Performance

The atomic structure of the SiP₂ monolayer was optimized with the lattice constant at 3.460 Å and 10.280 Å in the x and y directions, respectively, as is demonstrated in Figure 2a. The lattice constant of 3.460 Å is comparable with that of the TMDs materials [36] and the B₂P₆ monolayer (about 3.25 Å) [37], showing a promising application as a stable heterostructure. The simulated scanning tunneling microscopy (STM) images of the SiP₂ monolayer obtained are shown in Figure 2b, and such patterns in the simulated STM images display good agreement with a previous experiment [28]. Moreover, the dynamic stability of the SiP₂ monolayer was investigated by using the density functional perturbation theory as shown in Figure 2c; one can see that no imagery was found in phonon spectra, suggesting dynamic stability of the SiP₂ monolayer.

Then, the thermal stability of the SiP₂ monolayer under different temperatures was further investigated. Using ab initio molecular dynamics (AIMD) calculations, the Nosé–Hoover heat bath scheme was addressed to further evaluate the thermal stability of the SiP₂ monolayer. A 4 × 2 × 1 supercell of the SiP₂ was employed, considering the lattice translational constraints, which possesses 36 atoms in the simulations. After the total relaxation under 300–1200 K in 10 ps, the structure of the SiP₂ system was still intact, demonstrated by the inset image in Figure 2a. Such results represent a robust thermal stability of the SiP₂ monolayer even under 1200 K. In addition, a convergence was revealed by the fluctuations in temperature and total energy of the SiP₂ monolayer during the AIMD calculation under 300–1200 K as shown in Figure 3, further suggesting the accuracy of the obtained results.

3.2. Band Structure and Carrier Mobility

The projected band structure of the SiP₂ monolayer was calculated using the HSE06 functional expressed in Figure 4a. One can see that the SiP₂ monolayer is a semiconductor with an indirect bandgap of 2.277 eV, which displays good agreement with other reported results [28]. The conduction band minimum of the SiP₂ monolayer is mainly contributed to by the P atoms, while the valence band maximum is donated to by the P and Si atoms, as is demonstrated in Figure 4a. By comparing the vacuum level, the band edge positions of the SiP₂ monolayer were calculated, as is shown in Figure 4b. The obtained band alignment of the SiP₂ monolayer suggests a suitable band energy to promote the oxidations and reductions in water splitting; such decent band energy was also addressed by the WS₂ monolayer in some TMDs materials insinuated in Figure 4b. Furthermore, the light absorption capacity of the SiP₂ monolayer was investigated as a photocatalyst. The anisotropy optical performance of the SiP₂ monolayer is shown in Figure 4c, with the peak of the light absorption spectrum along the x (or y) direction as 12.8 × 10⁵ cm⁻¹ (or 10.2 × 10⁵ cm⁻¹) and with the wavelength as 207 nm (or 155 nm), which is higher than that of B₂P₆ (3.4 × 10⁴ cm⁻¹) [37], CdO (3.56 × 10⁵ cm⁻¹) [38] arsenene (3.01 × 10⁵ cm⁻¹) [39]. Such excellent light absorption characteristics also demonstrate the potential use as a photocatalyst to decompose water.

The carrier mobility of the SiP₂ monolayer is calculated by using the Bardeen–Shockley deformation potential theory [40], because the carrier mobility is also a critical target in photocatalytic water splitting. The effective masses (m*) of the electron and hole are obtained by:

$$m*=\pm {\hslash }^2{\left(\frac{{\mathrm{d}}^2{E}_k}{ \mathrm{d}{k}^2}\right)}^{-1},$$

(1)

where k and E_k are the wave vector and the corresponding electronic energy, respectively. In addition, the carrier mobility (μ) of the SiP₂ monolayer is calculated from:

$$\mu =\frac{e{\hslash }^{3}C}{k_{\mathrm{B}}{Tm}^{*}{m}_{\mathrm{e}}{E}_{\mathrm{d}}{}^2},$$

(2)

where the temperature, the electron charge and the Planck constant are expressed by T, e and $\hslash$, respectively. The Boltzmann constant is represented by k_B. The change of the band edge energy of the SiP₂ monolayer was evaluated by the deformation potential (E_d), which is calculated by comparing the vacuum level. In addition, the elastic modulus is used by C, which is calculated using $C=\left[{\partial }^{2}E/\partial {\epsilon }^2\right]/S$. The total energy of the SiP₂ monolayer is E and the area of the system is S. The energy difference and the band edge energy under the external strain of the SiP₂ monolayer were obtained, as is shown in Figure 5, and the fitted elastic modulus are summarized in

Table 1. The calculated effective mass (m*), elastic modulus (C), deformation potential constant (E_i) and mobility (µ) of the SiP₂ monolayer along the transport directions.

Material	Direction	Carrier	m* (me)	Ei (eV)	C (N/m)	μ (cm2·V−1·s−1)
SiP2	x	e−	0.138	2.600	454	14,254
		h+	–2.807	0.930		1926
	y	e−	1.713	0.190	70	33,153
		h+	–0.681	0.520		3915

.

The calculated hole carrier of the SiP₂ monolayer was 1926 cm²·V⁻¹·s⁻¹ and 3915 cm²·V⁻¹·s⁻¹ along the x and y directions, respectively. Particularly, the electron carrier presented ultrafast mobility at 14,254 cm²·V⁻¹·s⁻¹ and 33,153 cm²·V⁻¹·s⁻¹, respectively. Such excellent mobility was even higher than black phosphorus (10,000 cm²·V⁻¹·s⁻¹) [41] and Li₂B₆ (6800 cm²·V⁻¹·s⁻¹) [42]. The obtained hole carrier of the SiP₂ monolayer was also higher than that of recently reported 2D materials, such as GeS (1312 cm²·V⁻¹·s⁻¹) [27] and HfSi₂N₄ (1182 cm²·V⁻¹·s⁻¹) [7]. Furthermore, one can see that the mobility of the electron was about 10 times higher than that of the hole, suggesting a more advantageous ability to separate electron and hole in water splitting [43].

3.3. Hydrogen Evolution Reaction Performance

As a photocatalyst, the catalytic ability of the SiP₂ monolayer also played a significant role. The Gibbs free energy (∆G_H*) of the intermediate product in hydrogen evolution reaction (HER) is calculated by standard conditions from:

ΔG_H* = ΔE + ΔE_zpe + TΔS,

(3)

where the ΔE is used to represent the total energy of the H-adsorbed SiP₂ monolayer system, as shown in Figure 6a; the representative highly symmetrical adsorption sites are expressed by yellow balls, which contain 24 possibilities. The ΔE_zpe is the difference in the zero-point energies, and the ΔS shows the change in the entropy under the adsorption. T is set at 298 K. The active site is highlighted by the “*”. In addition, the hydrogen evolution reaction characteristic is addressed by two reactions:

∗ + H⁺ + e⁻ → H^∗,

(4)

H^∗ + H⁺ + e⁻ → H₂ + ∗

(5)

Furthermore, the most favorable hydrogen evolution reaction by the H-adsorbed site on the SiP₂ system is illustrated in Figure 6a as cyan balls, and the obtained Gibbs free energy of such an H-adsorbed SiP₂ system was calculated by using 1.11 eV, as shown in Figure 5b. Obviously, the SiP₂ monolayer possesses a novel and more advantageous hydrogen evolution reaction than the graphene [44], MoGe₂N₄ [7] and IV–VI monolayers [27].

4. Conclusions

In this study, the first-principles calculations were explored to systematically investigate the structural, electronic and optical properties and the carrier mobility and hydrogen evolution reaction of the SiP₂ monolayer. The SiP₂ monolayer is a semiconductor, which has a thermal stability even at 1200 K. The decent band edge positions and optical properties are addressed. Furthermore, the SiP₂ monolayer shows anisotropic carrier transport properties with ultrafast electron mobility at 33,153 cm²·V⁻¹·s⁻¹. The excellent hydrogen evolution reaction of the SiP₂ monolayer was calculated, which is more advantageous than that of graphene. All these things demonstrate the potential application for using SiP₂ as a photocatalyst to decompose water.