Xiaoshu Guo and Sandong Guo

1Xi'an University of Posts and Telecommunications, Xi'an 710121, China

2School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China

Abstract: A two-dimensional (2D) MA2Z4 family with α and β phases has been attracting tremendous interest, the MoSi2N4 and WSi2N4 of which have been successfully fabricated (Science 369, 670 (2020)). Janus monolayers have been achieved in many 2D families,soit isinterestingtoconstruct aJanusmonolayerfromtheMA2Z4family.In thiswork, JanusMSiGeN4 (M=Zrand Hf)monolayers arepredictedfrom β-MA2Z4,whichexhibitdynamic,mechanicalandthermalstabilities.Itisfound thattheyare indirect band-gap semiconductors by using generalized gradient approximation (GGA) plus spin-orbit coupling (SOC). With biaxial strain a/a0 from 0.90 to 1.10, the energy band gap shows a nonmonotonic behavior due to a change of conduction band minimum (CBM). A semiconductor to metal transition can be induced by both compressive and tensile strains, and the phase transformation point is about 0.96 for compressive strain and 1.10 for tensile strain. The tensile strain can change the positions of CBM and valence band maximum (VBM), and can also induce the weak Rashba-type spin splitting near CBM. For MSiGeN4 (M =Zr and Hf) monolayers, both an in-plane and out-of-plane piezoelectric response can be produced, when a uniaxial strain in the basal plane is applied, which reveals the potential as piezoelectric 2D materials. The high absorption coefficients in the visible light region suggest that MSiGeN4 (M = Zr and Hf) monolayers have potential photocatalytic applications. Our works provide an idea to achieve a Janus structure from the MA2Z4 family, and can hopefully inspire further research exploring Janus MA2Z4 monolayers.

Key words: Janus monolayers; piezoelectronics; MA2Z4 family

1. Introduction

Janus 2D monolayers have currently attracted increasing attention, which possess unique physical and chemical properties caused by their special crystal structure, such as strong Rashba spin splitting, the second harmonic generation response, and out-of-plane piezoelectric polarizations[1]. Experimentally, Janus monolayer MoSSe, which is constructed from MoS2/MoSe2, has been achieved by different experimental methods with an out-of-plane structural asymmetry[2,3]. In theory, many Janus 2D materials have been predicted by the first-principle calculations[4-12], such as Janus transition metal chalcogenides (TMDs), Janus transition-metal oxides, PtSSe,Janus MA2Z4, TiXY (X/Y = S, Se and Te), VSSe, SnSSe and Janus group-III monochalcogenide M2XY (M = Ga, In; X/Y = S,Se and Te). Some unique properties have also been predicted, such as an out-of-plane piezoelectric coefficient[13,14]and a significant Rashba spin splitting induced by intrinsic out-of-plane built-in electric field[10]. The Janus monolayer BiN and AsP field-effect transistors (FETs) possess sufficient competitiveness against other 2D FETs, which is confirmed by the benchmarking of the energy-delay product[15,16].

Recently, the high-quality 2D MoSi2N4and WSi2N4are successfully synthesized with excellent ambient stability by chemical vapor deposition (CVD)[17], which starts a new 2D material family. In the wake of MoSi2N4and WSi2N4, twelve kinds of 2DfamilyWSi2N4areproposed withαiandβi(i=1to6)phasesbyintercalatingMoS2-type MZ2monolayerintoInSetype A2Z2monolayer[18]. The MA2Z4with 32 or 34 valence electrons (VEC)are mostly semiconductors. Moreover,α2-WSi2P4forthe spin-valleypolarization,α1-TaSi2N4for Ising superconductor andβ2-SrGa2Se4fortopological insulator are predicted[18]. And then, spin-valley polarization are also investigated in MoSi2N4, WSi2N4and MoSi2As4[19,20]. Intrinsic piezoelectricity of the MA2Z4family along structure effect has been predicted by the first-principle calculations[21,22]. Coexistence of intrinsic piezoelectricity and ferromagnetism induced by small biaxial strain in the septuple-atomic-layer VSi2P4and VSi2N4has been achieved, which offers the opportunities for achieving multifunctional electronic devices[23]. 2D van der Waals electrical contact to monolayer MoSi2N4has been reported[24]. For example, the MoSi2N4/NbS2contact exhibits an ultralow Schottky barrier height[24]. High intrinsic lattice thermal conductivity in monolayer MoSi2N4has also been predicted by solving the phonon Boltzmann transport equation[25].

It is very worthy of intensive study to construct a Janus monolayer from the MA2Z4family. In our previous work,Janus MSiGeN4(M = Mo and W) monolayers have been predicted fromα1-MA2Z4[12]. The MSi2N4and MGe2N4(M = Zr and Hf) monolayers with aβ2phase are semiconductors[18]. And then, in this work, Janus monolayer MSiGeN4(M = Zr and Hf)are built by replacing the Si/Ge atoms of the top SiN/GeN bilayer in a MSi2N4/MGe2N4monolayer with Ge/Si atoms. Their crystal stability, electronic structures, piezoelectric and optical properties are investigated by the first-principle calculations.Calculated results show that MSiGeN4(M = Mo and W) monolayers are indirect gap semiconductors with dynamic, mechanical and thermal stabilities, and that tensile strain can induce weak Rashba-type spin splitting near CBM, and that MSiGeN4(M = Mo and W) monolayers have observable piezoelectric response and high absorption coefficients in the visible light region.

Table 1. For the ZrSiGeN4(HfSiGeN4) monolayer, the lattice constants a0; the physical quantities associated with elasticity (the elastic constants Cij, shear modulus G2D, Young's modulus C2D and Poisson's ratio ν); the gaps without/with SOC.

2. Computational detail

Within the density functional theory (DFT)[26], the projected augmented wave (PAW) method and GGA with the Perdew-Burke-Ernzerh (GGA-PBE) as the exchange-correlation functional are used, as implemented in the VASP code[27-30].It has been proved that GGA is more suitable for a gap of experimentally synthesized MoSi2N4monolayer than HSE06[17].So, we use GGA to study the electronic and optical properties of MSiGeN4(M = Zr and Hf) monolayers. The SOC is included to investigate electronic structures of MSiGeN4(M =Zr and Hf) monolayers. The plane-wave cutoff energy of 500 eV is used with a 16 × 16 × 1 k-mesh. We relax both the lattice constants and internal atomic positions until the maximal residual Hellmann-Feynman forces are less than 0.0001 eV/Å. We use the total energy as convergence criterion,which is set to 10−8eV. A vacuum space of larger than 30 Å is used to avoid interactions with other neighboring layers.After optimizing the crystal structure, 0.0001 eV/Å. We use the total energy as convergence criterion, which is set to with a supercell of 5 × 5 × 1, and the phonon dispersions of MSiGeN4(M = Zr and Hf) monolayers are calculated by using the PHONOPY code[31]. The ab-initio molecular dynamics(AIMD) simulations are performed with a supercell of size 4 × 4 × 1 for more than 3000 fs with a time step of 1 fs. The in-plane spin-textures are computed by using PYPROCAR code[32].

Fig. 1. (Color online) The crystal structures of MSiGeN4 (M = Zr and Hf)monolayers: (a) top view and (b) side view.

Fig. 2. (Color online)The phonon dispersion curves of MSiGeN4 (M =Zr and Hf) monolayers with GGA.

3. Structure and stability

The crystal structure of the Janus monolayer MSiGeN4(M = Zr and Hf) is shown in Fig. 1 with the rhombus primitive cell and the rectangle supercell marked by black and red frames. With MN2(M = Zr and Hf) triple layers sandwiched between the SiN and GeN bilayers, the symmetry of Janus monolayer MSiGeN4(M = Zr and Hf) is lower than that of the MSi2N4(M = Zr and Hf) or the MGe2N4(M = Zr and Hf) monolayer due to the lack of the vertical reflection symmetry. In other words, Janus monolayer MSiGeN4(M = Zr and Hf) can be built by replacing the Si/Ge atoms of the top SiN/GeN bilayer in the MSi2N4/MGe2N4monolayer with Ge/Si atoms. We use GGA to optimize lattice constants of monolayer MSiGeN4(M = Zr and Hf), and they are 3.110 and 3.097 Å, which are between the ones of MSi2N4(3.05 and 3.19 Å) and MGe2N4(3.04 and 3.18 Å)[18].

The dynamical stability of monolayer MSiGeN4(M = Zr and Hf) is studied by calculating their phonon band dispersions, which are shown in Fig. 2. It is clearly seen that the phonon branches are free from any imaginary frequencies, indicating the dynamical stability of these monolayers. They exhibit three acoustic and eighteen optical phonon branches due to seven atoms in the unit cell. In addition, the thermal stability is examined by AIMD simulations. During the simulations, the temperature is kept at 600 K, and the temperature and total energy fluctuations of only ZrSiGeN4monolayer are plotted in Fig. 3 due to similar results between ZrSiGeN4and HfSiGeN4. The crystal structures of ZrSiGeN4at 600 K after the simulation for 3 ps are also plotted in Fig. 3. It is found that monolayer ZrSiGeN4undergoes no structural reconstruction around 600 K, which indicates the thermal stability of these monolayers with the temperature and total energy fluctuating in the acceptable range.

Fig. 3. (Color online) (a) The fluctuations of temperature and total energy with the time obtained from MD simulation of ZrSiGeN4 monolayer at 600 K. (b, c) The snapshot of ZrSiGeN4 monolayer at the end of MD simulation at 600 K ((b): Top views, (c): Side views).

To verify the mechanical stability of MSiGeN4(M = Zr and Hf), the investigation of the mechanical properties are carried out. Due to hexagonal symmetry, using Voigt notation,the elastic tensor can be expressed as:

Fig. 4. (Color online) Band structures of MSiGeN4 (M = Zr and Hf) monolayers without/with SOC (GGA/GGA+SOC).

Phonon band dispersion calculations, elastic constants and AIMD simulations reveal the dynamical, mechanical and thermal stabilities of predicted monolayers. Monolayer MSi2N4(M = Mo and W) have been synthesized by introducing Si during CVD growth of M2N (M = Mo and W)[17]. We have proposed that the MSiGeN4(M = Mo and W) monolayers can be achieved by introducing Si and Ge during CVD growth of M2N (M = Mo and W)[12]. The same way may be used to achieve the MSiGeN4(M = Zr and Hf) monolayers.

4. Electronic structure

For Janus MSiGeN4(M = Mo and W) monolayers, the SOC can produce important effects on their electronic structures,like Rashba spin splitting and valley polarization[12]. Thus, the SOC is considered to investigate electronic structures of MSiGeN4(M = Zr and Hf) monolayers, and the corresponding energy bands without/with SOC are shown in Fig. 4. The results without/with SOC show that MSiGeN4(M = Zr and Hf)monolayers are indirect gap semiconductors with VBM at the Γ point and CBM at the M point. The GGA gap of ZrSiGeN4is 1.134, and 1.336 eV for HfSiGeN4. When including SOC, the gap of ZrSiGeN4/HfSiGeN4reduces to 1.115 eV/1.282 eV. The SOC can also remove band degeneracy, and we take spin-orbit splitting (Δ) at VBM to illustrate the strength of SOC. TheΔis 35 meV/81 meV for ZrSiGeN4/HfSiGeN4, which means that the SOC has more strong effects on HfSiGeN4.

Fig. 5. (Color online) Band structures of HfSiGeN4 monolayer with SOC (a/a0 from 0.90 to 1.10).

Fig. 6. (Color online) The band gaps of MSiGeN4 (M = Zr and Hf) monolayers vs a/a0 with SOC.

Strain can be used to tune the physical and chemical properties of 2D materials[39-41]. Here, we examine the biaxial strain effects on the electronic properties of MSiGeN4(M = Zr a ndHf)monolayers. Thea/a0isusedtosimulate compressive/tensilestrainwitha/a0<1/a/a0>1,whereaanda0arethe strained and unstrained lattice constants, respectively. Due to similar dependence on strain for electronic structures of Zr-SiGeN4and HfSiGeN4, we only show energy bands of Hf-SiGeN4as afunctionofa/a0in Fig.5,and thetheenergy bandgaps of MSiGeN4(M =Zr andHf)monolayerswitha/a0from 0.90 to 1.10 are plotted in Fig. 6. With strain from 0.90 to 1.10, the gap of monolayer MSiGeN4(M = Zr and Hf) firstly increases, and then decreases, which can be found in many 2D materials[12,41]. In the considered strain range, it is found that both compressive and tensile strains can induce semiconductor to metal transition. The critical point is about 0.92 for compressive strain, and about 1.10 for tensile one. For MSiGeN4(M = Mo and W) monolayers, no semiconductor to metal transition is observed in the same strain range[12]. Another difference is that the maximum of gap can be induced by compressive strain for MSiGeN4(M = Mo and W)[12], and tensile strain for MSiGeN4(M = Zr and Hf).

Fig. 7. The larger version around CBM for MSiGeN4 (M = Zr and Hf)monolayers with SOC at 1.04 strain.

It is found that tensile strain can tune the positions of VBM and CBM of MSiGeN4(M = Zr and Hf). Tensile strain can make CBM change from M point to Γ point, and VBM move from Γ point to one point along the M-K direction. These lead to that MSiGeN4(M = Zr and Hf) change from an indirect gap semiconductor to a direct one to an indirect one. For example, a direct gap semiconductor can be observed at 1.04 strain. The Rashba-type spin splitting near the CBM can be induced by tensile strain. At 1.04 strain, the enlarged views of the conduction bands near the Fermi level for MSiGeN4(M =Zr and Hf) monolayers using GGA+SOC are plotted in Fig. 7.It is clearly seen that a very weak Rashba-type spin splitting is produced. The constant energy 2D contour plots of spin texture of HfSiGeN4as a representative centered at the Γ point are plotted in Fig. 8 at an energy surface of 1.5 eV above the Fermi level. The spin-up (red) and spin-down (blue) electronic bands can be distinctly observed, which shows the Rashbatype spin splitting. Due to the pure 2D Rashba spin splitting,the concentric spin-texture circles are observed. In the Rashba spin split bands, the only in-planeSXandSYspin components are observed with the lack of out-of-planeSZcomponent. The tensile strain can tune the relative positions of valence band extrema (VBE), and can induce valence bands convergence, for example ata/a0= 1.06 point, which can produce an important influence on their electronic transport properties. However, the compressive strain produces small changes on electronic structures of MSiGeN4(M = Zr and Hf)monolayers except for the energy band gap.

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5. Piezoelectric properties

Theβ-MSi2N4or MGe2N4(M = Zr and Hf) monolayers (No.164) are centrosymmetric, which show no piezoelectricity.The MSiGeN4(M = Zr and Hf) monolayers (No. 156) lack inversion symmetry, and a reflection symmetry with respect to the central M atomic layer is broken. This leads to bothe11/d11ande31/d31being nonzero, and the piezoelectric stress and strain tensors become:

Fig. 8. (Color online) In-plane spin textures calculated at the iso-energy surface of 1.5 eV above the Fermi level for HfSiGeN4 monolayer with red/blue colours being spin-up/spin-down states.

Table 2. Piezoelectric Coefficients e11/e31 (10−10 C/m) and d11/d31 (pm/V)of β -MSiGeN4 (M = Zr and Hf) and α -MSiGeN4 (M = Mo and W) monolayers.

6. Optical properties

mined by a summation over empty band states as follows[42]:Here, the rhombus primitive cell is used to calculate the optical properties of MSiGeN4(M = Mo and W) monolayers. It is well known that the unit-cell volumeΩof a 2D material is not well-defined, which leads to some calculated physical properties of a 2D material depending on the the length of the unit cell along thezdirection, for example optical properties[34].Theε(ω) andα(ω) of MSiGeN4(M = Mo and W) monolayers are calculated alongxx/yyandzzdirections, and are shown in Figs. 9 and 10. Because of hexagonal symmetry, the optical spectra betweenxandydirections are isotropic for light polarization along the in-plane directions. Due to similar energy band structures, it is clearly seen that the ZrSiGeN4and HfSiGeN4show very similar optical spectra. Due to distinct optical selection rules, there is a strong anisotropy in the optical spectra alongxx/yyandzzdirections. The static dielectric constants for ZrSiGeN4/HfSiGeN4are 2.94/2.74 alongxx/yydirection and 2.74/2.56 alongzzdirection, which can be attained from the real part of the dielectric constant at zero energy.Itisfoundthata sharpincrease forε2(ω)atthefirst onsetof theopticaltransitionsbetweenxx/yyandzzdirections is almost the same, and is at about 1.31 eV/1.71 eV for Zr-SiGeN4/HfSiGeN4. From the ultraviolet to the visible light region, the calculated results imply that bothxx/yyandzzdirections show strong absorption intensity with the absorption coefficient values being more than 104cm−1in the visible region, which means high efficiency in the utilization of solar energy. It is found that the absorption intensity along thexx/yydirection has more smaller changes than one alongzzdirection in the visible light region, especially for ZrSiGeN4.

7. Discussions and conclusion

Fig. 9. (Color online) The calculated optical dielectric function of MSiGeN4 (M = Zr and Hf) monolayers with real parts (Left) and imaginary parts(Right) along xx/yy and zz directions.

Fig. 10. (Color online) The optical absorption coefficients ofMSiGeN4(M = Zr and Hf) monolayers along xx/yy and zz directions from 0 to 4 eV, and the visible light region (1.6-3.1 eV) is shown.

The Janusα1-MSiGeN4(M = Mo and W) andβ2-MSiGeN4(M = Zr and Hf) monolayers have been predicted by the reliable first-principle calculations. In fact, our works provide an idea to achieve Janus structures from the MA2Z4family, and many Janus MA2Z4can be further investigated. For example,α2-MSiGeP4(M = Cr, Mo and W) can be built, based on semiconducting MSi2P4and MGe2P4(M = Cr, Mo and W)[18]. In these Janus MA2Z4, both in-plane and out-of-plane piezoelectricity, Rashba-type spin splitting, valley polarization and second harmonic generation responses can be explored.

In summary, the electronic structures, piezoelectric properties and optical properties of Janus MSiGeN4(M = Zr and Hf)monolayers are systematically investigated by DFT. They exhibit mechanical, dynamic and thermal stabilities, and show indirect gap properties. It is found that strain can effectively tune their electronic structures, and can induce semiconductors to metal transition in the considered strain range. A very weak Rashba-type spin splitting near CBM can be induced by tensile strain. Both in-plane and out-of-plane piezoelectricity are predicted in MSiGeN4(M = Zr and Hf) monolayers. The high absorption coefficients in the visible light region can be found along bothxx/yyandzzdirections. Our works can stimulate further experimental works to synthesize Janus MA2Z4monolayers, and will motivate farther theoretical studies of other Janus MA2Z4, likeα2-MSiGeP4(M = Cr, Mo and W) monolayers.

Acknowledgements

This work is supported by Natural Science Basis Research Plan in Shaanxi Province of China (2021JM-456). We are grateful to the Advanced Analysis and Computation Center of China University of Mining and Technology (CUMT) for the award of CPU hours and WIEN2k/VASP software to accomplish this work.