Novel 2D Semiconductor SnP3 with High Carrier Mobility, Good Light

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C: Physical Processes in Nanomaterials and Nanostructures 3

Novel 2D Semiconductor SnP with High Carrier Mobility, Good Light Absorption and Strong Interlayer Quantum Confinement Li-ping Feng, Ao Li, Pei-chen Wang, and Zhengtang Liu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06211 • Publication Date (Web): 27 Sep 2018 Downloaded from http://pubs.acs.org on October 2, 2018

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The Journal of Physical Chemistry

Novel 2D Semiconductor SnP3 with High Carrier Mobility, Good Light Absorption and Strong Interlayer Quantum Confinement Li-ping Feng ∗, Ao Li, Pei-chen Wang, Zheng-tang Liu State Key Lab of Solidification Processing, College of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P. R. China Abstract: We propose a novel two-dimensional (2D) SnP3 crystal that possesses low indirect band gaps of 0.67 eV (monolayer) and 1.03 eV (bilayer) and high kinetic and thermal stability until 500 K. The 2D SnP3 shows strong interlayer quantum confinement effects, resulting in a band gap increase from mono- to bilayer, and then a band gap decrease from bi- to triple layer leading to a semiconductor-metal transition. Monolayer SnP3 has large hole mobility (992 cm2V-1s-1), whereas bilayer SnP3 has high electron mobility (8002 cm2V-1s-1) which is comparable to that of phosphorene. The static dielectric constants of mono- and bilayer SnP3 are 3.21 and 5.24, respectively. Both monolayer and bilayer SnP3 show strong light absorption in the visible and ultraviolet regions. The indirect band gap of monolayer SnP3 decreases under biaxial compressive strain and increases under biaxial tensile strain. Especially, when the biaxial compressive strain reaches to 6%, monolayer SnP3 has a transition from semiconductor to metal. These results indicate that mono- and bilayer SnP3 are promising novel 2D materials that have great potential applications in electronic and optoelectronic devices.

Keywords: 2D SnP3, electronic structure, carrier mobility, stability, optical properties, First-principles 1 Introduction It is well known that the emergence and development of two-dimensional materials began with the discovery of graphene.1-4 Researchers in all fields have turned their attention to this emerging two-dimensional material,5,6

∗

Corresponding author. Tel.: +86 29 88488013; fax: +86 29 88492642. E-mail: [email protected] (Dr. L. P. FENG) 1

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because of their compelling physical, chemical, electronic, and optical properties.7 In addition to graphene, atomic layer crystals such as silicene,8,9 germanane,10 hexagonal nitride (h-BN),11-14 transition metal sulfides (TMDs)15-17 transition metal borides (MBenes)18, arsenic trichalcogenides19, intrinsic ferromagnets (CrOX)20 and black phosphorus (BP)21,22 are also two-dimensional materials similar to graphene structures. They are diverse and complementary, covering from conductors, semiconductors, superconductors to insulators. Two-dimensional materials have penetrated into many existing research fields and have even opened up some emerging fields which are expected to be widely used in the next generation of information transmission devices and energy storage devices. However, existing 2D materials, in practice, some severe problems will still be encountered such as band gap hurdles, the lack of bandgap in the original graphene limits its practical application in field effect transistors (FETs).23,24 MoS2 has achieved an extremely high on/off ratio of up to 1×108 and ultra-low standby power dissipation; however, the carrier mobility of typical TMDC devices is still lower than 300cm2V-1s-1.25 The carrier mobility and on/off ratio of phosphorene have up to 10000 cm2V-1s-1 and 104-105, respectively. Nevertheless, phosphorene is unstable in air and is easily degraded.26 Accordingly, it is desirable to explore the new 2D semiconductor with high carrier mobility and excellent stability. As a member of a layered material family, a layered material composed of P and Sn with stoichiometry SnP3 has already been reported in the 1970’s, and it can be obtained by heat treatment at 575°C for 2 days and then slowly cooled to room temperature.27,28 SnP3 nanoparticles has been used for sodium ion battery anode material.29 Bulk SnP3 belongs to the space group R3� m, SnP3 crystal possesses the puckered arsenic-type honeycomb structure, and the corrugated layers are composed of puckered P6 rings, as illustrated in Figure 1. Along the c axis, the layer is connected to the layer by Van der Waals force. As far as we know, there is very little work focused on the theoretical aspects of SnP3, and the electronic structure and optical properties of its bulk and monolayers are still unknown. However, the electronic structure and optical properties of bulk and monolayers of SnP3 should be investigated thoroughly, which is very important for 2


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understanding the new type of 2D semiconductor as well as for designing and analyzing of the layered material applications in the optoelectronics and photovoltaics fields. In this work, by using first-principles calculations molecular dynamics simulations, the thermal stability, mechanical, electronic, and optical properties of SnP3 have been investigated in detail, ranging from the monolayer to quadruple layer to the layered bulk.

2 Computational methods First-principles calculations were performed by using Vienna ab initio simulation package (VASP)30,31 based on density functional theory (DFT). Projector augmented-wave (PAW) pseudopotential32 was used to account electron-ion interactions. The exchange and correlation terms were described using general gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional33 and the density functional dispersion correction (D2Grimme)34 was used to accurately describe the weak interactions of interlayers of SnP3. The valence electron configurations include Sn 5s25p2 electrons and P 3s23p3 electrons. A cutoff energy of 450 eV was used to expand the wave functions in plane waves. The convergence criteria were 1×10-2 eV/Å for the residual forces on ions and 1×10-6 eV for the energy difference in electronic self-consistent loop. Γ-centered Monkhorst-Pack schemes with kpoint mesh of 7×7×5 and 7×7×1 were adopted to sample the first Brillouin zone (BZ) of the conventional unit cell of bulk and multilayers of SnP3, respectively. In order to minimize the interlayer interactions periodic boundary condition, a vacuum of 20 Å perpendicular to the layer plane was constructed for multilayers. Electronic band structures were obtained by GGA-PBE and compared with those from the Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid functional,35 and HSE06 functional with a mixing parameter alpha value of 0.5 was employed to calculate their band structure and optical properties. Note that the default value alpha=0.25 may not predict the experimental value very accurately. Phonon band dispersions were calculated using a 3 × 3 × 1 supercell by using the PHONOPY package36 with the finite displacement method, where a 5×5×1 K-mesh was used. The Ab initio molecular dynamics (AIMD) simulation with a canonical ensemble were performed on a 3 × 3 × 1 supercell by using a canonical ensemble (NVT) with a Nose-Hoover thermostat37,38 and the temperature of the system was set at 3



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300 and 500K, respectively. The total simulation maintained 10 ps with a time step of 2 fs.

3 Results and discussions 3.1 Bulk and 2D SnP3 Structure Figure 1a-b show the structures of bulk SnP3. Figure 1c is the optimized structure of monolayer SnP3. Figure 1d is the band structure of bulk SnP3. Although there are some experiments on bulk SnP3, there is no available experimental data of multilayers of SnP3. Hence, in this work, the atomic structure and electronic properties of bulk SnP3 have been calculated firstly and compared to the available experimental values. The optimized lattice constants of bulk SnP3 are a=7.401 Å and c=10.403 Å, which are in good agreement with the experimental data of a=7.378 Å and c=10.512 Å.28 As shown in Figure 1a and b, SnP3 is a layered structure with a Van der Waals forces between the interlayers. In each layer of SnP3, a honeycomb-like six-membered ring structure with upper and lower folds consists of P and Sn atoms. The lattice constant, bond length and bond angle of bulk SnP3 are listed in Table 1 and compared with the results obtained from the experiments.28 It can be seen from Table 1 that the calculational values are consistent with the reported experimental data.28 In Figure 1d, bulk SnP3 is metallic with bands crossing the Fermi level. Monolayer SnP3 is established by removing one layer from the optimized bulk structure. The optimized lattice constant of monolayer SnP3 is 7.105 Å, which is smaller than that of the bulk phase and the lattice shrinkage is about 4%. This lattice contraction causes changes in bond lengths and bond angles, as shown in Table 1. The optimized lattice constant of bilayer and triple layer SnP3 are 7.221 Å and 7.283 Å, respectively. The monolayer SnP3 has a larger change in bond angle than bulk, it shows that the upper and lower folds of a monolayer are larger than bulk. As the number of layers increases, the structure of SnP3 cannot be relaxed completely due to the van der Waals interaction, and the lattice constant of SnP3 is more and more close to that of the bulk phase. Similar changes have also been found in black phosphorus and other 2D materials39,40. For instance, the lattice constant shrinkage of monolayer SnS is up to 4.6%40. This may be due to the lack of layer-to-layer van der Waals forces.39 4


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3.2 Stability of Monolayer SnP3 The phonon dispersion spectrum and molecular dynamics simulation of monolayer SnP3 are presented in Figure 2. The dynamic stability of monolayer SnP3 is evaluated with phonon spectrum calculation and the thermodynamic stability of monolayer SnP3 is examined by AIMD simulation. As shown in Figure 2a and b, it can be clearly seen that no imaginary frequency phonon is found at any wave vector, which confirms that the monolayer and bilayer SnP3 is dynamically stable. In order to evaluate the mechanical robustness of the P-P covalent bonds of monolayer SnP3, the highest frequency phonon mode of monolayer SnP3 was compared with that of MoS2 and silicone. The highest frequency phonon mode of monolayer SnP3 reaches 500 cm-1, which is smaller than that of monolayer silicene (580 cm-1)41 and higher than that of monolayer MoS2 (473 cm-1)42, indicating that the P-P covalent bonds of monolayer SnP3 are mechanical robustness.43,44 As indicated by the AIMD snapshots illustrated in Figure 2b, the planar puckered arsenic-type honeycomb networks are well maintained within 10 ps, demonstrating the monolayer SnP3 is stable at room temperature. It can be seen in Figure 2c that the overall structure maintains integrity, the total energy was observed to oscillate in a very narrow range, indicating that the thermal stability of monolayer SnP3 is good at 500 K. According to the previous studies, the chemical stability of material can be evaluated by its work function43,44 The work function of monolayer SnP3 is about 4.92 eV, which is higher than that of phosphorene (4.25 eV) and comparable to that of monolayer GeP3 (4.89 eV), indicating that monolayer SnP3 is chemically stable.43,44 3.3 Cleavage Energies and 2D Young's Modulus The cleavage energy and the stress-strain curve are illustrated in Figure 3. The most common methods currently used to prepare two-dimensional materials are mechanical cutting and liquid stripping. To begin with, the possibility of obtaining monolayer SnP3 is estimated using a mechanical exfoliation strategy. Figure 3a shows cleavage energy curve of monolayer and bilayer SnP3.The cleavage energy Ecl is defined as:45

5



𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑛𝑛𝑛𝑛 + 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏−𝑛𝑛𝑛𝑛 − 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

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(1)

where 𝐸𝐸𝑛𝑛𝑛𝑛 , 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏−𝑛𝑛𝑛𝑛 and 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 is the total energy of monolayer or bilayer SnP3, the total energy of the bulk after

exfoliation, and the total energy of the bulk before exfoliation, respectively. The separation of monolayer and bilayer SnP3 from a neighboring sevenfold layers has been calculated. As shown in Figure 3a, the cleavage energies of monolayer and bilayer SnP3 are ∼1.16 and 0.78 J/m2, respectively. The theoretical cleavage strength curve is further

obtained by taking the derivative of 𝐸𝐸𝑐𝑐𝑐𝑐 with respect to the separation distance. The cleavage strengths σ of

monolayer and bilayer SnP3 are estimated to be 5.6 and 3.31 GPa, respectively. The experimental exfoliation energy

of graphene is 0.37 J/m2,15 and the calculational exfoliation energy of graphene is 0.31 J/m2.46 The cleavage energy of InP3, GeP3, and CaN2 are 1.32 J/m2,43 1.14 J/m2,44 and 1.09 J/m2,47 respectively. Compared with the calculated cleavage energy and strength in typical 2D layered materials, monolayer and bilayer SnP3 are feasible to obtain by stripping method. In order to form a freestanding film, two-dimensional material must be able to withstand its own weight or external load, which is determined by the in-plane stiffness. Figure 3b shows stress-strain curve of monolayer SnP3. From the strain energy curve, the in-plane stiffness can be determined by the 2D Young’s modulus (Y2D) which is defined as:48 𝑌𝑌2𝐷𝐷 =

1

𝐴𝐴0

𝜕𝜕 2 𝐸𝐸

� 𝜕𝜕𝜀𝜀2𝑠𝑠�

𝜀𝜀=0

(2)

where E is the total energy per unit cell, ε is the axial strain and A0 is the area of the equilibrium surface. The calculated Y2D of monolayer SnP3 is 51.42 N/m, which is higher than MnPSe3 (36 N/m),48 and is about 14% of that for the ultra-strong material graphene.48 According to the elasticity theory, the typical out-of-plane deformation h

caused by gravity can be estimated by the following formula:48 ℎ⁄𝐿𝐿 ≈ (𝜌𝜌𝜌𝜌𝜌𝜌⁄𝑌𝑌2𝐷𝐷 )1⁄3

(3)

where ρ = 1.606 × 10-6 kg/m2 is the density of monolayer SnP3, L represents the size of monolayer SnP3 lamina. For a monolayer SnP3 lamina with the length L ≈ 100 um, h/L ≈3.128 × 10-4 can be obtained, which is comparable 6


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to that of NaSnP (10-3~10-4),49 indicating that 2D SnP3 crystal is able to withstand its own weight and keep freestanding planar structure.49 3.4 Electronic Properties of 2D SnP3 Figure 4a shows the unit cell structure of monolayer SnP3, and Figure 4b shows the energy band structure of monolayer SnP3. Because Sn is a relatively heavy element, spin-orbital-coupling (SOC) may influence the electronic properties of monolayer SnP3. Hence, the band structures of monolayer SnP3 were calculated with and without SOC. In Figure 4b, it is clear that the band structures with SOC are consistent with those without SOC. Therefore, SOC has little effect on the band structures. Accordingly, SOC has not been considered in the following band structure calculations. In Figure 4b, it can be seen that the monolayer SnP3 is an indirect semiconductor. The band gap of monolayer SnP3 is about 0.39 and 0.67 eV calculated by PBE and HSE06 functional, respectively, because the PBE function usually underestimates the band gap. For monolayer SnP3, the valence band maximum (VBM) is at the K point, and the conduction band minimum (CBM) is at a Γ Point. The projected density of states (PDOS) and the wave functions of CBM and VBM are presented in Figure 4c and d, respectively. As shown in Figure 4c, the multiple van Hove singularities (VHSs) can be observed in the DOS of monolayer SnP3. Additionally, the valence band top and the conduction band bottom are mainly contributed by the 3p orbital of P and the 5p orbital of Sn, it can be clearly seen that the 5p orbit of Sn and the 3p orbit of P show strong hybridization near the VBM and CBM. The covalent bonding in the monolayer SnP3 are further evidenced by the analysis of electron localization functions (ELFs) in Figure 4e, where the ELF values of Sn-P and P-P bonds are all larger than 0.85, showing that the valence electrons among adjacent atoms are localized and covalent bondings of Sn-P and P-P are formed. The electronic structures of bilayer to quadruple layer SnP3 were also studied in Figure 5, monolayer SnP3 becomes a semiconductor after being separated from the bulk and exhibits a strong quantum confinement effect.44 As shown in Figure 5a, the bilayer SnP3 is also an indirect band gap semiconductor with band gap of 0.61 eV and 1.03 eV calculated by GGA-PBE and HSE06, respectively. The VBM and CBM of bilayer SnP3 locate at K and Γ 7



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point, respectively. Figure 5b and c show the band structure of triple layer and quadruple layer SnP3, respectively. In Figure 5b, the CBM and VBM are in contact at point D between G-K points, and the energy bands near the intersection distribute linearly. The band structure of the triple layer of SnP3 is similar to that of topological insulator of 2D SiGe,50 indicating that the triple layer of SnP3 may be a new topological insulator. The trilayer and multilayer SnP3 have no band gap and exhibit metallic character. However, for monolayer and bilayer SnP3, the conduction bands shift upwards and thus a band gap is formed. This semiconductor to metal transition may be ascribed to two aspects. On one hand, the interlayer interaction depends greatly on the layer thickness, which plays an important role in the semiconductor to metal transition for layered SnP3.6 On the other hand, the quantum confinement effect is another main factor affecting the electronic structure transition.51 The similar phenomena can be also found in atomically thin arsenene and antimonene.51 3.5 Carrier Mobility of 2D SnP3 The carrier mobility of monolayer and bilayer SnP3 was studied using the following formula:52 2𝑒𝑒ħ3 𝐶𝐶2𝐷𝐷 ∗ 2 2 𝐵𝐵 𝑇𝑇|𝑚𝑚 | 𝐸𝐸1

𝜇𝜇2𝐷𝐷 = 3𝐾𝐾

(4)

where e is the electron charge, ħ is Planck’s constant divided by 2π, kB is Boltzmann’s constant, and T is the temperature. m* is the effective mass of electron or hole, which can be calculated from the derivatives of electronic bands using the formula 𝑚𝑚∗ = ħ2 [𝜕𝜕 2 𝜀𝜀(𝑘𝑘)/𝜕𝜕𝜕𝜕 2 ]−1. The elastic modulus C2D of zigzag or armchair directions is given by 𝐶𝐶2𝐷𝐷 = [𝜕𝜕 2 𝐸𝐸⁄𝜕𝜕𝜕𝜕 2 ]/𝑆𝑆0, where E is the total energy and S0 is the lattice volume at equilibrium for a 2D

system. E1 is the deformation-potential (DP) constant, defined as 𝐸𝐸1 = ∆𝑉𝑉𝑖𝑖 /(∆𝑙𝑙 ⁄𝑙𝑙0 ), where ΔV is the shift of the band edge positions with respect to the lattice dilation Δl/l0 along the zigzag and armchair directions of the

orthogonal cell. As shown in Figure 6a, in order to facilitate the display of carrier mobility in the armchair and zigzag directions, orthogonal grids are used. Figure 6b shows the variation of total energy (E) with uniaxial strain (δ) applied to monolayer SnP3 along armchair and zigzag directions, the elastic modulus C2D is obtained through fitting the energy-strain curves. The energy band structures of monolayer and bilayer SnP3 are shown in Figures 6c 8


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and 6d, respectively. The VBM of monolayer and bilayer SnP3 are located between the Y and Γ Points instead at one high-symmetry point. It can be seen from the band diagram of monolayer SnP3 that there is a light hole and a heavy hole at the top of the valence band. As presented in Figures 6c and d, the DP constant (E1) can be obtained by fitting the liner relationship of the band edge for VBM and CBM with the strain exertion (δ) along the zigzag and armchair directions, respectively. The calculated deformation potential constant, elastic modulus, effective mass, carrier mobility, and relaxation time (τ = μm*/e) are summarized in Table 2. As shown in Table 2, the C2D of monolayer SnP3 is 39.505 N/m and 39.585 N/m along the zigzag and armchair directions, respectively, indicating that the mechanical properties of monolayer SnP3 are isotropic. The monolayer SnP3 shows light and heavy effective masses for holes, along the armchair direction, the m* for electrons and light holes are 0.851 and 0.76 me, respectively. In the zigzag direction, and the m* for electrons and light holes are 0.847 and 0.72 me, respectively. The effective electron mass of bilayer SnP3 is 0.205 and 0.206 me along the armchair and zigzag directions, respectively. From Table 2, it is clear that the effective mass along the armchair and zigzag direction has a little difference for monolayer or bilayer SnP3. However, the E1 of electron is about 2 times larger than that of hole for both monolayer and bilayer SnP3. Comparing the effective mass, elastic modulus, and deformation potential constants, monolayer and bilayer SnP3 are isotropic. The obtained electron mobility of monolayer SnP3 is about 171 and 128 cm2V−1s−1 for armchair and zigzag direction, respectively. For light holes, the mobility is about 6 times larger than that of electrons, with a value of 941 (armchair direction) and 992 cm2V−1s−1 (zigzag direction), respectively. The electron mobility of bilayer SnP3 is estimated to be about 8002 and 6746 cm2V-1s-1 along the armchair and zigzag direction, respectively. Clearly, bilayer SnP3 has higher carrier mobility than monolayer SnP3. Comparing the band structures of monolayer and bilayer SnP3, the radius of curvature of VBM and CBM of bilayer SnP3 is smaller than that of monolayer SnP3, and thus the effective mass of the bilayer SnP3 is smaller than that of monolayer SnP3. Due to the big difference in the effective mass, there is huge difference in the carrier mobilities between monolayer and bilayer SnP3. Importantly, the electron 9



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mobility of bilayer SnP3 is significantly higher than that of monolayer MoS2 nanosheet (200 cm2V−1s−1)52 and is close to that of black phosphorus (10000 cm2V−1s−1).39 3.6 Strain of 2D SnP3 Figure 7 shows the variation of total energy with biaxial strain for a monolayer SnP3 system, and the change in band gap under biaxial stress. During the preparation process, the material is often subjected to stress from the substrate or the external environment. Therefore, it is of great importance to understand the properties of monolayer SnP3 under stress. In Figure 7a, the strain energy monotonically increases with the increase of compressive strain, and the strain energy also monotonically increases with the increase of tensile strain. There is no mutation in strain energy, it indicates that the system is within the elastic strain range. The phonon spectra of monolayer SnP3 under 6 and 6% were calculated and no imaginary phonon modes were found, indicating that monolayer SnP3 is dynamically stable under the strain range from -6 to 6%. As shown in Figure 7b, the band gap of monolayer SnP3 increases monotonously with the increase of tensile strain, and decreases monotonically with the increase of compressive strain. When the tensile strain is applied to 6%, the band gap of monolayer SnP3 increases to 0.845 eV. When the pressure strain is applied to 6%, the band gap of monolayer SnP3 becomes 0 eV, and the material changes from semiconductor to metal. Figure 8 shows the band structure of monolayer SnP3 under biaxial strain from -6% to 6%. It can be seen from the band diagram that the change of the band gap is caused by the change of the band edge position. The bottom of the conduction band is always kept at Γ point. With the increase of tensile strain, the position of the top of the valence band moves from point K to point M. As the compressive strain increases, the position of the top of the valence band moves from point K to point Γ. The value of the conduction band top increases with the increase of the tensile strain and decreases with the increase of the compressive strain. As the lattice parameters decrease, the repulsive force between the atoms increases and the degree of localization of electrons decreases. Hence, the interactions between the orbitals become stronger, and the valence and conduction bands become wider, which 10


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result in the decrease of the band gap and the transition from semiconductor to metal. Therefore, the electronic properties of monolayer SnP3 can be effectively adjusted by applying external strain, which may be useful for monolayer SnP3 applications in flexible electronics. 3.7 Optical properties of 2D SnP3 The light absorption abilities of monolayer and bilayer SnP3 were evaluated by calculating the imaginary part ε2 (ω) of the complex dielectric function, which is expressed by:43 1⁄2

α(𝜔𝜔) = √2𝜔𝜔 ��𝜀𝜀12 (𝜔𝜔) + 𝜀𝜀22 (𝜔𝜔) − 𝜀𝜀1 (𝜔𝜔)�

(5)

The optical absorptions of monolayer and bilayer SnP3 are shown in Figure 9a. The results for the calculated monolayer MoS2 are also presented in Figure 9a for comparison. The light absorption coefficient of monolayer and bilayer SnP3 are much higher than that of monolayer MoS2. Optical absorption is related to electronic transitions, and thus the light absorption intensity can be qualitatively explained by DOS. By comparing the DOS of SnP3 and MoS253, multiple VHSs can be observed in the DOS of monolayer and bilayer SnP3. It is well-known that the presence of VHS in DOS can lead to strong light-matter interactions, which causes strong light absorption.43,54 Therefore, the monolayer and bilayer SnP3 show much better optical absorption than MoS2. The complex dielectric functions of monolayer and bilayer SnP3 are presented in Figure 9b. As shown in Figure 9b, the dielectric constant of bilayer SnP3 (5.24) is greater than that of monolayer SnP3 (3.21). Figure 9c shows the optical absorption of monolayer SnP3 under strain ranging from -5 to 5%. In Figure 9c, under the tensile strain, the absorption edge of monolayer SnP3 gradually moves to the infrared direction, showing the range of light absorption is enlarged. These results indicate that the new 2D SnP3 may have the potential applications in photovoltaic fields.

4 Conclusion The stable, mechanical, electrical, and optical properties of novel 2D SnP3 have been studied systematically by first-principles calculations. The low cleavage energies of monolayer and bilayer SnP3 are 1.16 and 0.78 J/m2, respectively, indicating that mono- and bilayer SnP3 can be obtained by exfoliation. Monolayer SnP3 shows high 11



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stability until 500 K and good mechanical properties with 2D Young’s modulus of 51.42 N/m. Monolayer and bilayer SnP3 are semiconductor with indirect band gap of 0.67 and 1.03 eV, respectively. However, 2D SnP3 with triple layer and more layers are all metal. The hole mobility of monolayer SnP3 is greater than the electron mobility, whereas the electron mobility of bilayer SnP3 is greater than the hole mobility. The high electron mobility (8002 cm2V-1s-1) of bilayer SnP3 is comparable to that of phosphorene. Light absorptions of mono- and bilayer SnP3 in the visible and ultraviolet spectral range are excellent, which are much larger than that of monolayer MoS2. Strain effect can effectively adjust the band gap and light absorption performance of 2D SnP3. These theoretical results show that the novel 2D SnP3 may have great potential applications in nano-electronic, optoelectronic and photovoltaic devices.

Acknowledgments We acknowledge the National Natural Science Foundation of China under grant No. 11674265, the Natural Science Basic Research Project of Shaanxi Province under grant No. 2018JZ6003, and the Research Funds of the State Key Laboratory of Solidification Processing (NWPU) under grant No. KP201614. We would like to thank the Analytical & Testing Center of Northwestern Polytechnical University. References 1. Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666-9. 2. Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nature 2005, 438, 197-200. 3. Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183-91. 4. Rao, C. N.; Sood, A. K.; Subrahmanyam, K. S.; Govindaraj, A. Graphene: The New Two‐Dimensional Nanomaterial. Angew. Chem. Int. Ed. 2009, 48, 7752-7777. 5. Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. TwoDimensional Atomic Crystals. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 10451-3. 6. Sun, S.; Meng, F.; Wang, H.; Wang, H.; Ni, Y. Novel two-dimensional semiconductor SnP3: high stability, tunable bandgaps and high carrier mobility explored using first-principles calculations. J. Mater. Chem. A. 2018, 6, 11890-11897. 7. Tan, C.;Wu, X. J; etc. Recent Advances in Ultrathin Two-Dimensional Nanomaterials. Chem. Rev. 2017, 117, 6225-6331. 8. Kara, A.; Enriquez, H.; Seitsonen, A. P.; Voon, L. L. Y.; Vizzini, S.; Aufray, B.; Oughaddou, H. A Review on 12


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Page 16 of 22

Figures and tables captions list: Table 1. Calculated lattice parameters, bond lengths, and bond angles of monolayer, bilayer, triple layer and bulk SnP3 within D2-Grimme, compared to the experimental value. Table 2. Calculated effective mass |m*|, DP constant |E1|, elastic modulus C2D, relaxation time τ, carrier mobility μ for SnP3 monolayer and bilayer along the zigzag direction and armchair directions. NL represents the layer number of SnP3. Figure 1. (a, b) Side and Top Side view of the supercell structure of bulk SnP3, (c) the optimized structure of monolayer SnP3 (d) Calculated electronic band structure of bulk SnP3 at the PBE level. Figure 2. The phonon dispersion for monolayer (a) and bilayer SnP3(b). The evolution of the total energy and snapshot of monolayer SnP3 from AIMD was simulated at different temperatures (c) 300K and (d) 500K Figure 3. (a) Cleavage energy Ecl in J/m2 (blue line) and its derivative σ in GPa (red line) as a function of the separation distance d for a fracture in bulk SnP3. Solid and dash lines correspond to monolayer and bilayer, respectively. Inset (b) Elastic energy of the monolayer SnP3 under axial strain along a direction. Inset: Visualization of axial strain. The unit cell (dash line box) is stretched or compressed in a direction. Figure 4. (a) Monolayer SnP3 structure, (b) Band structures of monolayer SnP3 calculated at PBE, HSE06 and PBE+SOC levels of theory, (c) Partial density of states of monolayer SnP3, (d) Wave function at the CBM and VBM, the isosurface is set to 0.002 e/Å-3, (e) electron localization functions of the monolayer SnP3. Figure 5. Band structures of (a) bilayer layer, (b) triple layer, and (c) quadruple layer SnP3 calculated at the HSE06 level. Figure 6. (a) monolayer SnP3 in an orthogonal super cell, (b) Energy difference between the total energy of unstrained and strained monolayer SnP3 along the zigzag and armchair directions, the band structures of monolayer (c) and bilayer (d) SnP3 in orthorhombic lattices calculated by PBE. Shifts of CBM and VBM under uniaxial strain along armchair (e) and zigzag(f) direction. Figure 7. (a) Elastic energy of SnP3 monolayer under biaxial strain. (b) The band gap of monolayer SnP3 under biaxial strain calculated by PBE and HSE06, respectively. Figure 8. The band structure of monolayer SnP3 under biaxial strain from -6% to 6%, calculated by HSE06 functional. Figure 9. (a) Calculated absorption spectra of monolayer and bilayer SnP3 at the HSE06 level, calculated the light absorption spectrum of monolayer MoS2 at PBE level for comparison. (b) Calculated Dielectric function real part of monolayer and bilayer SnP3 (c) The absorption spectra of monolayer SnP3 under biaxial strain from -5% to 5%.

16


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Table 1. Calculated lattice parameters, bond lengths, and bond angles of monolayer, bilayer, triple layer and bulk SnP3 within D2-Grimme, compared to the experimental value.27 Structure

Clattice/Å

LP-P / Å

LSn-P / Å

angleP-P-P /°

angleP-Sn-P /°

1L SnP3

7.105

2.165

2.700

110.886

81.902

2L SnP3

7.221

2.217

2.668

96.551

94.324

3L SnP3

7.283

2.229

2.693

96.895

97.796

Bulk-SnP3

7.401

2.232

2.669

99.13

97.177

Bulk-exp

7.378

2.222

2.662

99.08

97.31

Table 2. Calculated effective mass |m*|, DP constant |E1|, elastic modulus C2D, relaxation time τ, carrier mobility μ for SnP3 monolayer and bilayer along the zigzag direction and armchair directions. NL represents the layer number of SnP3. Carrier type

NL

m*arm

m*zig

0.851

0.847

hole

1.35 (0.76)

1.998 (0.72)

electron

0.205

0.206

electron 1

2 hole

C2Darm (N/m)

39.505

89.593 0.783

C2Dzig (N/m)

E1arm (eV)

E1zig (eV)

µarm (cm2V -1s-1)

µzig (cm2V -1s-1)

τarm(fs)

τzig(fs)

2.124

2.275

171

128

82

61

1.101

1.041

254 (941)

131 (992)

195 (407)

149 (408)

1.945

2.109

8002

6746

994

791

0.748

0.790

3704

4151

1651

1656

39.585

89.694

0.701

17



(a)

(b)

c

b

a

a (c)

Page 18 of 22

(d)

Figure 1. (a, b) Side and Top Side view of the supercell structure of bulk SnP3, (c) the optimized structure of monolayer SnP3 (d) Calculated electronic band structure of bulk SnP3.

(a)

(b)

(c)

(d)

Figure 2. The phonon dispersion for monolayer (a) and bilayer SnP3 (b). The evolution of the total energy and snapshot of monolayer SnP3 from AIMD was simulated at different temperatures (c) 300K and (d) 500K 18


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(a)

(b)

Figure 3. (a) Cleavage energy Ecl in J/m2 (blue line) and its derivative σ in GPa (red line) as a function of the separation distance d for a fracture in bulk SnP3. Solid and dash lines correspond to monolayer and bilayer, respectively. Inset (b) Elastic energy of the monolayer SnP3 under axial strain along a direction. Inset: Visualization of axial strain. The unit cell (dash line box) is stretched or compressed in a direction.

(a)

(c)

(b)

P Sn

(d)

(e)

1 P

P P

Sn 0.5 VBM

Sn

P

CBM

P 0

Figure 4. (a) Monolayer SnP3 structure, (b) Band structures of monolayer SnP3 calculated at PBE, HSE06 and PBE+SOC levels of theory, (c) Partial density of states of monolayer SnP3, (d) Wave function at the CBM and VBM, the isosurface is set to 0.002 e/Å-3, (e) Electron localization functions of the monolayer SnP3.

19


P


(a)

(b)

Page 20 of 22

(c)

D

Figure 5. Band structures of (a) bilayer layer, (b) triple layer, and (c) quadruple layer SnP3 calculated at the HSE06 level.

(a)

(c)

(e)

(d)

(f)

Armchair (b)

Figure 6. (a) monolayer SnP3 in an orthogonal super cell, (b) Energy difference between the total energy of unstrained and strained monolayer SnP3 along the zigzag and armchair directions, the band structures of monolayer (c) and bilayer (d) SnP3 in orthorhombic lattices calculated by PBE. Shifts of CBM and VBM under uniaxial strain along armchair (e) and zigzag(f) direction.

20


Page 21 of 22

(a)

(b)

Figure 7. (a) Elastic energy of SnP3 monolayer under biaxial strain. (b) The band gap of monolayer SnP3 under biaxial strain calculated by PBE and HSE06, respectively.

(a)

2.0

-6%

(b)

-4%

(d)

(c)

-2%

0%

(e)

2%

(f)

4%

(g)

6%

1.5

1.0

Energy(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.5

0.0

-0.5

-1.0

-1.5

-2.0

Γ

K

M

Γ

Γ

K

M

Γ

Γ

K

M

Γ

Γ

K

M

Γ

Γ

K

Γ

M

Γ

K

M

Γ

Γ

K

M

Γ

Figure 8. The band structure of monolayer SnP3 under biaxial strain from -6% to 6% calculated by HSE06.

(a)

(b)

(c)

Figure 9. (a) Calculated absorption spectra of monolayer and bilayer SnP3 at the HSE06 level, calculated the light absorption spectrum of monolayer MoS2 at PBE level for comparison. (b) Calculated Dielectric function real part of monolayer and bilayer SnP3 (c) The absorption spectra of monolayer SnP3 under biaxial strain from -5% to 5%.

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Contents graphic

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Novel 2D Semiconductor SnP3 with High Carrier Mobility, Good Light

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