Abstract
Searching for new stable free-standing atomically thin two-dimensional (2D) materials is of great interest in the fundamental and practical aspects of contemporary material sciences. Recently, the synthesis of layered SiAs single crystals has been realized, which indicates that their few layer structure can be mechanically exfoliated. Performing a first-principles density functional theory calculations, we proposed two dynamically and thermodynamically stable semiconducting SiAs and SiAs2 monolayers. Band structure calculation reveals that both of them exhibit indirect band gaps and an indirect to direct band even to metal transition are found by application of strain. Moreover, we find that SiAs and SiAs2 monolayers possess much higher carrier mobility than MoS2 and display anisotropic transportation like the black phosphorene, rendering them potential application in optoelectronics. Our works pave a new route at nanoscale for novel functionalities of optical devices.
Background
Atomically thin two-dimensional (2D) crystals have become one of the most rapidly burgeoning field of contemporary material science. The versatile electronic properties, excellent electron mobility, and promising applications in nanoelectronics and optoelectronics are driving a large percentage of condensed-matter physicists to hunt for new 2D materials. Following graphene [1–4], a huge number of other 2D materials have been synthesized such as silicene [5–7], boron-nitride nanosheets [8, 9], transition-metal dichalcogenides (TMDs) [10, 11], black phosphorus [12, 13], borophene [14–16], arsenene [17, 18], tellurene [19], and their isoelectronic compounds [20–23]. The list of 2D materials is fast expanding, and more than thousands kinds of such materials are now known, encompassing the full spectrum of electronic and other properties. And their novel properties, different from or even better than those of their bulk counterparts, are theoretically predicted and experimentally confirmed firmly.
Although extensive and substantial efforts were invested in finding diverse 2D materials including some that already possess bandgaps or other desirable properties, consensus has not been reached. Graphene with marvelous carrier mobility, high mechanical stability, and massless dirac electrons has attracted much attention to date, but the lacking of an intrinsic band gap hinder its application in modern electronic devices industry. Although large efforts have been made, opening up a sizeable band gap without side-effect has not been reached [24, 25]. TMDs with high performance in optoelectronic devices indeed have intrinsic band gap, but exhibit poor in carrier mobility [26–28]. Black and blue phosphorus with a strain sensitive tunable band gap and anisotropic high carrier mobility can not keep stable in air [13, 29]. Recently, the synthesis of layered SiAs and SiAs2 single crystals has been realized [30–32], which indicates that few layer structure can be obtained by mechanically exfoliated.
In the present work, based on a first-principles density functional theory calculations (DFT), we proposed two dynamically and thermodynamically stable semiconducting monolayers SiAs and SiAs2. They both possess indirect band gaps (2.39 eV and 2.13 eV respectively). Application of isotropic strain along two in-plane directions practically transforms the SiAs (SiAs2) monolayer into a direct-gap 1.75 eV (1.60 eV) material. Moreover, we find that SiAs and SiAs2 monolayers possess much higher carrier mobility than MoS2 and display anisotropic transportation like the black phosphorene, rendering them potential application in optoelectronics. Our works paves a new route at nanoscale for novel functionalities of optical devices.
Computational Methods
The DFT calculations are performed using Vienna ab initio simulation package (VASP) code [33]. We used the Perdew-Burke-Ernzerhof (PBE) [34] exchange-correlation functional under the generalized gradient approximation(GGA). The projector augmented wave (PAW) method [35] was employed to describe the electron-ion interaction. A vacuum of 20 Å perpendicular to the sheets (along the c axis) was applied to avoid the interaction between layers. A kinetic energy cut-off of 500 eV is used for the plane wave basis set. The Brillouin-zone sampling is carried out with a 15 × 5 × 1 Monkhorst-Pack [36] grid for 2D sheets. Convergence criteria employed for both the electronic self-consistent relaxation and ionic relaxation are set to be 10−4 and 0.01 eV/Å for energy and force, respectively. The phonon calculations are carried out using the supercell method through the PHONOPY code [37, 38], and the real-space force constants of supercells are calculated in the density-functional perturbation theory (DFPT) as implemented in VASP. Moreover, a more strict energy (10−8 eV/atom) and force convergence criterion (10−4 eV/Å) are used during the vibrational spectra calculations. In the molecular dynamics(MD) calculations, (3×3×1) supercells are employed and the temperature is kept at 300 K for 6 ps with a time step of 2 fs in the moles-volume-temperature (NVT) ensemble. The raman spectra were calculated at the PBE level of theory using the CASTEP code [39–41].
Results and Discussions
The geometrical structures and electron density distribution of relaxed free-standing 2D SiAs and SiAs2 are presented in Fig. 1a, b, respectively, and their bulk structures are shown in Additional file 1: Figure S1 of the supplementary material. As shown in Additional file 1: Figure S1a and b, the bulk SiAs(SiAs2) possesses C2/m(Pbam) symmetry and consists of stacked Si-As layers weakly bound by van der Waals forces with a distance of 3.06 Å (1.66 Å). The unit cell of monolayer SiAs is rhombic and its optimized crystal parameters are a1 = 3.69Å and b1 = 10.83Å with φ=99.81°. SiAs contains 6 Si atoms and 6 As atoms. Each Si atom has four nearest neighboring atoms (3 As and 1 Si) while each As atom forms only three covalent bonds with neighboring Si atoms. It exists two kinds of bonds, namely, Si–Si and Si–As bonds. And the Si–Si bond length is about 2.35 Å and that of Si–As is in the range of 2.39 Å and 2.43 Å, and the buckled height is d1 = 4.86 Å. At the side view of monolayer SiAs, a eyeglass-stringed like structure is formed with double and single layers alternately bulked. Another monolayer structure of silicon and arsenic compound is SiAs2. Its prime cell contains 4 Si atoms and 8 As atoms, with a rectangular structure and the optimized crystal parameters are a2 = 3.68Å and b2 = 10.57 Å. Each As atoms has three nearest neighboring Si atoms or forms one covalent bond with neighboring Si atoms and two covalent bonds with themselves, while each Si atoms has only four nearest neighboring As atoms. Unlike the former, SiAs2 owns weaker As–As bond (2.50 Å) instead of Si–Si bond. And its Si–As bonds range from 2.41 Å to 2.45 Å, and the buckled height is d2 = 5.09 Å. From the electron density distribution, the As atoms attract electron from Si Atoms for their large electronegativity and have a larger electron density. In order to assist future experimental characterization, we further calculated and checked the Raman spectra of bulk and monolayer SiAs and SiAs2. Clear shifts between the monolayer and the full crystals have been seen in Additional file 1: Figure S2 of the supplementary material, whose origins have been identified as the influence of layers van der Waals interaction [42].
To learn the stability of SiAs (SiAs2), we first calculated the cohesive energy, defined as Ecoh = (nESi + mEAs−EMono)/(n + m), where ESi,EAs, and EMono are the total energies of a single Si atom, a single As atom, and one formula unit of monolayer SiAs (SiAs2), respectively, and n(m) is the number of As(Si) atom in the formula unit. Our calculations show that the SiAs monolayer has a cohesive energy of 5.13 eV/atom, which is a bit larger than that of SiAs2 monolayer 4.98 eV/atom. For comparison, at the same theoretical level, the cohesive energies of arsenene and silicene are 2.99 and 3.71 eV/atom, respectively [18, 43]. The high cohesive energies of SiAs and SiAs2 reveal that both of them are bonded strongly with high stability.
To further confirm the structural stabilities of monolayer SiAs and SiAs2, we also have performed vibrational phonon spectra calculations. As shown in Fig. 2a, positive frequencies account for a majority of modes except the transverse acoustic mode near the Γ point, which is due to the softening of phonons and has been reported in other similar systems [44, 45], indicating that the structures are both dynamically stable. Then, we carried out 6 ps first-principles MD simulations at room temperature (T=300K), as presented in Fig. 2b. The slight energy fluctuation and well kept sturctures suggest that they are thermally stable at room temperature. Our results imply that the monolayers SiAs and SiAs2 could be realized experimental at room temperature.
With the optimized structures of monolayer SiAs and SiAs2, now we pay attention to their electronic properties. The calculated orbital decomposition band structures of SiAs and SiAs2 monolayers are shown in Fig. 3. Our calculations clearly show that SiAs and SiAs2 monolayers are both indirect semiconductors with wide band gaps. For monolayer SiAs, the valence band maximum (VBM) is located at the Y point, while the conduction band minimum (CBM) is at the Γ (Fig. 3a). The indirect band gap of monolayer SiAs is Eg = 1.72 eV within the PBE scheme. One can also see that the VBM state at Y point comprises the py orbital, while the CBM of Γ point comprises mainly the s orbital, which means that the external deformation will have different effects on the two states and may lead to indirect–direct transition, as revealed in the following. Unlike SiAs, the monolayer SiAs2 is a nearly direct semiconductor with VBM located at side of the Y point and CBM is of a little displacement from it (Fig. 3b). The SiAs2 monolayer indirect band gap is Eg = 1.42 eV within the PBE scheme. And the VBM and CBM of SiAs2 monolayer are comprised of the py orbital and s orbital, respectively. In order to get more accurate band gap value, we also performed the hybrid functional calculations (HSE06)[46, 47] for SiAs and SiAs2 monolayers. From the calculated band structures (the right part of Fig. 3a, b), the sharps of band states from PBE and HSE are basically the same, and the indirect band gap is still predicted within the hybrid functional calculations, but the gap value is increased to 2.39 eV and 2.07 eV for SiAs and SiAs2, respectively.
The carrier mobilities, which is a key factor of the potential applications in modern electronic devices for the newly discovered 2D materials, is as important as the bandgap and location of CBM and VBM. To gain more details on the electronic structure properties of SiAs and SiAs2 monolayers, we then calculated their acoustic phonon-limited carrier mobilities (including electron and hole in both x and y directions) on the basis of deformation potential (DP) theory [48] at the room temperature (T=300 K). At the low-energy regime (300 K), the electron-acoustic-phonon scattering dominates the carrier transport, which makes the acoustic phonon-limited an effective way to predict the carrier mobilities of many 2D structures, such as the MoS2 monolayer [49], tellurene [19], phosphene [50], and few-layer MoO3 [51]. The calculated effective masses m∗ and carrier mobilities μ of SiAs and SiAs2 monolayers show that both of them are high-mobility and transport anisotropy (see Additional file 1: Table S1 and the Figures S3 and S4) like the black phosphorene [50]. To estimate the carrier mobility of SiAs and SiAs2, we firstly performed a fit of their bands using the nearly free electron model to get the effective carrier masses. For SiAs, we define x and y as the direction perpendicular to the lattice vectors b and a, respectively. The \(m_{e}^{*}\) and \(m_{h}^{*}\) along the x direction are about 0.15 m0 and 0.86 m0, respectively, and along the y direction are 0.80 m0 and 0.22 m0 (m0 is the free-electron mass), respectively. For SiAs2, the direction of lattice vector a is defined as x, while that of b is y. The \(m_{e}^{*}\) and \(m_{h}^{*}\) along the x direction are about 0.14 m0 and 0.65 m0, respectively, and along the y direction are 2.05 m0 and 1.82 m0, respectively. We further studied the elastic constants (C) and the deformation potentials (E1) (see Additional file 1: Figure S2 and S3). Based on the above obtained m∗, C and E1 values, we estimated the carrier mobility as listed in Table 1. The electron mobilities for SiAs(SiAs2) along x and y directions are 0.66(0.26) and 0.54(0.11) × 103 · cm2V−1S−1, while the hole mobilities along x and y directions are 3.90(0.13) and 0.30(0.65) × 103 · cm2V−1S−1, respectively, both of which are much higher than those of MoS2 [49].
To further shed light on the underlying bonding mechanism of Si and As atoms in monolayers SiAs and SiAs2, the total and partial density of states (PDOS) of them using PBE functional, with their electron density distribution corresponding to VBM and CBM, are provided in Fig. 4, respectively. One can see that the PDOS of As and Si atoms (Fig. 4a, c) shows strong hybridization of s and p orbitals, indicating the strong covalent bond between them. The distinctions between monolayers SiAs and SiAs2 are the localization of pz orbital, which are attribute to the different bonding coordination environment of As atom. The lone pair electron states, localized at As atom in both of SiAs and SiAs2 monolayers, augment the three nearest bonding orbitals to decide the monolayer structure buckling formation and to form the pz orbital localizing action. In monolayer SiAs, the lone pairs are apart by Si–As bond, which relax the repulsive effect and broaden the pz orbital. Whereas in monolayer SiAs2, As–As bond, remaining the situation which is very common in group V semiconductors, localizes the pz orbital in a deeper energy level.
As we know, the character of frontier states is not only of interest in a microscopic understanding of the conduction channels but also of great concern for the design of optimal contacts.[52] The charge densities corresponding to VBM and CBM of monolayers SiAs and SiAs2 are presented in Fig. 4b and d, respectively. The VBM is almost the hybridization of 3p orbitals of Si and As, while CBM is mainly from the contribution of 3s orbitals of Si and As, which are also consistent with PDOS results in Fig. 4a, c and the electronic orbital decomposition of band structures in Fig. 3.
Mechanical strain is an effective way to modulate the electronic properties of 2D materials, which are extensively used to modify the band structure of black and blue phosphorenes and other nanosheet materials [53–55]. Especially, for the buckled structure system, the energy cost is usually quite small to induce a marked strain. Here, the application of mechanical strain is simulated by varying the lattice constant as well as the internal degrees of freedom of each atom during the geometric optimization. The strain ε is defined as ε=(l−l0)/l0, where l and l0 are the strained and equilibrium lattice constants of monolayers SiAs and SiAs2. In Fig. 5a, b, the detailed variations of high buckling geometric structure of 2D SiAs and SiAs2 under strains are represented, respectively. One can see that their buckled heights are expanded or compressed by changed the buckled angle θ1(2) with biaxial compressive or tensile strains in nearly linear variations. And we also found that their high buckling geometric structure are both still kept well under quite large strains, whose phonon spectra, as shown in Additional file 1: Figure S5 and S6, exists no negative frequencies even at the large strain regime. The gap variations of monolayer SiAs and SiAs2 under biaxial compressive and tensile strains are shown in Fig. 5c, d, respectively. One can see that the electronic properties of SiAs and SiAs2 sensitively depend on the strain and undergo an indirect to direct band transition in certain strain region and then to metal at a large strain region.
The detailed variations of SiAs and SiAs2 band structures are exhibited in Figs. 6 and 7, respectively. Under biaxial compressive strains, the buckled height of monolayer SiAs is increasing and the CBM shifts from Γ to a point on the Y–S line and back to Y. While the VBM is kept still at Y point until the compressive strain reachs ε =− 10%. Therefore, with increasing compressive strain the band gap switches from indirect Y to Γ, via indirect Y to a point on the Y–S line, to direct Y to Y and back to indirect a point on the Γ–Y line to Y, as shown in Fig. 6. For tensile strains, the VBM at Y moves to a point on the Y–S line and the CBM at Γ moves to Y and the band gap remains indirect. For large strain, no matter compressive or tensile leads to a metal transition, as shown in the Fig. 5c.
In Fig. 7, a similar study has been carried out for 2D SiAs2. Instead of compression, tensile strains in the range of 8–10% result in direct band gaps. when the monolayer SiAs2 spreads with a decreasing of buckled height under the tensile strains, the VBM shift from a point on the Γ–Y line to Γ and keep still in the range of 8–10% and then shift apart to a point on the Γ–X line, while the CBM moves from a point on the Γ–Y line to Γ and hold on. Therefore, with rising tensile strain, the band gap switches from indirect on the Γ–Y line to direct Γ– Γ and then back to indirect a point on the Γ–X line to Γ, as illustrated in Fig. 7. Compressive strains remain the indirect band gap. And large strains have similar effects, leading to a metal transition as SiAs.
Representative direct band structures of strained SiAs and SiAs2 are also shown in Additional file 1: Figure S7a and b by the PBE and HSE calculations. For SiAs, a direct band gap of Eg = 1.75 eV(HSE) with the VBM and CBM localized at the Y points is obtained under a biaxial compressive strain of ε = − 7.5%. Unlike SiAs, a biaxial tensile strains of ε=8.5% induces the SiAs2 to a direct band of Eg = 1.60 eV(HSE). And the VBM and CBM are at the Γ point.
Conclusions
In summary, performing a first-principles DFT calculation, we have propsed two new kinds of 2D materials of silicon and arsenic compound, SiAs and SiAs2, which are both dynamically and thermodynamically stable. Our caculations show that SiAs and SiAs2 monolayers are indirect semiconductors with the band gaps of 2.39 eV and 2.07 eV, respectively. The band gap of SiAs and SiAs2 monolayers are sensitive to strain, which undergo an indirect to direct band transition and even to metal upon certain mechanical strain. SiAs and SiAs2 monolayers possess higher mobility than MoS2 and display anisotropic transportation like the black phosphorene. Our works pave a new route at nanoscale for novel functionalities of optical devies.
Abbreviations
- 2D:
-
Two-dimensional
- CASTEP:
-
Cambridge sequential total energy package
- CBM:
-
Conduction band minimum
- DFT:
-
Density functional theory
- DFPT:
-
Density functional perturbation theory
- DP:
-
Deformation potential
- GGA:
-
Generalized gradient approximation
- MD:
-
Molecular dynamics
- NVT:
-
Moles-volume-temperature
- PAW:
-
Projector augmented wave
- PBE:
-
Perdew-Burke-Ernzerhof
- PDOS:
-
Partial density of states
- TMDs:
-
Transiton-metal dichalcogenides
- VASP:
-
Vienna ab initio simulation package
- VBM:
-
Valence band maximum
References
Berger C, Song Z, Li X, Wu X, Brown N, Naud C, Mayou D, Li T, Hass J, Marchenkov AN, et al (2006) Electronic confinement and coherence in patterned epitaxial graphene. Science 312(5777):1191–1196.
Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA (2004) Electric field effect in atomically thin carbon films. Science 306(5696):666–669.
Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK (2009) The electronic properties of graphene. Rev Mod Phys 81:109–162.
Li X, Cai W, An J, Kim S, Nah J, Yang D, Piner R, Velamakanni A, Jung I, Tutuc E (2009) Others: Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324(5932):1312–1314.
Vogt P, De Padova P, Quaresima C, Avila J, Frantzeskakis E, Asensio MC, Resta A, Ealet B, Le Lay G (2012) Silicene: compelling experimental evidence for graphenelike two-dimensional silicon. Phys Rev Lett 108(15):155501.
Fleurence A, Friedlein R, Ozaki T, Kawai H, Wang Y, Yamada-Takamura Y (2012) Experimental evidence for epitaxial silicene on diboride thin films. Phys Rev Lett 108(24):245501.
Zhang WB, Song ZB, Dou LM (2015) The tunable electronic structure and mechanical properties of halogenated silicene: a first-principles study. J Mater Chem C 3(13):3087–3094.
Chopra NG, Luyken RJ, Cherrey K, Crespi VH, Cohen ML, Louie SG, Zettl A (1995) Boron nitride nanotubes. Science 269(5226):966–967.
Dean CR, Young AF, Meric I, Lee C, Wang L, Sorgenfrei S, Watanabe K, Taniguchi T, Kim P, Shepard KL, et al. (2010) Boron nitride substrates for high-quality graphene electronics. Nat Nanotechnol 5(10):722.
Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS (2012) Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nanotechnol 7(11):699.
Wilson JA, Yoffe AD (1969) The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties. Adv Phys 18(73):193–335.
Li L, Yu Y, Ye GJ, Ge Q, Ou X, Wu H, Feng D, Chen XH, Zhang Y (2014) Black phosphorus field-effect transistors. Nat Nanotechnol 9(5):372.
Liu H, Neal AT, Zhu Z, Luo Z, Xu X, Tománek D, Ye PD (2014) Phosphorene: an unexplored 2d semiconductor with a high hole mobility. ACS Nano 8(4):4033–4041.
Li WL, Chen Q, Tian WJ, Bai H, Zhao YF, Hu HS, Li J, Zhai HJ, Li SD, Wang LS (2014) The B35 cluster with a double-hexagonal vacancy: a new and more flexible structural motif for borophene. J Am Chem Soc 136(35):12257–12260.
Jiang HR, Lu Z, Wu MC, Ciucci F, Zhao TS (2016) Borophene: a promising anode material offering high specific capacity and high rate capability for lithium-ion batteries. Nano Energy 23:97–104.
Peng B, Zhang H, Shao H, Xu Y, Zhang R, Zhu H (2016) The electronic, optical, and thermodynamic properties of borophene from first-principles calculations. J Mater Chem C 4(16):3592–3598.
Zhang S, Yan Z, Li Y, Chen Z, Zeng H (2015) Atomically thin arsenene and antimonene: semimetal–semiconductor and indirect–direct band-gap transitions. Angew Chemie 127(10):3155–3158.
Kamal C, Ezawa M (2015) Arsenene: Two-dimensional buckled and puckered honeycomb arsenic systems. Phys Rev B 91(8):85423.
Zhu Z, Cai X, Yi S, Chen J, Dai Y, Niu C, Guo Z, Xie M, Liu F, Cho JH (2017) Others:Multivalency-driven formation of Te-based monolayer materials: a combined first-principles and experimental study. Phys Rev Lett 119(10):106101.
Zhu Z, Guan J, Liu D, Tománek D (2015) Designing Isoelectronic Counterparts to Layered Group V Semiconductors. ACS Nano 9(8):8284–8290.
Guan J, Liu D, Zhu Z, Tománek D (2016) Two-dimensional phosphorus carbide: Competition between sp2 and sp3 bonding. Nano Lett 16(5):3247–3252.
Zhang S, Guo S, Huang Y, Zhu Z, Cai B, Xie M, Zhou W, Zeng H (2016) Two-dimensional SiP: an unexplored direct band-gap semiconductor. 2D Mater 4(1):015030.
Zhang WB, Qu Q, Zhu P, Lam CH (2015) Robust intrinsic ferromagnetism and half semiconductivity in stable two-dimensional single-layer chromium trihalides. J Mater Chem C 3(48):12457–12468.
Elias DC, Nair RR, Mohiuddin TMG, Morozov SV, Blake P, Halsall MP, Ferrari AC, Boukhvalov DW, Katsnelson MI, Geim AK, et al. (2009) Control of graphene’s properties by reversible hydrogenation: evidence for graphane. Science 323(5914):610–613.
Han MY, Özyilmaz B, Zhang Y, Kim P (2007) Energy band-gap engineering of graphene nanoribbons. Phys Rev Lett 98(20):206805.
Radisavljevic B, Radenovic A, Brivio J, Giacometti IV, Kis A (2011) Single-layer MoS2 transistors. Nat Nanotechnol 6(3):147.
Fuhrer MS, Hone J (2013) Measurement of mobility in dual-gated MoS2 transistors. Nat Nanotechnol 8(3):146.
Weck PF, Kim E, Czerwinski KR (2013) Semiconducting layered technetium dichalcogenides: insights from first-principles. Dalt Trans 42(43):15288–15295.
Wood JD, Wells SA, Jariwala D, Chen KS, Cho E, Sangwan VK, Liu X, Lauhon LJ, Marks TJ, Hersam MC (2014) Effective passivation of exfoliated black phosphorus transistors against ambient degradation. Nano Lett 14(12):6964–6970.
Barreteau C, Michon B, Besnard C, Giannini E (2016) High-pressure melt growth and transport properties of SiP, SiAs, GeP, and GeAs 2D layered semiconductors. J Cryst Growth 443:75–80.
Wadsten T, Vikan M, Krohn C, Åke Nilsson, Theorell H, Blinc R, Paušak S, Ehrenberg L, Dumanović J (1967) The Crystal Structures of SiP2, SiAs2, and GeP. Acta Chem Scand 21(21):593–594.
Donohue P, Siemons W, Gillson J (1968) Preparation and properties of pyrite-type SiP2 and SiAs2. J Phys Chem Solids 29(5):807–813.
Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54(16):11169.
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865.
Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758.
Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13(12):5188.
Togo A, Oba F, Tanaka I (2008) First-principles calculations of the ferroelastic transition between rutile-type and CaCl 2-type SiO 2 at high pressures. Phys Rev B 78(13):134106.
Togo A. https://atztogo.github.io/phonopy/.
Clark SJ, Segall MD, Pickard CJ, Hasnip PJ, Probert MJ, Refson K, Payne MC (2005) First principles methods using CASTEP. Z Kristall 220:567–570.
Refson K, Tulip PR, Clark SJ (2006) Variational density-functional perturbation theory for dielectrics and lattice dynamics. Phys Rev B 73:155114.
Porezag DV, Pederson MR (1996) Infrared intensities and raman-scattering activities within density-functional theory. Phys Rev B 54:7830–7836.
Molina-Sánchez A, Wirtz L (2011) Phonons in single-layer and few-layer mos 2 and ws 2. Phys Rev B 84:155413.
Li Y, Liao Y, Chen Z (2014) Be2C Monolayer with quasi-planar hexacoordinate carbons: a global minimum structure. Angew Chemie Int Ed 53(28):7248–7252.
Zheng H, Li XB, Chen NK, Xie SY, Tian WQ, Chen Y, Xia H, Zhang SB, Sun HB (2015) Monolayer ii-vi semiconductors: A first-principles prediction. Phys Rev B 92:115307.
Şahin H, Cahangirov S, Topsakal M, Bekaroglu E, Akturk E, Senger RT, Ciraci S (2009) Monolayer honeycomb structures of group-iv elements and iii-v binary compounds: First-principles calculations. Phys Rev B 80:155453.
Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J Chem Phys 118(18):8207–8215.
Krukau AV, Vydrov OA, Izmaylov AF, Scuseria GE (2006) Influence of the exchange screening parameter on the performance of screened hybrid functionals. J Chem Phys 125(22):224106.
Bardeen J, Shockley W (1950) Deformation potentials and mobilities in non-polar crystals. Phys Rev 80(1):72.
Kaasbjerg K, Thygesen KS, Jacobsen KW (2012) Phonon-limited mobility in n-type single-layer mos 2 from first principles. Phys Rev B 85:115317.
Qiao J, Kong X, Hu ZX, Yang F, Ji W (2014) High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nat Commun 5:4475.
Zhang WB, Qu Q, Lai K (2017) High-mobility transport anisotropy in few-layer MoO3 and its origin,. Acs Appl Mater Interfaces 9(2):1702–1709.
Tománek D (2015) Interfacing graphene and related 2D materials with the 3D world. J Phys Condens Matter 27(13):133203.
Peng X, Wei Q, Copple A (2014) Strain-engineered direct-indirect band gap transition and its mechanism in two-dimensional phosphorene. Phys Rev B 90(8):85402.
Fei R, Yang L (2014) Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Lett 14(5):2884–2889.
Yu W, Niu CY, Zhu Z, Wang X, Zhang WB (2016) Atomically thin binary V-V compound semiconductor: a first-principles study. J Mater Chem C 4(27):6581–6587.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (nos. 11504332 and 11774078) and Innovation Scientists and Technicians Troop Construction Projects of Henan Province (no. 10094100510025) and the key Research Project for the Universities of Henan Province (19A140009) and Doctoral Foundation of Henan Polytechnic University (B2018-38). The calculations were performed on the High Performance Computational Center of Zhengzhou University.
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YJ and CYN conceived the idea. SYB performed the calculations, analyzed the result data, and wrote the manuscript. All authors have read and approved the final manuscript.
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Bai, S., Niu, CY., Yu, W. et al. Strain Tunable Bandgap and High Carrier Mobility in SiAs and SiAs2 Monolayers from First-Principles Studies. Nanoscale Res Lett 13, 404 (2018). https://doi.org/10.1186/s11671-018-2809-6
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DOI: https://doi.org/10.1186/s11671-018-2809-6