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Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

SnP3: A Previously Unexplored Two-Dimensional Material Barun Ghosh,†,§ Shivam Puri,‡,§ Amit Agarwal,† and Somnath Bhowmick*,‡ †

Department of Physics and ‡Department of Materials Science and Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

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S Supporting Information *

ABSTRACT: We predict SnP3 to be an easily exfoliable and dynamically stable twodimensional (2D) material with thickness-dependent electronic properties. On the basis of density functional theory calculations, we show that mono- and bilayer SnP3 has relatively low cleavage energies of 0.71 and 0.45 J m−2, lower than several other 2D materials and comparable to that of graphene (0.32 J m−2). Mono- and bilayer SnP3 have an indirect band gap of 0.83 and 0.55 eV, respectively, and the magnitude of the gap can be tuned by applying strain. Remarkably, pristine monolayer SnP3 has a relatively high carrier mobility in the range of 3000−7000 cm2 V−1 s−1, at par with well-known 2D semiconductors such as MoS2, phosphorene, and other phosphorus-based layered materials such as GeP3 and InP3. Mono- and bilayer SnP3 also show large optical absorption, resulting from the existence of the van-Hove singularities in the electronic density of states. The combined properties of layered SnP3, in particular, its high carrier mobility and tunable band gap, along with large optical absorption coefficient, open up interesting possibilities for nanoelectronic and nanophotonic applications.

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that of graphene (0.32 J m−2),34 MoS2 (0.29 J m−2),35 and phosphorene (0.36 J m−2).36 Density functional theory (DFT)based calculations predict SnP3 to have an indirect band gap of 0.83 eV for the monolayer and 0.55 eV for the bilayer (based on HSE06 calculations), whereas the metallic nature observed in bulk SnP3 returns only from trilayer onward. Remarkably, we find that pristine SnP3 has a very high carrier mobility in the range of 3000−7000 cm2 V−1 s−1, except for the hole mobility in the zigzag direction, which is 2 orders of magnitude smaller than this. Other than massless Dirac fermions in graphene, the charge-carrier mobility of SnP3 is significantly higher than some of the popularly known 2D semiconductors such as MoS2 and phosphorene (an overview of the data available in the literature is given in the Supporting Information). Comparing the in-plane elastic constant with MoS2 and graphene, we find that SnP3 is 4−10 times softer, which is an important criteria for applications in flexible electronic devices. We also find a large optical absorption coefficient (∼106 cm−1) for both mono- and bilayered SnP3, making them very promising for optoelectronic applications.

INTRODUCTION In the quest of new materials for next-generation electronic devices, atomically thin two-dimensional (2D) materials1−3 with gate tunable electronic and optical properties offer the highest promise, with proven potential applications in electronic,4−12 photonic,13−16 and plasmonic devices.17−19 Since the isolation of a single layer of graphite or graphene more than a decade ago,20,21 the family of 2D materials have grown significantly with new additions such as transition metal dichalcogenides,4 monolayer phosphorus or phosphorene,6−8 and several derivatives of phosphorus, predicted to be stable in atomically thin form.22−28 This includes the combination of phosphorus with group-II, III, and IV elements, resulting in easily exfoliable 2D materials with high mobility, such as calcium triphosphide (CaP3),23 indium triphosphide (InP3),24 phosphorous carbide, 25 and germanium triphosphide (GeP3).26 They are also predicted to have excellent absorption in the infrared to visible regime, with possible applications in photovoltaic solar cells. In this article, we introduce an easily exfoliable, new 2D material, SnP3, to the group-IV-based triphosphide family of 2D materials. The bulk binary compound of Sn and P can exist in several phases, such as Sn3P4, SnP, Sn4P3, and SnP3.29 Among the various known bulk phases, SnP3 is a well-known layered material, with studies reporting its synthesis, as well as electronic and structural properties.29,30 It is also used extensively as an anode material in Na- and Li-ion batteries.31−33 On the basis of ab initio calculations, we show that monolayer and bilayer SnP3 can be exfoliated easily from the bulk, with an estimated cleavage energy of 0.71 J m−2 for monolayer and 0.45 J m−2 for bilayer, which is comparable to © XXXX American Chemical Society

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METHODOLOGY We perform all of the DFT-based ab initio calculations using the projector-augmented wave pseudopotentials and a plane wave basis set, as implemented in the VASP suite of codes.37−39 We treat the exchange and correlation effects within the generalized gradient approximation (GGA) scheme, developed by Perdew−Burke−Ernzerhof (PBE) and incorporate the dispersion forces using the vdW-DF240,41 van der Received: July 12, 2018

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DOI: 10.1021/acs.jpcc.8b06668 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Waals correction. We used an energy cutoff of 500 eV for the plane-wave basis set and a k-mesh of 12 × 12 × 8 (6 × 6 × 1) for the Brillouin zone (BZ) integrations. Considering the wellknown underestimation of the band gap within the standard semilocal DFT functionals, we used the Heyd−Scuseria− Ernzerhof (HSE06) functional for the band structure calculations. The phonon calculation is performed in VASP using the LDA pseudopotentials.

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RESULTS AND DISCUSSIONS Bulk SnP3. Initially, the pseudopotentials and other simulation parameters are validated by reproducing the structural and electronic properties of bulk SnP3, which is a well-known layered material belonging to the trigonal space group R3̅m (no. 166).33,42 Each layer is composed of buckled honeycombs made of P atoms (similar to β allotrope of monolayer P43), and three such honeycombs are connected with each other via a common Sn atom [see Figures 1a,b and Figure 2. (a) Honeycomb crystal structure of monolayer SnP3 viewed from the top (below) and at an angle from the side (above). (b) Phonon-dispersion spectrum for monolayer SnP3. (c) Calculated cleavage energy of 1L and 2L SnP3 compared with the cleavage energy of monolayer graphene. (d) Total energy/unit cell of a 2L SnP3 structure plotted against the interlayer separation, d − d0. The DFT data (blue dots) for the total energy curve matches reasonably well with a Lennard-Jones (red line) potential, indicating the predominantly van der Waals nature of the interlayer interaction.

high-symmetry directions in the first BZ [see Figure 1c,d]. Evidently, bulk SnP3 is metallic in nature, with Fermi-levelcrossing electronic bands at several places along the Γ̅ A̅ , A̅ L̅ , K̅ Γ̅ , and Γ̅ M̅ directions, among others. Monolayer SnP3. One (1L), two (2L), and three (3L) layers of SnP3 are obtained by separating those many layers from the bulk, followed by adding a vacuum of 20 Å perpendicular to the plane to avoid the spurious interactions between the periodic replicas in the out-of-plane direction. The crystal structure of a monolayer of SnP3 is shown in Figure 2a. Multilayers such as 2L and 3L SnP3 are formed by stacking monolayers in the same sequence as in bulk SnP3. Lattice parameters and atomic positions of a monolayer SnP3 are given in the form of a POSCAR file in Tables SII and SIII in the Supporting Information. The in-plane lattice parameters are found to decrease with the number of layers [see Table SIV in the Supporting Information for detailed structural parameters]. In case of a monolayer, the calculated in-plane unit cell dimensions are found to be a = b = 7.37 Å. This is ∼5% smaller than the bulk values according to the DFT estimate, although it is very similar to the experimentally reported value for bulk SnP3. However, bond angles are found to differ significantly (∼11−14%) in 1L SnP3 from their bulk values [see Table SIV in the Supporting Information for details]. Stability of atomically thin film of SnP3 is checked by comparing the cohesive energy [see eqs S1 and S2 in the Supporting Information] of the monolayer and bulk SnP3. Because the cohesive energy of monolayer (−19.04 eV per formula unit) is comparable to that of the bulk (−19.71 eV per formula unit), we conclude SnP3 to be stable all the way down to 1L. The dynamical stability of the monolayer is further checked by calculating the phonon dispersion using a 3 × 3 × 1 supercell. Complete absence of any negative phonon frequency, as shown in Figure 2b, confirms the dynamical

Figure 1. (a) Top and (b) side view of the layered crystal structure of bulk SnP3. (c) BZ corresponding to the bulk reciprocal lattice, with the monolayer BZ on the top. Various high-symmetry points in the reciprocal lattice are marked by the red dots. For clarity, the bulk high symmetry points are marked by bar symbols. (d) Band structure of bulk SnP3, calculated within GGA, along various high symmetry directions in the BZ.

2a]. In the bulk unit cell, monolayers are stacked in such a fashion that every third layer is repeated by a translation vector perpendicular to the plane of layers. The smallest repeating unit has six formula units (three constituent layers, each having two formula units) in a nonprimitive hexagonal cell of dimension a = b = 7.80 Å and c = 11.11 Å, as per DFT calculations using the PBE along with the vdW-DF2 functional. Details of the structural relaxation are described and illustrated in section S1 and Figure S1 in the Supporting Information. Compared with the experimentally reported values for SnP330 (a = b = 7.38 Å and c = 10.51 Å), approximately 5% overestimation is observed, which is well-known for PBE functional.44 Similarly, 1−5% difference is observed between calculated and experimental values of bond angles and bond lengths of SnP3 [see Table SIV in the Supporting Information]. Electronic band structure of bulk SnP3 is plotted along various B


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The Journal of Physical Chemistry C

Novelty of a 2D material mainly lies in its electronic and optical properties, which can be predicted from the electronic band structure of the material. Given that PBE underestimates the band gap of a semiconductor, HSE06 (Heyd−Scuseria− Ernzerhof) functional is used to calculate the electronic band structures of 1L, 2L, and 3L SnP3. As shown in Figure 3a, 1L

stability of the monolayer SnP3. As shown in Figure 2b, the out-of-plane transverse acoustic mode has a parabolic dispersion, which is a distinctive feature of atomically thin materials.45 On the other hand, both the in-plane longitudinal and transverse modes have a linear dispersion near the Γ point. The longitudinal acoustic (LA) mode travels with a speed of ∼3.7 km/s, which is much smaller compared to that in graphene (21 km/s).46 This implies that the in-plane elastic stiffness of SnP3 should be much smaller than that of graphene, and it is explicitly confirmed below. Similar to other 2D materials, the elastic property of SnP3 is characterized by calculating the in-plane stiffness constant, defined as C =

1 ∂ 2E , A 0 ∂ε 2

where A0 is the equilibrium area of the

unit cell and E is the difference in energy between an unstrained layer and a layer under uniaxial strain of magnitude ε. Calculated C values are nearly equal in the armchair (C ≈ 31.19 N/m) and zigzag (C ≈ 31.26 N/m) direction of SnP3. Compared to many established 2D materials such as graphene (C ≈ 350 N/m),47,48 MoS2 (C ≈ 130 N/m),49,50 and hBN (C ≈ 267 N/m),51 SnP3 is very soft, although it is marginally stiffer than isostructural GeP3 (C ≈ 22.10 and ≈22.35 N/m in armchair and zigzag direction, respectively). 26 Such a remarkable softness in SnP3 can be attributed to its buckled crystal structure, enabling the monolayer to deform via change of bond angle at minimal energy expenses, without stretching or contracting the bond length. The latter mode of deformation, as observed in case of graphene or hBN, requires much higher energy, making them significantly more stiff than in SnP3. This can be further confirmed by comparing the structural parameters of SnP3 under strain, as reported in Table SIV of the Supporting Information. Although the bond lengths and P−P−P bond angle hardly change under strain from their equilibrium values, P−Sn−P bond angle changes by ∼10% (∼−10%) under tensile (compressive) strain. Efficient fabrication of a 2D material largely depends on how easily it can be separated from the bulk via commonly used mechanical or liquid-phase exfoliation methods. Ease of exfoliation is estimated by calculating the cleavage energy of 1L and 2L SnP3 from a 5L thick slab, approximated to be equivalent to the bulk [see Figure 2c]. We find the cleavage energy of the monolayer SnP3 to be 0.71 J m−2, which is much smaller than many recently proposed group V-based 2D materials such as GeP3 (1.14 J m−2),26 NaSnP (0.81 J m−2),52 Ca2N (1.09 J m−2),53 and InP3 (1.32 J m−2).24 Cleavage energy is further reduced to 0.45 J m−2, in case of bilayer SnP3, which is comparable to the exfoliation energy of graphene (0.32 J m−2)34 and other well-known 2D materials such as MoS2 and phosphorene [see Table SV in the Supporting Information for a detailed comparison]. Thus, it should be relatively easy to cleave 1L and 2L SnP3 from the bulk phase using either mechanical or liquid exfoliation processes. Generally, low cleavage energy is the signature of layered materials, which originates from the weak van der Waals type of interlayer interaction. In case of bilayer SnP3, this is confirmed by plotting the total energy as a function of the interlayer distance. As shown in Figure 2d, the energy profile is similar to a typical Lennard-Jones type potential, highlighting the predominantly van der Waals nature of the interlayer interaction. The depth of the potential energy curve gives a measure of the binding energy between two monolayers, which is found to be ∼1.1 eV (per unit cell), in this case.

Figure 3. (a) Electronic band structure and the DOS of (a) 1L, (b) 2L, and (c) 3L SnP3 calculated using the HSE06 functional. In panel (a), the HSE06 results are compared with the PBE results and the effect of spin−orbit coupling on the band structure is shown. Note that although 1L and 2L SnP3 are small-gap semiconductors, 3L SnP3 shows metallic behavior. The orbital PDOS plots suggest that near the VBM and CBM of 1L and 2L SnP3, the most prominent contribution arises from the p orbital of P and Sn atoms. Note that the flatness of the bands results in several VHS in the DOS. (d) Change of band gap as a function of strain applied in the zigzag and armchair direction.

SnP3 is an indirect band gap semiconductor, with the valence band maximum (VBM) and conduction band minimum (CBM) located near the K valley and at the Γ point, respectively. A twofold degeneracy is observed at the K point, with two valence bands crossing each other. The magnitude of the band gap is found to be 0.83 eV (HSE06 functional), which is in the near-infrared region. Nearly 1.5 times increase of the PBE-predicted band gap justifies the use of HSE06 functional. However, no significant change is observed by adding the spin−orbit coupling. Note that, similar to GeP3 and InP3, monolayer SnP3 as directly cleaved from bulk shows metallic nature in the absence of any surface relaxation.24,26 This suggests that the opening of a band gap in the monolayer is not only because of quantum confinement, but the surface relaxation also has an important role in it. After a second layer is added, SnP3 (2L) remains an indirect band gap semiconductor [see Figure 3b] with the VBM and CBM located at the K and Γ point, respectively. As expected, the band gap magnitude reduces to 0.55 eV in 2L SnP3. Finally, adding a third layer converts SnP3 (3L) to a metallic state, and it remains metallic with further increase in the number of layers similar to bulk SnP3. Projecting the calculated wave functions on the atomic wave functions, we find that the valence and conduction band edges in 1L and 2L SnP3 are composed of mainly p orbitals of P and C


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carrier effective mass (depending on the curvature of valence and conduction band edges) in the transport and its transverse direction, respectively. The scattering probability (λα) for the charge carriers is estimated from the deformation potential

Sn atom, as depicted in the projected density of states (PDOS) plot attached with the electronic band structure [see Figure 3a,b]. Multiple van Hove singularities (VHSs) can be observed in the DOS plots of atomically thin SnP3 layers. For example, in the case of 1L SnP3, the topmost valence band is almost flat along the MK direction resulting in a VHS in the DOS. Such VHSs result in strong light-matter interactions and are also known to be responsible for ferromagnetic and other manybody instabilities. For example, ferromagnetic ground state has been reported in case of monolayer InP3 via hole doping.24 Although SnP3 is isostructural to InP3, and it has VHS, we do not find any ferromagnetic ground state by hole doping in a single layer of SnP3. Analyzing the band structure further, we find significant anisotropy in terms of the curvature of the highest occupied valence band along the KM and KΓ direction in monolayer SnP3 [see Figure 3a]. A nearly flat valence band along the KM line leads to a very high effective mass of the positive charge carrier in this direction. In contrast, effective mass is much smaller in the KΓ direction because of the parabolic band dispersion. It should be noted that although the valence band is a twofold degenerate at the K point, the valence band maxima is not exactly at the K point. The two hills along KM and KΓ directions have slightly higher energy than the K point. A similar situation is observed for monolayer GeP3 with strain,54 where the heavy hole and light hole bands cross each other, rendering their classification unfeasible. When a second layer is added, effective mass changes significantly. Interestingly, although effective mass of electron decreases by a factor of ∼6 in bilayer SnP3 as compared to monolayer, effective mass of the hole shows an opposite trend and increases by a factor of ∼2.5 after the second layer is added. The carrier mobilities in different high symmetry directions are reported in Table SVI of the Supporting Information. In both 1L and 2L SnP3, although the effective mass of electron is found to be isotropic, a large anisotropy is observed in case of the hole effective mass. This anisotropy of the hole effective mass has a significant impact on the transport properties of monolayer SnP3, as discussed later. As described earlier, SnP3 is a relatively soft material, which makes it a potentially good candidate for strain-tunable electronic devices. A rectangular unit cell of monolayer SnP3 is subjected to uniaxial compressive and tensile strains along the zigzag and the armchair directions [see the inset of Figure 3d]. In the rectangular BZ, CBM (VBM) is located at the Γ point (near the X valley in the XΓ direction) [see Figure S2 of the Supporting Information]. Although the band gap reduces significantly under compressive strain (down to 0.6 eV at 6% strain from its pristine value of 0.85 eV), only a marginal increase occurs under tensile strain [see Figure 3d]. Other than band gap modification, two highest valence bands flip in energy as the strain changes from compressive to tensile [see Figure S2, Supporting Information]. This band-flipping in SnP3 is similar to that reported recently in GeP3.54 However, no indirect to direct band gap transition is observed within ±6% strain applied on monolayer SnP3. Electronic transport properties are characterized in terms of charge-carrier mobilities of monolayer SnP3, calculated along the zigzag and armchair directionsee the inset of Figure 3d. The acoustic-phonon-limited mobility of pristine SnP3 at room temperature (T = 300 K) along the α (α = x/y) direction is given by,55 μα =

eℏ3 λαmα* mα*mβ*

(Eiα) using,55 λα =

kBT (Eαi )2 , Cα

where Cα is the elastic constant in

the direction of propagation of the LA phonon, aligned along the transport direction. The calculated values of the effective mass, deformation potential, and elastic constant are reported in Table 1. Details Table 1. Elastic Constants and the Mobility of 1L SnP3 carrier

direction

C (N/m)

m*/m0

Ei (eV)

μ (103 cm2/V s)

Electron

zigzag armchair zigzag armchair

31.26 31.19 31.26 31.19

0.92 0.92 2.07 0.84

0.40 0.47 1.98 0.29

5.02 3.54 0.06 7.15

Hole

of their calculations are given in section SII and Figure S3 of the Supporting Information. Although the effective mass of the electron is equal in the zigzag and armchair directions, nearly 1.4 times higher mobility along the former direction is due to the smaller deformation potential, which signifies weaker electron−phonon coupling along the zigzag axis [see Table 1]. A large anisotropy is observed in the case of hole mobility which is nearly 119 times higher in the armchair direction. This is a consequence of both lower effective mass and deformation potential along the armchair direction as compared to the respective values in the zigzag direction. Noticeably, estimated values of charge-carrier mobility lie in a range of 3000−7000 cm2 V−1 s−1, other than the hole mobility in the zigzag direction, which is 2 orders of magnitude smaller. Despite the fact that we evaluate an upper limit of chargecarrier mobility, limited by only acoustic phonon scattering in a pristine material, the value of mobility in SnP3 definitely lies in a higher range among the known 2D semiconductors [see Table SV in the Supporting Information for a comparison] and possibly falls short only to the extremely high mobility of the massless Dirac fermions in graphene. The relatively high mobility of SnP3 coupled with the intrinsic band gap which restricts the problems associated with high off-current (as in graphene) renders it a solid candidate for field-effect transistor devices. In terms of optical properties, 1L and 2L SnP3 are small gap semiconductors, which implies light absorption in the infrared and visible regions. This is confirmed by calculating the optical absorption coefficient for SnP3 [for computational details, see section SIII of the Supporting Information]. As shown in Figure 4, for the in-plane polarized light, a strong absorption peak (α∥) is present around ∼1.6 eV for monolayer SnP3, which is marginally shifted in the case of bilayer SnP3. The next absorption peak is found near ∼4.5−5 eV for both 1L and 2L SnP3. Calculated values of the absorption coefficient are found to be around ∼106 cm−1, which is comparable to that of the perovskite solar cells.56 This large absorption coefficient obtained in a wide energy range suggests potential applicability of SnP3 in photovoltaic devices. On the other hand, for the case when light is polarized along the superlattice axis,57 there is a significant reduction of the absorption. Note that, we have renormalized the results obtained from VASP according to the formalism developed by Matthes et al.57 to exclude the effect of the vacuum region. A detail discussion is given in section SIII,

, where mα* and mβ* is the chargeD


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shows strong light absorption, resulting from the presence of VHS in the DOS. The combined properties of SnP3 make it a very interesting 2D material, with potential applications in nanoelectronic and nanophotonic devices, which need to be explored further.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b06668. Figure 4. Absorption coefficient of 1L and 2L SnP3 for light polarized along the in-plane (solid lines) and the out of plane (dashed lines) direction. The in-plane absorption peak centered around 1.6 eV originates primarily from the transitions between valence and conduction bands, dominated by the p orbitals of phosphorous.

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and a figure of absorption coefficient without renormalization is also shown in Figure S4 of the Supporting Information. Because optical absorption is closely related to the electronic transitions, DOS can qualitatively explain the origin of the peaks observed in the spectrum. It is also well-known that the presence of VHS in DOS leads to strong light-matter interactions. Comparing the absorbance shown in Figure 4 with the orbital projected DOS [see Figure S5 in the Supporting Information] of monolayer and bilayer SnP3, a clear correlation is observed. The initial peak occurring around ∼1.6 eV in monolayer SnP3 originates from the direct transition between the valence and conduction band states, both dominated by P-p orbitals [see Figure S5a in the Supporting Information]. On the other hand, the higher energy peak at ∼4.5 eV originates from the direct transition between the valence band and conduction states dominated by P-p and Sn-p orbitals, respectively [see Figure S5a in the Supporting Information]. For bilayer SnP3, in addition to the P-p orbital, significant contributions from Sn-p and Sn-s orbital are also observed for the states near the CBM, corresponding to the low-energy peak of optical absorption around ∼1.7 eV [see Figure S5b in the Supporting Information]. Before concluding, we note that in SnP3, every atom is bonded to three nearest neighbors. This means that, there are two valence electrons left, per P atom. These lone pair of electrons may have a tendency to bond with oxygen atoms. However, this hypothesis needs to be tested thoroughly, and we will investigate this in the near future. However, hBN encapsulation has become a standard procedure to protect atomically thin 2D materials from environmental perturbations, and the same technique can be used in the case of SnP3 as well.

Discussion and details of structural relaxations, cohesive and exfoliation energy calculations, band flipping under strain, mobility calculations, and optical property calculations (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Somnath Bhowmick: 0000-0003-4094-5204 Author Contributions §

B.G. and S.P. contributed equally to this paper.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the funding from DST INSPIRE scheme, SERB (EMR/2017/004970), and DST Nanomission project. We also thank the computer center, IIT Kanpur, for providing the HPC facility. B.G. acknowledges CSIR for the Senior Research Fellowship.

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SUMMARY AND CONCLUSIONS In conclusion, we predict an easily exfoliable and previously unexplored 2D materialSnP3, which is dynamically stable and has a relatively high charge-carrier mobility in the range of 3000−7000 cm2 V−1 s−1. We show that both mono- and bilayer SnP3 have remarkably low cleavage energy which makes it realistic for mechanical or liquid exfoliation from the bulklayered material. We find that electronic properties of SnP3 strongly depend on its thickness, with 1L and 2L being small band gap semiconductors, whereas from 3L onward SnP3 becomes metallic similar to the bulk material. We show that the most effective way of tuning the band gap is via uniaxial compression, which is very promising as SnP3 is remarkably soft in terms of elastic stiffness. We find that 1L and 2L SnP3 E


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NOTE ADDED IN PROOF After the submission of this paper, we came to know about two similar studies just published,58,59 all cited here for the readers’ benefit.

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