Gallium Thiophosphate: An Emerging Bidirectional Auxetic Two

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Gallium Thiophosphate: An Emerging Bidirectional Auxetic 2D Crystal with Wide Direct Band Gap Jun-Hui Yuan, Kan-Hao Xue, Jia-Fu Wang, and Xiangshui Miao J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b01611 • Publication Date (Web): 18 Jul 2019 Downloaded from pubs.acs.org on July 22, 2019

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The Journal of Physical Chemistry Letters

Gallium Thiophosphate: An Emerging Bidirectional Auxetic 2D Crystal with Wide Direct Band Gap

Jun-Hui Yuan,† Kan-Hao Xue, †,‡* Jia-Fu Wang,§ Xiang-Shui Miao† †Wuhan

National Laboratory for optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China ‡ Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, IMEP-LAHC,

38000 Grenoble, France §School

of Science, Wuhan University of Technology, Wuhan 430070, China

Corresponding Authors *E-mail: [email protected] (K.-H. Xue)

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ABSTRACT: Two-dimensional materials with negative Poisson’s ratio (NPR) attract considerable attention due to their exotic mechanical properties. We propose a new 2D material monolayer GaPS4, which shows NPR for both in-plane (-0.033) and out-ofplane (-0.62) directions. Such coexistence of NPR in two directions is extremely rare for 2D materials, which mainly originates from its particular corner- and edge-shared tetrahedra pucker structure. GaPS4 has a stable three-dimensional layered bulk counterpart, and monolayer GaPS4 has an ultra-low cleavage energy of 0.23 J m-2 according to our calculation, suggesting exfoliation of bulk material as viable means for the preparation of mono- and few-layer GaPS4. Direct wide band gap of 3.55 eV and moderate electron mobility have been revealed in monolayer GaPS4, while the direct gap feature is robust within a strain range of -6% to 6%. These findings render 2D GaPS4 a promising candidate for the applications in nanoelectronics and low dimensional electromechanical devices.


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TOC GRAPHICS

Poisson’s ratio and Young’s modulus are important intrinsic characteristics of materials.1–3 Usually, most materials exhibit a positive Poisson’s ration (PPR), meaning the expansion (shrink) in the transverse direction will occur when a compressive (tensile) strain is imposed along the longitudinal direction. In contrast to PPR materials, the so-called auxetic materials demonstrate unusual negative Poisson’s ratio (NPR), attracting enormous attention recently due to their intriguing features such as enhanced toughness, shear resistance, enhanced sound, and vibration absorption.4 NPR is mainly observed in engineered three dimensional bulk structures,

3,5

while two dimensional

(2D) auxetic materials are rather rare. Till now, 2D auxetic materials are mainly divided into two categories, either with (i) in-plane NPR or with (ii) out-of-plane NPR. The inplane NPR 2D materials include B2N4/B4N2,6 penta-graphene,7 silicon dioxide,8 Be5C2,9

SiC6,10

W2C,11

Zn2C/Cd2C,12,13

Be2C,14


Carbon

dioxide,15

-


phosphorene/arsenic/graphene,16,17 group V-V binaries,18 1T-MX2 (M = Mo, W, Tc, Re; X = S, Se, Te),19 α-BeH2,20 graphene-related structure,21–23 and the recently predicted MB2 (M = Ti, Hf, V, Nb, Ta)24. On the other hand, 2D auxetic materials with out-ofplane NPR mainly cover black phosphorous,25,26 SnSe,27 borophene,28 borophane,29 TiN,30 BP5,31 and ABP2X6 (A = Ag, Cu; B = Bi, In; X = S, Se).32 Most of these materials possess reentrant or hinged geometric structures, which is believed to be the main reason for the auxetic behavior. But for 1T-MX2 (M = Mo, W, Tc, Re; X = S, Se, Te) and MB2 (M = Ti, Hf, V, Nb, Ta), the auxetic behaviors are determined by their distinct electronic structures.19,24 Very recently, Peng et al. 33 predicted a new single-layer Ag2S with bidirectional NPR for both in-plane and out-of-plane directions, which greatly broadened the scope of 2D auxetic materials. However, most of the 2D auxetic materials are based on theoretical crystal structure predictions, where the missing of corresponding 3D bulk counterparts may hinder their experimental preparation. Therefore, it is highly demanded to search for new 2D auxetic materials that are easy to obtain in experiments, such as by chemical vapor deposition (CVD), mechanical or liquid exfoliation, similar to that of 1T-MoS2 and black phosphorous. In this letter, we report an unexplored 2D material monolayer (ML for short) GaPS4, which gives rise to NPR for both in-plane and out-of-plane directions according to first-principles calculations. Specially, it can be produced from its unknown GaPS4 3D bulk, which shows remarkably weak interlayer interactions with a low cleavage energy of 0.23 J m-2. As monodirectional NPR is rarely identified in 2D materials, the 4 ACS Paragon Plus Environment

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special bidirectional NPR phenomenon is super rare, rendering ML GaPS4 an attractive auxetic material with potential applications in nanoelectronics and micromechanics. Our density functional theory (DFT) calculations were performed using planewave-based Vienna Ab initio Simulation Package (VASP).34,35 The generalized gradient approximation (GGA) within the Perdew-Burke-Ernzerhof (PBE)36 functional form was used for the exchange-correlation energy, and projector augmented-wave pseudopotentials37,38 were used to replace the core electrons. The screened exchange HSE06 hybrid functional39 was used to calculate the band structures in order to overcome the band gap problem of GGA-PBE. The plane wave energy cutoff was fixed to be 500 eV. The van der Waals interactions were corrected by the DFT-D3 approach.40 For all structural relaxations, the convergence criterion for total energy was set to 1.0×10-7 eV, and structural optimization was obtained until the HellmannFeynman force acting on any atom was less than 0.001 eV/Å in each direction. The 2D Brillouin zones were sampled using 12×8×1 k-point meshes within the Monkhorst– Pack scheme41 for the geometry relaxation, which were enlarged to 16×12×1 for electronic structure calculations. In order to minimize the undesired interaction between neighboring layers, a vacuum slab of 20 Å along the z-axis was introduced for the 2D monolayers. The phonon dispersion was obtained from the force constants by means of the PHONOPY code.42 Ab initio molecular dynamics (AIMD) simulations were performed to examine the thermal stability of the structures within the temperature range of 300 K to 1000 K, where NVT canonical ensembles were used. The layered GaPS4 single crystal was initially reported in 1973 by Buck et al.43 5 ACS Paragon Plus Environment


Experimentally, single crystal GaPS4 can be obtained under chemical transport in a temperature gradient from 650 to 600 °C, which facilitates its mass production. As shown in Figure 1a-1c, the symmetry for bulk GaPS4 is monoclinic with space group P21/c (No.14), and the unit cell consists of four GaPS4 formula units. The structure can be derived from a hexagonal close-packed arrangement of S atoms, stacking along the (100) direction. Our optimized lattice parameters of bulk GaPS4 are a = 8.354 Å , b= 7.844 Å, c = 11.950 Å and =133.17°, in good accordance with the experimental results (a = 8.603 Å , b= 7.778 Å, c = 11.858 Å and =135.46°).43 Bulk GaPS4 is a typical van der Waals crystal with interlayer distance d=2.744 Å and layer thickness h=3.355 Å, respectively. In addition, Ga and P atoms are each surrounded by four S atoms at the corners of a distorted tetrahedron. The coordination tetrahedra of Ga and P are adjacent and linked together by edge-sharing, where the details of bond angles are shown in Figure 1d. Due to this cation distribution, the S layers are slightly puckered and not so planar as in ideal hexagonal close packing. The bond lengths of Ga-S and P-S are around 2.306~2.338 Å and 2.064~2.073 Å, respectively (details listed in Table S1). Moreover, bulk GaPS4 is a direct wide gap semiconductor with the predicted band gap values of 2.06 eV and 3.18 eV at the PBE and HSE06 levels, respectively (see Figure S1).


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Figure 1. Optimized crystal structure of bulk GaPS4 with 2×2×2 supercell demonstrated along (a) b-direction, (b) a-direction and (c) c-direction, respectively. The unit cell is marked in light red squares. (d) The corresponding atomic structures of GaS4, PS4 and GaS4-PS4 in bulk GaPS4. The S atoms are marked by numbers and the bond angels (∠) of Ga-S, P-S and Ga-S-P are listed as well. Structures were plotted using the VESTA software. 44

ML GaPS4 in our calculation was obtained by taking an atomic layer from bulk 7 ACS Paragon Plus Environment


GaPS4 along the (100) direction, as shown in Figure 2a. ML GaPS4 exhibits a nearly rectangular configuration ( = 89.65°,  =  = 90°). The optimized lattice parameters are a =8.24 Å and b = 12.15 Å, respectively. The Ga-S bond length ranges from 2.306 Å to 2.338 Å, while the P-S bond length is between 2.065 Å and 2.073 Å, both slightly larger than that of bulk GaPS4 (see Table S1). Furthermore, the layer thickness of ML GaPS4 is h=3.415 Å, also slightly larger than that of bulk GaPS4 (h=3.355 Å). As bulk GaPS4 is a typical van der Waals crystal, for 2D GaPS4 preparation it becomes very necessary to evaluate the possibility of mechanical cleavage and liquid phase exfoliation, which are powerful techniques to produce single and few layer flakes from the layered bulk materials.45–47 Hence, we have estimated the cleavage energies of ML and bilayer (BL for short) GaPS4 from a five-layer GaPS4 slab, resembling the bulk (see Figure S2). In addition, the calculated cleavage energies of graphite and black phosphorus are also given as comparison, as shown in Figure 2b. Fairly low cleavage energies of 0.23 J m-2 and 0.24 J m-2 for ML and BL GaPS4 have been revealed, even lower than that of graphene (0.32 J m-2) and black phosphorus (0.37 J m-2). The DFTestimated exfoliation energies for some other layered materials such as InP3,48 TlP5,49 Tl2O,50 GeP3,51 and KTlO52 are 1.32 J m-2, 0.39 J m-2, 0.43 J m-2, 1.14 J m-2 and 0.56 J m-2, respectively. Since we are only aware of the experimental cleavage energy of graphene, we can only compare our calculated value (0.32 J m-2) with the reported experimental value (0.37 J m-2) for graphene53, and conclude that theoretical calculation is a feasible way for cleavage energy estimation. Therefore, exfoliation from the bulk is feasible for monolayer and few layer GaPS4 preparation, as its ultra-low cleavage 8 ACS Paragon Plus Environment

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energy is comparable with the graphene and several other related 2D materials.

Figure 2. (a) Top and side views of structurally optimized ML GaPS4. (b) Cleavage energy estimation for the formation of ML and BL GaPS4. (c) The calculated phonon dispersion spectra of ML GaPS4. (d) The evolution of total energy of ML GaPS4 from AIMD simulations at 300K, 500K, 800K and 1000K, respectively, within the time scale of 10 ps. The insets show the snapshots of GaPS4 at 1000K.

Subsequently, we discuss the dynamic stability of ML GaPS4 through its phonon dispersion, where the calculated results are illustrated in Figure 2c. Only a tiny imaginary phonon mode (1.3 cm−1) near the Γ point is found, which arises from the systematic computational error, suggesting that ML GaPS4 is dynamically stable. The 9 ACS Paragon Plus Environment


maximal frequency mode of ML GaPS4 reaches 583 cm-1, which is higher than that of MoS2 (473 cm-1)54 and phosphorene (∼450 cm-1)55. The AIMD simulations are further performed to check the thermal stability of ML GaPS4. Figure 2d shows that the ML GaPS4 structure remains intact up to 1000 K after a 10 ps simulation time, indicating very high thermodynamic stability. In addition, air stability of ML GaPS4, especially for oxygen (O2) and water (H2O), of ML GaPS4 at room temperature has been investigated using AIMD simulation as well. As shown in Figure S3, ML GaPS4 shows excellent stability in oxygen or water environment, suggesting its broad application scope. Furthermore, a stable 2D structure should satisfy the Born−Huang criteria,56 which can be expressed as C11C22  C122  0 and C66  0 , where Cij are the elastic constants. Here C11, C22, C12 and C66 represent Cxxxx, Cyyyy, Cxxyy, and Cxyxy, respectively, since by convention the Voigt tag indicates xx→1, yy→2, zz→3, yz→4, xz→5, and xy→6.57,58 The calculated values are C11 = 4.45 N m-1, C22 = 19.22 N m-1, C12 = 3.63 N m-1, and C66 = 4.71 N m-1 for ML GaPS4, thus fully satisfying the mechanical stability criteria. To confirm the accuracy of our method, we also calculated the elastic constants of phosphorene and ML SnSe for benchmark. Our results of C11 = 108.44 N m-1, C22 = 23.73 N m-1, C12 = 16.03 N m-1, and C66 = 22.67 N m-1 for phosphorene and C11 = 42.82 N m-1, C22 = 22.67 N m-1, C12 = 17.98 N m-1, and C66 = 17.30 N m-1 for SnSe agree well with the available theoretical values.18,33 The unique staggered network structure of ML GaPS4 may lead to intriguing mechanical performance. Therefore, it is of great interest to explore the mechanical behaviors of ML GaPS4 by calculating the in-plane Young’s modulus Y(θ) and 10 ACS Paragon Plus Environment

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Poisson’s ratio υ(θ) on the basis of the elastic constants. The Young’s modulus Y(θ) and Poisson’s ratio υ(θ) along the in-plane θ can be expressed as follows:33

C11C12  C122 Y ( )  (1) C11 sin 4   A sin 2  cos 2   C22 cos 4 

 ( ) 

C12 sin 4   B sin 2  cos 2   C12 cos 4  (2) C11 sin 4   A sin 2  cos 2   C22 cos 4 

where A  (C11C22  C122 ) / C66 -2C12 and B  C11  C22  (C11C22  C122 ) / C66 . The results are plotted in Figure 3a and 3b. The Young’s modulus Y(θ) of ML GaPS4 exhibits strong anisotropy following its anisotropic structure, implying different mechanical responses against the same level of strain from different directions. The Young’s modulus reaches its highest value of 16.26 N m-1 at θ = 90° and 270° (Y22), while the lowest value is 3.76 N m-1 at θ = 0° and 180° (Y11). The relatively small Young’s modulus indicates that ML GaPS4 is a soft material against deformation along both aand b-directions. It is noteworthy that the Young’s modulus of ML GaPS4 along the adirection is lower than that of most reported 2D materials, and comparable to the recently studied single layer Ag2S (2.78 N m-1) by Peng et al.33 Such a small value implies extraordinary flexibility of ML GaPS4 along its a-direction. On the other hand, Poisson’s ratio is defined as the ratio of the strain in the transverse direction to that of the longitudinal direction, reflecting the mechanical responses of the system against uniaxial strains. The Poisson’s ratio υ(θ) of ML GaPS4 also shows obvious anisotropy with the maximum value of 0.81 achieved along the b-direction, as shown in Figure 3b. Most remarkably, the rare NPR is obtained in ML GaPS4 along the diagonal direction and nearby areas, reaching its highest value of −0.033 at 46°, which identifies 11 ACS Paragon Plus Environment


GaPS4 as an in-plane auxetic material. This in-plane NPR value is comparable to that of tetra-silicene (-0.044, -0.055)59 and PN (-0.078),18 but lower than that of Ag2S (0.12),33 Be5C2 (-0.16), 9 AsN (-0.176),18 and δ-phosphorene (-0.267).16

(a) 18

90°

Negative 135°

0.6

9 6 3 0 180°

0°

3 6

45°

0.3

225°

15

0.0 180°

225°

z

6

y = -0.16x y= -0.88x-0.01x2

4 2 0 -2 -4 -6 -8

-6

-4

-2

0

x (%)

0.06

225°

(d)

y

8

2

4

6

0°

0.03

0.3

315° 270°

315°

0.9

270°

10

45°

0° 0.00 180°

0.6

315°

18

135°

0.03

9 12

90°

0.06

Resultant strain  (%)

Young's modulus

45°

Poisson's ratio

135°

12

(c)

(b) 0.9

90°

15

Resultant strain  (%)

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270° 10

x

8

z

6

y = -0.66x+0.02x2 y = 0.62x+0.02x2

4 2 0 -2 -4 -6 -8

-6

-4

-2

0

y(%)

2

4

6

Figure 3. (a) Young’s modulus and (b) Poisson’s ratio of ML GaPS4 as a function of the angle θ. θ = 0° corresponds to the a-axis. Negative Poisson’s ratio is represented with red solid line. (c) Mechanical response of ML GaPS4 under uniaxial strain along a-direction. (d) Mechanical response of ML GaPS4 under uniaxial strain along bdirection.

On account of its unique puckered structure consisting of distorted tetrahedra, the mechanical response of ML GaPS4 from the out-of-plane direction may bring about new functional opportunities. Thus, it urges us to explore the out-of-plane mechanical properties of ML GaPS4 extensively. Following the previous studies,30,33 a strain range of -6% to 6% is considered here to estimate the Poisson’s ratio. The response of ML GaPS4 lattice parameters or buckling height (thickness) to uniaxial strains are shown in 12 ACS Paragon Plus Environment

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Figure 3c and 3d. The strain is defined as ε = (l - l0)/l0, where ε involves εx, εy, εz, which correspond to the relative strains along the a-, b-, and c-directions, respectively; l = a, b represent the lattice parameter along the a- and b-directions under strain, while l = h represents the buckling height (or thickness) of ML GaPS4 under strain, respectively; l0 = a0, b0, h0 are the corresponding lattice constants and buckling height of ML GaPS4 without strain, respectively. The Poisson’s ratio can be obtained by fitting y = -ν1x + ν2x2 + ν3x3, where y and x indicate applied strain and resultant strain, and ν1 can be regarded as the Poisson’s ratio.25 From Figure 3c one finds that the lattice parameter y decreases linearly upon increasing the value of x, and vice versa, consistent with the inplane PPR along a- and b-directions analyzed above. PPR is also observed between xdirection and perpendicular z-direction, since the layer thickness z is subject to a decrease when enlarging the lattice parameter x. Nevertheless, as shown in Figure 3d, the layer thickness z surprisingly increases upon enlarging the lattice parameter y, indicating extremely large NPR between b-direction and the perpendicular c-direction. Such NPR reaches up to -0.62, much larger than that of α-phosphorene (-0.027)25 and SnSe (-0.17),27 and comparable to that of ML Ag2S (-0.52).33 Therefore, pronounced NPR properties have been predicted in ML GaPS4. We further examined this conclusion by including the Ga 3d electrons in the valence, and the results confirm that bidirectional NPR is the intrinsic characteristic of ML GaPS4 regardless of the pseudopotential selection. The details of the finer calculation considering Ga 3d semicore electrons are provided in Figures S4 and S5. NPR of the ML GaPS4 structure originates from the particular corner- and edge13 ACS Paragon Plus Environment


shared tetrahedra pucker structure. It can be explained by the rotation and dilation deformation mechanisms.60 When the compressive (tensile) strain (Figure 4a) is applied to the b-direction, the angle  decreases (increases) with the strain whilst the angle α is robust against the strain. Thus, in order to release the strain energy along the b-direction, the system will expand along the a-direction, leading a positive Poisson’s ratio (υ > 0, cf. Figure 3d). Nevertheless, the compressive (tensile) strain will lead the tetrahedral volume compression (expansion), as shown in Figure 4b, causing the atomic distance along the c-direction to decrease (increase). This leads to the unusual NPR phenomenon (υ < 0). And Figure 4c demonstrate that the atomic distances dx along the c-direction vary in two opposite manners, among the four non-equivalent S atoms. The distances d1 and d4 decrease as the strain increases, where d2 and d3 show the opposite trend. Since d2 and d3 tend to increase sharply upon applying stronger strains, their influence outweighs that from d1/d4. Hence, the overall atomic distance along the c-direction will increase when applying tensile strains along the b-direction, which is exactly the NPR effect. Moreover, the applied strain yields the rotation of GaS4/PS4 tetrahedra in the process. For an intuitive understanding, the crystal structures of (i) -6% compressive strained, (ii) unstrained, and (iii) 6% tensile strained ML GaPS4 are plotted in Figure 4d, 4e and 4f, respectively. One can observe the expansion (compression) along the a-direction under the uniaxial compressive (tensile) strain along the b-direction. We have also marked the direction of atomic movement using curved arrows. The rotation and dilation deformation mechanism was firstly raised by Alderson et al. 60, with application to the -cristobalite tetrahedral framework structure. 14 ACS Paragon Plus Environment

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Compared to -cristobalite that is linked by corner-sharing tetrahedra, the structure of ML GaPS4 is much more complex with both corner-sharing tetrahedra and edge-sharing tetrahedra. The edge-sharing tetrahedra make ML GaPS4 more tough and resistant to rotation deformation. Therefore, only a small in-plane NPR along the diagonal direction persists as the corner-sharing tetrahedra dominate. However, the low dimensional effect is prominent for the out-of-plane direction (without symmetry confinement), along which a larger NPR has been obtained.

Figure 4. (a) Bond angles of ML GaPS4 under uniaxial strains along the b direction. (b) The DFT-optimized volumes of GaS4 and PS4 tetrahedra in ML GaPS4 under 15 ACS Paragon Plus Environment


uniaxial strains along the b direction. (c) Atomic distances of ML GaPS4 under uniaxial strains along the b direction. The crystal structures of (d) -6% compressive strained, (e) unstrained and (f) 6% tensile strained ML GaPS4 are illustrated respectively. Here dx (x=1, 2, 3, 4) indicates the corresponding inter-atomic vertical distance between the two x atoms on the top and bottom. The four non-equivalent S atoms are marked by colors and numbers.

For electronic structures, our HSE06 calculation indicates that ML GaPS4 exhibits a 3.55 eV direct band gap (2.38 eV at the PBE level), with both the valence band maximum (VBM) and conduction band minimum (CBM) located at the -point, as shown in Figure 5a. The wide band gap may be useful for power electronics and light emitting devices. In addition, the VBM is dominated by S-3p orbitals, while the CBM is mainly composed of Ga-4s, P-3p and S-3p states, according to the partial density of states (PDOS) plotted in Figure 5b. Moreover, strong s-p hybridization is evidently shown in the PDOS, which tends to stabilize the GaPS4 structure. To further investigate the characteristic of charge distribution, we demonstrate the partial charge density in Figure 5c and 5d. The results can vividly reflect the orbital distribution of the band edges, in well agreement with the information observed in band structure and PDOS. In order to elucidate the changes in the electronic properties of GaPS4 from the bulk to few layers, we have investigated the electronic band gaps of 2D GaPS4 with varying number of layers. As shown in Figure S7, the electronic structures of 2D GaPS4 multilayers indeed strongly depend on the number of layers. For instance, the band gap 16 ACS Paragon Plus Environment

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increases from 2.06 eV (bulk) to 2.38 eV (ML). Interestingly, the direct band feature of GaPS4 is maintained from bulk to ML, similar to that of black phosphorous.61

Figure 5. (a) Electronic band structures of ML GaPS4 calculated using GGA-PBE and HSE06 without considering SOC. (b) Computed density of states of ML GaPS4. (c) The charge distribution corresponding to the VBM of ML GaPS4. (d) The charge distribution corresponding to the CBM of ML GaPS4. The charge contours are set to critical charge densities of 0.02 e Å-3.

We also estimated the carrier mobilities (both electrons and holes) of ML and BL GaPS4 based on the deformation potential (DP) theory proposed by Bardeen and 17 ACS Paragon Plus Environment


Shockley,62 in order to explore the application potential of ML and BL GaPS4 in electronic devices. The details for the calculations are provided in Figures S8 and Table S3. Our calculations indicate that BL GaPS4 possesses higher electron mobilities than its ML counterpart. The carrier mobilities of BL GaPS4 are 2142 cm2 V-1 s-1 for electrons and 160 cm2 V-1 s-1 for holes along the a direction. However, the mobilities are strongly direction dependent, as the value changes to 818 cm2 V-1 s-1 for electrons and 331 cm2 V-1 s-1 for holes along the b direction. For ML GaPS4, the carrier mobilities are 1306 (411) cm2 V-1 s-1 and 14 (906) cm2 V-1 s-1 for electrons (holes) along the a (b) direction, respectively, where the maximal values are however still comparable to that of MoS2 (~200 cm2 V-1 s-1).63 Last but not least, we further studied the effects of in-plane compressive/tensile biaxial and uniaxial strains on the band structures of ML GaPS4, since applying elastic strain is an effective means of band structure engineering in 2D semiconductors.64,65 Figure S9 presents the PBE-predicted band structures and band gaps of ML GaPS4 under different strains in the range of -6% to 6%. Surprisingly, ML GaPS4 maintains its direct band gap feature within the range of strains being considered (see Figure S9ac), which is very beneficial for optical applications. On the other hand, the gap value increases linearly with either compressive or tensile uniaxial strain along a axis. Nevertheless, for uniaxial strain along b direction, the gap value decreases gradually when varying the strain from -6% to 6% (Figure S9d). In addition, under the biaxial strain, the gap value increases linearly until up to 3%, and then decreases linearly. The variable responses to the strain in ML GaPS4 may be utilized in flexible electronics 18 ACS Paragon Plus Environment

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applications. In summary, we propose a novel 2D semiconductor GaPS4 as an interesting auxetic material for nanoelectronics and mechanic devices. Synthesis of its layered bulk semiconductor species has been known since the 1970s, and the predicted 0.23 J m-2 cleavage energy indicates that exfoliation from the bulk is highly possible to obtain monolayer GaPS4. Its stability is confirmed by the phonon spectra, AIMD simulations and elastic constants. Monolayer GaPS4 shows a direct wide band gap of 3.55 eV with remarkable negative Poisson’s ration in both in-plane (-0.033) and out-of-plane (-0.62) directions, which are extremely rare in the 2D world. In addition, ML and BL GaPS4 show moderate electron mobility. Energy gap characteristics of GaPS4 can be modulated by strain engineering, but the direct band gap feature is robust against the strain.

ASSOCIATED CONTENT Supporting Information Additional figures, tables, methodology, and references (PDF)

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (K.-H. Xue) ORCID Jun-Hui Yuan: 0000-0002-3892-604X Kan-Hao Xue: 0000-0002-2894-7912 19 ACS Paragon Plus Environment


Xiang-Shui Miao: 0000-0002-3999-7421

Notes The authors declare no competing financial interest.

Acknowledgements This work was supported by the National Key Research and Development Program of China (Materials Genome Initiative, 2017YFB0701700), the National Natural Science Foundation of China under Grant Nos. 11704134 and 61874146, and the Fundamental Research Funds of Wuhan City under Grant No. 2017010201010106. K.-H. Xue received support from China Scholarship Council (No. 201806165012) and the Hubei “Chu-Tian Young Scholar” program. The authors acknowledge support from Hubei Engineering Research Center on Microelectronics.

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Gallium Thiophosphate: An Emerging Bidirectional Auxetic Two

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