Multifunctional Binary Monolayers GexPy: Tunable Band Gap

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Functional Nanostructured Materials (including low-D carbon)

Multifunctional binary monolayers GexPy: Tunable bandgap, ferromagnetism, and photocatalyst for water splitting Pengfei Li, Wei Zhang, Dongdong Li, Changhao Liang, and Xiao Cheng Zeng ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b05655 • Publication Date (Web): 24 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018

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ACS Applied Materials & Interfaces

Multifunctional binary monolayers GexPy: Tunable bandgap, ferromagnetism, and photocatalyst for water splitting Pengfei Lia,†, Wei Zhangb,†, Dongdong Lic, Changhao Liang*a and Xiao Cheng Zeng*b,d,e a

Key Laboratory of Materials Physics and Anhui Key Laboratory of Nanomaterials and

Nanotechnology, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China. b

Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, P. R. China

c

School of Science and Engineering of Materials, Hefei University of Technology, Hefei, Anhui 230009, China

d

Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States e

Department of Chemical & Biomolecular Engineering and Department of Mechanical &

Materials Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States *Corresponding author. E-mail: [email protected] (Changhao Liang) [email protected] (Xiao Cheng Zeng) Keywords: Two-dimensional, semiconductor, band structure, ferromagnetism, water splitting

Abstract The most stable structures of two-dimensional (2D) GexPy and GexAsy monolayers with different stoichiometry (e.g., GeP, GeP2, GeP3) are explored systematically through the combination of the particle-swarm optimization (PSO) technique and density functional theory optimization. For GeP3, we show that the newly predicted most stable C2/m structure is 0.16 eV/atom lower in energy than the state-of-the-art P-3m1 structure reported previously (Nano Lett.2017, 17, 1833). The computed electronic band structures suggest that all the stable and metastable monolayers of GexPy are semiconductors with highly tunable bandgaps under the biaxial strain, allowing strain engineering of their bandgaps within nearly the whole visible-light range. More interestingly, the hole doping can convert the C2/m GeP3 monolayer from nonmagnetic to ferromagnetic (FM) due to its unique valence band structure. For GeP2 monolayer, the predicted most stable Pmc21 structure is a (quasi) direct-gap semiconductor that possesses high electron mobility of ~800 cm2V-1s-1 along the ka direction, much higher 1

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than that of MoS2 (~200 cm2V-1s-1). More importantly, the Pmc21 GeP2 monolayer not only can serve as an n-type channel material in field effect transistors (FETs), but also can be an effective catalyst for splitting water.

2


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1. Introduction Two-dimensional (2D) materials with one or few atomic layers are not only flexible and light in weight, but also may possess novel physical properties not seen in their bulk counterparts. For examples, graphene exhibits unique quantum Hall effect and Dirac-corn band structures1-5. But the gapless property of graphene hampers its application in optoelectronic nanodevices. Over the past decade, extensive efforts have been devoted to exploration and study of other 2D materials with desired band gaps, e.g., boron-nitride (BN)6, transition-metal dichalcogenides (TMDCs)7-12, and transition-metal trichalcogenides (TMTCs)13, 14, among others, which have been utilized or predicted as channel materials in FETs or as light-detector and light–emitting optoelectronic materials. Recently, germanene (monolayer germanium)15, phosphorene (monolayer black phosphorus)16-18 and arsenene (monolayer gray arsenic)19 have been successfully fabricated in the laboratory, or predicted to be stable from first-principles computation. The three elemental 2D materials exhibit graphene-like honeycomb lattice with distinct puckered structures. While germanene can only be stabilized on metal substrates, free-standing phosphorene obtained from exfoliation has been demonstrated to be stable.

For 2D materials, alloying has been often used to modify materials’ properties for expanding their applicability. For example, 2D MoS2xSe2(1-x) and WS2xSe2(1-x) nanosheets20,

21

exhibit

tunable electronic and optical properties with changing composition of the binary nanosheets. The theoretically predicted binary 2D compounds SixCy22, BxCy23 and BxSiy24 possess novel structural, electronic and mechanic properties, different from those of pure graphene, silicene, and borophene. Since 2D Ge, P and As monolayers have been fabricated in the laboratory, it is natural to explore new properties of the most stable 2D germanium phosphide/arsenide alloys (GexPy/GexAsy) with various stoichiometry.

In this work, we report a comprehensive search, on the basis of density-functional theory (DFT) optimization combined with the PSO algorithm25, of the most stable structures of 2D GexPy and GexAsy binary monolayers with the Ge/P or Ge/As ratio ranging from 3:1 (i.e., Ge3P) to 1:3 (i.e., GeP3). The exhaustive search yields a number of low-lying GexPy/GexAsy monolayer structures that exist only for y/x≥ 1. Electronic structure computation indicates that all the stable or metastable binary monolayers are semiconductors. In particular, the Pmc21 GeP2 monolayer is a (quasi) direct-gap semiconductor with a finite band gap (G0W0-Eg) of 2.23 eV in the green-light region. Furthermore, based on the deformation potential (DP) theory, the electron mobility of the most stable Pmc21 GeP2 monolayer along the ka direction is predicted to be as high as 800 cm2V-1s-1, much higher than that of MoS2 (~200 cm2V-1s-1)7. 3



The bandgaps of these stable GexPy/GexAsy binary monolayers can be tuned over a wide range, covering almost the entire visible-light region, through applying biaxial strains. We also find that the hole doping can convert the most stable C2/m GeP3 from nonmagnetic to ferromagnetic (half-metallic). 2. Computational methods The global-minimum structures of 2D binary germanium phosphide/arsenide is searched based on the PSO algorithm implemented in the CALYPSO package25. The basic settings for the PSO algorithm are given in our previous work26. To assure a thorough search of the global-minimum structure for different 2D monolayers, various simulation cells consisting of one to eight GexPy/GexAsy units are taken into account. DFT calculations are performed using the Vienna Ab-inito Simulation Package (VASP) 5.3.5 code27. The projector-augmented-wave (PAW) pseudopotential was utilized to treat 4s24p2 and 3s23p3/4s24p3 valence electrons for Ge and P/As, respectively. Specifically, the Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional28 within the generalized gradient approximation (GGA) is used for describing the electron interactions. The cutoff energy for the plane-wave basis set is set to 400 and 360 eV, respectively, for Ge-P and Ge-As systems. A dense enough k point sampling in the first Brillouin zone is chosen with energy tolerance in 1 meV/atom. Both the lattice constants and atomic positions are relaxed during the geometric optimization, with the force convergence of 0.01 eV/ Å and accuracy of 1 × 10-5 eV for electronic minimization. For electronic structure computation, more accurate G0W0 method and HSE06 functional are adopted. The van der Waals interaction is considered based on the Grimme’s DFT-D3 method29. Phonon dispersion of the predicted 2D structures are calculated through the cooperation of VASP package and the PHONOPY program30, to confirm their dynamic stability. The carrier mobility (µ) of 2D structures is calculated based on the deformation potential (DP) theory as proposed by Bardeen and Shockley31, which has been proven to be reasonable in estimating µ of 2D materials32, 33. On the basis of DP theory, the carrier mobility can be expressed as:

2 D 

2e3C 2 D 2

3kbT m E12

,

(1)

where C2D, T and m* represent in-plane stiffness, ambient temperature (300 K), and the effective mass of carrier, respectively. The DP constant E1 is denoted as the band edges shift induced by strain. Lastly, to examine catalytic activity, the climbing nudged elastic band 4


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(cNEB)34-36 method is used to determine the reaction pathway for H2 generation. 3. Results and discussion Through the PSO search, numerous low-energy 2D binary structures of GexPy and GexAsy are obtained. The lowest-energy or second lowest-energy binary structures of GexPy and GexAsy possess the same crystal structure, except for Ge2P and Ge2As (Cm vs P1). Since the predicted 2D binary GexPy and GexAsy monolayers with x/y>1 are located high above the convex hull by more than 100 meV/atom (see below), hereafter, we only focus on properties of the 2D binary GexPy and GexAsy structures with x/y≤1.As shown in Figure 1, all the predicted low-energy 2D structures satisfy the general electron counting rule, i.e., Ge atoms are four-fold coordinated, while P or As atoms are three-fold coordinated, following the sp3 hybridization.

Table 1. The lattice parameters and calculated formation enthalpy of the GexPy monolayers. GexPy monolayers P-6m2-GeP

P-3m1-GeP

Pmc21-GeP2

P-421m-GeP2

C2/m-GeP3

Lattice parameters

Space group

a=b=3.66 Å, c=18.55 Å

P-6m2

α=β=90º, γ=120º

No.187

a=b=3.67 Å, c=18.48 Å

P-3m1

α=β=90º, γ=120º

No. 164

a=3.53 Å, b=10.51 Å,

Pmc21

c=16.34 Å, α=β=γ=90º

No. 26

a=b=5.03 Å, c=18.02 Å

P-421m

α=β=γ=90º

No. 113

a=b=6.74 Å, c=13.52 Å

C2/m

α=β=90º, γ=126.97º

No. 12

5


Formation enthalpy -0.245 eV/atom

-0.231 eV/atom

-0.167 eV/atom

-0.152 eV/atom

-0.068 eV/atom


(a) P-6m2 GeP/GeAs

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(b)P-3m1 GeP/GeAs

(e) C2/m GeP3/GeAs3

(c) Pmc21 GeP2/GeAs2

(d) P-421m GeP2/GeAs2

Figure 1. Top and side views of the atomic structures of the predicted low-energy GexPy and GexAsy binary monolayers: (a) P-6m2 GeP/GeAs, (b) P-3m1 GeP/GeAs, (c) Pmc21 GeP2/GeAs2, (d) P-421m GeP2/GeAs2, (e) C2/m GeP3/GeAs3. The heavy pink spheres represent P (As) atoms, and light pink spheres represent Ge atoms. Phase Stability and Formation Enthalpy The relative stability of 2D germanium phosphide/arsenide compounds can be assessed by computing the formation enthalpies, based on the following equation:

H  [ H (Gex X y )  xH (Ge)  yH ( X )] /( x  y)

(2)

Where X represents P or As, and H is the enthalpy of a compound or a constituent element at a specific

pressure

(0

GPa).

Here,

the

experimentally

synthesized

germanene15,

phosphorene16-18 and theoretically predicted arsenene19 structures are used to compute element enthalpies of Ge (H (Ge)), P (H (P)) and As (H (As)), respectively.

6


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Figure 2. Computed formation enthalpy vs concentration (y) for GexPy binary monolayers. The ground-state convex hull is denoted by blue solid line. To validate phase stability of these 2D monolayers, we plot the convex hull of the formation enthalpy (see Figure 2 and Figure S1). As discussed in the previous studies37, 38, a phase whose formation enthalpy value is at the local minimum of the convex hull can likely be fabricated in the laboratory. As Figure 2 and Figure S1 show, four 2D compounds are located at the local minima of the convex hull, namely, the hexagonal P-6m2 GeP/GeAs and orthorhombic Pmc21 GeP2/GeAs2. The predicted most stable P-6m2 GeP has the lowest ΔH value of -0.245 eV/atom, and its structure can be viewed as having two kinds of orthogonal periodic chains: one puckered armchair and another puckered zigzag chains (Figure 1a), the same as the atomic structure of monolayer GaSe39. The P-3m1 trigonal phase (Figure 1b), which exhibits a similar structure as the P-6m2 hexagonal phase whereas with inversion symmetry, has slightly higher ΔH value (14 meV/atom) than the P-6m2 phase. When the P composition is further increased to 2/3, an orthorhombic GeP2 phase, located at the local minima of the convex hull, arises in the diagram. The lowest-energy phase has the Pmc21 symmetry with ΔH value of -0.167 eV/atom. As plotted in Figure 1c, the Pmc21 GeP2 phase can be viewed as a stack of two Ge-P and one P-P zigzag chains on the puckered hexagonal GeP monolayer. The second lowest-energy structure, P-421m GeP2, has a higher ΔH value (-0.152 eV/atom) than the Pmc21 structure. Interestingly, a GeP4 (GeAs4) tetrahedron can be viewed as a basic building block for the P-421m phase, as shown in Figure 1d. For GeP3, we find a new lowest-energy C2/m phase near the convex hull with ΔH value of -0.068 eV/atom which is much lower than that of the recently reported P-3m1 GeP340 (by 7



0.1 eV/atom). Compared with 2D GeP and GeP2, the C2/m GeP3 exhibits more complex structural characteristic with two building blocks: one puckered Ge2P6 octagon and one GeP4 pentagon (Figure 1e). The lattice parameters and calculated formation enthalpy of the predicted monolayers are listed in Table 1 and Table S1. Furthermore, to confirm the predicted 2D binary GexPy (GexAsy) structures are dynamically stable, phonon spectra are calculated based on the supercell frozen phonon theory implemented in PHONOPY program30 (see Figure S2). According to the phonon theory41, a solid structure with negative phonon frequencies would be unstable and tends to transform to a structure with lower energy. Clearly, most of the predicted 2D GexPy (GexAsy) structures possess positive phonon frequencies over the entire first Brillouin zones, except for the C2/m GeAs3 structure that exhibits a negative frequency of ~0.1 THz near the Г point. High thermal stability of semiconducting materials is also crucial for their potential applications in electronic devices. Here, thermal stability of the predicted lowest-energy GexPy (GexAsy) 2D binary phases are examined by using ab initio molecular dynamics (AIMD) simulations. Large enough supercells (6×6 for P-6m2 GeP; 6×2 for Pmc21 GeP2; 4×4 for C2/m GeP3) are used in three independent AIMD simulations at T=600, 800, and 1000 K, respectively. At each given temperature, the AIMD time step and total simulation time are 1fs and 10-12 ps, respectively. The total energy and kinetic energy versus simulation step, and the final equilibrium structures at T=600 K of each lowest-energy 2D phase are shown in Figure S3. For T = 600 K, no chemical bond rupture is observed, and the GexPy (GexAsy) monolayers almost keep their original equilibrium geometry. However, when the temperature increases to 800 or 1000 K, the monolayer structures start to break down and gradually lost their structure integrity. Thus, the predicted lowest-energy GexPy (GexAsy) 2D binary monolayers are thermally stable at least at 600 K, allowing their potential applications in nanoelectronic device at elevated temperatures.

Electronic and magnetic properties The computed PBE and HSE06 band structures, partial density of states (PDOS) and partial charge density of the 2D GexPy /GexAsy binary phases are plotted in Figure 3 and Figure S4, S5. As shown in Figure 3(a) and Figure S4 (a), the P-6m2 Ge is an indirect semiconductor with a band gap (PBE-Eg) of 1.37 eV (HSE06-Eg=2.05 eV). The valence band maximum (VBM) is contributed by the hybridized Ge 4p and P 3p orbitals, while the conduction band minimum (CBM) derives from the hybridized Ge 4s and P 3p orbitals. Apparently, the valence band dispersion of P-6m2 GeP near the Г point and Fermi level (EF) is quite flat, 8


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given rather high DOS and a van Hove singularity around the VBM. P-3m1 GeP exhibits similar band structures as the P-6m2 counterpart, but with a smaller PBE-Eg of 1.24 eV. It is known that direct-gap semiconductors usually enable better optoelectronic performance than indirect-gap semiconductors. The Pmc21 GeP2 exhibits (quasi) direct-gap semiconducting character (Eg(direct)-Eg(indirect)=8 meV) with PBE-Eg of 1.34 eV (HSE06-Eg=2.21 eV) (see Figure 3(b), Figure S4(b)). Its VBM is mostly attributed to P 3p orbitals, while CBM is mainly contributed by P 3p orbitals, and less contributed by Ge 4s orbitals. P-421m GeP2 is an indirect-gap semiconductor with PBE-Eg of 1.99 eV, the largest band gap among all the predicted 2D GexPy binary phases.

VBM

CBM

(a) P-6m2 GeP

VBM

CBM

(b) Pmc21 GeP2

VBM

CBM

(c) C2/m GeP3

Figure 3. Computed HSE06 electronic band structures and partial charge density of VBM and CBM of the lowest-energy GexPy binary monolayers: (a) P-6m2 GeP, (b) Pmc21GeP2, (c) C2/m GeP3, The Fermi level (horizontal dashed line) is shifted to 0 eV. As shown in Figure 3(c) and Figure S4(c), C2/m GeP3 exhibits indirect-gap semiconducting character with PBE-Eg of 1.74 eV (HSE06-Eg=2.45 eV). The VBM of C2/m GeP3 is located at the Г point while CBM is located at N point. The VBM is mostly contributed by P 3p orbitals and CBM mainly derives from the hybridized P 3p and Ge 4s orbitals. Similar to P-6m2 GeP, a flat-band dispersion character around VBM also arise for C2/m GeP3, resulting in very high density of sates and a van Hove singularity. To obtain a more accurate value of band gap of the predicted monolayers, we performed more accurate quasi-particle G0W0 computation. As shown in Table 2 and Table S2, the band gaps of the 9



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lowest-energy 2D GexPy/GexAsy based on the G0W0 computation are about 0.5-1.0 eV larger than those based on PBE calculations and slightly larger (0.02-0.28 eV) than those based on HSE06 computation. For example, the G0W0-Eg of P-6m2 GeP is 2.33 eV, 0.96 eV larger than the corresponding PBE-Eg.

Table 2. The band gap of the lowest-energy 2D GexPy binary phases based on GGA-PBE, HSE06 and G0W0 calculations. Structure/gap P-6m2 GeP

Pmc21 GeP2

C2/m GeP3

PBE

1.37 eV

1.34 eV

1.74 eV

HSE06

2.05 eV

2.21 eV

2.45 eV

G0W0

2.33 eV

2.23 eV

2.64 eV

Based on the Stoner criterion, spontaneous ferromagnetism can arise if the loss in kinetic energy is smaller than the exchange splitting energy, i.e., if the density of states at EF is high enough. Due to the very high DOS around VBM (Figure 3(c)), the C2/m GeP3 may satisfy the Stoner criterion if its EF is shifted to a position with high DOS through hole doping. To examine stability of spin polarization, the spin polarization energy (Ep), defined by the energy difference between the non-spin-polarized state and spin-polarized state, is computed. As expected, the calculation result suggests that the C2/m GeP3 may be converted into a ferromagnetic ground state beyond the critical hole density (nh) (nh=mh/Scell, mh is the number of holes introduced in the primitive cell. Scell is the area of the primitive cell), as shown in Figure 4(a). The spin moment exhibits a steep trapezium-like relationship with the hole density, which rapidly increases for nh>0.4×1013 cm-2 as the DOS at EF increases, eventually reaching a stable value of ~0.5 μB/hole for 1.1×1013 cm-21, where D(Ef) is the density of sates at the Fermi level Ef, and J represents the strength of the exchange interaction44. When the hole density is close to zero, the Fermi level is located just at the VBM, while the D(Ef) is close to zero as well, giving rise to no spin moment due to D(Ef)J < 1. When more holes are formed, the Fermi level moves into the valence band and the D(Ef) value increases, proportional to m*3/2 EVBM  E f (where m* is the hole effective mass, the quite flat band dispersion correspond to a large effective mass). When the hole density becomes large enough so that D(Ef)J >1, the system becomes spin polarized and the spin moment reaches a stable maximum value in a range of hole density. However, as the D(Ef) decreases sharply at a certain hole density, the spin moment also rapidly decreases.

(a)

(b)

Figure 4. Magnetic properties of the C2/m GeP3 monolayer. (a) The spin moments and polarization energies versus hole density nh. (b) The computed valence band structure of C2/m GeP3 at nh=1.35×1014 cm-2. The spin-down and spin-up bands are shown in blue and red, respectively. The Fermi level is set to be 0 eV.

It is also interesting to investigate strain effects on the electronic properties of the 2D GexPy/GexAsy structures. Here, we apply isotropic in-plane strain for all the predicted lowest-energy 2D GexPy/GexAsy structures, and uniaxial strain for the P-6m2 GeP. Figure 5 and Figure S6 present the dependence of the computed bandgap (PBE-Eg) upon the isotropic 11



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strain ε. The bandgap of GexPy monolayers are significantly modulated, and correlated nearly parabolically with the isotropic strain ε. For example, the bandgap of P-6m2 GeP decreases from 1.37 eV to 0.4 eV with increasing the tensile strain up to ε=8%, first increasing from 1.37 eV to 1.46 eV for ε≥-2%, followed by decreasing from 1.46 eV to 0.49 eV for ε≤-2%. Considering the bandgap increment of about 0.5-1.0 eV based on the G0W0 computation, the range of tunable bandgap by in-plane strain almost covers the entire visible-light region. Through analysis of the band structure of P-6m2 GeP in rectangle supercell, we speculate that the two bands (one conduction band and one valence band) closest to Fermi level can be changed significantly along Г→X or Г→Y under uniaxial strain along x or y direction. Indeed, the flat band along Г→X is depressed and the energy of the lowest conduction band at the Г point is lowered with increasing the compressive strain along x direction, leading to indirect-to-direct transition at the compressive strain of εx=-4% (see Figure 5 (a), (b) and (c)), a useful feature for potential applications.

(a)

(b)

(c)

εx=0

(d)

εx=-2%

εx=-4%

Figure 5. Strain dependent electronic properties of 2D GexPy. (a) The bandgap of GexPy versus the in-plane biaxial strain. Computed band structure of P-6m2 GeP in rectangle supercell at a strain value of (b) εx=0, (c) εx=-2% and (d) εx=-4%. The Fermi level is shifted to 0 eV.

2D materials can also exhibit layer-number dependent electronic properties due to the van der Waals interaction between layers. Here, we choose P-6m2 GeP as an example to investigate the dependence of bandgap on the number of layers (N). Similar as 2D GaSe39, the P-6m2 GeP layers can also form four types of bulk crystal, i.e. β-, ε-, γ-, δ-GeP, according to different stacking sequence. The energy of the four types of GeP bulk crystals are almost degenerate. Figure 6 (a) shows the PBE-Eg of β stacking GeP layers (P63/mmc, inset of Figure 12


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6 (a)) versus N. Interestingly, as N increases, the bandgap is almost linearly decreased from 1.37 eV to 0 eV (negative Eg). The band-structure computation (Figure 6(b)) shows that as N increases, the CBM (M points) is shifted downward to the Fermi level and finally crosses the Fermi level at N=6, resulting in the semiconductor-to-metal transition. Moreover, our calculations show that this layer-number dependent semiconductor-to-metal transition is robust and generally exists in the other three types of GeP multilayers. The layer-number dependent Eg is much stronger than that observed for TMDs and phosphorene8, 45, 46, which can be desirable for applications that requests the semiconductor-to-metal transition.

(a)

(b)

Figure 6. (a) The computed bandgap of P-6m2 GeP versus the number of layers. Inset: a side view of the structure of bulk β-GeP. (b) The CBM and VBM band structures for different layers, i.e. blue (N=1), cyan (N=2), green (N=3), brown (N=4), yellow (N=5) and red (N=6).The Fermi level is shifted to 0 eV.

The effective masses of electron and hole associated with the (quasi) direct semiconducting Pmc21 GeP2 monolayer are also computed. As a comparison, the effective mass of electron and hole associated with MoS2 monolayer47 are also listed (see Table 3 in Figure 7). To gain more insight into the band structure near Fermi level, the 3D band structures around the VBM and CBM are plotted in Figure 7(a), where the drift of electron and hole along ka and kb directions is marked by gray lines. Interestingly, the effective mass of electron in ka direction (0.14 me) is much smaller than that in kb direction (1.29 me), indicating the easy drift of electrons in ka direction. However, the holes entail an effective mass of ≈1.54/0.38 me (ka/kb), suggesting easy drift of holes in kb direction. By fitting the change of total energy (E) versus the uniaxial strain (ε), as shown in Figure 7 (b), the in-plane stiffness 13



C2D (= ( 2 E /  2 ) / S0 , S0 is the area of 2D monolayer) along a and b direction are evaluated to be 106.3 and 14.6 N/m, respectively, showing high elastic anisotropy. The absolute DP constant E1 (=dEedge/dε) for electrons along a and b direction are calculated to be 10.0 eV and 4.0 eV, respectively. According to the calculated effective mass m*, C2D and E1, the electron mobility can be evaluated based on equation (1). Surprisingly, the electron mobility in ka direction can be as high as ~800 cm2V-1s-1, much higher than that of MoS2 (~200 cm2V-1s-1 in experiments7 and ka~80 cm2V-1s-1 and kb~140 cm2V-1s-1 from our DFT computation). In contrast, the electron mobility is just about ~8 cm2V-1s-1 in kb direction. Therefore, in view of the highly anisotropic electron mobility, accurate control of current direction is required when involving fabrication of high-performance electronics or optical devices based on the Pmc21 GeP2 monolayer.

(a)

Table 3 Pmc21 GeP2

MoS2

me* (me)

0.14 (ka) 1.29 (kb)

0.49 (ka) 0.47 (kb)

mh*(me)

1.54 (ka) 0.38 (kb)

0.55 (ka) 0.62 (kb)

(b)

εa εb

Figure 7. (a) Surface plot of valleys around VBM and CBM for the Pmc21 GeP2 monolayer. Calculated effective mass of electron and hole for Pmc21 GeP2 and MoS2 are listed in Table 3, where the ka and kb refer to Г-X and Г-Y directions, respectively. (b) The energy of Pmc21 GeP2 monolayer versus uniaxial stain.

GeP2 monolayer as photocatalyst for water splitting. As shown above, the (quasi) direct semiconducting Pmc21 GeP2 monolayer has a G0W0 band gap of 2.23 eV, a value within the visible-light region. Hence, the monolayer could be a potential photocatalyst for water splitting, if suitable band-edge alignment is met, i.e., its 14


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CBM energy is higher than the reduction potential of H+/H2 and its VBM energy is lower than the oxidation potential of O2/H2O48, 49. Here, the standard water redox potential in previous studies50, 51 is adopted for discussion. Due to the high computational cost of GW computation, the band-edge alignment of the Pmc21 GeP2 monolayer under various biaxial strains (from -4% to 4%) is computed on the basis of HSE06 functional, as the HSE06-Eg of strain-free Pmc21 GeP2 monolayer is 2.21 eV, very close to the G0W0-Eg of 2.23 eV. It can be shown that the CBM energy of the strain-free Pmc21 GeP2 monolayer is -3.82 eV, ~0.62 eV higher, respectively, than the H+/H2 reduction potential (see Figure 8). With increasing the tensile (compressive) strain, the CBM level moves downward (upward) and gets close to (away from) the H+/H2 potential. However, the CBM level of the monolayer is still located ~0.09 eV above the H+/H2 potential, even at a strain up to 4%. Meanwhile, the strain induced variation of the VBM level ensures the alignment of the VBM below the H2O/O2 potential, except in the case of ε=-4%. Hence, for the Pmc21 GeP2 monolayer under the biaxial strain from -3% to 4%, suitable band-edge alignment ensures the redox potential of water splitting being located within the band gap, thereby allowing wide overlap with visible light from green-to-red region. Such a desirable band-edge alignment renders the Pmc21 GeP2 monolayer a possible effective visible-light-driven photocatalyst for water splitting reaction.

-3.82

H+/H2

H2O/O2 -6.03

Figure 8. Band alignment, calculated at the HSE06 level, of the Pmc21 GeP2 monolayer. The dashed lines represent the redox potential of water splitting reaction with respect to the vacuum potential level.

To gain deeper insight into the mechanism of water splitting reaction on the Pmc21 GeP2 monolayer, we computed the water-splitting reaction pathway by using the climbing nudged elastic band (cNEB) method with consideration of van der Waals interaction. Note that there 15



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are two kinds of P atoms (namely, P1 and P2) and one kind of Ge atom in the surface of the Pmc21 GeP2 structure (Figure S7). To characterize the H2O splitting reaction on Pmc21 GeP2, we explore all the possible adsorption sites for the H2O molecule. Table 4 lists all possible adsorption sites and corresponding adsorption energies. It turns out that the adsorption energies of H2O on different adsorption sites on the Pmc21 GeP2 surface are very close, within the range of -1.89 eV～-0.22 eV. Note also that the adsorption energy of H2O on the Pmc21 GeP2 surface is very small, compared to the adsorption energy of the reaction intermediate in H2O splitting reaction (Table 4). Besides H2O molecule, we also optimized the OH group, and O and H atoms in various adsorption configurations on the Pmc21 GeP2 monolayer. P2 is the most favorable site for the adsorption of OH group, O and H atoms, and their adsorption energies are -3.16 eV, -2.09 eV, and -2.42 eV, respectively. Based on the difference between the H2O and the reaction intermediate (OH, H, and O), we can confirm that 2D GeP2 is a good catalyst for the H2O splitting.

Table 4. The adsorption site and corresponding adsorption energy of O, H, OH, and H2O (“/” denotes non-existent, and “U” denotes unstable). H2O -OH -O

Ge -0.204 -2.647 -1.845

P1 -0.189 -2.648 -1.618

P2 -0.199 -3.156 -2.092

Ge-P1 -0.190 -2.526 U

P2-P2 -0.192 U U

-H

-2.417

-2.627

-2.688

/

/

Figure 9. Calculated relative energies and the most favorable reaction pathway for H2 16


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generation via H2O splitting on the Pmc21 GeP2 monolayer. Here, * refers to adsorption site on the monolayer.

Using the most stable structures as reactants, we explore the water-splitting reaction pathway52. The reaction pathway and potential energy surface of water-splitting reaction are shown in Figure 9. The most favorable adsorption sites of OH molecule, and O and H atoms are at the P2 site. As such, we choose the P2-H2O structure as the initial state for the H2O splitting reaction. Because of the interaction between the O atom and the P atom, the O-H bond of H2O becomes weaker, which facilitates the splitting of water. The barrier for the first H splitting from H2O is 1.93 eV, and this reaction process is an endothermic reaction. It follows that the dissociated H atom can react with the H atom of OH adsorbed on P atom to form the H2 molecule. In this process, the H2 molecule can directly form, with 3.09 eV reaction barrier. This reaction barrier for the H2 formation is quite high on GeP2 surface. Therefore, we suggest a use of photo excitation to excite electron to a higher electronic state to overcome the reaction barrier. 4. Conclusion In conclusion, we have identified several most stable and metastable GexPy (GexAsy) monolayers with the ratios of x:y=1:1, 1:2 and 1:3, based on the PSO algorithms combined with DFT optimization. Phonon spectra calculations and AIMD simulations confirm that all the predicted 2D monolayers are dynamically and thermally stable. Electronic band structure calculations show that all the predicted monolayers are semiconducting with highly tunable bandgap under the biaxial strain. Besides, these multifunctional monolayers also possess novel electronic and magnetic properties: (i) The P-6m2 GeP monolayer exhibits interesting layer-number dependent semiconductor-to-metal transition. (ii) The Pmc21 GeP2 monolayer possesses very high electron mobility of ~800 cm2V-1s-1 along ka direction, much higher than that of MoS2 (~200 cm2V-1s-1). (iii) Hole doping can convert the ground state of C2/m GeP3 from a nonmagnetic state to a ferromagnetic (half-metallic) state, due to its unique valence band structure. Finally, the computed water splitting reaction pathway suggests that Pmc21 GeP2 monolayer can be a promising photocatalyst for the H2O splitting. These desirable properties of the multifunctional 2D GexPy (GexAsy) materials provide promising opportunities for diverse application in electronics, spintronics and catalysis.

Acknowledgments

17



This work was financial supported by the National Basic Research Program of China (No.2014CB931704), the National Natural Science Foundation of China (NSFC, No.11604320, No. 51371166, No.51571186). X.C.Z. was supported by US NSF through the Nebraska Materials Research Science and Engineering Center (MRSEC) (grant No. DMR-1420645) and by UNL Holland Computing Center.

Supporting information Formation enthalpy vs concentration (y) for GexAsy binary monolayers (Figure S1). The phonon spectra and MD simulations of the GexPy and GexAsy monolayers (Figure S2-S3). The PBE electronic band structures of the GexPy and GexAsy monolayers (Figure S4-S5). The band gaps of GexAsy monolayers versus the in-plane biaxial strain (Figure S6) and the possible adsorption sites for H2O and OH group, and H atom on the Pmc21 GeP2 monolayer (Figure S7). The lattice parameters and calculated formation enthalpy of the GexAsy monolayers (Table S1) and the bandgap of the lowest-energy 2D GexAsy structures, based on GGA-PBE and G0W0 computation (Table S2).

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Multifunctional Binary Monolayers GexPy: Tunable Band Gap

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