Electronic Structures and Li-Diffusion Properties of Group IVâV

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Electronic Structures and Li-Diffusion Properties of Group IV-V Layered Materials: Hexagonal Germanium Phosphide and Germanium Arsenide Fazel Shojaei, and Hong Seok Kang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07903 • Publication Date (Web): 20 Sep 2016 Downloaded from http://pubs.acs.org on September 22, 2016

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The Journal of Physical Chemistry

Electronic Structures and Li-Diffusion Properties of Group IV-V Layered Materials: Hexagonal Germanium Phosphide and Germanium Arsenide

Fazel Shojaei Department of Chemistry and Bioactive Material Sciences and Research Institute of Physics and Chemistry, Jeonbuk National University, Jeonju, Chonbuk 561-756, Republic of Korea and Hong Seok Kang* Department of Nano and Advanced Materials, College of Engineering, Jeonju University, Hyoja-dong, Wansan-ku, Chonju, Chonbuk 560-759, Republic of Korea

*Corresponding author: Hong Seok Kang; email: [email protected]; ☎ 82-63-220-2525

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ABSTRACT

Based on density functional theory (DFT) calculations that includes an empirical van der Waals interaction, we propose a layered hexagonal phase of bulk GeP and GeAs that is marginally less stable than monoclinic phase experimentally observed. Both types of monolayers are dynamically stable semiconductors. Application of 2% isotropic stretching along two in-plane directions practically transforms the GeAs monolayer into a direct-gap (= 1.60 eV) material, rendering it useful in optoelectronics. In addition, comparison of effective masses shows that the GeAs monolayer can function better as n-type materials, especially when it is subject to the in-plane strain. Furthermore, a detailed comparison of the activation barriers for the rate-determining steps along the different paths on the GeP surface indicates that the Li atom can diffuse on the surface ~ 1,000 times faster than on graphene. Another comparison of the barriers allows us to identify a preferred diffusion path in the interlayer region of bulk hexagonal GeP. The diffusion is expected to occur as fast as in graphite, suggesting that its bulk can be useful as an anode material in lithium ion battery.

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1. INTRODUCTION

As alternatives to the gapless graphene and the wide-gap boron nitride, other types of fewatom-thick two-dimensional (2D) materials have been extensively pursued for novel transistor applications. When MoS2 and WS2 are exfoliated down to a monolayer, they experience indirect-to-direct transitions of the band gap.1,2 A field-effect transistor (FET) based on the MoS2 monolayer exhibits an excellent on/off current ratio of ~108.3 The WS2 monolayer can be used in a tunneling transistor, in which current modulation exceeds 106 at room temperature for a very high ON current.4 Black phosphorene can also be exfoliated from black phosphorus into monolayers or bilayers.5,6 This material exhibits a direct band gap in the near IR region, depending on the number of layers.6 In addition, it possesses a high carrier mobility on the order of 103-104 cm2V-1s-1, which is more than one order of magnitude larger than that of MoS2 (~200 cm2V-1s-1).7,8 Specifically, black phosphorene monolayer exhibits anomalous elastic properties that reverse the anisotropy of the hole mobility.9 The energy barrier of Li diffusion (0.08 eV) is much shallower along the zigzag direction on the phosphorene monolayer, leading to an ultrahigh diffusivity.10 When used as an anode material in the sodium ion battery, few-layer phosphorene sandwiched between graphene layers shows a high specific capacity of 2440 mA/g at a current density of 0.05A/g.11

A theoretical proposal of hexagonal phosphorene, also known as blue phosphorene, triggered research on various layered materials derived from hexagonal phases.12 The material exhibits an indirect band gap of 2.76 eV, which is much larger than the 1.59 eV gap in black phosphorene.13,14 Its hole mobility is expected to be much larger than its electron mobility, indicating that the material will be hole-dominated.15 A calculation showed that other group V hexagonal materials of arsenene and antimonene display indirect band gaps of 2.49 and 2.28 eV, respectively.16 Specifically, hexagonal arsenene can be transformed from a spinnonpolarized semiconductor to a spin-polarized semiconductor, a half-metal, or even a metal.17 In binary group V monolayers of AsSb, a weak Rashba band splitting is expected to be introduced due to the asymmetric structure.18 Namely, there is an obvious band flip from 3



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the band states, which might find applications in spintronic devices. As group III-VI binary materials, ultrathin GaS and GaSe nanosheets were shown to be useful for photodetectors in the UV-visible region.19,20 Even hexagonal silicon was fabricated, which is stable up to 9 GPa. 21

Dynamically stable group II-VI semiconductors with hexagonal structures were also

predicted, such as ZnO, CdO, CaS, SrS, SrSe, BaTe, and HgTe.22 The quantum anomalous Hall phase can be achieved by rationally engineering the hexagonal structure of a newly synthesized covalent organic framework.23

In the bulk forms of IV-V monolayers of GeP and GeAs, the binary materials have been known to crystalize in the monoclinic (ML) phase, as evidenced by X-ray and Raman measurements.24-28 They are 2D layered materials stacked by van der Waals interaction. Their electric resistivity follows 2D-variable Range Hopping conduction.27They also exhibits highly anisotropic electric and thermal conductivities along in-plane and out-of-plane directions.28 Although little attention has been paid, there can be other kinds of bulk phases for the materials. In this work, we will propose that they can also exist in hexagonal phase based on the estimation of its relative stability with respect to the ML phase. In this regard, we want to mention that blue phosphorene is not merely a theoretical prediction. Although it is less stable than black phosphorene, its single layer was indeed synthesized via epitaxial growth.29 We will also investigate dynamical stability, electronic structures, and optical properties of the hexagonal GeP and GeAs. Furthermore, we will compare the Li diffusion properties in their bulk with that in graphite, because the latter material is not only cheap and chemically stable but also exhibits a high charge carrier mobility,30 a large surface area,31 and broad electrochemical windows.32

2. THEORETICAL METHODS

Geometry optimizations were performed using the Vienna ab-initio simulation package (VASP).33,34 The electron-ion interactions were described using the projector-augmented 4


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wave (PAW) method, which is primarily a frozen-core all-electron calculation.35 Attractive van der Waals interactions were included using Grimme’s correction for the PBE-D3 method.36 For structure optimization, atoms were relaxed in the direction of the HellmannFeynman force using the conjugate gradient method with an energy cut-off of 400 eV until a stringent convergence criterion ( of 0.01 eV/Å) was satisfied.

Lattice constants were optimized using the PBE-D3 exchange-correlation functional. Subsequent structure optimizations and band structure calculations were performed using the HSE06 functional.37 We maintained a sufficiently large vacuum space of 17 Å along the direction normal to the monolayer plane to ensure that no appreciable interactions occurred between two adjacent supercells. We defined the 2D layers to be located on the XY plane so that the Z axis is parallel to the c axis along which the layers are stacked. The k-point sampling was performed using a mesh of 21×21×1 points, which guarantees that the accuracy of the total energy less is than 1 meV. Phonon dispersion calculations were performed using the supercell finite-displacement method implemented in the PHONOPY package38, with VASP used as the force-constant calculator.39 Force evaluations were performed on 7×7×1 supercells using reduced k-point sampling meshes of 6×6×1 points. Nose-Hoover molecular dynamics (MD) simulations are performed in constant NVT systems for 5×5×1 supercells using k-point sampling meshes of 2×2×1 points with a time step of 1.0 fs.40-42

Neglecting local field effects, the imaginary part of the frequency-dependent dielectric matrix is determined from the equation:

ε αβ 2 (ω ) =

4π 2e 2 1 limq→0 2 ∑ 2wk δ (ε ck − ε vk − ω ) < uck +eα q | uvk >< uck +eβ q | uvk >* , (1) Ω q c ,v ,k

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where indices c and v refer to conduction and valence band states, respectively; wk is the weight of the k-point; and uck is the cell periodic part of the orbitals at the k-point. The real part of the tensor ε αβ 1 (ω ) is obtained from the Kramers-Kronig relation. The absorption coefficient is calculated from the relation:

α (ω ) =

2ω | ε (ω ) | +ε 1(ω ) , (2) c 2

2

2

where | ε (ω ) |= ε 1 + ε 2 .

3. RESULTS AND DISCUSSION

First, we investigate the relative stability of GaSe-like phase (H11) proposed by Hart et al.

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with that of the experimental ML phase. As shown in Figure 1(a), the H11 phase is

composed of H1 monolayers stacked along the c axis in the AA pattern. In the H1 monolayer, Ge1-P1 and Ge2-P2 bonds belonging to the upper and the lower sublayers of the monolayer are staggered with respect to each other, which is achieved by rotating one of them by 60° around the c axis. Therefore, the H11 phase does not adopt the hexagonal phase but a monoclinic phase. However, Figure S1 shows that the chemical structure of the phase is clearly different from that of the ML phase. For example, there are five-membered rings which consists of three and two Ge and P atoms in the latter phase, while this is not in the former.

For bulk GeP and GeAs, Table 1 shows that the H11 phase is less stable (by 0.02 and 0.03eV, respectively, from the PBE-D3 calculation) than the ML phase which they did not consider. We recall that our result is based on the PBE-D3 calculation, while Hart et al.43 relied on the PBE calculation without including van der Waals interaction. In the next paragraph, we will demonstrate that the relative stabilities (Erel) of various hexagonal phases 6


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indicate that another hexagonal phase (H21) is more stable than H11 by 11 and 9 meV/atom for GeP and GeAs, respectively. (Erel is defined with respect to the ML phase.) In its bulk form, Table 1 shows that it is less stable than the ML phase only by 13 and 24 meV/atom for GeP and GeAs, respectively, which is comparable to the corresponding energy difference (10 ~ 40 meV/atom) between bulk black phosphorus and blue phosphorus.13 We have made additional calculation on the relative stability of the ML and H21 phases using the fully ab inito TSMBD, which properly implements the long-range many-body nature of correlation and dispersion interactions.44,45 In the case of the GeP, Table S1 shows that the H21 phase is again marginally less stable than the ML phase. We recall that a nearly equivalent performance of the DFT-D3 and TS-MBD was also noted for graphene/Ni(111) system.46 This observation suggests that the hexagonal GeP and GeAs can be also experimentally synthesized by a proper method. Different from the case of the H1 layer, Figure 1(b) shows that, in each H2 layer of the H21 phase, Ge1-P1 and Ge2-P2 bonds belonging to different sublayers are exactly eclipsed. Here, the H2 layers denote monolayers that form the bulk H21 phase when they are stacked along the c axis.

To build the bulk phase, we have considered six different stacking patterns of the H2 layers. The H21 phase is characterized by the AB' stacking pattern, in which B' indicates that the B stacking is rotated by 180° with respect to the c axis. For GeP, this phase is marginally more stable (~3 meV/atom) than the H22 phase shown in Figure 1(c), which adopts the AB stacking pattern as in graphite. A comparison of the c constant for the two phases indicates that the AB' stacking is more compact than the AB stacking along the c axis. The H23 phase shown in Figure 1(d) is also less stable than the H21 phase by the same amount. This phase corresponds to the experimental γ phase of GaSe, where B" and C" in Table 1 represent the B stacking patterns rotated by 120° and 240° with respect to the c axis, respectively. The H24 phase shown in Figure S2(a) is even less stable; it corresponds to the β phase of GaSe with the AA' stacking pattern, where A' indicates the A stacking rotated by 180° with respect to the c axis. There were other less stable phases investigated in this work, which are built by 7



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stacking H2 layers, i.e., H25 and H26. [See Table 1 and Figures S2(b) and (c).] The H11 and H12 phases are also two of the least stable phases investigated: in the later phase, H1 layers are stacked in AB pattern. Table 1 shows that the relative stability of various H2 phases generally correlates with the interlayer distance, which is defined by the difference between the maximum and the minimum Z coordinates of the lower and the upper layers, respectively. The interlayer binding energies (Elayer = 53 and 65 meV/atom for H21 GeP and GeAs, respectively ) are slightly smaller than those for the ML phase and are comparable to that for graphite. Table 1 shows that the stability order of various phases for GeAs is similar to that for GeP, although the H23 phase is marginally more stable than the H22 phase. It may be more difficult to exfoliate bulk GeAs into monolayers because its interlayer interaction is larger than that for GeP.

Now, we turn our attention to the H2 monolayers. In Figures 2(a) and (b), our phonon calculation shows that there is no imaginary frequency in neither of the materials, and both are dynamically stable. Our MD simulation further demonstrates that the two kinds of monolayers remain chemically intact after 2ps even at elevated temperature (400 oK).

The a

constant (=b) is unaltered within 0.01 Å as the number of layers is reduced to one. For the GeP monolayer, the HSE06 band structure shown in Figure 3(a), indicates that it is a semiconductor with an indirect gap of 2.08 eV for the Κ '→ M and M' → M transitions, where Κ ' and M' denote the k-points located at 13% along the Γ → Κ and Γ → M paths, respectively. At the Κ ' and M' points, the valence band (VB) states are almost degenerate (< 1 meV) to each other. In addition, the VB is nearly dispersionless within 10 meV along the Κ' → Γ → M' path. Carrier mobility is expected to be anisotropic along different directions. In fact, Table S2 shows that the effective mass of holes ( mh * / me ≈ 1.7) along the Γ → Κ and Γ → M directions, respectively) is appreciably larger than that ( me * / me = 0.3 and 0.1 along the directions) of electrons, and the hole mobility will be lower than the electron mobility. Consequently, the carrier transport of the material can be dominated by electrons rather than by holes.

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For the GeP monolayer, Figures S3(a) and (b) show that the VBM( Κ ' ) represents π1 (Ge3P3) states hybridized with σ (Ge-Ge) states, where π1 (Ge3P3) indicates the lowest π state of the six-membered ring composed of Ge3P3 units with no nodal planes parallel to the c direction. [Here, we adopt a notation for the states of the ring similar to that for the π orbitals of benzene. One major difference is that an adjacent Ge-P pair is defined as having the same phase when the upper lobe of the pz(Ge) orbital can experience a bonding interaction with the lower lobe of the pz(P) orbital, not with the upper lobe of the latter. This is because the ring is puckered in such a way that Ge atoms are located below P atoms along the c axis.] The VBM( M' ) has a similar π character, because the M' point is close to the

Κ ' point in the 1st Brillouin zone. Figures S3(c) and (d) show that the conduction band minimum, i.e., CBM(M), corresponds to the π 4 (Ge3P3) state with two nodal planes. Figure 4 shows the absorption coefficient α (ω) of the GeP monolayer for the incident light polarized along the X (or Y) direction. Although the first peak at ~2.92 eV indicates that the absorption corresponding to the first direct gap at the Γ point is active, the material has much higher absorption in the UV region.

The HSE06 band structure shown in Figure 3(b) indicates that the GeAs monolayer exhibits a slightly smaller band gap (= 1.89 eV) than the GeP monolayer for the same indirect transitions. Again, Table S2 shows that the effective mass of holes ( mh * / me ≈ 1.8) along the Γ → Κ and Γ → M directions, respectively) is appreciably larger than that ( me * / me = 0.3

and 0.1 along the directions) of electrons, and carrier transport can be again dominated by electrons. In Figure 4, a comparison of its absorption coefficient with that of the GeP monolayer indicates that it has a higher absorption in the visible region. The first shoulder at ~2.45 eV corresponds to the VB-1( Γ ) → CB( Γ ) and VB-2( Γ ) → CB( Γ ) transitions. At the point, the two bands below the VB are degenerate, now representing the bonding and antibonding interactions of the σ states of the two sublayers. [Here, VB-n represents the (n1)th band below the VB.] Note that the corresponding transition (= 3.43 eV) occurs in the UV region for GeP, which appears as a shoulder in the absorption curve. A higher absorption shoulder of GeAs at ~2.85 eV seems to correspond to VB-3 → CB and VB-4 → CB transitions 9



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at the same k-point, where the two bands are also degenerate. We also recall that the CB( Γ ) and CB+1( Γ ) represent bonding and antibonding interactions of the highest π states, i.e., π 6 (Ge3X3) (X = P, As) states, belonging to different sublayers. Namely, π 6 (Ge3X3) is characterized by three nodal planes, as shown in Figures S3(e) and (f). In short, the GeAs monolayer displays a higher absorption than GeP in the visible region because (1) the π → π * transition corresponding to the direct gap (= 2.15 eV) of the former at the Γ point

is significantly smaller than that of the latter and (2) the σ → π * transitions for VB-n ( Γ ) (n = 1~4) → CB( Γ ) excitations are also active. It is quite easy to understand that the smaller direct gap can be ascribed to the lower electronegativity of As atoms than P atoms, considering that their VB( Γ ) and CB( Γ ) have π and π * characteristics of Ge3X3 rings, respectively.

For the GeAs monolayer, we note that the difference ( ∆Eg ) of 0.25 eV in the direct gap at the Γ

point and the indirect gap is appreciably smaller than the corresponding difference of 0.83

eV for the GeP monolayer. Therefore, it will be interesting to investigate the effect of inplane strain on its electronic structure. In fact, a comparison of Figures 5(a) and 5(b) shows that an application of 2% isotropic stretching along the two in-plane directions practically transforms the GeAs into a direct-gap (= 1.60 eV at the Γ point) material, while the GeP still remains an indirect-gap material. In this regard, we have already noted that the VB of the monolayer is nearly dispersionless (< 10 meV) along the Κ'→ Γ → M' path, when compared to thermal energy at room temperature. Therefore, the GeAs monolayer will be useful in optoelectronics, while the GeP will not. In addition, Table S2 shows that the electron mobility can be enhanced under the strain, because its effective mass ( me * / me = 0.1 along both of Γ → Κ and Γ → M directions) will be decreased from that at zero strain. Recalling that the material practically turns into a direct-gap semiconductor under the strain, the strained GeAs monolayer can be useful in semiconductor devices when used as an n-type material. Figure 4 indicates that the strained material exhibits red-shift in the absorption, displaying higher absorption in the visible region than at zero strain. Again, the first shoulder

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at 2.15 eV is originated from VB-1( Γ ) → CB( Γ ) and VB-2( Γ ) → CB( Γ ) transitions, and the second shoulder at 2.70 eV is due to VB-3 → CB and VB-4 → CB transitions.

Herein, we investigate the diffusion of a Li atom on the surfaces of the 3 × 3 monolayers. We can easily find that there are three different sites for the adsorption of a Li atom in Figure 6(a): the top of a Ge atom (GeT), the top of a hollow site at the center of a hexagon ring (HT), and the top of an X (= P or As) atom (XT). Table 2 shows that the adsorption energies (Ed) of the Li atom on GeP are -1.97, -1.92, and -1.48 eV at GeT, HT, and PT, respectively. For comparison, the GeT site is as favorable as the most stable site in phosphorene and MoS2,47,48 Our Bader charge analysis shows that there is almost a complete charge transfer from the Li atom to the monolayer. The Ed value on GeAs is ~0.2 eV smaller at each site. [Here, the chemical potential of a Li atom is taken from an isolated atom, and a negative value designates an exothermic process.]

Therefore, we can easily find that the diffusion will follow the GeT1 → HT1 → GeT2 path (P1) between different hexagons, as shown in Figure 6(a). [Here, superscripts 1 and 2 are used to distinguish between different but equivalent sites.] In fact, our nudged elastic band (NEB) calculation49 indicates that the activation barrier (Ea1) for three equivalent GeT1 → HT1 steps (S1) is 0.12 eV, as shown in Figure 6(b). The next step will be HT1 → GeT2 (S2) at 120° to the first step, for which the activation barrier of 0.07 eV is smaller. Therefore, the diffusion rate of the P1 path is determined by the barrier of step S1, which is appreciably smaller than the corresponding barriers of 0.31 and 0.23 eV for graphene and MoS2, respectively.47,48,50 For comparison, we note that the transition state is exactly located at the PT site for an alternative GeT1 → PT1 → HT2 path (P2) at 0° to the first step, and its activation barrier (Ea2) of 0.49 eV is much larger. In summary, the Li atom can diffuse on the GeP surface much faster than on graphene or MoS2 via the zigzag path of GeT1 → HT1 → GeT2. Diffusion on the GeAs monolayer is quite similar to that on the GeP monolayer, as discussed above. One minor difference is that the activation barriers for the corresponding steps are only 0.01 eV higher: Ea1 = 0.13 and Ea2 = 0.50. Estimating the diffusion coefficients (D) from the Arrhenius 11



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equation, i.e., D ~ e − Ea / kT , we can find that the diffusion on the GeP (GeAs) along the P1 path will be 1000 (700) and 70 (50) times faster than that on graphene and MoS2, respectively.

It is more informative to investigate the Li diffusion in the interlayer region of the bulk H21 crystals. Again, a three-dimensional supercell is adopted for one Li atom which consists of 3 × 3 × 1 primitive cells. We recall that the supercell contains two layers along the c direction

with an AB' stacking pattern: a Li atom is placed between the two layers. Upon structure optimization, the lithiation appreciably increases the c constant for the bulk GeAs. Namely, the constants are (15.16, 15.18) Å and (14.54, 15.21) Å for GeP and GeAs, respectively, where the two numbers inside the parentheses denote the values before and after lithiation. Table 3 shows that the adsorption energies (Ed) at two inequivalent sites are larger than those for the corresponding monolayers discussed in the previous paragraph. As expected, the energy is the largest at the GeT1GeT2 site, at which the Li atom is on top of two Ge atoms in different layers. [Here, subscripts 1 and 2 are used to distinguish atoms in different layers.] The Li-X (X = P or As) distances are slightly longer than those for the monolayers, and the positive charge on the Li atom is slightly smaller.

We first focus on the Li diffusion through bulk GeP. The PT1HT2 site, which is equivalent to the HT1PT2 site, designates that the Li atom is on top of a P atom of the one layer and on top of a hollow site of the other layer. It is less stable than the GeT1GeT2 site by 0.30 eV. As in the case of the adsorption on the monolayers, the Li-X distances are shorter than the Li-H (H = hollow site) distances. The positive charge on the Li atom is slightly smaller than that on the monolayer. Figure 6(c) shows two possible paths for the Li diffusion. Figure 6(d) shows that the diffusion along GeT11GeT21 → PT11HT21 step (S1B) is subject to the activation barrier of 0.33 eV, which is appreciably larger than that for the diffusion on the monolayer discussed above. The diffusion in the bulk phase is much more difficult than that on the monolayer. The next step (S2 B) will again be PT11HT21 → GeT12GeT22, for which there are three equivalent steps including the backward step to GeT11GeT21. Figure 6(c) indicates that the Li atom can 12


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diffuse along this step much faster than along the S1 step, because its barrier of 0.03 eV is much smaller. In short, the Li diffusion will follow a zigzag path (P1B) which consists of two steps S1B and S2B in sequence: GeT11GeT21 → PT11HT21 → GeT12GeT22, where the S1B is the rate-determining step. Again, we consider a straight path (P2B) alternative to P1B which consists of three steps (S1B, S2B', and S3B') in sequence: GeT11GeT21 → PT11HT21 → HT11PT21 3

3

→ GeT1 GeT2 . Note that two sites in step S2

B'

should be distinguished from each other,

although they are equivalent. In Figure 6(d), we find that the path is again much less favorable than the P1B because the barrier for the S2B' is 0.16 eV higher. In short, the Li diffusion in the bulk crystal will follow the zigzag path P1B, which is similar to that on the surface.

The diffusion through bulk GeAs is similar to that through GeP. However, the activation barriers for the S1B and S2B steps (= 0.42 and 0.09 eV) are 0.09 and 0.06 eV higher, respectively. The barrier for the S2B' step (= 0.60 eV) is still higher than that for the S2B step. In regard to this observation, we recall that a comparison of Tables 3 and 4 shows that the Ed values at various sites are much larger than those on the monolayer in the case of the GeAs system. This is less pronounced in the GeP system. For comparison, we have also calculated the diffusion barrier in the interlayer region of graphite. Figure S4(a) shows two possible steps for the Li diffusion on the 4×4 supercell, where the lattice constants (a = b = 9.88 Å) are comparable to those for GeP (a=b= 10.95 Å). As shown in Figure S4(b), the activation barrier for step H1 → H2 (S1G) is 0.33 eV, which follows the shortest path between two adjacent hollow sites. The diffusion along step S2G is subject to the barrier (= 0.35 eV) of a similar height, which can be an alternative to the next available hollow site through a C=C bond. Therefore, the Li diffusion in the graphite will follow a complicated path composed of the two steps. These observations indicate that the diffusion barriers in the GeP crystal are almost the same as those for the two paths in graphite. In another calculation, the barriers for the two paths are also comparable to each other, although their numerical values depend on 13



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the treatment of the van der Waals interaction.51 Considering that the barrier for the S1B is 0.33 eV, we can expect that Li atoms will diffuse in the interlayer region of the hexagonal GeP as fast as in graphite. On the one hand, the diffusion will be somewhat slower in the hexagonal GeAs, because the corresponding barrier (= 0.42 eV) is higher.

4. CONCLUSION

We have found that the H21 phase is the most stable for both bulk GeP and bulk GeAs among various hexagonal phases, in which two layers are stacked in the AB' pattern. The pattern is different from that of graphite in that the B layer is rotated 180° with respect to the c axis. The H21 phase is marginally less stable than the experimental ML phase (by 13 and 24 meV/atom for GeP and GeAs, respectively). The interlayer binding energies (~53 and 65 meV/atom, respectively) are slightly smaller than those for the ML phase and comparable to that for graphite. A comparison of the interlayer energy of the two materials suggests that it will be more difficult to exfoliate GeAs than GeP. Our phonon calculation shows that both types of monolayers are dynamically stable. Their monolayers are semiconductors with indirect gaps of 2.08 and 1.89 eV within the HSE06 calculation, respectively. Neglecting the local field effect, the GeAs monolayer is expected to display a higher absorption in the visible region. Application of 2% isotropic stretching along the two directions practically transforms the GeAs monolayer into a direct-gap (= 1.60 eV at the Γ point) material, while it still leaves as GeP an indirect-gap material. Therefore, the GeAs monolayer will be useful in optoelectronics, especially when it is subject to stretching. In both kinds of monolayers, carrier transport can be dominated by electrons, because the effective mass of electrons is appreciably smaller than that of holes. The GeAs monolayer can be useful in n-type semiconductor devices under the in-plane strain, since the strain can enhance the electron mobility.

A detailed analysis of the activation barriers for various paths shows that a Li atom can diffuse on the surface of the GeP (GeAs) monolayer about 1000 (700) and 70 (50) faster than on graphene and MoS2, respectively. The preferred zigzag path is a combination of steps 14


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connecting the top sites (GeT) of Ge atoms and the hollow sites (HT) at the center of a hexagon, i.e., GeT1 → HT1 → GeT2. A similar analysis displays that the diffusion in the interlayer region of their bulk crystals also follows a zigzag path (P1B) which consists of two steps S1B and S2B in sequence: GeT11GeT21 → PT11HT21 → GeT12GeT22, where the S1B is the rate-determining step. A comparison of the barriers for the rate-determining steps suggests that the Li diffusion in the GeP will occur as fast as that in graphite, while it can be slower in the GeAs. Hence, the bulk hexagonal GeP can be a better candidate than the bulk hexagonal GeAs for anode in lithium ion battery. We hope that our prediction would stimulate their experimental synthesis either in bulk or as monolayers.

Supporting Information. A full list of authors for Refs. 4, 19, 21 and 29; comparison of cell parameters and the relative stability of the H21 phase with those of the ML phase obtained from different methods (Table S1); comparison of the effective masses of electron and hole for the GeP and GeAs monolayers with those for black phosphorene (Table S2); two different views for the ML phase of GeP (Figure S1); less stable hexagonal phases of bulk GeP (Figure S2); two different views of the charge density plot of the GeP monolayer for the VBM at the Κ ' point, the CBM at the M point, and the CB at the Γ point (Figure S3); two possible diffusion steps of a Li atom in the interlayer region of the graphite (Figure S4).

ACKNOWLEDGMENTS This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) and funded by the Ministry of Education, Science and Technology (Grant NRF-2015R1D1A1A01057606). We would also like to thank Jeonju University for partial financial support.

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Table 1. Structural and energetic parameters for various hexagonal phases of bulk GeP and GeAs in comparison with those for the ML phase. Lengths are in Å units.

GeP

Phase

Stacking Pattern

MLa

-

H21 H22 H23

AB' AB

H24 H25 H26 H11f H12 MLa H21 H23 H22 H24 H25 H26 H11f H12

AB"C" (γ) AA'(β) AC' AA AA AB AB'

Cell Parameters

Erel(eV/atom)

15.05,3.68,9.17 β=99.9° 3.65,15.16 3.65,15.54 3.65,23.06 3.65,15.72 3.65,16.99 3.65,17.01 3.72,6.44 ,6.86 3.66,6.33,16.21 15.49,3.86,9.52 β=99.6° 3.81,14.54 3.81,23.47 3.81,15.62 3.81,15.86 3.81,17.25 3.81,17.24 3.89,6.74,7.14 3.81,6.61, 17.38

b

Elayer (eV/atom)

dlayerc

l (GeGe)d

l (GeX)e -

0.00

0.072

-

-

0.013 0.016 0.016

0.053 0.050 0.050

2.94 3.14 3.05

2.50 2.50 2.50

2.36 2.36 2.36

0.018 0.034 0.034 0.024 0.037 0.00

0.049 0.033 0.033 0.057 0.043

3.21 3.85 3.86 2.29 3.90

2.50 2.50 2.50 2.49 2.48

2.35 2.36 2.36 2.39 2.37

0.081

-

-

-

0.024 0.028 0.029 0.031 0.050 0.050 0.033 0.059

0.065 0.060 0.060 0.058 0.039 0.039 0.056 0.039

2.52 2.49 3.07 2.49 AB"C"(γ) AB 3.04 2.49 GeAs 3.15 2.49 AA'(β) AC' 3.84 2.49 AA 3.84 2.49 AA 2.48 2.49 AB 4.42 2.48 a The ML phase corresponds to the experimental monoclinic phase, and the β angle is also shown.

b

2.48 2.48 2.48 2.48 2.48 2.48 2.48 2.48

The relative energy is defined with respect to that for the monoclinic phase. Interlayer distance defined by the difference between the maximum and the minimum Z coordinates of the lower and the upper layers in the two adjacent layers, respectively. d Ge-Ge bond length belonging to the same layer. e Ge-X (X=P, As) bond length belonging to the same layer. f The GaSe-like hexagonal-like phase proposed in Ref. 43. c

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Table 2. Energetic and structural parameters for the adsorption of a Li atom on various sites of the 3 × 3 supercells of the GeP and GeAs monolayers.

GeP

Site GeT HT

Ed a −1.97

l(Li-X)b

q(Li)c

2.58

0.87

−1.92

2.59

0.88

PT

−1.48

2.35

0.90

−1.85

2.49

0.88

d

T1 GeT HT AsT T1d

-1.77 2.65 0.86 -1.72 2.66 0.87 GeAs -1.28 2.42 0.90 -1.65 2.56 0.88 a Adsorption energy of the Li atom. b Li-X distance. For the HT site, the distance to the center of a hexagon. c Bader charge of the Li atom. d Transition state configuration for the GeT → HT step.

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Table 3. Energetic and structural parameters for the adsorption of a Li atom at various sites of the interlayer region of 3 × 3 supercells for GeP and GeAs crystals in the H21 phase.

GeP

GeAs

Site GeT1GeT2 PT1 HT2

Eda −2.28

l(Li-X)b

q(Li)c

2.65

0.84

−1.98

2.31,2.49

0.82

HT1PT2

−1.98

2.49,2.31

0.82

T1d

−1.95 −2.44 −2.06 −2.06 −2.02

2.30,2.42

0.82

2.68 2.36,2.50 2.50, 2.36 2.34,2.44

0.83 0.81 0.81 0.82

GeT1GeT2 AsT1HT2 HT1AsT2 T1d

a

Adsorption energy of the Li atom. Li-X (X= P, As, H) distances. For example, two numbers represent Li-PT1 and Li-HT2 distances in sequence, where PT1 is the P atom on the first layer and HT2 is the center of a hexagon on the second layer. c Bader charge of the Li atom. d Transition state configuration for the GeT11GeT21 → PT11HT21 step (S1B). b

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Figure 1. Two different views for the H1 phase (a) and three most stable hexagonal phases of bulk GeP: H21 (b), and H22 (c), and H23 (d). The first Brillouin zone and points of special symmetry are also shown in (e). The green color represents the germanium (Ge) atoms. For better understanding, phosphorus (P) atoms belonging to different layers are distinguished from each other by different colors.

(e)

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Figure 2. Phonon dispersion curves for the H2 monolayers of GeP (a) and GeAs (b). (a)

(b)

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Figure 3. The HSE06 band structures of the H2 monolayers of GeP (a) and GeAs (b). (a)

(b)

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Figure 4. The frequency-dependent absorption coefficients of the H2 monolayers of GeP (dashed line) and GeAs (solid lines). For GeAs, the corresponding curve at 2% biaxial strain is also shown (red line).

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Figure 5. The HSE06 band structures of the H2 monolayers of GeP (a) and GeAs (b) at 2% biaxial stretching strain. (a)

(b)

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Figure 6. Various diffusion steps of a Li atom on the GeP monolayer (a) and in the interlayer region of the hexagonal GeP crystal (c). Corresponding activation barriers are also shown in (b) and (d), respectively. (a)

(b)

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(c)

(d)

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TOC Figure:

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Electronic Structures and Li-Diffusion Properties of Group IVâV

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