Band Gap Opening in 8-Pmmn Borophene by ... - ACS Publications

Article Cite This: ACS Appl. Electron. Mater. XXXX, XXX, XXX−XXX

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Band Gap Opening in 8-Pmmn Borophene by Hydrogenation Zhi-Qiang Wang,†,§ Tie-Yu Lü,† Hui-Qiong Wang,†,|| Yuan Ping Feng,*,§ and Jin-Cheng Zheng*,†,‡,|| †

Department of Physics and Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices and ‡Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen 361005, China § Department of Physics, National University of Singapore, Singapore 117542, Singapore || Xiamen University Malaysia, 439000 Sepang, Selangor, Malaysia

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S Supporting Information *

ABSTRACT: A first-principles calculation has been performed to explore the adsorption and dissociation of hydrogen on 8-Pmmn borophene. Different hydrogen adsorption sites, coverage, and dissociation reaction pathways have been considered. The results show that for one hydrogen atom adsorption the top site is the most stable adsorption site with an adsorption energy of 3.13 eV/H. Under high hydrogen coverage, the adsorption energy of hydrogen in BH1/2 is of the largest value (3.44 eV/H) among the five different hydrogen coverages (BH1/48, BH1/24, BH1/4, BH1/2, and BH3/4). Before the hydrogenation, 8-Pmmn borophene is a gapless semiconductor. Unexpectedly, BH1/4 and BH1/2 are both semiconductors. More specifically, BH1/4 is an indirect semiconductor with a 0.82 eV band gap while BH1/2 is a direct semiconductor with a 0.78 eV band gap. The band gap opening for 8-Pmmn borophene has been achieved by hydrogenation. Furthermore, the electronic band gap of BH1/2 is sensitive to mechanical strains, and more interestingly the direct to indirect band gap electronic phase transition in BH1/2 has been found under the three applied tensile strains. KEYWORDS: 8-Pmmn borophene, hydrogen adsorption, H2 dissociation, band gap opening, strain engineering

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INTRODUCTION Two-dimensional (2D) materials, such as graphene,1−8 BN,9 silicene,10,11 germanene,12 phosphorene, and transition metal dichalcogenides,13,14 have drawn lots of attention in the past decade. Because of the unique physical and chemical properties (like linear band structure near the Fermi level, high electrical, thermal conductivity, and its stiffness), 2D materials show vast application prospects in electronic devices. Recently, borophene was synthesized on Ag and Al substrates.15−17 Many theoretical studies on the mechanical properties, electronic structure, lattice thermal conductivity, superconducting properties, optical properties, magnetic properties, atomic adsorption, and surface reactivity of borophenes are reported.18−28 Four phases (2-Pmmn, β12, χ3, and honeycomb phases) of borophene that have been synthesized in the experiments are all metallic. It is reported that the fully hydrogenated 2-Pmmn borophene possesses a Dirac cone along the X-Γ direction in the Brillouin zone. In our previous study, another four more stable fully hydrogenated borophenes all possess a Dirac cone.29 To broaden the application of 2D boron-based materials for semiconductor devices, the band gap opening is crucial. Generally speaking, applying mechanical strain is an effective approach to achieved the band gap opening of 2D materials. The band gap opening of borophane is achieved by applying a shear strain.30 It is interesting that the shear strain can convert the gapless 8-Pmmn borophene into an indirect band gap semiconductor. Moreover, chemical adsorption is © XXXX American Chemical Society

another effective way to open the band gap of 2D materials. For example, hydrogenation can convert graphene, silicene, and germanene from a gapless semiconductor to a large band gap semiconductor. More specifically, the band gaps of chairlike configuration fully hydrogenated graphene, silicene, and germanene are 4.6, 4.0, and 3.6 eV, respectively.31−33 A natural question to ask is, can the band gap opening for 8Pmmn borophene be achieved by hydrogenation? By now, the effect of hydronation on the atomic and electronic structure of 8-Pmmn borophene is not clear. In this work, the band gap opening for 8-Pmmn borophene by hydrogenation has been investigated by first-principles calculations. Different adsorption sites and hydrogen coverage have been considered. Before the hydrogenation, 8-Pmmn borophene is a gapless semiconductor. However, the band gap has been opened by the hydrogenation. The band gaps of BH1/4 and BH1/2 are 0.82 and 0.78 eV, respectively. Furthermore, the band gap of BH1/2 can be tuned by external mechanical strains. It is interesting that the direct to indirect band electronic phase transition of BH1/2 under mechanical strains are observed. Moreover, the mechanical properties of hydrogenated 8-Pmmn borophene have also been studied. Received: January 10, 2019 Accepted: April 25, 2019 Published: April 25, 2019 A

DOI: 10.1021/acsaelm.9b00017 ACS Appl. Electron. Mater. XXXX, XXX, XXX−XXX

Article

ACS Applied Electronic Materials

Figure 1. Crystal structures of 8-Pmmn borophene: (a) top view, (d) side view; 8-Pmmn borophene with one hydrogen atom adsorption: (b) top view, (e) side view; 8-Pmmn borophene with one hydrogen molecule adsorption: (c) top view, (f) side view.

Figure 2. (a−c) Energy profiles of H2 dissociation on 8-Pmmn borophene along different reaction pathways. The crystal structures of the initial, transition and final state have been shown as illustrated. (d) H2 dissociation barrier and the energy difference ΔE between the initial and final state of the H2 dissociation reaction along reaction path 3 with different charge states.

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METHODOLOGY

on the 8-Pmmn borophene, the semiempirical DFT-D2 van der Waals interaction was included.

34

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The Quantum-Espresso package is used for all calculations. The ultrasoft pseudopotentials35 are used, and the exchange correlation is represented by the Perdew−Burke−Ernzerhof functional.36 The kinetic energy cutoff of plane waves is set as 50 Ry. The k-point mesh is 5 × 7 × 1 for the unit cell which contains 12 boron atoms and 3 × 3 × 1 for the supercell which contains 48 boron atoms. We fully relaxed the atomic positions, and the convergence criterion is 0.01 eV/Å. To eliminate the interlayer interactions, we add a vacuum layer (20 Å) in all models along the z-direction in our calculations. For the calculation of H2 molecule adsorption and dissociation

RESULTS AND DISCUSSION Hydrogen Atom Adsorption and Hydrogen Molecule Dissociation. First, we calculated the 8-Pmmn borophene with a single hydrogen atom adsorption on the 2 × 2 × 1 supercell that contains 48 boron atoms. Four different adsorption sites (B1, B2, B3, and T sites) that have been marked by the red characters in Figure 1a are considered. Our results show that the most stable adsorption site is the top site, and the adsorption energy is 3.13 eV. The adsorption energy is calculated using the formula B


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Figure 3. Crystal structures of borophane with different coverages of hydrogen: (a, d) BH1/4, (b, e) BH1/2, and (c, f) BH3/4.

borophene. The crystal structure of the final state is two hydrogen atoms coadsorbed on 8-Pmmn borophene. For the three initial states as shown in Figure 2, the adsorption energy is 64.2, 71.7, and 40.1 meV per H2 molecule, respectively. The dissociation energy barriers of the three different reaction pathways have been shown in Figure 2. The results show that the energy barrier along path 3 is much smaller than that along path 1 and path 2, indicating that the dissociation reaction along path 3 is much more favorable from the view of dynamics. The H2 dissociation reaction process on 2D materials can be tuned by the charge state. It has been reported that the H2 dissociation barrier on neutral 2-Pmmn borophene is 0.76 eV; however, the barrier can be reduced to 0.36 and 0.27 eV respectively under the one and two positive charge state.37 The effect of the charge state on the H2 dissociation barrier has been shown in Figure 2d. Under the neutral states, the dissociation barrier is 1.04 eV. However, under the 0.5, 1, and 1.5 positive charge states, the dissociation barriers are 0.86, 0.68, and 0.52 eV, respectively. From the view of dynamics, the dissociation reaction process can be accelerated under the positive charge state and suppressed under the negative charge state. From the view of thermodynamics, the energy difference ΔE between the initial and final state is increased under the positive charge state. Under the neutral case, the energy difference ΔE is 0.32 eV. However, under the 0.5, 1, and 1.5 positive charge states, the energy difference ΔE is 0.45, 0.53, and 0.60 eV, respectively, indicating that the thermodynamic driving force of the dissociation reaction is enhanced under the positive charge state. Hence, from both the view of dynamics and thermodynamics, the H2 dissociation reaction can be accelerated under the positive charge state. Hydrogen Atom Adsorption under High Coverage. Then the hydrogen adsorption under high coverage has been

Figure 4. Adsorption energies of hydrogen atoms under different hydrogen coverages.

Ead =

E(BHx) − E(B) − xE(H) x

(1)

where E(BHx) and E(B) are the total energy of 8-Pmmn borophene with and without hydrogen adsorption, respectively, E(H) is the total energy of an isolated hydrogen atom, and x is the ratio of the number of H and B atoms. After the H adsorption at the top site, the shift of the boron atom is 0.55 Å along the positive z-direction. However, for the two nearest B atoms of the B atom bonded with H atom, the shifts are 0.16 and 0.09 Å along the negative z-direction, respectively. The shift of the B atoms will lead to the change of the buckling height of 8-Pmmn borophene directly. The impact of H adsorption on the crystal structure is significant, which will lead to the change of the charge distribution and band structure. Then we study the dissociation of H2 on 8-Pmmn borophene. For the H2 dissociation process, the crystal structure of the initial state is the H2 molecule adsorbed on 8-Pmmn

Table 1. Lattice Parameter in Å, Buckling Heights dBuckling in Å, B−B Bond Lengths d1 and d2 in Å (Figure 1), B−H Bond Lengths d3 and d4 in Å (Figure 3), and Adsorption Energy Ead in eV/H

8-Pmmn BH1/4 BH1/2 BH3/4

a

b

dBuckling

d1

d2

d3

d4

Ead

4.50 4.53 4.50 4.56

3.24 6.37 3.14 4.37

2.19 3.54 3.33 1.91

1.60 1.69−1.71 1.72 2.52

1.64 1.61−1.69 1.76 1.85

1.20 1.20 1.22

1.34 1.35 1.30

3.40 3.44 2.94

C


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Figure 5. Deformation charge density distribution of (a, d) BH1/4, (b, e) BH1/2, and (c, f) BH3/4. Electron accumulation areas are demonstrated by the yellow isosurface, and electron depletion areas are demonstrated by the blue isosurface.

direction. A similar phenomenon has been reported in hydrogenated graphene38 and 2-Pmmn borophene.29 Furthermore, the changes of the B−B bond lengths have been calculated and are shown in Table 1. For 8-Pmmn borophene, bond length d1 is 1.60 Å. The bond lengths gradually increase with the increasing hydrogen coverage. For BH1/2, d1 is 1.72 Å. However, for BH3/4, the B−B distance d1 changes to 2.52 Å, indicating that the B−B bond has been broken. Hence, the full hydrogenation is irrational. To study the charge transfer between 8-Pmmn borophene and hydrogen, we calculated the deformation charge density of BH1/4, BH1/2, and BH3/4. The deformation charge density is defined as the formula Figure 6. Band structures of (a) 8-Pmmn borophene, (b) BH1/4, (c) BH1/2, and (d) BH3/4. The Fermi energy is set at 0 eV.

Δρ = ρ(BHx) − ρ(B) − ρ(H)

(2)

where ρ(BHx) is the charge density of hydrogenated 8-Pmmn borophene, ρ(B) is the charge density of borophene whose atomic coordinates are directly obtained from hydrogenated 8Pmmn borophene, and ρ(H) is the charge density of hydrogen whose atomic coordinates are also directly obtained from hydrogenated 8-Pmmn borophene. As displayed in Figure 5, the charge transfer between 8-Pmmn borophene and hydrogen atoms is from 8-Pmmn borophene to H atoms. From the view of electronegativity (2.2 for hydrogen and 2.04 for boron), the charge transfer result is rational. A similar phenomenon has been reported in hydrogenated 2-Pmmn borophene.29 Band Structures. To verify whether hydrogenation can open the band gap, we calculated the band structures of 8Pmmn borophene with and without hydrogen adsorption. The band structures of 8-Pmmn borophene, BH1/4, BH1/2, and BH3/4 are shown in Figure 6. 8-Pmmn borophene is a gapless semiconductor. However, BH1/4 is an indirect semiconductor with a 0.82 eV band gap. BH1/2 is a direct semiconductor, and the band gap is 0.78 eV. Because of the fact that PBE exchange functional underestimates the band gap, we provide the additional values of band gaps of BH1/4 and BH1/2 with hybrid functionals (HSE06). Under the HSE06 level, the band gap values of BH1/4 and BH1/2 are 1.42 and 1.67 eV, respectively. The band gap values under the HSE06 level are much larger than that under the PBE level. A similar phenomenon has been reported in chlorographene,39 fluorographene,39 and strained borophanes.19 The band gap of chlorographene under the PBE

calculated. Three different H/B ratios (1/4, 1/2, and 3/4) have been taken into consideration. The crystal structures of the most stable configuration are shown in Figure 3. The atomic structures and adsorption energies of different isomers of BH1/4 and BH1/2 are displayed in the Supporting Information (Figures S1 and S2). The adsorption energies of hydrogen under five coverages are shown in Figure 4. For BH1/4 and BH1/2, half of the H atoms adsorb on the top sites and the remaining half of H atoms adsorb on the B3 bridge sites. For BH1/4 and BH1/2, the adsorption energies of hydrogen are 3.40 and 3.44 eV/H, respectively. The adsorption energies of hydrogen in BH1/4 and BH1/2 are much larger than that in BH1/48, indicating that the interactions between H atoms and 8-Pmmn borophene are enhanced, which will lead to a more significant change in the electronic structure. However, for BH3/4, all the top site and the B3 bridge sites have been saturated by hydrogen; in other words, it is the fully hydrogenated 8-Pmmn borophene. The adsorption energy of hydrogen in BH3/4 is 2.94 eV/H, which is much smaller than that in BH1/2 and BH1/4, indicating that the fully hydrogenated 8-Pmmn borophene configuration is irrational. From the above analysis, we can find that the adsorption of hydrogen atoms will cause the B atom bonded with the hydrogen atom to shift along the positive z-direction and the neighboring B atoms shift along the negative zdirection. Hence, the hydrogen adsorption on the neighboring B atoms will suppress its movement along the negative zD


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Figure 7. Electronic band structure of BH1/2 under (a) a-direction and (b) b-direction uniaxial and (c) biaxial tensile strain. The Fermi energy is set at 0 eV. (d) Schematic drawings of the electronic structure phase transition of BH1/2 under εa, εb, and εBi. The blue, yellow, and green rectangles represent that BH1/2 is a direct semiconductor (DS), indirect semiconductor (IS), and metal (M) under the corresponding tensile strain.

Figure 8. Band gap (a) and stress (b) of BH1/2 under the stress-free state: εa, εb, and εBi.

Under the a-direction uniaxial tensile strain, when εa ≤ 0.09, the conduction band minimum (CBM) locates at the Γ point; however, when the εa increases to 0.11, the CBM shifts away from the Γ point. The valence band maximum (VBM) still locates at the Γ point. The shift of the CBM induces the electronic structure phase transition of the direct band gap to the indirect band gap. Similar electronic phase transitions also have been found under εb and εBi. As displayed in Figure 7b, a relatively small tensile strain (0.05) along the b-direction can shift the CBM away from Γ point and induce the direct to indirect band structure phase transition. The schematic drawings of the electronic structure phase transition of BH1/2 under the three applied tensile strains are shown in Figure 7d. A similar indirect band structure phase transition of BH1/4 under εa and εb has been found. The band structures of BH1/4 and BH3/4 under the three applied strains are shown in Figures S6 and S7. Furthermore, the band gap of BH1/2 under the three applied strains is shown in Figure 8a. Under εa, the band gap increases with the increasing strain when εa ≤ 0.09 and then decrease with the increasing strain. Finally, BH1/2 changes to be metallic when the strain increases up to 0.29. A similar

Table 2. PBE and HSE06 Level Band Gap (in eV) of BH1/2 under the Stress-Free State: 0.09 a- and b-Direction Uniaxial and 9% Biaxial Tensile Strain strain

PBE

HSE06

stress-free 0.09 a-direction uniaxial 0.09 b-direction uniaxial 0.09 biaxial

0.78 1.28 0.29 0.95

1.67 2.07 1.16 1.78

level is 1.41 eV; however, that value changes to 2.81 eV under the HSE06 level. For fluorographene, the band gap under the PBE level is 3.09 eV; however, under the HSE06 level, the band gap value is 4.93 eV. So far, we have successfully demonstrated that hydrogenation is a feasible approach to open the band gap of 8-Pmmn borophene. As we know, the band structure of 2D materials can be tuned by mechanical strain. Hence, the band structure of BH1/2 under a-direction (εa) and b-direction (εb) uniaxial and biaxial (εBi) tensile strains are calculated. The band structures of BH1/2 under the three applied strains are shown in Figure 7. E


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Table 3. Elastic Constants cij, Shear Modulus G, Young’s Modulus Y in N/m, and Poisson’s Ratio ν of Hydrogenated 8-Pmmn Borophene, 2-Pmmn, α Sheet, β12, χ3, and Pmmm Borophenes 40

8-Pmmn BH1/48 BH1/8 BH1/2 2-Pmmn40 α sheet40 β1240 χ340 Pmmm40

c11

c22

c12

c66 = G

Ya

Yb

νa

νb

249.00 250.00 230.00 243.00 398.00 219.00 185.50 201.00 333.50

322.50 296.50 235.75 219.50 170.00 219.00 210.50 185.00 576.00

15.50 14.50 14.63 16.50 −7.00 43.00 37.00 21.50 21.50

108.00 104.00 81.00 41.50 94.00 94.00 68.50 60.50 157.00

248.26 249.29 229.09 241.76 398.00 210.56 179.00 198.50 332.70

321.54 295.66 234.82 218.38 170.00 210.56 203.12 182.70 574.61

0.048 0.049 0.062 0.075 −0.040 0.196 0.176 0.116 0.037

0.062 0.058 0.064 0.068 −0.020 0.196 0.199 0.107 0.064

Figure 9. Polar diagrams for Young’s modulus (a) and shear modulus (b) of 8-Pmmn borophene, BH1/48, BH1/4, and BH1/2. The angle is measured relative to the a-direction.

parallel to the b-direction, we can find that the B−B bond lengths d1 and d2 are 1.60 and 1.64 Å, respectively; however, for BH1/2, the two bond lengths increase to 1.70 and 1.76 Å, respectively. Furthermore, in 8-Pmmn borophene, the two B− B bonds are parallel to the b-direction, but not in BH1/2. Because of the compensation of the B−B bond angles, the stress in BH1/2 will be less than that in 8-Pmmn borophene under the same b-direction uniaxial strain. Both of the two factors induce the decrease of the Young’s modulus along the b-direction. The polar diagrams for Young’s modulus and shear modulus of 8-Pmmn borophene, BH1/48, BH1/4, and BH1/2 are shown in Figure 9. The highly anisotropic shear modulus of BH1/2 has been found. The ratio of the largest and smallest shear modulus along the different direction is up to 2.58. However, for 8-Pmmn borophene, BH1/48, and BH1/4 the shear modulus is more isotropic.

tendency has been found for the band gap of BH1/2 under the biaxial tensile strain. However, under the εb, the band gap decreases and becomes zero when the strain is up to 0.15. The band gap value under the HSE06 level is listed in Table 2. Under the stress-free state, the band gap of BH1/2 is 1.67 eV. The band gaps under the 0.09 εa, εb, and εBi are 2.07, 1.16, and 1.78 eV, respectively. The band gap of BH1/2 can be tuned in a large range, from 0 to 2.07 eV, by mechanical strain. Then, we calculate the stress−strain curve of BH1/2 under the three applied tensile strains. The results are shown in Figure 8b. Under εa, the stress increases with the increasing strain until the strain is 0.15, beyond which the stress decreases. Under εb, the stress increases with the increasing strain until the strain is 0.17, beyond which the stress decreases sharply. When εb is 0.17, the stress is 21.85 N/m. However, the stress changes to 1.52 N/m when strain reaches 0.21, indicating the mechanical instability of BH1/2 once the εb reaches 0.21. The stress−strain curve under the biaxial strain is similar to that under the b-direction uniaxial strain. The ultimate strains along a-direction, b-direction, and biaxial direction are 0.15, 0.17, and 0.15, respectively. Mechanical Properties. The mechanical modulus of hydrogenated 8-Pmmn borophene, 2-Pmmn, α sheet, β12, χ3, and Pmmm borophenes are listed in Table 3. For 8-Pmmn borophene, Y a and Y b are 248.26 and 321.54 N/m, respectively. With the increasing hydrogen coverage, Yb decreases significantly. Yb of BH1/2 is 218.38 N/m. The reduced proportion is ∼32%. For the shear modulus, the reduced proportion from 8-Pmmn borophene to BH1/2 is ∼62%. From the view that the corresponding B−B bonds are

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CONCLUSIONS The adsorption and dissociation of hydrogen on 8-Pmmn borophene are studied. Different adsorption sites, hydrogen coverage, and H2 dissociation pathways have been considered. The adsorption energies of BH1/48, BH1/24, BH1/4, BH1/2, and BH3/4 are 3.13, 3.33, 3.40, 3.44, and 2.94 eV/H, respectively. The adsorption energy of hydrogen in BH1/2 is largest among the five different hydrogen coverages. Before the hydrogenation, 8-Pmmn borophene is a gapless semiconductor. However, BH1/4 and BH1/2 are both semiconductors. More specifically, BH1/4 is an indirect semiconductor with a 0.82 eV band gap and BH1/2 is a direct semiconductor with a 0.78 eV band gap. The band gap opening for 8-Pmmn borophene has F


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been achieved by hydrogenation. Furthermore, the electronic band gap of BH1/2 is sensitive to mechanical strains. The direct to indirect band gap phase transition has also been found under the three applied tensile strains. Furthermore, the mechanical properties of 8-Pmmn borophene and hydrogenated 8-Pmmn borophene have been calculated. Hydrogenation can decrease the b-direction Young’s modulus and the shear modulus of 8-Pmmn borophene.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsaelm.9b00017. Crystal structures of BH1/4 (Figure S1) and BH1/2 (Figure S2) with different configurations; phonon dispersions of BH1/2 under the a-direction (Figure S3) and b-direction (Figure S4) uniaxial and biaxial (Figure S5) strains; electronic band structures of BH1/4 (Figure S6) and BH3/4 (Figure S7) under the a- and b-direction uniaxial and biaxial strains (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Zhi-Qiang Wang: 0000-0003-4915-5727 Yuan Ping Feng: 0000-0003-2190-2284 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work is supported by the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) under Grant U1501501, and the National Natural Science Foundation of China (Nos. 51661135011). Z.W. thanks the financial support from the China Scholarship Council (No. 201706310088).

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