Tuning Electronic Properties of Germanane Layers by External Electric

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Tuning Electronic Properties of Germanane Layers by External Electric Field and Biaxial Tensile Strain: A Computational Study Yafei Li*,† and Zhongfang Chen*,‡ †

College of Chemistry and Materials Science, Jiangsu Key Laboratory of Biofunctional Materials, Nanjing Normal University, Nanjing, Jingsu 210046, China ‡ Department of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico, Rio Piedras Campus, San Juan, PR 00931, United States S Supporting Information *

ABSTRACT: Comprehensive density functional theory computations with van der Waals (vdW) correction demonstrated that there exists strong hydrogen bonding between twodimensional (2D) germanane layers. Especially, germanane layers all have a direct band gap, irrespective of stacking pattern and thickness. The band gap of germanane bilayer can be flexibly reduced by applying an external electronic field (Efield), leading to a semiconducting-metallic transition, whereas the band gap of germanane monolayer is rather robust in response to E-field. In contrast, the band gaps of both germanane monolayer and bilayer can be reduced to zero when subjected to a biaxial tensile strain. These results provide many useful insights for the wide applications of germanane layers in electronics and optoelectronics.

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INTRODUCTION In a rather long time it was believed that a strictly twodimensional (2D) crystal is physically impossible. The successful isolation of graphene, a single layer of graphite, by Geim and Novoselov et al. in 2004,1,2 totally refreshed our minds. The past decade has witnessed the rise of graphene as one of the hottest stars in materials science due to its unique properties and wide applications in various fields.3−8 Just similar to the case of inorganic fullerenes and nanotubes,9−12 such planar structure is not limited to carbon. In recent years, more and more inorganic layered materials, including boron nitride (BN)13−16 and transition-metal dichalcogenides (TMD)17−19 have been mechanically or chemically exfoliated into monolayer or few layers, and have been well investigated.20−26 Similar to graphene, these 2D materials also present different properties from their bulk phases. For example, bulk MoS2 is a well-known semiconductor with an indirect band gap (1.29 eV), whereas its monolayer structure has a direct band gap of ∼1.80 eV,27 which would facilitate the application in optoelectronics. More interestingly, some monolayer structures that were once considered to be rather hypothetical, such as silicene28−31 and MXenes,32−34 also have been realized experimentally. These 2D structures are bringing us revolutions to many advanced materials we desire. For example, MXenes have found many important applications in lithium ion batteries (LIBs)35,36 and electrochemical capacitors.37 Germanium is in the same row of the periodic table as carbon and silicon. As the monolayer structures of carbon and © XXXX American Chemical Society

silicon have been realized experimentally, the monolayer structure of germanium (germanene) still exists only in the theory.38,39 Quite recently, by means of topochemical deintercalation of Zintl phase CaGe2 , Bianco et al. 40 successfully fabricated stable germanane monolayer (GeH), which can be seen as the fully hydrogenated germanene. Germanane monolayer may have many potential applications in electronics and optoelectronics as it has a direct band gap as well as high carrier mobility.40 However, at present, some interesting issues still need to be addressed for this novel material. For example, the high level ab initio computations revealed that there is strong hydrogen bonding between graphane layers,41 does the similar interlayer coupling also exist between the thicker germanane layers that have already been obtained experimentally?40 If the answer is yes, would the direct band gap of germanane monolayer be tuned into indirect band gap with the increase of thickness, just similar to the case of MoS2 layers? Moreover, the controllable band gap engineering of semiconductors is always highly desirable for a wide range of energy and sensing applications. Wen et al.42 theoretically demonstrated that insulating graphane layers can be tuned into metallic under the external pressure, can we also efficiently engineer the electronic properties of germanane layers using some feasible approaches? Received: December 1, 2013 Revised: December 29, 2013

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In this work, by means of vdW corrected density functional theory (DFT) computations, we systematically investigated the structural and electronic properties of germanane layers. Our computations revealed that there is strong hydrogen bonding between germanane layers. Encouragingly, germanane layers can retain the direct band gap regardless of the stacking pattern and thickness. Especially, the electronic properties of germanane layers can be efficiently engineered by applying an experimentally feasible external electric field (E-field) or a biaxial tensile strain.

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COMPUTATIONAL DETAILS The computations employed an all-electron method within a generalized gradient approximation (GGA) for the exchangecorrelation term, as implemented in the DMol3 code.43,44 The double numerical plus polarization (DNP) basis set and PBE functional45 were adopted in all computations. It is known that weak interactions are out of the framework of standard PBE functional, so we adopted the PBE+D2 (D stands for dispersion) method with the Grimme vdW correction46 to describe the weak interactions. The accuracy of DNP basis set is comparable to that of People’s 6-31G** basis set,47 and the accuracy of PBE-D2/DNP on describing the weak interactions was well validated in our previous studies.48,49 Self-consistent field (SCF) calculations were performed with a convergence criterion of 10−6 a.u. on the total energy and electronic computations. To ensure high quality results, the real-space global orbital cutoff radius was chosen as high as 4.6 Å in all the computations. We set the x and y directions parallel and the z direction perpendicular to the plane of germanane layers and adopted a supercell length of 30 Å in the z direction. The Brillouin zone was sampled with a 6 × 6 × 1 Γ centered k points setting in geometry optimizations, and a 20 × 20 × 1 grid was used for electronic structure computations.

Figure 1. (a) Top (upper) and side (bottom) views of geometric structures of chairlike germanane monolayer. Ge and H atoms are denoted by green and white balls, respectively. (b) Band structure of germanane monolayer. (c) The partial charge densities of the VBM (left) and CBM (right). The isovalue is 0.04 e/A3.

fold degenerated. According to our computations, the VBM and CBM are contributed by the electronic states of Ge−Ge bonds and Ge atoms, respectively (Figure 1c). Previously Lu et al.54 revealed that the CBM of graphane monolayer is a highly delocalized state, which is known as the near free electronic (NEF) state. However, the CBM of germanane monolayer is highly localized and is not the NFE state. So what makes the difference for graphane monolayer and germanane monolayer? As mentioned above, in germanane monolayer, the H atoms are all negatively charged, which is repulsive to electrons and unfavorable for the formation of NFE state. In contrast, the H atoms of graphane monolayer are almost neutral, which is favorable for the stabilization of NFE state. Moreover, the neighboring H−H distance of germanane is as long as 4.05 Å (2.54 Å for graphane monolayer), which is also unfavorable for the formation of delocalized NFE state. A germanane bilayer can be constructed by pairing two germanane monolayers together. To determine the most stable configuration of germanane bilayer, we performed a set of lateral shifts of one germanane monolayer to the basal plane of the other monolayer and finally obtained four stable configurations (see Supporting Information) with energy difference in the range of 41−150 meV/unit. The energetically most favorable configuration of germanane bilayer (Figure 2a) has two Ge skeletons in A−B stacking; at the interface, each H atom of one monolayer points to the center site of three H atoms of the other monolayer. In this case, each H atom at the interface is involved in three hydrogen bonding. The PBE+D2 method predicts a rather pronounced binding energy of 260 meV/unit cell, an interlayer distance (between two Ge skeletons) of 3.18 Å, and an average H···H length of 2.34 Å for germanane bilayer. As a comparison, computed at the same theoretical level, the binding energies of graphene bilayer, graphane bilayer, and graphane/fluorographene bilayer are 132, 66, and 86 meV/unit cell, respectively. Note that the unit cell area of germanane bilayer is much larger than the abovementioned three bilayer structures. However, the average binding energy of germanane bilayer (18.2 meV/ Å2) is still larger than those of graphane bilayer (11.8 meV/Å2) and

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RESULTS AND DISCUSSION Structural and Electronic Properties of Germanane Monolayer and Bilayer. We first studied the structural and electronic properties of germanane monolayer. Similar to graphane,50 our computations revealed that the most stable configuration of germanane monolayer favors the chairlike form with hydrogen atoms alternating on both sides of the plane, which is 10 and 31 meV/atom lower in energy than the boat and stirrup-like forms (see Supporting Information), respectively. Figure 1a presents the optimized structure of chairlike germanane monolayer in a 4 × 4 supercell. One unit cell of germanane monolayer consists of 2 Ge atoms and two H atoms with the lattice parameters optimized to be a = b = 4.05 Å. The lengths of Ge−Ge and Ge−H bonds are 2.45 and 1.56 Å, respectively, in good agreement with previous theoretical studies.51−53 According to Hirshfeld charge population analysis, Ge and H are charged with 0.065 and −0.065 |e|, respectively. Computed at PBE/DNP theoretical level, gemanane monolayer is semiconducting with a direct gap of 1.50 eV (Figure 1b), which is quite close to that computed using the hybrid HSE06 functional (1.55 eV)40 but lower than that computed using the GW approximation (2.4 eV).51−53 The valence band maximum (VBM) and conduction band minimum (CBM) of germanane mononolayer are both located at the Γ point, and because of the symmetry, they are both 2B

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that the band gap of MoS2 bilayer monotonically decreases with increasing the vertical E-field,56,57 the electronic and magnetic properties of armchair and zigzag MoS2 nanoribbons can be feasibly manipulated by applying a transverse E-field,58,59 and both the interfacial binding and band structures in hydrogenfunctionalized BN bilayers and nanoribbons can be tuned by external electric field.60,61 Inspired by these studies, we explored the effect of external vertical E-field on the electronic properties of germanane layers. Figure 3a presents the band gaps of germanane monolayer and bilayer as a function of E-field magnitude. When Figure 2. (a) Top (upper) and side (bottom) views of geometric structures of germanane bilayer. The black double arrow denotes the interlayer distance. (b) Band structure of germanane bilayer.

graphane/fluorographane bilayer(15.4 meV/Å2), but lower than that of graphene bilayer (25.2 meV/Å2). Therefore, the interlayer coupling between germanane bilayer is rather strong, once formed, germanane bilayer will be highly stable against thermal perturbation. Next, we computed the band structure of germanane bilayer. As shown in Figure 2b, germanane bilayer still has a direct band gap of 1.36 eV, which is 0.14 eV lower than that of germanane monolayer. Compared with germanane monolayer, a slight energy level splitting in both the conduction and valence bands can be observed in the band structure of germanane bilayer, which removes the 2-fold degeneracy of VBM and CBM and decreases the band gap correspondingly. So what is the driving force for the energy level splitting? According to Hirshfeld charge analysis, there is no charge transfer between two monolayers. In contrast, induced by the interlayer coupling, an intralayer charge redistribution occurs in both monolayers (see Supporting Information), which should be responsible for the energy level splitting. Moreover, since there is no spontaneous interlayer polarization between two monolayers, the energy levels of two monolayers are not separated from each other, and VBM and CBM are contributed equally by two monolayers (see Supporting Information) We also explored the effects of stacking pattern and thickness on the electronic properties of germanane layers. First, we computed the band structures of the other three metastable configurations of germanane bilayer (see Supporting Information). According to our computations, these three metastable configurations also have a direct band gap in the range of 1.36− 1.44 eV. Then, we investigated the electronic properties of thicker germanane layers with layer numbers up to 5 and threedimensional (3D) bulk germanane. The germanane layers and bulk germanane were constructed by adopting the same stacking pattern as the most stable configuration of germanane bilayer. Our computations revealed that all these germanane layers have a direct band gap, irrespective of the thickness (see Supporting Information). Therefore, we conclude that the direct band gap is an essential property of germanane layers, which is an advantage over MoS2 layers for the applications in optoelectronics. Effect of External Electric Field on the Electronic Properties of Germanane Monolayer and Bilayer. The external E-field is a powerful tool to achieve tunable properties in nanostructures. For example, by applying an external E-field, a considerable gap can be opened in the band structure of graphene bilayer.55 Recent theoretical studies demonstrated

Figure 3. (a) Band gaps of germanane monolayer and bilayer as a function of external E-field. (b) Band structure of germanane bilayer with an E-field of 0.5 V/Å (left) and the corresponding partial charge densities of the VBM (right bottom) and CBM (right upper).

germanane monolayer is applied with an external E-field of even up to 0.5 V/Å, its band gap is almost unchanged, indicating that the electronic properties of germanane monolayer are rather robust in response to E-field. In contrast, the band gap of germanane bilayer decreases monotonically as the magnitude of E-field increases. With an E-field of 0.5 V/Å, the band gap of germanane bilayer is closed with VBM and CBM touching each other at the Fermi level (Figure 3b). For larger E-field, the system then becomes metallic with energy levels crossing the Fermi level. Interestingly, Ma et al.62 demonstrated quite recently that the electronic properties of wrinkled germanane monolayer are also quite sensitive to the external E-field. The above-discussed band gap modulation of germanane bilayer under external E-field should be attributed to the wellknown Stark effect, which has been observed in BN nanostrucutres63,64 and MoS2 bilayer.56,57 Explicitly, the external E-field could induce an electrostatic potential difference between two germanane monolayers. As a result, the energy levels of two monolayers would be separated from each other, causing a shifting of energy levels and thus decreasing the C

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band gap. With increasing magnitude of E-field, the energy level shifting becomes more and more pronounced and finally leads to a semiconducting-metallic transition. To validate our above analysis, we computed the partial charge densities corresponding to VBM and CBM of germanane bilayer under an E-field of 0.5 V/Å. As shown in Figure 3b, the VBM and CBM, which distribute over both monolayers under zero E-field, now are localized at upper and bottom monolayer, respectively. Note that GGA method may underestimate the value of band gap, but the trend predicted here should be solid and that the GW correction would only increase the threshold value of E-field for gap closure. Effect of Biaxial Strain on the Electronic Properties of Germanane Monolayer and Bilayer. Our above studies revealed that the electronic properties germanane monolayer is rather robust in response to external E-field. Can we engineer the electronic properties of germanane monolayer using other low-cost approach? One promising route toward the continuously tunable band gap is elastic strain engineering, which has been demonstrated experimentally65−67 and theoretically68−70 to be efficiently on tuning the electronic properties of MoS2 layers. Thus, we also studied the effect of biaxial strain on the electronic properties of germanane monolayer as well as bilayer. Computationally, the biaxial strain can be imposed on germanane layers by changing the lattice parameters of x−y plane (a and b, equally) and reoptimized the structures along the z direction. Here the strain (ε) is defined as ε = (a − a0)/ a0, where a and a0 are the strained and the equilibrium lattice constants of germanane layers, respectively. In this work we only considered the tensile strain as it is experimentally more feasible, and the largest tensile strain is chosen to be 15%. Our computations demonstrated that the biaxial strain has a significant impact on the electronic properties of germanane monolayer. With a tensile strain, the band gap of germanane monolayer decreases monotonically as the increase of strain (Figure 4a), even a 2% strain, can result in a 0.3 eV gap reduction. This trend is in stark contrast to the case of graphene, as Topsakal et al.71 demonstrated that the band gap of graphane monolayer increases with increasing biaxial tensile strain up to 15%. When tensile strain reaches 12%, the band gap of germanane monolayer is closed with VBM and CBM touching each other at the Fermi level (Figure 4b), denoting a semiconducting−semimetallic transition. Interestingly, the further increase of strain up to 15% does not change germanane monolayer into metallic as it retains as semimetallic. Note that when the tensile strain is lower than 12%, germanane monolayer is always semiconducting with a direct band gap. In contrast, the tensile strain not only leads to a band gap reduction but also causes a direct-indirect band gap transition for MoS2 monolayer.67,68 The overall trend for the electronic properties of germanane bilayer in response to biaxial tensile strain is quite similar to those of germanane monolayer. The main difference is that germanane bilayer has a smaller critical strain for band gap closure (9%) than that of germanane monolayer since germanane bilayer has a lower band gap. Especially, with a tensile strain of 9%, germanane bilayer directly becomes metallic rather than semimetallic with an energy level crossing the Fermi level (Figure 4c). What’s the underlying mechanism for strain-tunable electronic properties of germanane layers? As above-mentioned, the VBM of germane monolayer is mainly localized at the Ge−

Figure 4. (a) Band gaps of germanane monolayer and bilayer as a function of biaxial tensile strain. (b) Band structure of germanane monolayer with a strain of 12%. (c) Band structure of germanane bilayer with a strain of 9%.

Ge bonds. With a biaxial tensile strain, the length of Ge−Ge bonds is stretched gradually with increasing strain. As a result, the hybridization between electronic states of Ge atoms would be smaller and smaller, leading to an energy shifting of VBM and, consequently, a reduced band gap. Moreover, we are aware that PBE functional generally underestimates the band gap. Therefore, we also investigated the effect of biaxial tensile strain on the electronic properties of germanane monolayer and bilayer using hybrid HSE06 functional72,73 as implemented in VASP software package.74 As shown in Figure S5, Supporting Information, computed with HSE06 functional, the band gaps of germanane monolayer and bilayer also decrease with increasing biaxial tensile strain, and the critical strains required for gap closure are 13% and 10% for monolayer and bilayer, respectively, which are slightly higher than those obtained from PBE functional. Therefore, HSE06 functional actually predicted qualitatively the same results as PBE functional. Note that HSE06 is still not the ultimate solution for band gap and that an accurate first-principles computation of band gap requires a quasiparticle approach (the GW method). However, the basic physics discovered here should not be changed though the GW method might further increase the critical strains required for gap closure. Experimentally, the biaxial tensile strain can be achieved by depositing germanane layers on an elastic substrate. Then, we have to address another important issue: are germanane layers strong enough to bear a 15% tensile strain? To answer this question, we computed the phonon density of states of germanane monolayer with a tensile strain of 15% (see Supporting Information). No imaginary phonon modes were observed, indicating the good kinetic stability of the strained structure. Therefore, the above predicted semiconducting− semimetallic and semiconducting−metallic transitions for D

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germanane layers can be realized in real experimental conditions.

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CONCLUSIONS To summarize, by means of vdW corrected DFT computations, we systematically investigated the structural and electronic properties of germanane layers. There exists strong interlayer coupling between germanane bilayer, which is even stronger than that of graphane bilayer. Encouragingly, germanane layers all have a direct band gap, which is an advantage over MoS2 layers. The electronic properties of germanane bilayer can be efficiently tuned from semiconducting to metallic under an external E-field due to the Stark effect, whereas the band gap of germanane monolayer is rather robust in response to the external E-field. By applying a biaxial tensile strain, the band gap can be closed for both germanane bilayer and monolayer. Overall, our results provide two very promising approaches, namely, by external electric field and by biaxial tensile strain, toward engineering the electronic properties of 2D germanane layers, which would widen their potential applications in electronics and optoelectronics.

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ASSOCIATED CONTENT

S Supporting Information *

Geometric structures and relative energies of three configurations of germanane monolayer; geometric structures and band structures of four stable configurations of germanane bilayer; the partial charge densities of the VBM and CBM for germanane bilayer; schematic of charge redistribution of germanane bilayer; geometric structures and band structures of thicker germanane layers and 3D bulk germanane; band gaps of germanane monolayer and bilayer as a function of biaxial tensile strain computed using HSE06 functional; phonon density of states of germanane monolayer with a tensile strain of 15%. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*(Y.L.) E-mail: [email protected]. *(Z.C.) E-mail: [email protected]. Tel: 1-787-7640000, ext. 3119. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support in China by startup funds of Nanjing Normal University (184080H20145) and in USA by Department of Defense (Grant W911NF-12-1-0083) and partially by NSF (Grant EPS-1010094) is gratefully acknowledged.

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REFERENCES

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