Electrical and Optical Properties of Germanene on Single-Layer BeO

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The Electrical and Optical Properties of Germanene on Single-Layer BeO Substrate xianping chen, Xiang Sun, Junke Jiang, Qiuhua Liang, Qun Yang, and Ruisheng Meng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06161 • Publication Date (Web): 26 Aug 2016 Downloaded from http://pubs.acs.org on August 29, 2016

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The Journal of Physical Chemistry

The electrical and optical properties of germanene on single-layer BeO substrate

Xianping Chen,‡*ab Xiang Sun,‡a Junke Jiang,a Qiuhua Liang,b Qun Yang,b and Ruisheng Meng*b a

Faculty of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, 541004 Guilin, China b Key Laboratory of Optoelectronic Technology & Systems, Education Ministry of China, Chongqing University and College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China

Supporting Information

■ ABSTRACT A comprehensive first-principles study has been employed to investigate the geometric structures, electrical properties, and optical properties of two-dimensional (2D) Ge/BeO heterostructure. The results show that there is weak interaction between germanene and BeO monolayer via van der Waals force without any site selectivity. Therefore, most of the outstanding properties of germanene are conserved especially a linear band dispersions near the K point. The energy gap of ~49 meV can be opened for the heterostructure, which is a pretty large value for the gap opening at room temperature. Meanwhile, the band gap can be tuned by the interlayer distance, external strain, as well as the external electric field, and the electric field has been found to be the most effective way (14 – 382 meV). All of these methods for band gap modulation can maintain the characteristics of a Dirac cone with a linear band dispersion relationship of germanene. Moreover, the enhanced optical properties are also observed after the formation of the heterobilayer system. In general, the calculated results indicate that the Ge/BeO heterostructure holds great potential in the electrical and optoelectronic applications. BeO monolayer, the excellent candidate of germanene substrate, can attract more attention in substrate materials researches.

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■ INTRODUCTION As attracted by the unique physical and electrical properties of experimental achieved graphene,1-2 researchers are exploring other graphene-like 2D materials such as silicene,3 stanene,4 and germanene,4 etc. Among these materials, germanene (the graphene analog of germanium) is especially deeply studied both theoretically and experimentally.5 Since the fact that both of C and Ge atoms have four electrons in the valence band, which makes the properties of germanene very similar to those of graphene.6-10 The high carrier mobility, ferromagnetism, half-metallic and quantum hall effect make germanene a promising 2D material after graphene.11-12 Furthermore, compared to graphene, germanene is more preferable for the present novel functional electronic devices such as room temperature field effect transistors.13 Different from sp2 hybridization that is energetically more favorable for C atoms in graphene, germanene is contributed by sp2 and sp3 hybridization leading to slightly buckled structure. The buckled nature has induced many novel properties such as spin Hall effect and modulation of its band gap under an external electric-field.14 However, the gapless characteristic of germanene limits its utilizations in nanoelectronic and optoelectronic devices.15 In order to solve the problem, a suitable substrate can effectively help germanene open its energy gap, although it may also deteriorate the excellent properties of germanene. Thus, it is important to find an ideal substrate for germanene to not only achieve a tunable band gap but also maintain its intrinsic properties. The new predicted material, Beryllium Oxide (BeO) monolayer with graphene-like structure comes into our line of sight. BeO with a sp3 hybridization is a member of alkali earth oxides group crystallized in wurtzite phase. It has been researched theoretically by many researchers.16-17 Moreover, the endeavor to the fabrication of BeO monolayer has been investigated and achieved some initial results, such as the research of Reinelt et al.18-19 BeO monolayer possesses a large surface area and shows similar structure with germanene. Besides, it is an wide band gap semiconductor with special magnetic and optical properties.20-21 All these excellent properties make the BeO monolayer a potential substrate to support germanene. In the present work, the structural and electrical properties of superlattice made with the stacking materials of germanene and BeO monolayer are systematically investigated by using density functional theory calculation with the van der Waals (vdW) correction. The two monolayers of heterostructure could complement each other, and the new formed heterostructure


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exhibits an opened band gap along with the preservation of carrier mobility contrasting to pristine germanene. The finite band gap of Ge/BeO heterostructure is opened due to the sublattice symmetry breaking of germanene induced by the introduction of the BeO monolayer. Besides, the biaxial strains and external electric field can effectively tune the band gap of Ge/BeO heterostructure while there are few papers studying about it systmatically. In this paper, we provide some results about it. The optical properties of the heterostructure are also improved compared to that of the constituent layers. Our results show that the BeO monolayer could be an appropriate substrate for germanene, which can form the germanene/BeO heterostructure akin to the Ge/BN ones22 and graphene/BN.23-24

■ COMPUTATIONAL METHODS The first-principles density-functional theory plus dispersion (DFT-D) calculations were performed using the DMol3 module in Materials Studio. All of the structures were all fully optimized using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional. The weak interaction was also described by adopting the Grimme scheme for the vdW corrections.25-26 An all-electron double numerical atomic orbital augmented by d-polarization functions (DNPs) was used as the basis set.27 The self-consistent field (SCF) procedure was used with a convergence threshold of 10-6 a.u.28 on the energy and electron density. Geometry optimizations are performed with a convergence threshold of 0.002 Ha/Å on the gradient, 0.005 Å on displacements, and 10-5 Ha on the energy. The real-space global cutoff radius was set to be 4.7 Å. A vacuum layer of 20 Å was used in the direction normal to the interface, representing the isolated slab boundary condition. The k-point was set to 15 × 15 × 1 for the structural optimizations and 16 × 16 × 1 for the electrical properties calculations, and the smearing value was 0.005 Ha (1 Ha = 27.2114 eV). The external electric field was applied in the direction perpendicular to the heterostructure plane from -1.0 to 1.0 VÅ-1 with the geometry relaxation carried out. This method for applying the electric density is similar to a previous report.11 To discuss the relative stabilities of the superlattices, the binding energy (Eb) between the stacking sheets in the superlattice is defined as, Eb = Etotal − Egermanene − EBeO



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where Etotal, Egermanene and EBeO are the total energies of the composite, the free-standing pristine germanene and the BeO monolayer, respectively. Based on this definition, a more negative Eb represents a more energetically favorable interaction between germanene and BeO monolayer.

■ RESULTS AND DISCUSSION The calculated lattice parameters of the pristine germanene and BeO monolayer are 4.018 Å and 2.694 Å, respectively, which are in agreement with the previous results.11, 20 Considering the mismatch between two crystal lattice, the combination of 2 × 2 lateral periodicity of germanene (a = b = 8.036 Å, containing 8 atoms) and 3 × 3 lateral periodicity of the BeO monolayer (a = b = 8.082 Å, containing 18 atoms) is used for the simulation. The lattice parameters of stacking structure are chosen to be a =b = 8.059 Å, the average value of two lattice parameters, resulting in a mismatch of around 0.29% for two monolayers that is acceptable and can obtain credible simulation results.22 Our test computations show that for the pristine germanene, the elongation of the lattice constant by 0.29% induced a negligible effect on the band gap (Eg) because of the preservation of sublattice symmetry, which is consistent with previous results.29 The shrink of BeO monolayer also does not show noticeable differences of electrical properties compared with pristine BeO monolayer.30 The stacking patterns of the heterostructure would play a very important role in determining the stability and the electrical properties, therefore, it is worthy to study the possible effects of different stacking patterns. Three stacking models, Pattern I-III, are listed at Fig. 1 (a), (b) and (c), respectively. In the Pattern I configuration, the center of germanene hexatomic ring points directly to the bridge of Be-O bond while one top Ge and bottom Ge in this ring place above the center of BeO hexatomic ring. In the Pattern II configuration, the O atom are placed just below the hollow of hexatomic ring of germanene; the pattern III shows that the hollow site of germanene sits above the Be atom of BeO monolayer. The calculated results show that the differences of Eb between these three models are very small (about 0.3 to 0.5 meV), which indicates that the energy of superlattice is not sensitive to the stacking patterns of the atomic layers. Moreover, the three stacking patterns share the similar electric properties, for the sake of simplicity, we still chose the energy-lowest model, pattern I, with the binding energy of -1.088 eV to represent the most stable one to research in this paper. The electrical properties of other patterns are available in supporting


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information. To examine the optimum spacing between two adjacent layers, the binding energies and band gaps of heterobilayer systems with different interlayer distances (D) are calculated and shown in Fig.1 (e). The optimum D is consistent with the calculated binding energy value, which proves the correctness of our calculations. The value of D for the optimized structure is 3.144 Å corresponding to the binding energy of -1.088 eV and the band gap of 0.149 eV. Analyzing the binding energy diagram, it is obvious that the changes of D have a clearly effect on Eb altering the stability of heterostructure and short D will introduce a stronger interaction that can make the band gap opened larger. Therefore, the suitable interlayer distance is extremely important for heterostructures research. And the D is beyond the sum of covalent radii of the Ge and Be or O atoms, which means the bond between these atoms are not formed. The buckled distance (△) of germanene is 0.705 Å, being a little larger than individual germanene (△=0.693 Å), which suggests a slight structural distortion in germanene induced by the substrate. Thus, the weak interaction is found between the substrate BeO monolayer and up-layer germanene similar to the interaction between germanene and h-BN at Ge/BN superstructure.22

Fig. 1. Top and side views of Ge-BeO stacking configurations. (a) Pattern I; (b) pattern II; (c) pattern III; (d) side view of configurations. Ge, Be, O atoms are presented by green, yellow, and red balls, respectively. The unit cells are shown by dashed lines. (e) Binding energies (Eb) and band gap (Eg) of heterostructure systems as functions of the interlayer spacing between the BeO monolayer and its nearest germanium.



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It was reported that the electronic properties of graphene-related materials can be modulated notably by weak interlayer interactions.31-33 In order to compare the band structure variation, the band gaps of pristine germanene, BeO monolayer and Ge/BeO heterostructure are shown in Fig. 2(a)-(c), respectively. The germanene has an electronic structure resembling that of graphene with a linear energy dispersion around the K point in which the linear π and π* bands contact each other at the Fermi level and result in the zero band gap (Fig. 2(a)).7, 31, 34-35 The band structure of BeO monolayer shows a distinct band gap character with a large band gap value for 6.520 eV, almost a kind of insulator. The valence band maximum (VBM) and the conduction band minimum (CBM) are all located at the Γ point (Fig. 2(b)). Apparently, the band structure of germanene/BeO heterostructure seems to be mainly contributed by germanene especially around the Fermi level (Fig. 2(c)), as expected on the basis of relatively weak interlayer interactions. Impressively, the curvature of the band dispersion around the Dirac point of germanene/BeO is almost linear, which indicates massless fermion charge carriers. The band gap diagrams indicate that there is little effect on the high carrier mobility of germanene induced by BeO substrate, the unique characteristic has been preserved. Comparing with the Ag (111) surface substrate, the impressive property of BeO substrate for Dirac cone retainability is attracting our attention.22

Fig. 2. Band structures of (a) isolated germanene, (b) BeO monolayer and (c) a germanene/BeO heterostructure. More importantly, a tunable band gap can be opened at the Dirac point in the structure with a great potential for field effect transistors. The opened impressive band gap is 49 meV located at


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K point, which is larger than that of the room temperature thermal scale (26 meV) and slightly larger than the band gap of Ge/h-BN heterostructure.22 The considerable opened band gap can effectively improve the on-off current ratio property in germanene/BeO made logical devices.31, 36 Meanwhile, how the germanene contribute to the band gap of new structure that needs us to analyze further. The density of states (DOS) of the isolated germanene and BeO from the heterostructure is plotted in Fig. 3 (a). It is found that the states of germanene/BeO near the EF are dominated by the π and π* bands of germanene, the DOS diagram confirms that the electrical properties of hybrid structure are mainly determined by the germanene as the green line is corresponding to the black line representing the total DOS of the system. In Fig. 3 (b)-(e), the partial densities of states (PDOS) for germanene/BeO monolayer are further displayed. As clearly shown in the PDOS in Fig. 3(b), the total DOS of the heterostructure is mainly contributed by the p orbital. Comparing with diagram (e), the p orbital of germanene at the range of -3 to 3 eV corresponds to the total DOS at that range in p orbital. Therefore, the DOS of heterostructure around Fermi level is dominated by germanene where the most attractive electrical properties are retained. O and Be atoms are also assets to the total DOS, the O atoms cause the peaks around -5 eV, Be atoms induce the peaks around 5 eV, which show at diagram (c), (d). From these PDOS diagrams, we can confirm that the most unique electric properties of germanene are well preserved in heterostructure.

Fig. 3. The total and partial densities of states for germanene/BeO monolayer. (a) The total DOS of heterobilayer structure, (b) partial density of states (PDOS) for heterobilayer structure, (c) the PDOS for O atoms, (d) the PDOS for Be atoms, (e) the PDOS for germanene.



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As mentioned above, the band gap of germanene is opened due to the introduction of BeO sublattice. To gain more insights into this phenomenon, it is necessary to study its charge density difference diagram to gain a comprehensive analysis. The formula expressed as

△ρ = ρ (Ge/BeO) – ρ (Ge) – ρ (BeO) where ρ (Ge/BeO), ρ (Ge), and ρ (BeO) are the total charge densities of the Ge/BeO hybrid structure, isolated germanene, and BeO monolayer, respectively. As shown in the Fig. 4, there is charge accumulation in the interspace near the BeO monolayer, while it is dissipated under the bottom Ge atoms. This suggests that the charge redistribution is mainly caused by the electrostatic repulsion,37 which has also be found in the graphene/BN heterostructure.38 Thus, it also produces an intrinsic electric field between interlayer, which points from germanene to BeO monolayer. Electron dissipation are observed at the interspace of heterostructure, which is close to the bottom Ge. The top and bottom Ge show different electric potential energies, which results in the onsite energy difference causing a band gap open. Through electron transfer analysis, the average Mulliken populations of top and bottom Ge (etop and ebottom) are -0.447 and 0.752 |e|, respectively. The electron redistribution occurring at an interface often leads to an intrinsic interface dipole, which is common for a heterostructure with a vdW interlayer interaction.31, 39 Totally, germanene lost nearly 0.305 |e| that corresponding to the charge density difference results. The O atoms carry the transferred electrons rather than Be atoms, it attributes to the biggest electronegative of oxygen comparing to these elements.

Fig. 4. Side (a) and top (b) view for the charge density difference (△ρ) of germanene/BeO, and the isosurface value is 0.002 V/Å. The blue (magenta) distribution corresponds to charge


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accumulation (depletion). Actually, as the mechanism of band gap opening for germanene/BeO is induced by the intrinsic interface dipole, the electron redistribution would continually be modulated by an external electric field (Ef), the charge transfer will easily be affected by the direction of Ef and eventually change the band gap, as reported for the free-standing graphene and BN monolayer hybrid.40 In order to achieve this proposal, an external electric field is adopted to the germanene/BeO heterostructure. Fig. 5 plots the band gap as a function of external electric field which is perpendicular to the plane of heterostructure with its positive direction aligned upward. Under the electric field, the structure of the heterobilayer can be slightly affected. The buckling of germanene and the interlayer distance change from 0.699 Å to 0.711 Å and 2.966 Å to 3.083 Å, respectively, under the electric field strength from -1 to 1 V/nm. Whereas, the electrical properties of the germanene/BeO heterostructures can be significantly tuned by the external electric field. The band gap value as a function of external electric field is displayed in Fig. 5 while the original band gap is 49 meV under zero electric field. When the positive electric field is applied, the band gap changes linearly. The band gap rises up to 382 meV as a result of setting the electric field to 5 V/nm. The value of band gap decreases and almost become 0 eV (0.014 eV) at the electric field of -1 V/nm, then it progressively increases up almost linearly to 265 meV as the electric field reach to -5 V/nm. The linear Ef - Eg effect in two ranges of -1 ~ -5 V/nm and 0 ~ 5 V/nm can be used to tune band gap for a practice application.

Fig. 5. (a) Eg and (b) Mulliken charges of the top Ge, bottom Ge, and the total germanene as a function of electric field for germanene/BeO heterostructure.



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To better understand the relationship between band gap and external electric field, etop, ebottom, and the average Mulliken populations of germanene are displayed as a function of electric field. From the diagram analysis, as the composite structure has formed, the electrical neutrality of germanene would be perturbed. The different Mulliken charges of different Ge atoms, etop= -0.447 |e| and ebottom= 0.752 |e|, completely destroy the symmetry structure of germanene and induce a band gap opening. It may further explain why the heterostructure has an impressive band gap and maintain the excellent electrical properties of germanene. Moreover, the positive electric field makes a larger amount of electrons escape from germanene. When Ef = 5 V/nm, the escaping electrons reaching to 0.38 |e|. The positive electric field will break the symmetry of free-standing germanene causing a band gap opening.11, 41 In light of the discussion above, the positive electric field finally lead to the band gap increase. On the contrary, when the external electric field is applied in the negative direction, the electrons transfer from germanene to BeO monolayer is decreased while the charge difference is enlarged from 1.354 |e| (etop= -0.531 |e|, ebottom= 0.823 |e|) when Ef =-1 V/nm to 1.994 |e| (etop= -0.882 |e|, ebottom= 1.112 |e|) when Ef = -5 V/nm. In other word, the symmetry of germanene is destroyed seriously which finally also leads to band gap increase.31 Thus, applying external electric field is an effectively way to tune the band gap to a satisfactory value.

Fig. 6. (a) The band gap of Ge/BeO heterobilayer structure versus different strain conditions. (b) Strain applied on heterostructure.

Using strain is also a regular method for band gap modulation. We investigate the two types of mechanical strain (uniaxial and biaxial) to modulate Ge/BeO heterostructure. In the first case,


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biaxial strains are used to stretch and compress the lattice. The other method is applying strain by stretching and compressing the heterostructure in a or b direction. We apply the strain by changing the in-plane cell parameters (a and b), relaxing the structure along the c-axis (the direction perpendicular to the sheets). The strain is calculated by ε = △ l/l0, △ l =l-l0 is the change parameter.37 As illustrated in Fig. 6, the biaxial strains don’t show significant influence in tuning band gap. The largest bang gap modulation is just 13 meV, and the band gap tuning is nearly linear during compression of -8% ~ -1% and expansion of 1% ~ 5%. Therefore, we come into conclusion that the biaxial strain can’t produce a large influence on electrical properties of heterostructure. When the strain is lower than -9% or larger than 6%, the band gap will significantly reduce to zero that the large strain may destroyed the Ge/BeO heterostructure. As for single-axial strain, the tuning effect is obvious. The stretch makes the band gap almost linear in the range of 0 ~ 6 % and the largest bang gap is 0.239 eV at 6%, which is quite a good result for band gap tuning. Compression can also tune band gap in pretty large extent. The largest band gap appeared at -8 % is 0.193 eV then suddenly decrease to 0.131 eV along the strains enhancement. Under single-axial strain, the impressive band gap modulation may cause by the symmetry broken of germanene. All of the strain induced band gap modulations do not lead to a direct-indirect band gap transition in heterostructure.

Fig. 7. Imaginary part of dielectric function of the separate Ge, BeO, and Ge/BeO heterostructure for (a) the polarization vector perpendicular (εʹʹ1) to the surface and (b) the parallel (εʹʹ2) to the surface. Finally, optical properties of Ge/BeO nanocomposites are studied whereas others just



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research the properties of these materials, respectively,19, 42 rather than that of the heterostructure (such as Ge/h-BN). Individual germanene43 and BeO monolayer19 themselves display unique optical properties. Meanwhile, interlayer interactions in Ge/BeO nanocomposites may cause new optical transitions.44 The imaginary parts of dielectric functions for the light polarization perpendicular/parallel to the plane of Germanene are shown at Fig. 7. For the perpendicular polarization, the pure germanene shows four peaks located at about 120, 145, 190, and 280 nm, respectively. The main adsorption parts are located at ultraviolet region and the largest strength of adsorption appeared at 145 nm while the second highest peak locating at 190 nm. The BeO monolayer shows a bad light adsorption ability. It can only harvest ultraviolet light at a low strength comparing with germanene. The photoabsorption efficiency of heterostructure are mainly contributed by germanene showing at Fig. 7 that exhibits a similar morphology of adsorption curves and there is overlap occurred at 140-150 nm. The Ge/BeO heterostructure displays a better adsorption efficiency in UV adsorption and enhanced visible light response, compared with germanene. Redshift of the adsorption edge is as large as 15 nm for Ge/BeO heterostructure. Besides, for the parallel polarization, the BeO monolayer just adsorbs light at the range of 80 ~ 280 nm with a low adsorbed strength showing at Fig. 7(b). The Ge/BeO heterostructure doesn’t change the basic optical absorption trend of germanene, moreover, the enhancement of heterostructure in dielectric function occurred after 300 nm. The redshift of the adsorption edge is as large as 70 nm for heterostructure when light is parallel to the plane. The expansion from UV light into the visible and the enhancement adsorption capacity indicate that the hybrid Ge/BeO nanoconposite could harvest a broad range of visible light efficiently. The extended adsorption region of the Ge/BeO heterostrucure, especially the enhancement and redshift to the visible light region would make them have a better performance as a photocatalyst.

■ CONCLUSION In summary, a comprehensive first-principles study is performed on the structure, electronic, and optical properties of Ge/BeO heterostructure. Through our investigation, the tiny differences on binding energies between possible stacking patterns indicate the insensitive property of Ge/BeO for different stacking patterns. A sizable band gap is opened with the Dirac cone preserved


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because of the destroyed symmetry of the two sublattices in germanene induced by the weak interaction. According to our calculations, the BeO monolayer not only lead to the band gap opening, more importantly, it can also maintain the various excellent electrical and optical properties of germanene in the largest extent. That implies the BeO monolayer can be an ideal substrate for germanene and it may help to conquer the main obstacle, similar to graphene, as lacking of intrinsic band gap to apply germanene as an electronic device. The opened band gap can be further modulated by the interlayer distance and in-plane strain in the Ge/BeO heterostucture. In addition, the external electric field is also an impactful way to tune band gap in a relatively linear way integrating with the Dirac cone of germanene retained. Furthermore, the composite structure helps to enhance the light adsorption properties of germanene, induces a redshift to visible light region. These findings may inspire the experimental developments in the Ge/BeO heterostructure with small energy gaps and enable their use in novel integrated functional nanodevices.

■ ASSOCIATED CONTENT

Supporting Information Supporting Information Available： Data of other stacking patterns as Band structure of other stacking patterns, band gap as a function of electric field, and band gap of Ge/BeO heterostructure versus biaxial and single-axial strain (PDF) This material is available free of charge via the Internet at http://pubs.acs.org/

■ AUTHOR INFORMATION

Corresponding Authors *E-mail, [email protected]; phone, +86-23-65111178. *E-mail: [email protected]

Author Contributions *X.C. and X.S. contributed equally to this work.

Notes



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The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS The research is co-supported by the National Natural Science Foundation of China under Grant No.

51303033

and

the

Guangxi

Natural

Science

Foundation

under

Grant

No.

2014GXNSFCB118004. Junke Jiang is supported by the Innovation Project of Guangxi Graduate Education under Grant No. YCSZ2015142.

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Electrical and Optical Properties of Germanene on Single-Layer BeO

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