Structural and electronic properties of hydrogen-functionalized armchair germanene nanoribbons: A first-principles study

Structural and electronic properties of hydrogen-functionalized armchair germanene nanoribbons: A first-principles study present the critical physical quantities to analyze the structural and electronic properties are fully developed through the first-principles calculations, including the functionalization energy, optimal structural parameters, orbital- and atom-decomposed electronic band structures and density of states, charge density, and charge density difference.

Structural and electronic properties of hydrogen-functionalized armchair germanene nanoribbons: A first-principles study

Nguyen Thanh Phuong1 and Nguyen Duy Khanh1,*

1Information Technology Center, Thu Dau Mot University, Binh Duong Province, Vietnam

*Corresponding at khanhnd@tdmu.edu.vn

Abstract

Structural and electronic properties of hydrogen-functionalized armchair germanene nanoribbons (AGeNR) are investigated using the first-principles calculations The critical physical quantities

to analyze the structural and electronic properties are fully developed through the first-principles calculations, including the functionalization energy, optimal structural parameters, orbital- and atom-decomposed electronic band structures and density of states, charge density, and charge density difference Under hydrogen functionalization, the functionalization energy is achieved around -2.59 eV, and the structural parameters are slightly distorted as compared to the pristine system This evidences for good structural stability of the functionalized system Besides, the very strong H-Ge bonds are created by the strong charge transfer of electrons from Ge atoms to

H atoms that generates free holes in the functionalized system, which can be considered as p-type doping As a result, the π bonds of Ge-4pz orbitals at low-lying energy are fully terminated

by the strong H-Ge covalent bonds, in which the strong hybridizations of H-1s and Ge-(4s, 4px, 4py, and 4pz) orbitals are occurred at deep valence band The termination of π bonds leads to the opened bandgap of 2.01 eV in the hydrogen-functionalized AGeNR that belongs to the p-type semiconductor The feature-rich electronic properties of the hydrogen-functionalized AGeNR identify that the hydrogen-functionalized AGeNR will be the very potential 1D semiconductor for high-performance optoelectronic applications

Keywords: graphene, germanene, armchair germanene nanoribbons, hydrogen functionalization, DFT calculation, band structure, and charge transfer

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TÓM TẮT

Các đặc tính cấu trúc và điện tử của các dải nano germanene cạnh ghế bành chức hóa hydro (AGeNR) được nghiên cứu bằng cách sử dụng các tính toán nguyên lý đầu tiên Các đại lượng vật lý quan trọng để phân tích các đặc tính cấu trúc và điện tử được phát triển đầy đủ thông qua các tính toán nguyên lý đầu tiên, bao gồm năng lượng chức năng hóa, các thông số cấu trúc tối

ưu, cấu trúc vùng điện tử phân tách theo quỹ đạo và nguyên tử và mật độ trạng thái, mật độ điện tích và sai khác mật độ điện tích Trong quá trình chức hóa hydro, năng lượng chức năng hóa đạt được khoảng -2,59 eV, và các thông số cấu trúc bị biến dạng rất ít so với hệ nguyên sơ Đây là bằng chứng cho sự ổn định cấu trúc tốt của hệ thống được chức năng hóa Bên cạnh đó, các liên kết H-Ge rất bền được tạo ra do sự chuyển điện tích mạnh của các electron từ nguyên tử Ge sang nguyên tử H tạo ra các lỗ trống tự do trong hệ cơ năng, có thể được coi là sự pha tạp loại p Kết quả là, các liên kết π của các obitan Ge-4pz ở năng lượng thấp bị kết thúc hoàn toàn bằng các liên kết cộng hóa trị mạnh H-Ge, trong đó các liên kết lai hóa mạnh của H-1s và Ge- (4s,4px, 4py và 4pz) các quỹ đạo xuất hiện ở vùng hóa trị sâu Sự kết thúc của liên kết π dẫn đến độ rộng vùng cấm mở ra là 2,01 eV trong AGeNR chức hydro thuộc bán dẫn loại p Các đặc tính điện tử phong phú của AGeNR chức năng hydro xác định rằng AGeNR chức năng hydro sẽ là chất bán dẫn 1D rất tiềm năng cho các ứng dụng quang điện tử hiệu suất cao

Từ khóa: graphene, germanene, dải nano germanene cạnh ghế bành, chức năng hóa hydro, tính toán DFT, cấu trúc dải vùng điện tử và chuyển điện tích

1 Introduction

Since the first two-dimensional (2D) graphene monolayer made of carbon elements arranging in a planar hexagonal lattice has been successfully synthesized by Novoselov et al through the top-down approach in 2004 [1], it strongly motivates for many studies of graphene-like 2D materials owing to its novel and unique properties to significantly enhance performance for applications as compaered with the traditional bulk materials [2-5] As a close anolog of graphene, germanene made of germanium (Ge) elements arranging in a low-buckled hexagonal lattice has attracted plenty of efforts because the Ge constituents have a good compatibility with the silicon elements in the current semiconducting industry and the low-buckled structure of

germanene also possesses better stability than the planar graphene in devices [6-8] However, the zero-gap feature of 2D germanene is a critical drawback that prevents great potential of germanene for electronic applications Thus, opening bandgap for germanene is an essential issue for practical applications that has recently drawn much attention in scientific community [9] Various approaches have been utilized to open bandgap for germanene, including functionalization [10], adsorption [11], substitution [12], inducing defects [13], forming stacking configurations [14], applying external electric or magnetic fields [15], and creating finte-size confinements [16] Among these methods, the finite-size confinements of the 2D germanene resulting in the one-dimensional (1D) germanene that can enhance bandgap without any serious deformations in geometries is the very effective way to open bandgap for germanene

This 1D germanene is termed as germanene nanoribbons (GeNRs), in which the different edge terminations can create two typical germanene nanoribbons are armchair (AGeNR) and zigzag (ZGeNR) germanene nanoribbons [17, 18] It should be noted that the bandgaps of GeNRs strongly depend on its widths, and the different edge configurations exhibit different electronic and magnetic behaviors The AGeNR presents the direct bandgap at band-edge states and exhibits non-magnetic states Meanwhile, the ZGeNR displays the direct bandgap at far band-edge states and presents the anti-ferromagnetic states across the edges, in which each zigzag edge presents opposite ferromagnetic states Nevertheless, the opened bandgaps of GeNRs are too narrow to have a good compatibility with the optoelectronic applications that needs bandgaps larger than 0.7 eV [19] Thus, enhancing the bandgap of GeNRs is an essential topic for electronic and optoelectronic applications that has interested in many recent studies Many methods to enhance bandgap for GeNRs has been studied, including the inducing defects [20], external fields [21], stacking configurations [22], atom dopings [23], and edge or surface functionalizations [24, 25] Among these methods, the surface functionalizations by hydrogen atoms can significantly enhance bandgap of GeNR with good structural stability owing to strong H-Ge bonds that is worthy for a detailed investigation In this work, the structural and electronic properties of hydrogen-functionalized AGeNRs are thoroughly studied using the first-principles calculations Through the first-principles calculations, a generalized theoretical framework to determine the studying properties are fully developed, including the functionalization energies, optimal lattice parameters, atom- and orbital-projected electronic band structures and density of

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states, charge density, and charge denstiy difference The developed first-principles theoretical framework can be fully generalized to other functionalization systems

2 Computational detials

Structural and electronic properties of hydrogen-functionalized armchair germanene nanoribbons are investigated using the density functional theory (DFT) method, implemented in Vienna Ab Initio Simulation Package (VASP) [26] In VASP calculations, the electron-electron Coulomb interactions coming from the many-body exchange and correlation energies are calculated using the Perdew-Burke-Ernzerhof (PBE) functional under the generalized gradient approximation [27] The intrinsic electron-ion interactions are evaluated by the projector-augmented wave (PAW) pseudopotentials As to the complete set of plane waves, the kinetic energy cutoff is set to be 500 eV, being suitable for evaluating Bloch wave functions and electronic energy spectra A vacuum space of 20 Å is used to create the free-standing monolayer The first Brillouin zone is sampled by 1×1×12 and 1×1×100 k-point meshes within the Monkhorst-Pack scheme for geometric optimizations and electronic structure calculations, respectively The energy convergence is equal to 10-5 eV between two consecutive steps, and the maximum Hellman-Feynman force acting on each atom is less than 0.01 eV/Å during the ionic relaxations

3 Results and Discussions

3.1 Structural properties

The atomic structures of pristine and hydrogen-functionalized armchair germanene nanoribbons (AGeNR) displayed in top-view and side-view are shown in Figs 1(a) and 1(b), respectively, in which the ribbon width of six dimer lines is used in the calculations The dangling bonds along armchair edges are eliminated by passivation of the hydrogen atoms at the edges Under the optimal calculations, the hydrogen atoms are flavorably functionalized at the top sites of AGeNR among other sites, and the only double-side functionalization of AGeNR can lead to the stable structure that is evaluated by the functionalized energy (Efunc), while the single-side functionalization generates the unstable structure The Efunc is calculated as follows:

E = E −E −nE n (1)

Whereas Etot, Epris, and EH are the ground-state energy of the hydrogen-functionalized AGeN, pristine AGeNR, and isolated hydrogen atoms, respectively; and n is the total number of functionalized hydrogen atoms The calculated Efunc is valued at -2.59 eV as shown in Table 1 This Efunc value is large enough to form the stable functionalized structure Under the double-side functionalization effect, it creates very short H-Ge bond lengths of 1.55 Å that is very shorter than Ge-Ge bond lengths of 2.37 Å shown in Table 1 This means that the generated H-Ge covalent bonds are very stronger than the Ge-Ge bonds Due to effect of finite-size termination, the Ge-Ge bond lengths near edges (1st Ge Ge) are larger than the Ge-Ge bond lengths far edges (2nd Ge-Ge) as shown in Table 1, in which the 1st Ge of 2.39 Å and 2.37 Å and the 2nd

Ge-Ge of 2.36 Å and 2.35 Å correspond to the pristine and H-functionalized AGe-GeNRs Also, it can

be identified that the Ge-Ge bond lengths of the H-functionalized system are slightly shorter than that of the pristine system The buckling height of 0.91 Å in the H-functionalized system is shorter than that of 1.08 Å in the pristine system, confirming that the buckling is reduced under the H functionalization The shorter bond lengths and buckling result in the larger Ge-Ge-Ge bond angle of 114.25 9 (˚) in the H-functionalized system This implies that the double-side H functionalization can create better symmetric structure It should be mentioned that the pristine AGeNR exhibits a mix of sp2/sp3 hybridization in buckled Ge-Ge bonds, in which it exists the strong bonded σ network of Ge-(4s, 4px, and 4py) orbitals and the weak π bonds of Ge-4pz orbitals Such weak π bonds are fully terminated under the double-side H functionalization that creates the hybridization mechanism of 1s-sp3 in H-Ge bonds

Table 1: Functionalization energy [E func (eV)], Ge-Ge bond lengths near edges [1 st Ge-Ge] and far edges [2 nd Ge-Ge], H-Ge bond length (Å), buckling height (Å), Ge-Ge-Ge bonds (˚), and bandgap [E g (eV)] of

the pristine and hydrogen-fucntionalized armchair germanene nanoribbons at the with of six dimer lines

Configurations E func (eV) 1 st Ge-Ge

(Å)

2 nd Ge-Ge (Å)

H-Ge (Å)

Ge-Ge-Ge angle (˚)

Buckling (Å)

E g (eV)

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Figure 1: Atomic models of the pristine AGeNR and hydrogen-functionalized AGeNR shown in top-view

and side-view

3.2 Electronic properties

The 1D electronic band structures of the pristine and H-functionalized AGeNR systems are presented in Fig 2, in which the Fermi level is set at the zero energy to determine the energy gaps and electronic states illustrated by short dot black lines As for the band structure of the pristine AGeNR in Fig 2(a), it presents a direct bandgap of 0.23 eV (shown in Table 1) that is determined by the highest occupied vanlence band and lowest unoccupied conduction band at Г point All 1D subbands are asymmetric from the Fermi level, and they belong to the anti-crossing weakly dispersed bands Different dominations of Ge-orbitals in 1D subbands are identified by the orbital-decomposed band structure Specifically, Ge-4pz orbitals shown by red circles in Fig 2(a) significantly dominate at the long-range energies near the Fermi level from -2.6 eV to 2.6

eV that indicates for long-range π bands, in which the co-domination of Ge-4pz and Ge-(4px+4py) orbitals shown by the blue circles exists at the valence band from -2.6 eV to the Fermi level, and the strongest domination of Ge-4pz is from the lowest unoccupied conduction band to 2.6 eV

From the middle valence band of -2.6 eV to deeper range energies, the Ge-(4px+4py) orbitals are strongly dominated and co-dominated with the Ge-4s orbital shown by the green circles at the deepest range energies, whereas the domination of Ge-4pz orbitals is disappeared It should be noted that the co-domination of Ge-4s and Ge-(4px+4py) orbitals implies for sp2 hybridization and the co-domination of the Ge-4s, Ge-(4px+4py), and Ge-4pz orbitals illustrates for the sp3 hybridizaton This can clarify that the hybridization mechanism in AGeNR is a mix of sp2/sp3, which is responsile for the weak separation of σ and π bands Under the hydrogen functionalization, the 1D band structure of the pristine AGeNR is dramatically changed, as shown in Fig 2(a), in which the bandgap is much enlarged at 2.01 eV The Ge atoms fully dominate at long-range energies from -3.2 eV to 4 eV illustrated by pink circles in Fig 2(a), which determine the opened bandgap, while the hydrogen atoms strongly dominate at deep valence energies from -3.2 eV to -5 eV shown by the cyan circles This is due to that the H-Ge bond lengths are very shorter than the Ge-Ge bond lengths

Figure 2: Orbital- and atom-projected band structures of (a) pristine AGeNR and (b)

hydrogen-functionalized AGeNR

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The orbital-projected density of states (DOSs) is utilized to verify all main features of the electronic band structures The DOSs of the pristine and H-functionalized AGeNRs are presented

in Figs 3(a) and 3(b), respectively, in which the Fermi energy is illustrated by the black short dot lines As for the DOSs of the pristine AGeNR shown in Fig 3(a), the vacant region between the highest occupied valence and lowest unoccupied conduction peaks is responsible for the energy gap The dominant peaks made of Ge-4pz orbitals (red curves)) at long-range energies near the Fermi level are resulted from the long-range π bands, in which the 4pz peaks are stronger than the peaks made of Ge-4s (green curves) and Ge-(4px+4py) orbitals (blue curves) above the Fermi level, while the Ge-(4px+4py) peaks become more dominant than the 3pz peaks below the Fermi level; however, the peaks of Ge-4s, Ge-4pz, Ge-(4px+4py) orbitals are simutaneously appeared in the long-range π regions This confirms for the sp3 hybridization Below the middle valence energy of -2.6 eV, the 3pz peaks are almost disappeared, and there only exist the merged peaks of Ge-4s and Ge-(4px+4py) orbitals, whereas the second one is more dominant than the first one, indicating for the sp2 hybridization In the whole energy range, it can show that there is a mix of

sp2/sp3 hybridizations Under the H functionalization, the DOSs is fully reshaped as shown in Fig 3(b) The appearance of the strong H-Ge bonds creates the very strong peaks at the deep valence band merged by the H-1s (cyan shot dot curves) and Ge-4s (green curves), Ge- 4px+4py (blue curves), and 4pz (red curves), in which the H-1s peaks are stronger than the other peaks This illustrates for the hybridization of 1s-sp3 in H-Ge bonds The π peaks at long-range energies

in Fig 3(a) are fully destroyed due full termination of π bonds in Fig 3(b), whereas the Ge-4s and Ge-(4px+4py) peaks fully dominate in the long-range energies

The bonding magnitute and hybridization mechanism are verified through the charge density distribution The charge density distribution of the pristine and H-functionalized AGeNRs is presented in Figs 4(a) and 4(b), respectively The highest and lowest charge densitties are used to display for strongest and weakest bonds, as illustrated by the red and blue colors, respectively As for the charge density of the pristine AGeNR in Fig 4(a), the charge density is strongly distributed between two Ge atoms in (x,y) plane illustrated by the red region that is due to the strong σ Ge-Ge bonds Meanwhile, the charge density is much lower along z direction displayed by the green region between two Ge atoms that is owing to the weak π Ge-Ge

bonds From the clear information in the charge density, it can be mentioned that the σ bonds are very stronger than the π bonds, and the strong σ bonds form the stable monolayer structure The

H functionalization causes much change in the charge density as shown in Fig 4(b), in which the

π bonds of Ge-Ge are fully terminated by forming in the very strong H-Ge covalent bonds, and the H-Ge bonds (dark red region) are stronger than the Ge-Ge bonds since the H-Ge bond lengths are very shorter than the Ge-Ge bonds as indentified in Table 1, while the σ bonds of Ge-Ge in the H-functionalized system are enhanced as compared with the pristine σ bonds owing to the Ge-Ge bond lengths shortened under the H-functionalization as identified in Table 1 To observe the charge transfer mechanism, the charge density difference of the H-functionalized AGeNR is presented in Fig 4(c), whereas the red and blue regions are responsible for vanished and gained electrons, respectively This indicates that the electrons are transferred from Ge atoms to H atoms to generate the very strong H-Ge bonds This charge transfer process creates the free holes

in the functionalized system that can be regarded as the p-type doping

Figure 3: Orbital-projected density of states of (a) pristine AGeNR and (b) hydrogen-functionalized

AGeNR

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Figure 4: Charge density distributions of (a) pristine AGeNR and (b) hydrogen-functionalized AGeNR;

and charge density difference distribution of (c) hydrogen-functionalized AGeNR

4 Conclusion

The structural and electronic properties of the pristine and H-functionalized AGeNRs are fully revealed in the physical quantities developed under the DFT calculations, including the functionalization energies, optimal structural parameters, atom- and orbital-decomposed electronic band structures, density of states (DOSs), charge density, and charge density difference The calculated functionalization energies demonstrate that the H functionalization can create the stable 1D structure The created H-Ge bonds are very stronger than the Ge-Ge bonds that fully terminate the π bonds and slightly distort the σ bonds The formation of strong H-Ge bonds is due to the transfer of electrons from Ge atoms to H adatoms that create the 1s-sp3 hybridization mechanism A a close relationship, the significantly change in geometric structure

in the H-functionalized system results in their enriched electronic properties The bandgap of 2.01 eV is opended in the H-functionalized AGeNR, and this bandgap is determined the σ orbitals of Ge atoms The enriched properties under the H functionalization effect are very potential for optoelectronic applications that requires bandgap larger than 0.7 eV