Optical Identification of Topological Defect Types in Monolayer

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Optical Identification of Topological Defect Types in Monolayer Arsenene by First-Principles Calculation Xiaoxu Liu, Lizhe Liu, Lun Yang, Xinglong Wu, and Paul K Chu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10303 • Publication Date (Web): 13 Oct 2016 Downloaded from http://pubs.acs.org on October 18, 2016

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The Journal of Physical Chemistry

Optical Identification of Topological Defect Types in Monolayer Arsenene by First-Principles Calculation

Xiaoxu Liu, † Lizhe Liu, † Lun Yang, † Xinglong Wu*, † and Paul K. Chu‖

†

Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics and

Collaborative Innovation Center of Advanced Microstructures, National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China ‖

Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

ABSTRACT Recent theoretical researches have demonstrated that a new two-dimensional material, the monolayer of gray arsenic (arsenene), can respond to the blue and ultraviolet light leading to possible optoelectronic applications. topological defects often affect various properties of arsenene.

However, some

Here we theoretically

investigate the arsenene with monovacancy (MV), divacancy (DV) and Stone-Wales (SW) defects.

Three kinds of MVs are identified and the reconstructed structures of

DV and SW defects are confirmed. The dynamical stability, rearrangement, and migration for these defects are investigated in details. Optical spectral calculations indicate that the MVs enhance optical transitions in the forbidden bands of arsenene and two new characteristic peaks appear in the dielectric and absorption spectra.

1

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However, there is only one new peak in the spectrum induced by DV and SW defects. Calculations of band structures indicate that the MV induces two defect bands in the forbidden bands of pristine arsenene, which are responsible for the two new peaks in the dielectric and absorption spectra.

Our findings suggest that the optical dielectric

and absorption spectra can help identify the types of topological defects in arsenene.

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INTRODUCTION Since the isolation of a monolayer of carbon atoms (graphene),1 researches on two-dimensional (2D) materials have aroused much interest.

Although graphene has

high electron mobility, the intrinsic zero bandgap restricts its application in optoelectronics.

In order to overcome this disadvantage, other 2D materials with the

proper bandgaps and unique properties such as boron nitride (h-BN),2 silicene,3 germanene,4 phosphorene5,6 and transition metal dichalcogenides (TMDs)7 have been studied theoretically and experimentally.

During synthesis and processing of 2D

materials, topological defects appear inevitably and affect the materials properties and performance and so it is important to characterize these defects.

It has been theoretically demonstrated that the monolayer of gray arsenic (arsenene) can be transformed from indirect to direct bandgap semiconductor under biaxial strain.8-10 The weak interaction between the gray arsenic layers makes the mechanical exfoliation possible9 and arsenene exhibits interesting interactions with blue and ultraviolet light leading to possible optoelectronics applications.

However,

since defects affect the properties of arsenene, they must be better understood. Transmission electron microscopy11 and scanning tunneling microscope12 are commonly used to examine topological defects in the 2D materials and Raman scattering and photoluminescence13,14 are often employed to study defects. to fathom the origin and evolution of defects, theoretical studies are critical.

In order In this

work, first-principles calculation is performed to determine the optical properties and electronic structure of arsenene with monovacancy (MV), divacancy (DV), and 3



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Stone-Wales (SW) defects. The density functional method is adopted to investigate the effects of several kinds of defects on the optical properties of arsenene.

Since arsenene, graphene, and

silicene have the same hexagonal geometry, we build the initial configurations with special defects according to the similar defective structures in graphene and silicene demonstrated by experiments and theory. Six types of initial defect configurations are constructed and optimized to form the final stable ones energetically.

The formation

energy of each configuration is calculated so that we can predict which type of defects most likely appears. Subsequently, the dielectric functions and absorption coefficients of the optimized configurations are derived.

It is found that each type of defect

produces characteristic peaks in the curves of the imaginary part of the dielectric function but the absorption coefficient curves are similar.

Hence, the different kinds

of defects in arsenene can be identified from the optical spectra.

To determine the

causes for these changes in the optical properties, the band structures of the supercells of arsenene with different types of defects are studied and our results reveal that the defects indeed alter the dielectric and absorption spectra.

METHODS The first-principles calculation is based on the density functional theory (DFT) in the Vienna ab-initio simulation package (VASP).15,16 The projector augmented wave method17 is adopted and the total energy of each supercell is calculated by generalized gradient approximation (GGA) in the framework of the Perdew–Burke–Eruzerhof 4


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(PBE)18 exchange-correlation functional. The electron–ion interaction is described by the norm-conversing pseudopotential and the As 4s24p3 orbitals are treated as valence bands.

To expand the plane-wave, the cut-off energies in the calculation are set to

325 eV and the van der Waals (vdW) interactions are considered using the DFT-D2 method of Grimme.19 Since the semiconductor bandgap is underestimated in local density approximation (LDA), the hybrid (HSE06)20 functional is implemented to overcome this limitation.

The vacuum region in the z direction between two

adjacent As slabs is 16 Å to avoid the interaction.

Three kinds of hexagonal

supercells 4×4×1, 5×5×1, and 6×6×1 are adopted and MV, DV, and SW are introduced.

The Monkhorst-Pack21 method is used to sample the Brillouin zone and

the k-point meshes are set to be 5×5×1 in all the supercells.

The self-consistent field

(SCF) tolerance is 1.0×10−5 eV/atom in the energy calculation and all the atom positions and supercell lattices are relaxed.

The optimized geometries are adopted to

calculate the associated optical properties and electronic structures.

RESULTS AND DISCUSSION We first construct a 4×4×1 supercell of the pristine monolayer arsenene consisting of 32 atoms.

The supercell is optimized with and without vdW correction.

Due to the

optimization, the length difference of the lattices along the x direction is only 0.023 Å. When the vdW correction is not introduced, the optimized geometric structure of the pristine monolayer arsenene has a buckled height of h = 1.398 Å in the z direction and As-As bond length of 2.509 Å.

The two parameters are similar to those found 5



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previously.10,22 We then remove one As atom and relax the supercell and the final configuration is shown in Figure 1a, named MV-1. optimized structures without vdW correction.

Here we only depict the

The equivalent three atoms A, B, and

C move towards the vacancy center by the same distance consequently deforming the configuration slightly. The distance between any two of the three atoms decreases from 3.608 to 3.297 Å.

The side-view of the structure in Figure 1a indeed shows a

small change compared to the pristine geometry.

The similar MV-1 configurations

also exist in graphene23 and silicene24,25 but have a higher symmetry than any other types of MV structures.

The reconstructed structure of the second MV, denoted

MV-2, is shown in Figure 1b.

The initial configuration of MV-2 is constructed by

referring to the self-healing MV in silicene.25 In the MV-2 structure, atom A moves towards the y direction while atoms B and C move in the opposite direction. displacement of atom A is larger than that of atom B or C.

The

The distance between

atoms B and C decreases from 3.608 to 3.490 Å but it is still longer than that (3.297 Å) in the MV-1 structure. The equivalent Si atom in the self-healing MV structure25 of silicene bonds with its nearest four Si atoms and lengths of four Si-Si bonds are equal to each other.

The Si atom in the center forms a saturated valence state by sp3

hybridization, and there are no dangling bonds.

However, one As atom in arsenene

tends to form valence bonds with the near three As atoms to achieve the saturated state.

Finally, atom A shown in Figure 1b is not located at the center of the vacancy.

The third kind of MV structure (MV-3) is depicted in Figure 1c and the top view of this configuration resembles that of the MV (5-9 type) configuration in graphene and 6


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carbon nanotubes containing one pentagon and one nonagon ring.

As shown by the

side view of the MV-3 structure in Figure 1c, atom A moves a little in the y and –z directions.

However, the Si atom in the corresponding MV configuration in silicene

moves upward from the silicene plane.25 Although the top views of the MV-3 structures of arsenene and silicene are similar, the side views are different from each other.

The distance between atoms B and C decreases to 2.832 Å and is much

shorter than those in the MV-1 and MV-2 structures.

Because the shorter distance

between atoms B and C eliminates the dangling bonds in MV-3, it is inferred that MV-3 is in the ground state and more stable than MV-1 and MV-2.

In order to

investigate the SW defects in arsenene, we construct the initial structure by rotating the two adjacent As atoms by 90° with regard to the midpoint of their bond.

The

most notable feature of this optimized structure is that in the top view, the bond orientation of atoms A and B and the y axis forms a 23° angle instead of being parallel to each other.

The shape of the two five-membered rings and two seven-membered

rings in the final SW structure is more irregular than those in the graphene26 and silicene.27 The side view in Figure 1d clearly shows this characteristic of SW structure. The two kinds of DVs, named DV-1 and DV-2, are shown in Figures 1e and 1f, respectively.

The relaxed DV-1 structure shows a 5-8-5 pattern which is similar to

that in graphene.28 DV-1 can be derived from the coalescence of two MVs or formed when the two nearest atoms are lost.

The reconstructed DV-2 (555-777) defect

contains three pentagons and three heptagons, which can stem from transformation of DV-1 by rotating a bond. The DV-2 defects also exist in the graphene28 and silicene29. 7



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In the same way, the defective configurations are constructed in the 5×5×1 and 6×6×1 supercells and the reconstructed defective structures in the supercells are similar. The differences mainly originate from the interactions of adjacent defects and it is inferred that the defect structure will converge when the volume of the supercell is increased. The defect formation energy ∆Ef of each configuration is calculated to determine which kind of defects is more stable and the results are listed in Table I. The defect formation energy is defined as ∆Ef = Esupercell − N×EAs, where Esupercell is the total energy of the supercell with defects, N is the number of the As atoms in the supercell, and EAs is the energy of the As atom in pristine arsenene.

The defect formation

energy ∆Ef increases when the vdW correction is included.

As the defect

concentration goes up, the enhanced interactions between defects relax the system to a lower energy state.

For instance, in the MV-0 defect structure, ∆Ef of the 4×4×1

supercell is the smallest and that of the 6×6×1 supercell is the largest in the cases with or without vdW correction.

MV-3 is more stable than the other two MVs and MV-1

is the most unstable. ∆Ef of SW is about 1.0 eV which is the smallest because only bonds are rotated and no atoms are lost in this defect structure.

Compared with

silicene29 and graphene,24,26,30 arsenene with the same kind of defect has smaller ∆Ef, indicating that it is more likely to form defects in arsenene.

The reported ∆Ef of

phosphorene31 is close to ∆Ef of arsenene based on our calculation. There are other important problems associated with the thermal stability of the defects in arsenene.

We study the stability of vacancies and SW defect in arsenene 8


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by the first-principles MD simulations in which the canonical ensembles are selected. The simulation time and time step are set to be 10.0 ps and 1.0 fs, respectively.

It is

found that MV-3, DV and SW configurations are thermally stable and can keep themselves at room temperature (300 K).

The temperature fluctuation of MV-3, SW

and DV configurations in the MD simulations at 300 K are shown in Figures S1a-d (Supporting Information).

The previously reported result also demonstrated that

MV-3 can keep itself at room temperature (300 K),32 which is consistent with our conclusion.

However, MV-1 and MV-2 quickly transform into MV-3 at low

temperature (30 K) in the initial 2.0 ps and several hundred femtoseconds, respectively.

This suggests that the MV-1 and MV-2 possible transform into MV-3

when there is thermal perturbation and MV-2 is changed more easily. At the low temperature, it is still possible to observe the MV-1 and MV-2 defects. In addition, we are interested in the rearrangement and migration of the defects in the monolayer arsenene. Figures 2a-c show the energy barriers and structure transformation of MV-3.

It can be seen that TS, TS1 and TS2 denote the saddle

points and IM respects the metastable hollow site.

As shown in Figure 2a, the defect

structure rotates by overcoming a rather low barrier (0.054 eV), which is lower than the barrier (0.1 eV) of graphene.33 Hence, the rotation of MV-3 is easy to occur by the thermal perturbation. Figure 2b.

The second structure transformation of MV-3 is depicted in

The As atom climbs over the 0.373 eV barrier and reaches the location of

the lost As atom.

The two kinds of structure transformations do not involve in the

migration of the MV-3 defect. There is another more complicated structure 9



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transformation in Figure 2c. It causes the center of MV-3 to move toward down-right. The brown atom diffuses from the initial to final position with a distance of 3.7 Å. The

diffusion

coefficient

D

is

obtained

by

the

formula

of

D ∼ ga 2ν 0 exp( − E / k BT ) ,25 where g is the geometrical factor and is set to 1, a is the distance of 3.7 Å, ν 0 is the vibration frequency of 1012 Hz, E is the energy barrier of 0.744 eV, kB is the Boltzmann constant, and T is set to 300 K. We finally obtain the diffusion coefficient of 1.33×10-11 cm2/s, which is much lower than that of MV in silicene,25,29 but higher than that of MV in graphene.34 In Figure 3a, the activation barrier and path for SW defect are shown, and SW defect transforms from the pristine arsenene by rotating the As-As bond. The forward barrier is 1.136 eV, which is lower than those in graphene (10 eV)30 and silicene (2.64 eV)29.

Compared to graphene and silicene, arsenene more easily generates the SW

defect.

In addition, the reverse barrier is 0.056 eV, which is much smaller than those

in graphene (5.0 eV)30 and silicene (0.5 eV).29

It is inferred that the SW defect can

be eliminated by rapid annealing and the material transforms into the pristine arsenene. As shown in Figure 3b, the DV-1 (5-8-5) defect can also transform into the DV-2 (555-777) defect by rotating the As-As bond. The energy of DV-1 is 0.061 eV lower than that of DV-2, which is opposite to the case in graphene30 and silicence.29 Though the structure transformations in Figures 3a and 3b both involve in the As-As bond rotations, the difference of the curves is obvious, which indicates that the shapes of the potential energy surfaces in these two cases are different. Because the shape of the curve in Figure 3b is almost symmetrical and both forward and reverse energy 10


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barriers are approximately equal to 1.4 eV, the probability of mutual transformation between DV-1 and DV-2 is almost the same. To find an effective method to examine these defects, we calculate the optical properties of the pristine and defective arsenene described in the independent-particle picture.

The imaginary part

ε 2 (ω) of the dielectric function ε (ω ) can be

determined by the following equation,35

ε 2 (ω ) =

2e 2π Ωε 0

∑

r k ,c,v

r r Ψ ckr u ⋅ r Ψ kvr

2

δ ( E c − E v − hω ) , r k

(1)

r k

where the real part ε1(ω) is obtained by the Kramer–Kronig relationship.

The

absorption coefficient α (ω) can be derived from the dielectric function by the 1/ 2

equation α (ω ) = 2ω  ε12 (ω ) + ε 22 (ω ) − ε1 (ω )   

spectra, the HSE06 hybrid functional is adopted. parts

.

To obtain accurate optical Figures 4a-g plot the imaginary

ε 2 (ω) of the dielectric functions of the pristine and defective structures using

the 4×4×1 supercells.

The black and red curves correspond to the two polarization

directions of the electric field of the incident light along the x and y axes of the supercells, respectively, and the incident light is perpendicular to the arsenene plane. As shown in Figure 4a, the two curves of ε 2 (ω) coincide completely because of the geometric symmetry of the pristine arsenene.

Despite the absence of an As atom in

the MV-1 structure, the reconstructed supercell retains the highest symmetry among the three MV defect structures.

Therefore, the two curves in Figure 4b also coincide

completely.

As shown in Figures 4b-d, there are two main peaks induced by MV in

each curve.

In Figure 4b, the top left and lower right peaks are at 0.40 and 1.54 eV,

respectively, and the height ratio is about 3.0.

With regard to the MV-2

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configuration in Figure 4c, there is clear separation between the two lines because of the geometric asymmetry along the x and y directions.

The height ratio of the two

main peaks on the x curve is larger (2.31) than that (1.39) in the y curve. peak in the curves of MV-2 is smaller than that in the curves of MV-1.

Each main In the MV-3

structure in Figure 4d, the height ratio of the two main peaks in the x curve is less than 1.0, whereas the height ratio of the two main peaks in the y curve is greater than 1.0.

As shown in Figures 4e-g, there is only one main peak in each curve when the

energy of incident photon is less than 3.0 eV.

Figure S2a (Supporting Information)

presents the curves of the pristine and SW configurations and the main peaks at different locations are denoted by arrows E1 and E2.

The shapes of the curves in the

pristine and SW configuration are different from each other and the difference can be used to identify the existence of the SW defects. Figure S2b (Supporting Information) shows the curves of the pristine and DV-2 configurations and the main peaks of DV-2 is indicated by arrow E3.

The difference of the shapes of these curves can also be

utilized to identify the DV-2 defect. In order to determine the reliability of the results from the independent-particle approximation, we adopt 3 × 3 × 1 supercells to calculate the optical properties of the MV-1, SW and DV configurations with and without local field effects.

It is found that the local field corrections reduce the

intensities of the main peaks in the curves of the imaginary part of the dielectric function from the pristine arsenene, while the intensities of the peaks associated with the defects decrease slightly.

The most important is that all the peak positions do not

change when the local field effects are included, and no new peak is induced by the 12


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local field corrections.

This means that the conclusions are reliable if the local field

corrections are not included in the calculations.

Because the calculations become

very time consuming, we no longer calculate all the larger supercells when the local field corrections are included.

All the analyses of the optical properties are based on

the calculation results in the independent-particle picture. The absorption coefficients of the various configurations using 4×4×1 supercells are calculated and shown in Figures 5a and 5b.

For the polarization direction of the

electric field of the incident light along the x axis, the corresponding curves are plotted in Figure 5a. Arrows 1 and 2 represent the two main peaks of the curve of the MV-1 structure and the curve of the other MV structure also has two peaks in Figure 5a. The shapes of the curves of the SW and DV structures differ from that of the curve of the pristine structure.

When the polarization direction of the electric field of the

incident light is along the y axis, a similar feature occurs as shown in Figure 5b.

In

general, we can also use the absorption spectra to determine the types of the defects in arsenene and it is a better strategy if both of these two spectra are employed to identify the defects.

Considering that the optical properties may change with defect

concentrations, the 5×5×1 supercells are constructed to derive the dielectric and absorption spectra. Information).

The results are shown in Figures S3 and S4 (Supporting

There are still two main peaks in each curve of the MV structure but

the intensity and position of each peak change slightly with decreasing defect concentration.

When the concentrations of the MV-2 and MV-3 defects decrease, the

change of the imaginary part of the dielectric function is more obvious and so 13



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information about the defect concentrations can be obtained from the optical spectra. In general, the dielectric and absorption spectral characteristics impart information about the types of topological defects. Since the optical properties are dominated by the band structure, the energy bands are derived to determine the origin of the spectral changes.

We calculate the

band structure of primitive cell of monolayer arsenene and obtain the bandgap (2.22 eV) to compare with the previous research results.9,22 It is found that they are consistent.

The band structures of the pristine and MV-1 4×4×1 supercells are

shown in Figures 6a and 6b, which are plotted along the high symmetrical path Γ−Μ −K −Γ.

The horizontal blue dash line represents the Fermi level of which the

energy is set to zero.

The MV defect introduces two defect bands (red lines) in the

forbidden energy range of the pristine structure.

With regard to the pristine arsenene,

the conduction band minimum (CBM) is located at a point on the ΓΜ line and the valence band maximum (VBM) corresponds to the Γ point.

When MV is

introduced, the valence band edge around the K point moves up and the VBM at Γ moves down slightly. and K points.

Finally, the VBM of the MV-1 structure corresponds to the Γ

In contrast, the conduction band edge changes little.

passes through the defect band below.

The Fermi level

Because the optical transition between the

parallel conduction and valence bands is high, the transition denoted by the arrow in Figure 6b between the two red bands around K point is responsible for the left peak at 0.40 eV in Figure 4b.

The other two arrows around M and Γ represent the

transitions which induce the peak at 1.54 eV in Figure 4b. 14


The band structures of the

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other defect structures are shown in Figure S5 (Supporting Information,).

There are

two defect bands in the MV-2 and MV-3 structures, and the lower bands are intersected by the Fermi levels.

However, the two defect states at Γ are no longer

degenerate because of the lower symmetry than MV-1 configuration.

In the SW and

DV structures, the Fermi levels do not pass through the defect bands, which are close to the conduction and valence band edges. responsible for the single peak in Figures 4e-g.

These band characteristics are In general, the topological defects in

arsenene induce the defect states and significantly alter the optical spectra. charge distribution in the defect states is also studied.

The

The charge density isosurface

belonging to the two defective bands of MV-1 is depicted in Figure 6c by integrating the whole path Γ − Μ − K − Γ in the Brillouin zone.

The charge is mainly around

the vacancy and therefore these electronic states are quite localized.

The shape of

the isosurface is symmetrical due to the geometrical symmetry of the MV-1 structure. For the MV-2 and MV-3 structures, the shape of the charge density isosurfaces (Supporting Information, Figure S6) is similar to that of the MV-1 structure.

The

local differences in these isosurfaces originate from structural changes in MVs.

CONCLUSION In the buckled monolayer arsenene, the MV-3 configuration with the minimal defect formation energy is the most stable and the DV and SW defects show the reconstructed structures.

First-principles MD simulations show that MV-1 and

MV-2 easily convert to MV-3 at low temperature, and MV-3, DV and SW 15



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configurations are thermally stable at room temperature. Several energy barriers and paths are found by the transition state searches when the structure transformations take place. The diffusion coefficient of MV-3 is 1.33×10-11 cm2/s, which is much lower than that of MV in silicene, but higher than that of MV in graphene. Producing a SW defect requires overcoming a barrier of 1.136 eV, while eliminating a SW defect is much easier. The probability of mutual transformation between DV-1 and DV-2 is almost the same. Calculations of the imaginary part of the dielectric function and absorption coefficient show that MV can enhance optical transitions in the forbidden bands of pristine arsenene and two characteristic peaks emerge from the spectrum of the MV structures but the DV and SW defects produce rather different features in the optical spectra.

These spectroscopic properties provide information

about the topological defects in arsenene.

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AUTHOR INFORMATION Corresponding Author E-mail: [email protected] (X.L.W).

Fax: 86-25-83595535. Tel: 86-83686303.

Notes The authors declare no competing financial interest.

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Acknowledgments This work was jointly supported by National Basic Research Programs of China under Grants Nos. 2014CB339800 and 2013CB932901 and National Natural Science Foundation of China (No. 11374141 and 11404162).

Partial support was from City

University of Hong Kong Applied Research Grants (ARG) No. 9667122.

We also

acknowledge the computational resources provided by High Performance Computing Center of Nanjing University.

Supporting Information 17



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Temperature fluctuation, imaginary part of the dielectric function, absorption coefficient, band structure, charge density isosurface. This material is available free of charge via the Internet at http://pubs.acs.org.

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73, 045112.

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Figure 1. Top and side views of six optimized defect configurations of arsenene in the 4×4×1 supercells: (a-c) Three kinds of MVs denoted by MV-1, MV-2 and MV-3, respectively. (d) Stone-Wales defect called SW. (e,f) Divacancy defects called DV-1 (5-8-5) and DV-2 (555-777).

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Figure 2. Energy barrier and structure transformation of MV-3. (a,b) The defect with no migration and (c) the defect with migration.

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Figure 3. Energy barrier and transformation path from pristine to SW configuration (a) and from DV-1 (5-8-5) to DV-2 (555-777) (b).

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Figure 4. Imaginary part of the dielectric function of the pristine and defect 4×4×1 supercells: (a) Pristine, (b) MV-1, (c) MV-2, (d) MV-3, (e) SW, (f) DV-1, and (g) DV-2.

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Figure 5. Absorption coefficients of the pristine and defect structures.

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The

polarization direction of the electric field of the incident light is along the x axis (a) and y axis (b) of the 4×4×1 supercell, respectively.

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Figure 6. Band structures of (a) pristine and (b) MV-1 4×4×1 supercells. arrows represent the optical transitions.

The

(c) Charge density isosurfaces of the two

red defect bands of the MV-1 configuration.

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Table I. Defect formation energies calculated with and without vdW corrections. The defect formation energy unit is eV.

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TOC Graphics

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Optical Identification of Topological Defect Types in Monolayer

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