Raman Spectra and Strain Effects in Bismuth Oxychalcogenides - The

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C: Physical Processes in Nanomaterials and Nanostructures

Raman Spectra and Strain Effects in Bismuth Oxychalcogenides Ting Cheng, Congwei Tan, Shuqing Zhang, Teng Tu, Hailin Peng, and Zhirong Liu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05475 • Publication Date (Web): 03 Aug 2018 Downloaded from http://pubs.acs.org on August 4, 2018

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The Journal of Physical Chemistry

Raman Spectra and Strain Effects in Bismuth Oxychalcogenides Ting Cheng, †,‡ Congwei Tan, †,‡ Shuqing Zhang, £ Teng Tu † Hailin Peng, †,‡,§,* and Zhirong Liu †,‡,§,* †

College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China. Center for Nanochemistry, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China £ The Low-Dimensional Materials and Devices Laboratory, Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen 518055, Guangdong, China § State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Beijing National Laboratory for Molecular Sciences, Peking University, Beijing 100871, China * Address correspondence to [email protected] and [email protected] ‡

ABSTRACT A new type of two-dimensional layered semiconductor with weak electrostatic but not van der Waals interlayer interactions, Bi2O2Se, has been recently synthesized, which shown excellent air stability and ultrahigh carrier mobility. Herein, we combined theoretical and experimental approaches to study the Raman spectra of Bi2O2Se and related bismuth oxychalcogenides (Bi2O2Te and Bi2O2S). The experimental peaks lie at 160 cm−1 in Bi2O2Se and at 147 cm−1 and 340 cm−1 in Bi2O2Te. They were fully consistent with the calculated results (159.89 cm−1, 147.48cm−1 and 340.33 cm−1), and were assigned to the out-of-plane A1g, A1g and B1g modes, respectively. Bi2O2S was predicted to have more Raman-active modes due to its lower symmetry. The shift of the predicted frequencies of Raman active modes was also found to get softened as the interlayer interaction decreases from bulk to monolayer Bi2O2Se and Bi2O2Te. To reveal the strain effects on the Raman shifts, a universal theoretical equation was established based on the symmetry of Bi2O2Se and Bi2O2Te. It was predicted that the doubly degenerate modes split under in-plane uniaxial/shear strains. Under a rotated uniaxial strain, the changes of Raman shifts are anisotropic for degenerate modes although Bi2O2Se and Bi2O2Te were usually regarded as 1

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isotropic systems similar to graphene. This implies a novel method to identify the crystallographic orientation from Raman spectra under strain. These results have important consequences for the incorporation of 2D Bismuth oxychalcogenides into nanoelectronic devices.

exposure to air for months.6 Actually, Bi2O2Se

1. INTRODUCTION on

was initially studied in its bulk (ceramics) form

two-dimensional (2D) materials, some “star

as potential n-type thermoelectric material.7-10

materials” such as graphene,1-2 transition-metal

After Bi2O2Se was synthesized into ultrathin

dichalcogenide3 and black phosphorene4-5 have

crystal films with a thickness between tens to

attracted great interest due to their fascinating

two layers,6, 11 it was recognized as a superior

properties and potential applications. They can

semiconductor, e.g., field-effect transistors

all be categorized as van der Waals (vdWs)

made from it exhibit a current on/off ratio

materials considering the existence of vdWs

larger than 106 at room temperature.6 There

interaction between layers in their parent

exists a strong spin–orbit interaction in 2D

counterparts. Very recently, a new type of 2D

Bi2O2Se sheets,12 and they were shown to have

material with weak interlayer electrostatic

excellent

interactions instead

photodetectors.13-14 The ultrathin thickness may

With

the

boom

of

of

vdWs

studies

interaction,

optoelectronic

performance

as

Bi2O2Se, has been successfully synthesized.6

also

Bi2O2Se was found to possess both a suitable

properties.15 Inspired by the synthesis of

bandgap and an ultrahigh Hall mobility at low

Bi2O2Se sheets, attentions were also paid to the

temperatures, and more importantly, to exhibit

related class of bismuth oxychalcogenides such

excellent environmental stability even after

as Bi2O2Te and Bi2O2S,16-17 which were

greatly

2


enhance

thermoelectric

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predicted to possess intriguing piezoelectricity

theoretical analyses on the Raman properties

and ferroelectricity.17 They have adjustable

of the bismuth oxychalcogenides are still

bandgaps in a range between 0.2 eV and 1.5

lacking.

eV,17-19 and have little mismatched lattice parameters,

yielding

their

This work is also motivated by the

outstanding

importance of strain effect. The presence of

contributions to the 2D material family.

strain in low-dimensional materials modifies

For the studies of 2D materials, Raman

the crystal phonons, band structure and

spectroscopy is a valuable tool in analyzing

carrier mobility.26-31 The strain effects are

structure, defect and phase transition.20-22

important in understanding the performance

Incorporated

experimental

of nanoelectronic devices, particularly in the

measurements, theoretical calculations can

flexible electronics. Usually, tensile strains

provide

insights

result in mode softening, while compressive

which are essential for interpreting and

strains result in mode hardening. The shift of

utilizing

spectroscopic

phonon frequencies with hydrostatic strain

information. In the previous works on the

could also give the Grüneisen parameter,

AT2X2 (A= K, Rb, Cs, Tl; T= Fe, Co, Ni and

which

X= S, Se, Te) family which adopt a tetragonal

thermomechanical properties.32 In addition,

layered

group

combining the applied strain and Raman

I4/mmm, No.139) similar to Bi2O2Se and

shifts, one may identify the crystallographic

Bi2O2Te, the combination of experimental

orientation as previously shown in graphene,

and

MoS2 and WS2.27, 31, 33

with

additional

the

crystal

theoretical

microscopic

Raman

structure

Raman

(space

spectra

shows

remarkable advantages.23-25 So far, detailed

is

closely

related

with

In this work, we studied the Raman 3



Page 4 of 32

spectra of Bi2O2Se, Bi2O2Te and Bi2O2S as

2.

THEORETICAL

AND

well as the corresponding strain effects. We

EXPERIMENTAL METHODS

firstly briefly discussed the geometric and

2.1 First-principle calculations electronic structures of these materials, and The

calculations

of

the

geometric

then systematically studied the first-order optimization and electronic structure were Raman active modes using the group factor carried out within density functional theory analysis

combined

with

first-principle (DFT), and the phonon frequencies were

calculations

and

unpolarized

Raman obtained

within

the

density

functional

scattering experiments. To further compared perturbation

theory

(DFPT)

method

with the experiments, the experimental implemented in QUANTUM ESPRESSO geometry

configuration and

polarization

package.34 To obtain the phonon frequencies,

Raman scattering were also discussed here. we

adopted

the

norm-conserving

Lastly, we explored the Raman shifts in the pseudopotentials with the local density bulk and monolayer Bi2O2Se and Bi2O2Te approximation (LDA) exchange correlation with

applied

mechanical

in-plane function which is more suitable to phonon

uniaxial/shear strains. Rotational uniaxial

calculation.35

However,

LDA

usually

strain was also considered to reveal the underestimates the bandgap. Therefore, to anisotropic effect and provide a novel better verify the electron density using in the potential

method

to

identify

the DFPT method, we calculated the band

crystallographic orientation of samples by dispersion under LDA, and compared the means of the Raman shifts of split degenerate trend

with

the

results

using

Raman modes. Perdew-Burke-Ernzerhof-modified 4


the

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Becke-Johnson

(PBE-MBJ)

Ry/a.u. for the phonon calculations. For

exchange-correlation function which is more

monolayer calculations, interactions between

suitable to obtain an accurate gap.36 For the

the adjacent layers were limited by setting

reason of computational efficiency, we

vacuum intervals of at least 15 Å. All the

performed the MBJ calculation implemented

Raman spectra shown are plotted after

in Vienna ab initio simulation package

uniform Gaussian broadening.

(VASP).37-38

Spin-orbit

coupling

(SOC)

2.2 Material synthesis and spectra effects were also considered in both LDA and

measurements PBE-MBJ calculations. In the self-consistent The bulk Bi2O2Se and Bi2O2Te were field calculation, the kinetic and charge synthesized using an oxygenation method. In density energy cutoffs were set to 80 Ry and this case, the O2 was directly introduced to 320

Ry,

respectively,

when using

the induce a phase transformation from Bi2Se3 to

Quantum Espresso package, whereas the Bi2O2Se and from Bi2Te3 to Bi2O2Te (Figure cutoff kinetic energy was set to 520 eV when S1). Herein, bulk Bi2Se3 and Bi2Te3 were using the VASP. The Brillouin zones were employed and the trace amount of O2 was sampled with a 24×24×24 and 8 × 8 × 1 controlled by using a gas flow meter. The Monkhorst-Pack k-space mesh for the bulk pressure of the system was kept at 200 Torr primitive cell and monolayer Bi2O2Se and and the synthesis temperature range was Bi2O2Te, respectively, and with a 27×27×9

about 590-620oC. Raman spectra were

mesh for bulk Bi2O2S. The convergence collected

with

a

confocal

Raman

−9

criterion for the total energy was set to 10

spectrometer (Jobin Yvon LabRAM HR800) −5

Ry and atomic forces were smaller than 10

using a He-Ne laser (632.8 nm). 5



Page 6 of 32

3.RESULTS AND DISCUSSIONS 3.1

Geometric

and

electronic

structures We

investigated

three

bismuth

oxychalcogenide materials: Bi2O2Se, Bi2O2Te and Bi2O2S. Their optimized bulk crystal structures are shown in Figure 1 (a-c) and all possess the inversion symmetry. The typical structures consist of stacked BiO layers, Figure 1. Geometric structures of (a) the unit sandwiched by X (X=Se, Te and S) ions cell of Bi2O2Se (Bi2O2Te), (b) the primitive arrays with relatively weak electrostatic cell of Bi2O2Se (Bi2O2Te), and (c) Bi2O2S, (d) interactions. In each BiO layer, one O atom is the monolayer Bi2O2Se (Bi2O2Te). The dotted bonded to four Bi atoms to form an OBi4 lines in the side view are for the convenience tetrahedral. to mark the central axes. Bi2O2Se

and

Bi2O2Te

were

both

experimentally observed to be tetrahedral

adopted

with space group I4/mmm,18,

which have

constraint in our calculations so that the

ten atoms in the unit cell. Although

resulting Raman spectra below can be used to

ferroelectric phases with lower symmetry

interpret experimental results. As seen from

were predicted elsewhere,17 they have not

Figure 1 (a), the Se/Te atoms locate at the

been observed in experiments yet. Here we

vertexes and the center of the cell, Bi atoms

39

the

I4/mmm

symmetry

as

a

locate at the vertical edges and the vertical 6


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axis of the cell, while the O atoms locate at

it could withstand the temperature of

vertical middle lines of the side faces. In

800℃.

other

words,

at

Different from the highly symmetrical

high-symmetry points or lines. However, the

Bi2O2Se and Bi2O2Te, the primitive cell of

tetrahedral cell is not the smallest repeating

bulk Bi2O2S is not rhombohedral but

unit. Actually, it is composed with two

orthorhombic (with space group Pnnm) with

formula units. The smallest primitive unit cell

anisotropic lattice parameters (a ≠ b in the x-y

is rhombohedral and contains five atoms

plane) as revealed in the experiment.40 S

[Figure 1 (b)], which will be used to perform

atoms still locate at the vertexes and the

the Raman calculation. The monolayer

center of the unit cell, but Bi and O atoms all

Bi2O2Se and Bi2O2Te were also studied in

deviate from the high-symmetry lines [Figure

our

previous

1 (c)]. More specifically, the upper BiO layer

experimental structure,6 to preserve the point

shifts to the left (minus x axis) with a

symmetry D4h of the bulk, Se layers

displacement of 0.08 Å for Bi atoms and

terminate both the top and bottom surfaces

0.059 Å for O atoms (in our relaxed structure

and hydrogen atoms were adopted to

using LDA method), while the lower BiO

passivate the outermost Se

layers for

layer shifts to the right with the same

balancing the non-stoichiometry due to the

displacements. Therefore, Bi2O2S has a

additional Se layer [Figure 1 (d)]. The

slightly distorted structure. The calculated

thermal stability of monolayer Bi2O2Se has

structural parameters (both in LDA and PBE

been verified by Yu and Sun using the ab

method) agree to better than 2% with the

initio molecular dynamics simulation where

experimental

work.

all

atoms

Following

the

locate

15

7


values,18,

39-40

which

are


summarized

in

Table

1.

The

lattice

Page 8 of 32

method was displayed in Figure 2. It

parameters of three systems are close,

indicates

making

semiconductors with indirect bandgaps of

it

possible

to

fabricate

that

three

systems

are

all

0.87, 0.24 and 1.34 eV, respectively, agreeing

heterostructures with little lattice mismatch. The computed band dispersion by MBJ

Table 1. The optimized lattice constants for Bi2O2Se, Bi2O2Te and Bi2O2S calculated using LDA and GGA methods.

Family Bi2O2S Bi2O2Se Bi2O2Te

Atom

Space group

10 5 5

Pnnm I4/mmm I4/mmm

a (Å) b (Å) c (Å) a a LDA PBE Exp. LDA PBE Exp. LDA PBE Exp.a 3.77 3.83 3.93

3.90 3.92 4.01

3.87 3.88 3.98

3.74 3.83 3.93

3.87 3.92 4.01

3.84 3.88 3.98

11.73 12.02 12.54

12.05 12.38 12.88

11.92 12.16 12.70

a

The experimental values of Bi2O2S, Bi2O2Se and Bi2O2Te were adopted from reference [40], [39] and [18], respectively, to provide a comparision.

Figure 2. Electronic band structures calculated by MBJ method of (a) Bi2O2Se, (b) Bi2O2Te, (c) Bi2O2S and (d) their corresponding first Brillouin zone (following the notation rules in ref.41). SOC effect was considered here. 8


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well with the recent reported experiments on

A1g, B1g and Eg are Raman active. The other

Bi2O2Se (0.8 eV)6 and Bi2O2S (1.5 eV)42 and

A2u and Eu are infrared active. Here the letter

previous theoretical calculations17 (0.89, 0.16

“E” denotes the doubly degenerate modes in

and 1.25eV, respectively). Compared with the

the xy plane. For Bi2O2S crystals, due to the

MBJ method, the LDA method gives similar

lower symmetry (D2h point group) and more

band dispersion, although the gaps are

atoms (10 instead of 5) in the primitive cell,

obvious underestimated as usual (Figure S2).

there are more vibrational modes at the Γ

Γ=4Ag+3Au

point:

3.2 Raman spectra

+4B1g+3B1u+2B2g+6B2u+2B3g+6B3u, 3.2.1

Factor

group

analysis

and

where

one B1u, one B2u and one B3u are acoustic

first-principle calculations

modes, while Ag, B1g, B2g and B3g are Raman

Factor group analysis on the D4h (Bi2O2Se,

modes.

Bi2O2Te) and D2h (Bi2O2S) point group yields

The

a normal mode distribution and Raman

typical

vibrational

modes

of

Raman-active phonons and the predicted

tensors at the Brillouin zone center, which are

Raman scattering spectra of the Bi2O2Se,

collected in Table 2. For bulk Bi2O2Se and

Bi2O2Te and Bi2O2S are illustrated in Figure

Bi2O2Te with D4h point group symmetry, five

3. Because Bi2O2Se and Bi2O2Te share the

atoms in the primitive cell results in 15

similar

vibrational modes. Γ-point phonons could be

structure

with

I4/mmm

group

symmetry, they exhibit similar vibrational

represented by the irreducible representations

modes at the Γ-point and four modes (A1g,

of D4h as: Γ=A1g+3A2u+B1g+2Eg+3Eu, where

B1g, Eg1 and Eg2 ) among them are Raman

one A2u and one Eu are acoustic modes, while 9



Table 2. The types of atoms together with their Wyckoff positions and each site’s irreducible representations in the Γ-point phonons, as well as Raman tensors, phonon activites and selection rules for Bi2O2Se (Bi2O2Te) and Bi2O2S.

Atoms

Wyckoff position

Irreducible representations

Bi

4e (0, 0, z)

A1g + A2u + Eg + Eu

O

4d (0, 1/2, 1/4)

B1g + A2u + Eg + Eu

Se/ Te

2a (0, 0, 0)

A2u +Eu

Bi2O2Se (Te)

Raman Tensors Rˆ A1g

a =  0 0 

0 a 0

0 c 0  0  Rˆ B1g =  0 − c 0 0 b  

0 0 0 e 0    0  Rˆ E1 =  0 0 0  Rˆ E 2 =  0 g g  e 0 0 0 0    

0 0 f

0 f  0 

Activity and selection rules Γ Raman-active = A1g (α xx + yy , α zz ) + 2 E g (α xz , α yz ) + B1g (α xx − α yy )

Γacoustic = A2u + Eu Atoms

Wyckoff position

Irreducible representations

Bi, O

4g (x, y, 0)

2Ag + A2u +2B1g + B2g + B1u + 2B2u + B3g

S

2a (0, 0, 0)

B1u + Au + 2B2u + 2B3u

Raman Tensors

Bi2O2S

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 32

 a 0 0 0   ˆ ˆ R Ag =  0 b 0  RB1g =  d 0 0 c 0   

d

0 0

0 0  ˆ 0  R B2g =  0 e 0  

0

0 0

e 0  ˆ 0  RB3g =  0 0 0  

0 0 f

Activity and selection rules Γ Raman-active = 4 Ag (α xx , α yy , α zz ) + 4 B1g (α xy ) + 2 B2 g (α xz ) + 2 B3g (α yz )

Γacoustic = B1u + B2u + B3u

10


0 f  0 

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Figure 3. Raman spectra of bismuth oxychalcogenides. (a) The atomic displacements of all Raman-active vibrational modes in Bi2O2Se (Bi2O2Te) with a unit cell (top) or a primitive cell (bottom). (b) Four typical Raman-active modes in Bi2O2S, which are similar to those in Bi2O2Se (Bi2O2Te), while the other Raman-active modes can be found in Figure S3. (c) The predicted Raman spectra of Bi2O2Se, Bi2O2Te and Bi2O2S. The frequencies of presented Raman modes in (a, b) are labelled in (c).

active. The atomic displacements associated

the motions of Bi and O atoms along the

with the Raman active modes in the primitive

crystallographic z-axis, respectively. On the

and unit cells are both illustrated in Figure 3

other hand, the vibrations of Bi and O atoms

(a). For the A1g and B1g mode, they involve

within the xy-plane give rise to two groups of 11



Page 12 of 32

degenerate Eg modes. Therefore, we may

respectively.

identify the A1g and B1g phonons as the

symmetry, the predicted Raman frequencies

breathing modes whereas the two Eg modes

are in a sequence of 20.52 (B2g), 29.23 (Ag),

as the interlayer shear modes. In the case of

64.34 (B2g), 68.23 (Ag), 82.86 (Ag), 154.20

Bi2O2S, because of its lower symmetry, it

(Ag), 263.85 (B1g), 273.27 (B3g), 386.85 (B1g),

possesses more complicated atomic motions

407.76 (B1g), 417.30 (B3g) and 520.28 (B1g)

(four Ag, four B1g, two B2g and two B3g) at the

cm−1. It is noted that all Raman-active

Γ-point. We just choose four typical modes

vibrations come from the BiO layer while

among them to shown in Figure 3(b), which

there is no contribution from Se, Te or S

are similar with those in Bi2O2Se and

atoms. Therefore, the Raman frequencies of

Bi2O2Te. The other Raman-active modes can

three systems nearly appear in the same range

be found in Figure S3. The predicted Raman

(< 600 cm−1). Besides, the predicted peak

spectra are shown in Figure 3 (c). The

intensity is expected to be less accurate than

frequencies of four Raman modes in Bi2O2Se

the frequency since the experimental peak

are 67.99 ( Eg1 ), 159.89 (A1g), 364.02 (B1g) and

intensity is usually affected by many factors,

428.68 cm−1 ( Eg2 ), respectively, which are in

such as the substrate, the energy of the

line with the recently calculated results (72,

incident light, and so on.

For

Bi2O2S

with

lower

165.7, 369.4 and 444 cm−1, using the PBE 3.2.2 Experimental confirmations method).

43

The corresponding frequencies in In general, whether a Raman mode in

Bi2O2Te are a litter smaller than those in crystals could be observed in experiments is 1 g

Bi2O2Se, which are 67.01 ( E ), 147.48 (A1g), determined by its Raman tensor and the 2 g

−1

340.33 (B1g) and 386.15 ( E ) cm , experimental configuration. In the usual 12


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back-scattering configuration, one can only

results and the predictions is provided in

observe two intrinsic Raman peaks (A1g and

Figure 4 for the unpolarized Raman spectra

B1g) for Bi2O2Se and Bi2O2Te according to

of Bi2O2Se and Bi2O2Te in a back-scattering

the Raman tensors shown in Table 2, while

configuration.

for Bi2O2S, only Ag and B1g modes (eight

located at about 160 cm−1 in Bi2O2Se and 147

peaks)

observed.

cm−1 in Bi2O2Te could be assigned as the A1g

Observation of the Eg modes for Bi2O2Se

mode, which are in good match with our

(Bi2O2Te) or B2g and B3g modes for Bi2O2S

predictions (159.89 cm−1 and 147.48 cm−1,

requires measurement in the xz or yz planes

respectively). The experimental peak at the

of the sample, which would be hard for thin

340 cm−1 in Bi2O2Te (which is much less

2D sheets but easy for bulk samples.

sharp) could be assigned as the B1g mode,

are

expected

to

be

A comparison between the experimental

The

experimental

peaks

also being consistent with the prediction

Figure 4. Unpolarized Raman scattering spectra of (a) Bi2O2Se and (b) Bi2O2Te sheet samples (red) measured at room temperature in a back-scattering configuration compared with the theoretical results (blue). The frequencies of peaks are labelled. 13



Page 14 of 32

(340.83 cm−1). In the experiment we did not

additional Raman peaks.24,

observe a peak near 364 cm−1 (the predicted

evidence, in a previous high-quality Bi2O2Se

B1g mode) in Bi2O2Se. It is unclear whether

sample, only one Raman peak located at

the B1g peak is absent because the intensity is

about 160 cm−1 was also reported,11 where

too weak (noting that the detected intensity of

the peak at 160 cm−1 can be assigned to the

B1g mode is much lower than A1g mode in

A1g mode In the current case, no additional

Bi2O2Te) or for other unknown reasons. In a

peaks rather than the intrinsic Raman peaks

recent study of Bi2O2Se under high pressure

were observed, indicating the high quality of

by Pereira et al., the B1g mode was also not

our synthesized sample. On this occasion, the

observed

spectrum

reason for the disappearing of B1g in Bi2O2Se

measurement and only A1g mode (at about

requires further verification of experimental

159.2 cm−1) existed.43 They explained the

and theoretical studies.

in

the

Raman

44-45

As an

absence of B1g mode in terms of the

A better way to distinguish and assign

plasmon-phonon coupling L+ or L− bands of

different Raman modes in experiments is to

B1g modes caused by the large carrier

adopt polarized configurations. According to

concentration in n-type semiconductor.43

the selection rules, Ag and B1g modes of

According to previous Raman experiments

Bi2O2S could be easily distinguished in

and calculations on AT2X2 structures with

parallel

I4/mmm

configurations,

symmetry

(such

as

and

crossed while

more

polarization complicated

iron-chalcogenide compounds), defects such

configurations are required to distinguish A1g

as vacancy ordering, consequently, symmetry

and B1g modes in Bi2O2Se and Bi2O2Te (see

lowering, may lead to the appearance of

SI and Figure S4 for more details). Raman 14


Page 15 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. The calculated and experimental Raman frequencies for Bi2O2Se, Bi2O2Te, Bi2Se3 and Bi2Te3. The frequencies for Bi2O2Te and Bi2Te3 are listed in brackets. The structures were fully or partially relaxed depending on whether the lattice parameters were fixed to the experimental values in calculations or not, resulting in different frequency values as listed. Bi2O2Se (Bi2O2Te) space group I4/mmm Eg1

Bi2Se3 (Bi2Te3) space group R3 m Eg2

B1g

A1g

Eg

A1g

Eg

A1g

Fully 72.21 166.83 376.20 449.60 44.4 75 142.7 180.6 relaxed (72.84) (154.25) (352) (408.03) (43.2) (64.4) (112.8) (140.8) Partially 67.99 159.89 364.02 428.68 40.4 68 135 174.2 relaxed (67.01) (147.48) (340.33) (386.15) (40) (58.8) (108.9) (138.5) (-) 160 37 69 131 174 Exp.a (-) (147) (340) (-) (36) (62) (102) (133) a The frequency values of Bi2O2Se and Bi2O2Te are chosen from our experiments. And the experimental values of Bi2Se3 and Bi2Te3 are chosen from Ref. [47] and [48], respectively. modes in similar systems AT2X2 (with

to the values of lattice constants. Therefore,

I4/mmm

been

two schemes of structural optimization were

successfully distinguished with such an

adopted in our calculations. In the first

approach.24, 46 Limited by the current sample

scheme, the structure was fully relaxed where

condition, we did not pursue polarized

both the lattice constants and the atomic

Raman experiments here.

coordinates were optimized. In the second

group

symmetry)

have

To further verify the reliability of the

scheme, the structure was partially relaxed,

calculation methods, we performed extra

where only the atomic positions were

calculations on Bi2Se3 and Bi2Te3 to compare

optimized while the lattice parameters were

with the reported experimental results.47-48

kept at their experimental values. Similar

The Raman frequencies are usually sensitive

schemes were also applied for Bi2O2Se and 15



Page 16 of 32

are

366.10 and 409.95 cm−1 for Bi2O2Se, and

summarized in Table 3. It can be seen that the

59.20, 141.10, 340 and 364.35 cm−1 for

values obtained with fully relaxed structures

Bi2O2Te, all exhibiting red shifts from the

are obviously larger than the experimental

bulk except the E g1 mode (80.44 cm−1 vs.

values, owing to the fact that LDA usually

72.21 cm−1) in Bi2O2Se. Similar mode

underestimates the lattice parameters. In

softening has also been found in many vdWs

comparison, the results obtained under the

layer materials such as Bi2Se3 and Bi2Te3,

partially relaxed structure (with experimental

which may be explained by the weaker

lattice constants) are more consistent with the

interlayer restoring forces in the vibrations

observed values, with an average deviation as

when the number of layer decreases.47-48

Bi2O2Te.

The

obtained

results

small as 3.5 cm−1. Similar trend was also

3.3 Strain dependence of Raman 49

found in other systems such as MoS2.

spectra Therefore, to compare with the Raman In

this

section,

we

theoretically

experiments, it is better to adopt the investigated the Raman shift of monolayer experimental

lattice

parameters

in and bulk Bi2O2Se and Bi2O2Te (all with D4h

calculations. The calculated Raman spectra in symmetry) under the mechanical in-plane Figures 3 and 4 for Bi2O2Se and Bi2O2Te also strain. The applied strain tensor is written as: adopted such a scheme.

ε xx γ  ε=  ,  0 ε yy 

Apart from the bulk materials, we

(1)

calculated the Raman frequencies in fully

where εxx and εyy represent the uniaxial strain

relaxed monolayer Bi2O2Se and Bi2O2Te. The

along the x and y directions, respectively, and

resulting frequencies are 80.44, 153.59,

γ is the engineering shear strain which is 16


Page 17 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ω(ε xx , ε yy , γ ) = ω0 + k (ε xx + ε yy )

related to the usual (symmetric) shear strain

+ (high-order terms)

εxy as γ = 2εxy.30 Here, we focus on the linear

(3)

with only one independent parameter k effect of strain on vibration frequencies. under the linear expansion. When the mode is 3.3.1 In-plane uniaxial and shear strain

degenerate, it will split into two bands under

The Raman frequency ω is a function of

strains and the relationship between ω and ε

applied strain ε. For a non-degenerate

should be analyzed by examining the strain

vibrational mode such as A1g and B1g, the

response of the corresponding Hamiltonian.50

frequency ω could be generally expanded as

Under the D4h symmetry, the splitting of

a Taylor series of ε components:

degenerate modes such as Eg is given as (the

ω (ε xx , ε yy , γ ) = ω0 + k xε xx + k y ε yy + kγ γ + (high-order terms)

detailed deduction is given in the SI):

, (2)

ω1,2 (ε xx , ε yy , γ ) = ω0 + k (ε xx + ε yy )

where kx, ky and kγ are the linear coefficients,

± [∆k (ε xx − ε yy )]2 + (kγ γ )2 + (high-order terms)

which could be determined by separately , (4) applying the strain εxx, εyy and γ. Under the where k , ∆ k and kγ are three independent

D4h symmetry of Bi2O2Se and Bi2O2Te, the

parameters under the D4h symmetry. It is x-axis and y-axis are equivalent, which noted that the number of independent

requires that k x = k y ≡ k . Moreover, under a

parameters is determined by the symmetry. mirror reflection with a normal direction For

example,

graphene,

graphyne

and

along x- or y-axis, γ changes into −γ, and the graphdiyne have a higher symmetry (D6h), so

symmetry requires that kγ = 0 . Therefore,

∆k = kγ and there are only two independent

with the D4h symmetry, Eq. (2) is simplified

parameters for strain effect of Eg mode.50 into We conducted first-principle calculations 17



Page 18 of 32

respectively).55

on monolayer and bulk Bi2O2Se and Bi2O2Te with various εxx, εyy and γ strains up to േ4%. Before discussing the behaviors of the Raman spectrum, we first briefly survey the mechanical properties of the studied systems. The elastic constant C11 is critical in determining the mobility.51-52 The calculated C11 of monolayer Bi2O2Se was 100 J m−2 (see Figure S5 for the fitted curve), which compares well to the previous calculation with PBE method (92

J m−2).15 For Figure 5. The evolutions of Raman shift with

monolayer Bi2O2Te, it was a little smaller, 95 (a-d) uniaxial strain and (e-h) shear strain for J m−2. The shear modulus C66 of these two bulk Bi2O2Se. The calculated data points −2

materials are 54 and 50 J m , respectively. (squares and triangles) are fitted with a The obtained C11 of monolayer Bi2O2Se and parabolic equation (solid lines) and the fitted Bi2O2Te is only about one-third of that for linear coefficients (unit: cm−1/%) are also −2 53

graphene (358 J m ), and also smaller than shown in the panels. Red and blue are used to -2

that of graphyne (207 Jm ), graphdiyne (159 denote the

results under εxx and εyy,

Jm-2) or 8B-Pmmn borophene (253 Jm-2).50, 54 respectively. For the degenerate modes, the But it is comparable or even higher than that open and filled symbols are used to of monolayer black phosphorous (29

and distinguish the two splitting frequencies

102 Jm-2 along the x and y direction, under the uniaxial strain. 18


Page 19 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The calculated shift and splitting of

compressive strains. The E g2 mode shows

Raman frequencies under various strains

the largest slope, indicating that it is the most

were displayed in Figure 5 for bulk Bi2O2Se.

affected under uniaxial strain. Different from

The data points were fitted with parabolic

the effect of uniaxial strain where two

curves and the resulting linear coefficients

splitting branches of doubly degenerate Eg

(slopes) were listed in the figure. The fitting

modes always shift along the same direction,

works well. Under the D4h symmetry, the x-

a shear strain would soften one branch while

and

For

harden another with opposite slopes [Figure 5

with

(g, h)] as predicted by Eq. (4). For

respective to εxx and εyy were practically

non-degenerate A1g and B1g modes, they are

identical (−2.32 ≈ −2.33 for A1g mode and

unaffected by shear strain.

y-directions

nondegenerate

are

modes,

equivalent. the

slopes

−3.00 ≈ −3.07 for B1g mode), being

We have systematically investigated the

consistent with the analysis in Eq. (3). For

strain effects in Bi2O2Se and Bi2O2Te in both

each doubly degenerate Eg mode, it splits into

bulk

two

linear

calculated results were shown in Figure S6-8,

coefficients under εxx and εyy in a direct fitting.

and the extracted coefficients k , ∆ k and kγ

They are well grouped into two values (e.g.,

were summarized in Table 4. The coefficients

−2.37 ≈ −2.38 and −0.66 ≈ −0.63 for E g1

of Bi2O2Se are close to those of Bi2O2Te no

mode), which agrees well with our Eq. (4)

matter in the bulk form or the monolayer

and can be combined to give k and ∆ k .

form, owing to their similar structures and

Overall, all Raman modes show redshifts

vibration modes. For the differences between

under tensile strains and blueshifts under

the bulk and the monolayer, the coefficients

branches

and

gives

four

and

19


monolayer

forms.

Detailed


Page 20 of 32

Table 4. Determined coefficient k , ∆k and kγ (in units of cm−1/%) for four Raman-active modes in bulk and monolayer Bi2O2Se and Bi2O2Te under applied strains.

E 1g

Bi2O2Se Bi2O2Te

A1g

B1g

E g2

k

∆k

kγ

k

k

k

∆k

kγ

Bulk

−1.51

0.85

0.81

−2.33

−3.04

−7.72

0.75

6.33

Mono

−2.15

0.43

1.86

−2.31

−1.65

−5.97

0.56

6.59

Bulk

−1.88

0.95

1.05

−2.32

−3.53

−7.68

0.93

5.78

Mono

−1.61

0.41

1.56

−2.32

−1.67

−6.07

0.31

6.38

for B1g mode in monolayer are obviously

Therefore, based on Eqs. (3, 4), we have

smaller than the bulk ones, whereas those for

γ m = − k / ωm

the A1g mode keep nearly unchanged.

non-degenerate modes. Then, the γm that we

for

both

degenerate

and

The above extracted coefficients of

found for each mode were: 2.67, 1.50, 0.45

phonon shift under strains could give the

and 1.46 for Eg1 , A1g, B1g and E g2 modes in

Grüneisen parameter γm, which is a parameter

monolayer Bi2O2Se, respectively, and 2.72,

related with thermodynamic properties and

1.64, 0.49 and 1.67 for monolayer Bi2O2Te.

have been discussed in isotropic 2D materials

These values are comparable to those for the

such as graphene and 2H-MoS2.27-28 The

G (γm= 1.72) and 2D (γm=2.0) peaks of

Grüneisen parameter for a mode m, γm, is

graphene,27,

defined as:32

monolayer 2H-MoS2 (0.54, 0.65, and 0.21 for

γm = −

1 ∂ω m , ω m ∂ε

56

and are larger than those in

28 E ′′ , E′ , and A′1 modes) .

where the strain ε = εxx + εyy is the hydrostatic component of the applied uniaxial strain.

20


Page 21 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the Raman frequencies do not depend on the

3.3.2 In-plane rotated uniaxial strain When a uniaxial strain with a magnitude

direction of strain, which is different from

ε is applied along a direction with angle θ to

anisotropic

the x-axis, the stain tensor can be expressed

phosphorus.29 For degenerate modes such as

by a rotation transformation as:

E 1g and E g2 , Eq. (4) evolves into

ε xx ε xy  T ε(ε ,θ ) =  =R ε ε yy   xy

 ε cos2 θ =  −ε sin θ cos θ

ε 0  0 0 R  

−ε sin θ cos θ   ε sin 2 θ 

systems

such

as

black

ω1,2 (ε , θ ) = ω0 + {k ± [ ∆k cos(2θ )]2 + [ kγ sin(2θ )]2 }ε

, (8)

, (5) taking into account γ = 2εxy. Hence, the change rate of the frequency versus strain is

where R is the 2D rotation matrix:

cos θ R=  sin θ

angle-dependent:

− sin θ  . cos θ 

(6) k1,2 =

∂ω1,2 ∂ε

= k ± [ ∆k cos(2θ )]2 + [ kγ sin(2θ )]2

We could then obtain the variation of Raman (9)

frequencies under a rotated uniaxial strain by The change rates of Raman frequencies under

substituting Eq. (5) into Eqs. (3, 4). a rotating strain were demonstrated in Figure

Considering

the

linear

effects,

for

a 6 for Bi2O2Se. It was recognized from Eq. (4)

non-degenerate vibrational mode, Eq. (3) that the anisotropy depends on the relative

evolves into

ω (ε , θ ) = ω0 + k ε .

1 values between ∆ k and kγ . For the E g

(7) mode, the anisotropy is weak [Figure 6(a)]

Therefore, the strain effect on non-degenerate since its ∆ k and kγ , are close (0.85 vs.

modes such as A1g and B1g is isotropic, i.e., 0.81). In contrast, ∆ k and kγ are markedly

21



Figure 6. The changes of Raman frequencies under a rotated uniaxial strain for degenerate (a)

E g1 and (b) E g2 modes in bulk Bi2O2Se. The data were calculated from Eq. (9) with the values of k , ∆ k and kγ listed in Table 4. Red and blue lines represent k1 and k2 for two splitting bands, respectively. 2 different (0.75 vs. 6.33) for the E g mode,

that degenerate Eg modes in graphene or

so the

graphynes also split under a uniaxial strain,

[Figure

resulting anisotropic effect is strong 6(b)].

Such

a

difference

may

but the therein frequencies are isotropic since they have ∆ k = k γ due to the symmetry.

2 originate from the fact that the E g mode is

an in-plane vibration and is more sensitive to

The anisotropic strain effect can be

1 the applied strain, while the E g mode

utilized to determine the crystallographic

involves the motion of interlayer Bi atoms.

orientation of Bi2O2Se and Bi2O2Te in

The anisotropic effects under a rotated strain

experiments. When an experimental sample

were also found in monolayer Bi2O2Se and

is stretched along a fixed direction, k1,2 can

Bi2O2Te

supporting

be readily measured as the ratio between the

information (Figure S9). It is worth noted

change of frequency and the magnitude of

as

shown

in

the

22


Page 22 of 32

Page 23 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


strain, and then the orientation angle θ can be

predicted the Raman spectra of Bi2O2Se,

solved from Eq. (9) with the known

Bi2O2S and Bi2O2Te, and determined their

parameters k , ∆ k and kγ listed in Table 4.

response to mechanical strain. Bi2O2Se and

A practical scheme is provided here. Denote

Bi2O2Te share the similar structure with D4h

a = cos2 (2θ )  2  b = sin (2θ )

point symmetry and four Raman-active

(10)

modes (A1g, B1g and 2Eg). Experimental work then a recombination of Eq. (9) gives

(k1 − k2 )  ( ∆k ) = 2  2 (k1 + k2 )   k 2

2

(kγ ) k2

2

 a     b

was carried out to give the Raman spectra of (11)

Bi2O2Se and Bi2O2Te. The observed peaks

After a and b are solved from Eq. (11), θ is

(160 cm−1 in Bi2O2Se and 147 cm−1 and 340

determined to be

cm−1 in Bi2O2Te) were fully consistent with

  0o  45o θ =  a  1 arccos  2 a+b

(if b < 0) (if a < 0)

the

calculated

results

(159.89

cm−1,

147.48cm−1 and 340.33 cm−1) and were

(12)

(otherwise)

assigned to the out-of-plane A1g, A1g and B1g

The strain efficiency, i.e., the efficiency of a

modes, respectively. Bi2O2S, on the other

strain to transfer from the substrate to the

hand, possesses a lower symmetry (D2h) and

sample, does not affect the accuracy of the

more atoms in its unit cell, so it has more

determined θ as the previous study on black

Raman-active modes (4Ag, 4B1g, 2B2g and

phosphorus.29

2B3g). From bulk to the monolayer Bi2O2Se and Bi2O2Te, most Raman frequencies show

4. CONCLUSIONS redshift, which may result from the decrease In summary, based on group-theory

of the interlayer interactions as that in other

analysis and first-principles calculations, we

2D materials. To reveal the strain effects on 23



the Raman shifts, a universal theoretical

Page 24 of 32

ASSOCIATED CONTENT

equation was established based on D4h

Supporting Information.

symmetry. All Raman modes show redshifts under

the

tensile

strain.

The

The Supporting Information is available free

doubly

of

degenerate modes split under uniaxial and

charge

via

the

Internet

at

http://pubs.acs.org.

shear strains. Under a rotated uniaxial strain, the frequency variation of degenerate modes

SEM imagining, calculated bandstructure

is anisotropic although the x- and y-axes are

using

equivalent under the D4h symmetry, being in

Raman-active modes in Bi2O2S, polarization

contrast to the isotropic case of graphene

configuration in theory, detailed deducing

with D6h symmetry. This provides a novel

process of equations, calculated 2D elastic

method to identify the crystallographic

constant and remaining evolutions of Raman

orientation of the D4h system by measuring

shifts with strain.

the

LDA

method,

remaining

the changes of degenerate Raman modes under an applied uniaxial strains. Overall, the

AUTHOR INFORMATION

changes of Raman shift under strain and the

Corresponding Author

good match in the lattice constants are * E-mail: [email protected] beneficial

for

bismuth * E-mail: [email protected].

oxychalcogenides-based nanoelectronics and mechanical systems.

Author Contributions The

manuscript

was

written

through

contributions of all authors. All authors have 24


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TOC Graphic

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TOC 62x46mm (300 x 300 DPI)


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474x453mm (300 x 300 DPI)



450x355mm (300 x 300 DPI)


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Raman Spectra and Strain Effects in Bismuth Oxychalcogenides - The

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