Infrared and Raman spectra of Bi₂O₂X and Bi₂OX₂ (X = S, Se, and Te) studied from first principles calculations

Abstract

The bismuth oxychalcogenide compounds contain many different kinds of materials, such as Bi₂O₂X and Bi₂OX₂ (X = S, Se, and Te). These materials have different but similar layered crystal structures and exhibit various interesting physical properties. Here, we have theoretically investigated their Raman and infrared spectra by first principles calculations based on density functional theory. It is found that in Bi₂O₂Se the calculated frequency of the A_1g Raman active mode is in good agreement with the experimental measurements while the other three modes are ambiguous or not observed yet. The Raman and infrared spectra of other materials are also presented and need further confirmation. Our work provides the structural fingerprints of these materials, which could be helpful in identifying the crystal structures in future experiments.

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1 Introduction

In recent years, bismuth oxychalcogenide materials Bi–O–X (X = S, Se, and Te) have attracted more and more attention. Among these materials, Bi₂O₂Se, synthesized more than forty years ago,¹ is one of the most studied materials and has now become a very hot topic due to its various and interesting physical properties. First, Bi₂O₂Se was suggested to be a good thermoelectric material.^2–7 In 2010, Ruleova et al. reported the thermoelectric properties of Bi₂O₂Se and they found that Bi₂O₂Se is an n-type semiconductor with a very low thermal conductivity and a relatively high figure of merit ZT about 0.2 at 800 K.² Several theoretical works were also conducted to explore its thermoelectric properties.^8–11 Second, Bi₂O₂Se has an ultrahigh electron mobility.^12–17 An earlier work in 2012 found that the room temperature Hall mobility of Bi₂O₂Se single crystal was on the order of 300 cm² s⁻¹ V⁻¹.¹² Recently, it was found that the low temperature (about 2 K) Hall mobility can reach more than 2.0 × 10⁴ cm² s⁻¹ V⁻¹ in Bi₂O₂Se thin film^13–15 and 4.0 × 10⁴ cm² s⁻¹ V⁻¹ in Bi₂O₂Se single crystal.¹⁶ Very recently, we have observed a superior Hall mobility of 2.2 × 10⁵ cm² s⁻¹ V⁻¹ at 2 K in a high quality Bi₂O₂Se single crystal.¹⁷ The high mobility in Bi₂O₂Se is possibly due to the self-modulation doping, i.e. the electron donor states lie above the lowest conduction band, not in the middle of the band gap.¹⁸ Furthermore, high mobility usually induces a large magnetoresistance (MR),¹⁹ which was also observed in Bi₂O₂Se. A longitudinal MR of about 600% (at 15 Tesla and 2 K) and 9000% (at 9 Tesla and 2 K) in Bi₂O₂Se single crystals was observed in two recent experiments.^16,17 Third, due to its high mobility and suitable band gap (about 0.8 eV), Bi₂O₂Se was used in optoelectronic devices and infrared (IR) photo-detectors.^20–22

Bi₂O₂Te has the same crystal structure as that of Bi₂O₂Se, but it is much less studied. Luu and Vaqueiro found that Bi₂O₂Te ceramics is an n-type semiconductor with a smaller band gap (0.23 eV), electron mobility (47 cm² s⁻¹ V⁻¹ at room temperatures), and ZT (0.13 at 573 K), compared with those of Bi₂O₂Se.²³ The similar compound Bi₂O₂S is also less studied. Bi₂O₂S was first synthesized in 1984 and it has a different crystal structure to that of Bi₂O₂Se.²⁴ There are only a few studies on its optical properties.^25–27 For example, it was found that Bi₂O₂S has an indirect band gap of 1.12 eV and it is an excellent photoelectric material.²⁷

On the other hand, there is another kind of bismuth oxychalcogenides Bi₂OX₂ (X = S, Se, and Te), which all share the same tetragonal lattice system. Among them, Bi₂OS₂ has been experimentally synthesized recently and it was a candidate as an optoelectronic material in the near-IR region.²⁸ First principles calculations indicated that the two-dimensional Bi₂OS₂ nanosheet possesses a direct band gap and an ultrahigh electron mobility (up to 2.6 × 10⁴ cm² s⁻¹ V⁻¹).²⁹ To the best of our knowledge, Bi₂OSe₂ and Bi₂OTe₂ have not been synthesized experimentally. However, first principles calculations showed that they have the same crystal structure as that of Bi₂OS₂.³⁰ In particular, the calculated electron and hole effective mass of Bi₂OX₂ is very small. For example, the effective mass of Bi₂OTe₂ is only 0.02 and 0.012 for electron and hole.³⁰ Another theoretical study indicated that Bi₂OX₂ materials show promising characteristics in applications for solar cells and thermoelectric devices.³¹

Besides Bi₂O₂X and Bi₂OX₂, the first BiS₂ family superconductor Bi₄O₄S₃ was studied over the past few years.^32,33 Later, it was found that Bi₄O₄S₃ is a mixture of the two phases, Bi₂OS₂ and Bi₃O₂S₃.³⁴ The former is non-superconducting, while the latter is superconducting.^34–36

Therefore, we can see that the Bi–O–X system contains many kinds of materials with various interesting physical properties. From the experimental point of view, it is of course very important to identify the structure of the grown crystal from the many similar Bi–O–X materials. In this regard, Raman and IR spectra are convenient and powerful methods to provide the structural fingerprints of materials. However, we find that the Raman and IR studies of these materials are quite lacking. Only a few works about the Raman spectra of Bi₂O₂Se and Bi₂O₂Te have been reported until now.^14,16,37,38 For this reason, we have systematically calculated the phonon, irreducible representations, Raman and IR spectra, vibrational eigenvectors of optical phonons, and polarized Raman configurations of six materials: Bi₂O₂X and Bi₂OX₂. We mainly present the results of Bi₂O₂Se and Bi₂O₂Te since they can be compared with other works. The Raman and IR spectra of the other four materials are also given briefly and could be referenced by future experiments.

2 Computational details

The vibrational properties of Bi₂O₂X and Bi₂OX₂ (X = S, Se, and Te) are calculated by density functional theory (DFT) implemented in the Vienna ab initio simulation package (VASP).^39,40 The projected augmented wave method^41,42 and the generalized gradient approximation with the Perdew–Burke–Ernzerhof exchange–correlation functional⁴³ are used. The DFT-D3 method^44,45 is used to correct the van der Waals interactions in these layered materials. The plane-wave cutoff energy is 520 eV for all materials. Both the internal atomic positions and the lattice constants are allowed to relax until the maximal residual Hellmann–Feynman forces on atoms are smaller than 0.002 eV Å⁻¹. The k-mesh is 8 × 8 × 2 for Bi₂O₂S and Bi₂OX₂ and 8 × 8 × 8 for Bi₂O₂Se and Bi₂O₂Te. The Phonopy package⁴⁶ is used to calculate the phonon frequencies, eigenvectors and irreducible representations of the materials. The crystal structures and eigenvectors are plotted by the VESTA program.⁴⁷

The IR and Raman activity of phonon modes can be analyzed by their irreducible representations. However their intensities need additional calculations. The IR intensity of a phonon mode is given by the corresponding oscillator strength:⁴⁸

where the e_β(s,v) is the normalized vibrational eigenvector of the νth phonon mode of the sth atom in the unit cell. α and β are the Cartesian coordinates: x,y,z. is the Born effective charge tensor of the sth atom. The Born effective charge tensor and the phonon eigenvectors are calculated by the density functional perturbation theory (DFPT) implemented in the VASP code. This method has been applied to different material systems.^48–51

The off-resonance Raman intensity of a phonon mode can be estimated by calculating the derivative of the macroscopic dielectric tensor with respect to the normal mode coordinate:⁵²

where the ε^∞ is the macroscopic high-frequency dielectric constant and Q(v) is the normal mode coordinate of the νth phonon mode. In practice, the derivative is replaced by the central difference based on the macroscopic dielectric matrix evaluated at positive and negative displacement along the phonon mode Q(v). The macroscopic dielectric matrix is also calculated by the DFPT method in the VASP code. This method has also been applied to different material systems.^53,54

3 Results and discussions

3.1 Crystal structures of Bi₂O₂X and Bi₂OX₂

The six materials Bi₂O₂X and Bi₂OX₂ (X = S, Se, and Te) have three different crystal structures. Bi₂O₂S belongs to a primitive orthorhombic lattice with a space group Pnnm (no. 58),²⁴ while Bi₂O₂Se and Bi₂O₂Te possess a body centered tetragonal lattice with a space group I4/mmm (no. 139).^1,13,23 On the other hand, Bi₂OX₂ have a primitive tetragonal lattice with a space group P4/nmm (no. 129).^28,55 All the materials show layered structures as shown in Fig. 1. Bi₂O₂X consists of two Bi₂O₂ and two X layers, while Bi₂OX₂ is composed of one Bi₂O₂ and two BiX₂ layers in a unit cell. Although the symmetries of Bi₂O₂S and Bi₂O₂Se are totally different, the structure of Bi₂O₂S is a slightly distorted form of Bi₂O₂Se.²⁴ Therefore, the difference between the two structures shown in Fig. 1(a) and (b) is hardly visible to the naked eye. All the structures shown in Fig. 1 contain ten atoms in the unit cell. However, Bi₂O₂Se and Bi₂O₂Te shown in Fig. 1(b) is a conventional cell, which in fact contains two primitive cells.

Fig. 1 Layered crystal structures of (a) orthorhombic Bi₂O₂S, (b) tetragonal Bi₂O₂Se and Bi₂O₂Te, (c) tetragonal Bi₂OS₂, Bi₂OSe₂, and Bi₂OTe₂. The purple, red, and yellow balls represent Bi, O, and S/Se/Te atoms respectively.

It is noted that among the six materials, to the best of our knowledge, Bi₂OSe₂ and Bi₂OTe₂ have not been synthesized experimentally. Their crystal structures are predicted to be the same as that of Bi₂OS₂ by first principles calculations.³⁰

The calculated lattice constants in this work with the DFT-D3 correction are listed in Table 1. It is obvious that our calculated results are well consistent with the experimental measurements with the largest difference less than 1%. Our results are also in good agreement with other theoretical work.³⁰

Table 1 Calculated lattice constants of Bi₂O₂X and Bi₂OX₂ (X = S, Se, and Te) in the unit of Å. Other theoretical and experimental results are also given for comparison

Symmetry	Material	Reference	a	b	c
Orthorhombic Pnnm	Bi2O2S	This work	3.837	3.848	11.94
		Experiment^24	3.840	3.874	11.92
		Theory^30	3.87	3.89	11.99
Tetragonal I4/mmm	Bi2O2Se	This work	3.891	3.891	12.20
		Experiment^1	3.891	3.891	12.21
		Experiment^13	3.88	3.88	12.16
		Theory^30	3.91	3.91	12.38
	Bi2O2Te	This work	3.984	3.984	12.65
		Experiment^23	3.980	3.980	12.70
		Theory^30	4.01	4.01	12.63
Tetragonal P4/nmm	Bi2OS2	This work	3.950	3.950	13.84
		Experiment^28	3.961	3.961	13.80
		Experiment^55	3.964	3.964	13.83
		Theory^30	3.96	3.96	13.69
	Bi2OSe2	This work	4.044	4.044	14.56
		Theory^30	4.05	4.05	14.46
	Bi2OTe2	This work	4.193	4.193	15.81
		Theory^30	4.17	4.17	15.99

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With the optimized structures, the zone-centered phonon modes, irreducible representations, IR and Raman spectra of the six materials are calculated. In the following subsections, we first present the detailed results of Bi₂O₂Se and Bi₂O₂Te since both materials have the same crystal structure and the Raman spectrum of Bi₂O₂Se is better studied than other materials. Then the brief results of Bi₂O₂S and Bi₂OX₂ are also given.

3.2 I4/mmm tetragonal Bi₂O₂Se and Bi₂O₂Te

The calculated zone-centered optical phonon frequencies of Bi₂O₂Se and Bi₂O₂Te are listed in Table 2. The highest phonon frequency of Bi₂O₂Se is about 433.3 cm⁻¹, while it is only 396.1 cm⁻¹ in Bi₂O₂Te due to the heavier atom mass. Bi₂O₂Se and Bi₂O₂Te have the same space group of I4/mmm (point group D_4h), and their irreducible representations at the Γ point in the Brillouin zone are:

Γ_acoustic = E_u + A_2u

Γ_optic = 2E_u + 2A_2u + 2E_g + A_1g + B_1g

There are five atoms in the primitive cell of Bi₂O₂Se, therefore we can find three acoustic and twelve optical modes. These irreducible representations are also assigned to each optical phonon mode as shown in Table 2. According to the character table of the D_4h point group, the E_u and A_2u modes are IR active, while the E_g, A_1g, and B_1g modes are Raman active in Bi₂O₂Se and Bi₂O₂Te. Therefore, both materials have four Raman active (two double degenerated E_g mode and two non-degenerated A_1g and B_1g modes) and four IR active modes (two double degenerated E_u modes and two non-degenerated A_2u modes), as indicated in Table 2.

Table 2 Calculated frequencies and Mulliken symbols of zone-centered optical phonon modes of Bi₂O₂Se and Bi₂O₂Te. The theoretical frequencies in other works by Pereira³⁷ and Cheng³⁸ are also listed for comparison. Raman or IR activity of each mode is also indicated by “Raman” and “IR”. The unit of the phonon frequency is cm⁻¹

Symmetry	Bi2O2Se			Bi2O2Te		Activity
	This work	Pereira^37	Cheng^38	This work	Cheng^38
Eu	54.8	59.2		56.4		IR
A2u	65.0	64.5		63.3		IR
Eg	67.3	72.0	67.99	69.1	67.01	Raman
A1g	162.9	165.7	159.89	150.4	147.48	Raman
Eu	268.0	293.9		243.6		IR
B1g	354.3	369.4	364.02	336.0	340.33	Raman
A2u	377.8	402.8		347.3		IR
Eg	433.3	444.0	428.68	396.1	386.15	Raman

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Recently, there have been two joint experimental and theoretical works by Pereira et al.³⁷ and Cheng et al.,³⁸ in which the phonon frequencies of Bi₂O₂Se and Bi₂O₂Te are also calculated. We listed their data in Table 2 for comparison. It is found that most of the calculated frequencies are in good agreement with ours, except for the two high-frequency IR active modes (E_u and A_2u) in Bi₂O₂Se, which have a maximal discrepancy of about 25 cm⁻¹. Phonon frequencies depend on the second derivative of the total energy, therefore the accuracy of the phonon calculation is usually not as good as the ones of the total energy calculations. Many parameters, such as the exchange–correlation functional, will affect the theoretical phonon frequencies. Therefore, we think such differences between these works are acceptable in phonon calculations.

We also illustrate the vibrational eigenvectors of Bi₂O₂Se in Fig. 2. It is found that the two low-frequency Raman active modes (E_g and A_1g) are related to the in-plane and out-of-plane vibrations of Bi atoms, respectively. While the two high-frequency Raman active modes (B_1g and E_g) represent the out-of-plane and in-plane vibrations of O atoms, respectively. Vibrations of Se atoms are not involved in any Raman active modes. The two low-frequency IR active modes (E_u and A_2u) are related to the in-plane and out-of-plane vibrations of Bi and Se atoms, respectively. While the two high-frequency IR active modes (E_u and A_2u) mainly represent the in-plane and out-of-plane vibrations of O atoms, respectively. The vibrational eigenvectors of Bi₂O₂Te are similar to those of Bi₂O₂Se, which are not shown here.

Fig. 2 Vibrational eigenvectors of the zone-centered optical phonon modes shown in the primitive cell of Bi₂O₂Se. The purple, red, and yellow balls represent Bi, O, and Se atoms respectively.

Then we present a detailed analysis about the polarized configurations for the Raman active modes of Bi₂O₂Se and Bi₂O₂Te. The Raman tensors of the D_4h point group can be written as:

Qualitatively, the Raman intensity I of a phonon mode can be calculated by the formula I ∞ |e_i·P·e_s|², where e_i and e_s are polarization directions of the incident and scattered light and P is the Raman tensor given above. In Table 3, we present the non-equivalent polarized configurations for the Raman active modes of Bi₂O₂Se and Bi₂O₂Te. In the configuration notation A(BC)D, A and D represent the propagation directions of the incident and scattered light respectively, while B and C represent the polarization directions of the incident and scattered light respectively. In the right angle scattering geometry, the propagation directions of the incident and scattered light are orthogonal (first five configurations in Table 3). In the back scattering geometry, the propagation directions of the incident and scattered light are anti-parallel (last four configurations in Table 3).

Table 3 The right angle and back scattering geometries in the polarized configurations of Raman active modes of Bi₂O₂Se and Bi₂O₂Te. The modes that can be observed in the configuration are indicated by the mark ✓

Configurations	A1g	B1g	Eg
X(YY)Z	✓	✓
Z(XX)Y	✓	✓
X(ZZ)Y	✓
X(YZ)Y			✓
Z(XZ)X			✓
−Z(XX)Z	✓	✓
−Y(XX)Y	✓	✓
−X(ZZ)X	✓
−X(YZ)X			✓

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From Table 3, it is interesting to find that the E_g mode cannot be observed with the A_1g and B_1g ones simultaneously under the same polarized configuration. Also, only one A_1g mode can be observed in the polarized configurations: X(ZZ)Y or −X(ZZ)X. Therefore, all of the Raman active modes can be well identified under different polarized configurations. Of course, in this case, the frequencies of the four Raman active modes in Bi₂O₂Se and Bi₂O₂Te are well separated and therefore it is quite easy to identify these modes in experiments according to their frequencies without considering their polarized configurations.

IR and Raman intensities of Bi₂O₂Se and Bi₂O₂Te are also calculated directly by first principles calculations based on the equations in Section II, which are shown in Fig. 3. From Fig. 3(a) and (c), we can see that the two high-frequency IR active modes (E_u and A_2u) have relatively higher intensities than those of the low-frequency modes (E_u and A_2u). On the other hand, in Fig. 3(b) and (d), the Raman active mode B_1g has the highest intensity for both materials, while the other three modes have much lower intensities.

Fig. 3 Calculated IR and Raman intensities (arbitrary unit) of Bi₂O₂Se and Bi₂O₂Te.

Recently, there have been four experimental works,^14,16,37,38 in which the Raman spectrum of Bi₂O₂Se was given. Wu et al. have synthesized the atomically thin two-dimensional and the bulk Bi₂O₂Se crystals and they observed two Raman peaks located at about 100 and 159 cm⁻¹.¹⁴ Tong et al. have grown high-quality Bi₂O₂Se single crystals and found two main Raman peaks located at around 90 and 159 cm⁻¹, which are associated with the symmetries of E²_g and A²_1g respectively.¹⁶ However, it seems that the E²_g mode in their Figure is made up of two adjacent peaks located at 84 and 90 cm⁻¹.¹⁶ Pereira et al. studied the physical properties of Bi₂O₂Se at high pressure, in which they only observed one most intense Raman peak at around 159.2 cm⁻¹ at room pressure.³⁷ The theoretical low-frequency E_g mode (near 70 cm⁻¹) can only be observed at high pressure.³⁷ Cheng et al. have measured the Raman spectra of Bi₂O₂Se and Bi₂O₂Te.³⁸ These results are summarized in Table 4, from which we can see that the Raman active mode A_1g at about 160 cm⁻¹ can be well confirmed, while the E_g mode below 100 cm⁻¹ is ambiguous. The discrepancy of the low-frequency E_g modes in the two experiments^14,16 is more than 10 cm⁻¹, and meanwhile both observed frequencies of the E_g modes are about 20–30 cm⁻¹ higher than the theoretical result. Furthermore, the two high-frequency Raman active modes (B_1g and E_g) have not been observed in all the experiments^14,16,37,38 in spite of the high intensity of the B_1g mode in our calculations. The possible reason is due to the phonon damping caused by the large carrier concentration in Bi₂O₂Se, as indicated in Pereira’s work.³⁷

Table 4 Comparison between calculated and experimental Raman frequencies of Bi₂O₂Se

	Raman frequency (cm^−1)
This work	67.3 (Eg), 162.9 (A1g), 354.3 (B1g), 433.3 (Eg)
Experiment^14	100, 159
Experiment^16	84/90 (E^2g), 159 (A1g)
Experiment^37	159.2 (A1g)
Experiment^38	160 (A1g)

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The Raman spectrum of Bi₂O₂Te was also measured in Cheng’s work,³⁸ which is listed in Table 5. The two observed Raman modes (A_1g and B_1g) are well consistent with our calculations. However, the two E_g modes are not observed in their work. It is interesting to point out that the missing B_1g mode in Bi₂O₂Se was observed in Bi₂O₂Te, although in a relatively low intensity compared to that of the A_1g mode. Therefore, the Raman spectra of Bi₂O₂Se and Bi₂O₂Te need further investigations. For example, one could try to measure the Raman spectrum of Bi₂O₂Se with a lower carrier concentration by doping or at low temperatures in a proper Raman polarized configuration.

Table 5 Comparison between calculated and experimental Raman frequencies of Bi₂O₂Te

	Raman frequency (cm^−1)
This work	69.1 (Eg), 147.48 (A1g), 336.0 (B1g), 396.1 (Eg)
Experiment^38	147 (A1g), 340 (B1g)

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3.3 Pnnm orthorhombic Bi₂O₂S

Although Bi₂O₂S has a very similar crystal structure to the one of Bi₂O₂Se shown in Fig. 1(a) and (b), they have a different symmetry. In fact, Bi₂O₂S has an orthorhombic crystal structure with a space group of Pnnm (point group D_2h). There are ten atoms in the unit cell of Bi₂O₂S resulting in thirty phonon modes. Its irreducible representations at the Γ point are presented as follows:

Γ_acoustic = B_1u + B_2u + B_3u

Γ_optic = 3A_u + 2B_1u + 5B_2u + 5B_3u + 4A_g + 4B_1g + 2B_2g + 2B_3g

The calculated zone-centered optical phonon frequencies of Bi₂O₂S and their symmetries are listed in Table 6. It is found that all of the modes are non-degenerate. According to the character table of the D_2h point group, the B_1u, B_2u, and B_3u modes are IR active, while the A_g, B_1g, B_2g and B_3g modes are Raman active. The A_u modes are neither IR nor Raman active. From our calculation, Bi₂O₂S should have twelve Raman and twelve IR active modes, as shown in Table 6.

Table 6 Mulliken symbols and frequencies of zone-centered optical phonon modes of Bi₂O₂S. Raman or IR activity of each mode is also indicated by “Raman” and “IR”. The A_u mode is neither Raman nor IR active. The unit of the phonon frequency is cm⁻¹

Symmetry	Bi2O2S	Activity	Symmetry	Bi2O2S	Activity
B2g	9.5	Raman	B3u	218.8	IR
Ag	13.9	Raman	Ag	285.2	Raman
Au	53.7		B3u	286.3	IR
B2u	54.9	IR	B2g	287.7	Raman
B3u	60.7	IR	B1u	288.5	IR
B1u	64.9	IR	B3u	364.4	IR
B3g	65.2	Raman	Ag	367.8	Raman
B1g	67.9	Raman	B2u	404.2	IR
B2u	75.7	IR	Au	448.9
B1g	83.0	Raman	B1g	450.6	Raman
Au	113.1		B3g	452.4	Raman
B2u	113.4	IR	B2u	457.5	IR
B3u	144.7	IR	B1g	519.1	Raman
Ag	170.6	Raman

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The vibrational eigenvectors of all the zone-centered optical modes and the polarized configurations of the Raman active modes are shown in Fig. S1 and Tables S1 and S2 in the ESI.†

IR and Raman intensities of Bi₂O₂S are also calculated directly by first principles calculations, which are shown in Fig. 4. It is found that the IR modes near 60, 290 and 400 cm⁻¹ have the highest intensities. In the Raman spectrum, the three A_g modes near 170, 285, and 370 cm⁻¹ have the highest intensities.

Fig. 4 Calculated IR and Raman intensities (arbitrary unit) of orthorhombic Bi₂O₂S.

It is noted that Bi₂O₂S has been synthesized in experiments,^24–26 however no Raman spectrum was measured yet. Recently, Cheng et al. have also calculated the Raman spectrum of Bi₂O₂S by the density functional perturbation theory in the local density approximation and norm-conserving pseudopotentials implemented in Quantum Espresso (QE) software.³⁸ We listed their data in Table 7 as well as ours for comparison. From the frequency perspective, we can see that the two calculations are in general consistent with each other. For example, in both works, there are five Raman modes below 100 cm⁻¹, one mode between 100–200 cm⁻¹, two modes between 200–300 cm⁻¹, and etc. Although the largest difference in a B_1g mode reaches 43 cm⁻¹ (about 10%), we still think it is acceptable since the two works use totally different methods in their calculations.

Table 7 Comparison between the theoretical Raman frequencies of Bi₂O₂S. For each row, the Raman modes are arranged according to their frequencies. The unit of the phonon frequency is cm⁻¹

This work	B2g	Ag	B3g	B1g	B1g	Ag	Ag	B2g	Ag	B1g	B3g	B1g
	9.5	13.9	65.2	67.9	83.0	170.6	285.2	287.7	367.8	450.6	452.4	519.1
Cheng^38	B2g	Ag	B2g	Ag	Ag	Ag	B1g	B3g	B1g	B1g	B3g	B1g
	20.52	29.23	64.34	68.23	82.86	154.20	263.85	273.27	386.85	407.76	417.30	520.28

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However, we noted that the Mulliken symbols in the two works are quite different. In particular, the four A_g modes in Cheng’s work are all below 200 cm⁻¹, while we have two A_g modes below 200 cm⁻¹ and two other ones above 200 cm⁻¹. The highest A_g mode in our work is more than 210 cm⁻¹ higher than theirs. This cannot be explained by the inaccuracy of the phonon frequency induced by the different parameters. It is possibly due to the different classification of the Mulliken symbols. In the D_2h point group, the assignment of B_1g, B_2g, and B_3g depends on the three mutually perpendicular 2-fold axes along the z, y, and x directions.⁵⁶ We have tested that QE software will give different Mulliken symbols (B_1g, B_2g, and B_3g) depending on the orientations of the orthorhombic unit cell of Bi₂O₂S. However, the assignment of the A_g mode should be unambiguous, which is independent of the directions of the unit cell. Therefore, we think the discrepancy of the A_g Raman modes in our work and Cheng’s work needs further investigations.

3.4 P4/nmm tetragonal Bi₂OS₂, Bi₂OSe₂, and Bi₂OTe₂

In experiment, Bi₂OS₂ has a space group of P4/mmm (point group D_4h).^28,55 However, to the best of our knowledge, Bi₂OSe₂ and Bi₂OTe₂ have not been synthesized in experiment. First principles calculations indicate that they share the same crystal structure as Bi₂OS₂.³⁰ There are ten atoms in the unit cell of Bi₂OX₂ (X = S, Se, and Te) as shown in Fig. 1(c), resulting in thirty phonon modes. The irreducible representations of Bi₂OX₂ at the Γ point are:

Γ_acoustic = E_u + A_2u

Γ_optic = 4E_u + 4A_2u + 5E_g + 4A_1g + B_1g

The zone-centered optical phonon frequencies and their symmetries of Bi₂OX₂ are listed in Table 8. The vibrational eigenvectors of Bi₂OS₂ are shown in Fig. S2 in the ESI.† The polarized configurations of the Raman spectra of Bi₂OX₂ should be the same as those of Bi₂O₂Se (Table 3) since they all belong to the D_4h point group.

Table 8 Mulliken symbols and frequencies of zone-centered optical phonon modes of Bi₂OX₂ (X = S, Se and Te). Raman or IR activity of each mode is also indicated by “Raman” and “IR”. The unit of the phonon frequency is cm⁻¹

Symmetry	Bi2OS2	Bi2OSe2	Bi2OTe2	Activity
Eu	26.0	18.8	6.5	IR
Eg	30.7	25.9	20.0	Raman
Eg	63.2	55.8	41.1	Raman
A2u	63.9	54.6	50.6	IR
A1g	73.2	64.1	53.5	Raman
Eu	97.7	73.2	49.2	IR
Eg	111.4	80.5	54.8	Raman
Eu	126.6	89.4	83.5	IR
A2u	129.4	97.2	84.5	IR
A1g	132.2	88.6	75.1	Raman
Eg	138.4	100.2	101.1	Raman
A1g	149.7	138.6	123.9	Raman
Eu	262.1	228.1	183.7	IR
A2u	286.0	182.3	140.9	IR
A1g	346.5	217.9	163.2	Raman
B1g	363.5	342.2	311.2	Raman
Eg	415.0	376.0	321.9	Raman
A2u	466.0	420.0	372.1	IR

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According to the character table for the D_4h point group, the E_u and A_2u modes are IR active, while the E_g, A_1g, and B_1g modes are Raman active. Therefore, there are ten Raman active (five double degenerated E_g modes, five non-degenerated A_1g and B_1g modes) and eight IR active modes (four double degenerated E_u modes and four non-degenerated A_2u ones) in Bi₂OX₂.

The IR and Raman intensities of Bi₂OX₂ are also calculated directly by first principles calculations, which are shown in Fig. 5. It is found that in the IR spectrum of Bi₂OS₂, there are six modes (E_u modes around 98, 127, 262 cm⁻¹ and A_2u modes around 129, 286, 466 cm⁻¹) which have relatively high intensities. For the Bi₂OSe₂ and Bi₂OTe₂, only four modes have high intensities. For the Raman spectra of Bi₂OS₂ and Bi₂OSe₂, there are two promising A_1g peaks around 132 and 346 cm⁻¹ for Bi₂OS₂, and 89 and 218 cm⁻¹ for Bi₂OSe₂. For Bi₂OTe₂, the A_1g Raman mode around 163 cm⁻¹ has the highest intensity.

Fig. 5 Calculated IR and Raman intensities (arbitrary unit) of tetragonal Bi₂OX₂ (X = S, Se, and Te).

Since the tetragonal Bi₂OSe₂ and Bi₂OTe₂ have not been synthesized in experiments, we also calculated their phonon dispersion and densities of state, which are not shown here. No imaginary frequencies are found in both materials. Therefore we think the tetragonal phases of Bi₂OSe₂ and Bi₂OTe₂ are stable and they could possibly be synthesized in future experiments.

4 Conclusions

We have systematically calculated the Raman and infrared spectra of six Bi–O–X materials: Bi₂O₂X and Bi₂OX₂ (X = S, Se, and Te). For each material, we present their optical phonon frequencies, Raman and infrared activities and intensities, Raman polarization configurations, and vibrational eigenvectors. In particular, the Raman spectra of Bi₂O₂Se and Bi₂O₂Te are compared with the existing experimental results. In Bi₂O₂Se, only one A_1g Raman mode is confirmed in experiments, while the other three are ambiguous or not observed yet. In Bi₂O₂Te, both A_1g and B_1g modes are well consistent with the experiments, while two E_g modes are not observed yet. Due to the various and important physical properties in these materials, our work could be helpful in identifying the crystal structure in future experiments.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by the National Key R&D Program of China (Grant No. 2016YFA0201104), National Basic Research Program of China (Grant No. 2015CB659400), National Natural Science Foundation of China (Grant No. 51872134, No. 51890860, No. 11890702, and No. 51721001), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20171343). Y. Y. Lv acknowledges the financial support from the Innovation Program for the Talents of China Postdoctoral Science Foundation (BX20180137). The use of the computational resources in the High Performance Computing Center of Nanjing University for this work is also acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ra02584g

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