Influence of Ch substitution on structural, electronic, and thermoelectric properties of layered oxychalcogenides (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te): a new insight from first principles

Abstract

We study the structural, electronic, and thermoelectric properties of p-type layered oxychalcogenides (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) from first principles. Ch substitution from S to Te enhances the local-symmetry distortions (LSDs) in CuCh₄ and OLa₂Bi₂ tetrahedra, where the LSD in OLa₂Bi₂ is more pronounced. The LSD in CuCh₄ tetrahedra comes from the possible pseudo-Jahn–Teller effect, indicated by the degeneracy-lifted t_2g and e_g states of Cu 3d¹⁰ orbital. The Ch substitution decreases bandgap from 0.529, 0.256 (Γ → 0.4Δ), to 0.094 eV (Z → 0.4Δ), for Ch = S, Se, Te, respectively, implying the increasing carrier concentration and electrical conductivity. The split-off energy at Z and Γ points are also increased by the substitution. The valence band shows deep O 2p states in the electron-confining [LaBiO₂]²⁺ layers, which is essential for thermoelectricity. (La_0.5Bi_0.5O)CuTe provides the largest thermoelectric power from the Seebeck coefficient and the carriers concentration, which mainly come from Te 5p_x/p_y, Cu 3d_zx, and Cu 3d_zy states. The valence band shows the partial hybridization of t_2g and Chp states, implied by the presence of nonbonding valence t_2g states. This study provides new insights, which predict experimental results and are essential for novel functional device applications.

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1. Introduction

Renewable energy sources are globally researched but maximizing their energy efficiency is challenging. Moreover, energy waste as thermal energy cannot be avoided in energy conversion processes. This condition leads to an increase in energy consumption. For the utilization of the energy waste, the thermal energy can be recovered and provide clean energy using the thermoelectric effect, which generates electric power from temperature (T, in K) gradient.^1–5 The thermoelectric effect is measured by the figure of merit (ZT) formulated bywhere S is the Seebeck coefficient (in V K⁻¹), σ is the electrical conductivity (in S m⁻¹), and κ is the thermal conductivity (in W m⁻¹ K⁻¹).^1,6 S can be expressed by the Mott formula,^7,8 which is formulated bywhere q is the elementary charge (q = 1.602 × 10⁻¹⁹ C), k_B is the Boltzmann constant (k_B = 1.381 × 10⁻²³ J K⁻¹), and μ(E) is the mobility (in m² V⁻¹ s⁻¹). Furthermore, S, σ, and κ are dependent on each other as the functions of the carrier concentration (n, in m⁻³) and the electronic properties. Notably, κ is contributed by two sources, that are transporting heat of electrons and holes (κ_e), which is a function of σ, and phonons passing through crystal lattices (κ_l). This condition leads to the challenging attempts for finding the optimum values of these parameters for obtaining the high ZT.^1,9

The superlattice structures are promising in generating the thermoelectric effect. The p-type Bi₂Te₃/Sb₂Te₃ superlattice structure shows the high thermoelectric power with ZT up to 2.4 at room temperature (RT), which is the result of the optimum control of electrons and phonons.¹⁰ The similar superlattice structure, accompanied by n-type δ-doped Bi₂Te_3−xSe_x in the superlattice thermoelectric modules, show the high cooling fluxes, which is potentially useful for modern device applications.¹¹ Furthermore, the hybrid inorganic–organic superlattice is promising for the flexible thin-film thermoelectric material.¹² Moreover, the natural superlattice (SnS)_1.2(TiS₂)₂ has its thermoelectric performance improved in the in-plane direction. Moreover, σ along the in-plane is higher than that of the cross-plane directions, showing the anisotropic behavior. On the other hand, the lattice κ of this system is low because of the phonon scattering in the modulating periodic layers.¹³

The layered oxychalcogenides (RO)TmCh (R = La, Ce, Nd, Pr, Bi; Tm = Cu, Ag; and Ch = S, Se, Te) are the p-type semiconductors. The systems provide potential applications in thermoelectrics and optoelectronics¹⁴ and are considered as the natural superlattice systems consisting of the insulating oxide and conducting chalcogenide layers.^15–17 The systems have (LaO)AgS-type crystal structure with the space group of P4/nmm (no. 129), in which Ag (O) is tetrahedrally surrounded by S (La) atoms.^18,19 For example, the layered oxychalcogenides (LaO)CuCh show the wide bandgap (E_g) of 2.3 to 3.1 eV by substituting Ch from Te to S, providing potential applications in optoelectronics.^20–25 Also, the excitonic emission at RT has been observed.²⁶ Our previous report has shown that the dielectric constant (ε₀), the optical dichroism, and the plasmonic states of (LaO)CuCh systems can be tuned by the Ch substitution.²⁷ However, despite possessing the natural superlattice structure, (LaO)CuCh systems exhibit the low σ, indicating that these systems are not suitable for the thermoelectric application.²⁵

Regarding the layered oxychalcogenides, (BiO)CuCh (Ch = Se, Te) are more suitable for the thermoelectric application. (BiO)CuSe show ZT of 0.50 at 923 K, while (BiO)CuTe show ZT of 0.42 and 0.66 at 373 and 673 K, respectively.^6,15 From the experimental and first-principles perspectives, our previous report shows that, in spite of having the lower S than that of (BiO)CuSe system, (BiO)CuTe system provides the larger thermoelectric power due to the high σ and the metallic behavior. Intriguingly, Sr²⁺ and Ca²⁺ doping at Bi site and Ba doping modulation can enhance ZT of (BiO)CuSe system.^28–31 The previous report shows that La doping in (BiO)CuSe increases both σ and κ but decreases S as the La doping concentration (x) increases, leading to the maximum ZT of 0.74 at 923 K for x = 0.08. The increase of σ is induced by the significant increase of μ.³² It has also been shown that the increasing x from 0.02 to 0.06 enhances σ and n but reduces μ at high T. It is suggested that the increase of n is induced by the presence of Bi vacancies due to the doping.³³ On the other hand, the other report shows the increment of μ due to the increasing x.³⁴ However, doping (BiO)CuTe system for tuning the thermoelectric performance is still a few. For example, the enhancement of the thermoelectric power factor of 16% by Bi addition in (BiO)CuTe system at 723 K has previously been reported.³⁵ Moreover, structural properties and contributions of orbital states toward the thermoelectric properties of doped (BiO)CuCh are still yet to be explored.

In this paper, we investigate structural, electronic, and thermoelectric properties of layered oxychalcogenides (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems calculated by first principles. As the small x tunes the thermoelectricity of La-doped (BiO)CuSe,^32,33 we are interested in the possible role of the same portion of La and Bi elements in inducing new structural, electronic, and thermoelectric properties of (La_0.5Bi_0.5O)CuCh. The results are comprehensively discussed to investigate the effect of Ch substitution on the properties, which are compared to that of (LaO)CuCh and (BiO)CuCh systems. The structural properties were fully optimized to obtain their most stable condition, followed by calculations of band structure, total density of states (TDOS), and projected density of states (TDOS). This study reveals the local-symmetry distortion (LSD) at CuCh₄ and OLa₂Bi₂ tetrahedra, as well as the effect of Ch substitution on both electronic and thermoelectric properties.

2. Computational methodology

The structural and electronic properties of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems (space group: P4/nmm)^18,19 were calculated using Quantum-ESPRESSO package code.^36,37 Fig. 1 shows the crystal structure model of (La_0.5Bi_0.5O)CuCh unit cell. In the unit cell, the system consists of [LaBiO1O2]²⁺ and [Cu1Cu2Ch1Ch2]²⁻ layers showing CuiCh1₂Ch2₂ (i = 1, 2) and OkLa₂Bi₂ (k = 1, 2) tetrahedra. Ch1 and Ch2 element are also denoted by Chj (j = 1, 2). Table 1 summarizes the initial structural parameters based on that of (LaO)CuCh.³⁸ The use of i, j, and k is due to the structural symmetry distortion with the presence of two different layers, that are La and Bi layers. The term ‘distortion’ refers to the fact that the top and the bottom sides of [Cu1Cu2Ch1Ch2]²⁻ layers are located between different La and Bi layers, leading to the decrease of the structural symmetry degree. The structural symmetry distortion will be later discussed in Results and discussions.

Fig. 1 Crystal structures of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems. The corresponding unit cell consists of [LaBiO1O2] and [Cu₂Ch1Ch2] layers. Notations Ch1 (Ch2) represents Ch between Cu and Bi (La) layers. Blue and red shades denote CuiCh1₂Ch2₂ (i = 1, 2) and OkLa₂Bi₂ (k = 1, 2) tetrahedra, respectively.

Table 1 Initial structural parameters of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems

Initial lattice parameter (Å)		(La0.5Bi0.5O)CuS	(La0.5Bi0.5O)CuSe	(La0.5Bi0.5O)CuTe
a		3.9938	4.0670	4.1808
c		8.5215	8.8006	9.3441
Atoms (site symmetry symbol)	Initial atomic positions
Cui: Cu1 (xCu, −yCu, zCu), Cu2 (−yCu, xCu, zCu) (2b)	(xCu, yCu, zCu)	(1/4, 1/4, 1/2)	(1/4, 1/4, 1/2)	(1/4, 1/4, 1/2)
Ok: O1 (xO, −yO, zO), O2 (−yO, xO, zO) (2a)	(xO, yO, zO)	(1/4, 1/4, 0)	(1/4, 1/4, 0)	(1/4, 1/4, 0)
La (xLa, xLa, zLa), Bi −(xBi, xBi, zBi) (2c)	(xLa = xBi, zLa = zBi)	(1/4, 0.14763)	(1/4, 0.13963)	(1/4, 0.1267)
Chj: Ch1 (xCh1, xCh1, zCh1), Ch2 −(xCh2, xCh2, zCh2) (2c)	(xCh1 = xCh2, zCh1 = zCh2)	(1/4, 0.6623)	(1/4, 0.6698)	(1/4, 0.6754)

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The calculation employs the plane-wave method within the generalized gradient approximation (GGA), which includes the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functionals.³⁹ The previous reports have successfully carried out this method for various systems.^40,41 The norm-conserving pseudopotential methods are used to approach all-electron potentials. For Cui, Chj, and Ok atoms, the Troullier–Martins (TM) method^42–44 are used, while for La and Bi atoms, the Goedecker–Hartwigsen–Hutter–Teter (GHHT) method^45,46 are used. Note that we use the different pseudopotential methods since this technique can minimize deviations between experimental and calculated structural properties. This technique has been used in our previous report in investigating the structural and electronic properties of (LaO)ZnPn (Pn = P, As, Sb) systems.⁴⁷ The calculation is initiated by the full structural optimization by means of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method^48–51 with threshold force of ∼0.03 eV Å⁻¹. The corresponding command is variable-cell relaxation (vc-relax). Notably, the BFGS method is suitable for large molecular systems.⁵² Using this method, the optimized lattice parameters of several systems^53–56 are comparable with that of the corresponding experimental results. Hence, this method is also suitable for small systems. The Broyden mixing method⁵⁷ was used for the corresponding self-consistent field (SCF) calculation. The SCF calculation employed threshold and cut-off kinetic energies of ∼3.0 and ∼1088 eV, respectively, as well as k-point mesh of and 9 × 9 × 4. The SCF calculation was followed by the band structure calculation. A k-point path of Γ–X–R–Z–Γ–M–A–Z is used in the corresponding Brillouin zone. In the whole paper, visualizations of all crystal structures and calculations of LSD parameters are performed using VESTA.⁵⁸ Any term of ‘Ch substitution’ refers to the Ch substitution from S to Te.

3. Results and discussion

3.1. Structural properties

Table 2 presents the calculated structural parameters of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems compared with that of the previous experimental reports of (LaO)CuCh and (BiO)CuCh systems.³⁸ The structural parameters include the lattice parameters a and c. We use a general term Δη to represent Δa and Δc, which is the difference percentage between calculated data (η_calc) and experimental results (η_exp). This term is expressed as

Δη = [(η_calc/η_exp) − 1] × 100% (dimensionless). (3)

Table 2 Calculated structural parameters of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems (Calc) compared with the previous experimental results denoted by Exp₁ and Exp₂ for (LaO)CuCh and (BiO)CuCh,³⁸ respectively

Parameter		(La0.5Bi0.5O)CuS			(La0.5Bi0.5O)CuSe			(La0.5Bi0.5O)CuTe
		Calc	Exp1	Exp2	Calc	Exp1	Exp2	Calc	Exp1	Exp2
a (Å)		3.9699	3.9938(2)	3.8691(1)	4.0413	4.0670(1)	3.9287(1)	4.1442	4.1808(2)	4.0411(2)
c (Å)		8.5791	8.5215(4)	8.5602(4)	8.9197	8.8006(8)	8.9291(2)	9.4662	9.3441(8)	9.5237(5)
Δa (%)		—	−0.5981	2.6056	—	−0.6329	2.8651	—	−0.8746	2.5522
Δc (%)		—	0.6759	0.2207	—	1.3532	−0.1054	—	1.3072	−0.6033
Vcell (Å^3)		135.2083	135.9217	128.1456	145.6745	145.5662	137.8178	162.5799	163.3264	155.5267
Cu1 (xCu, −yCu, zCu)	xCu	0.2477	1/4		0.2481	1/4		0.2502	1/4
Cu2 (−yCu, xCu, zCu)	yCu	0.2481	1/4		0.2480	1/4		0.2501	1/4
	zCu	0.5016	1/2		0.4987	1/2		0.4988	1/2
O1 (xO, −yO, zO)	xO	0.2500	1/4		0.2500	1/4		0.2502	1/4
O2 (−yO, xO, zO)	yO	0.2502	1/4		0.2503	1/4		0.2503	1/4
	zO	−0.0014	0		0.0000	0		0.0004	0
La (xLa, xLa, zLa)	xLa	0.2497	1/4	—	0.2496	1/4	—	0.2499	1/4	—
	zLa	0.1566	0.14763(7)	—	0.1458	0.13963(6)	—	0.1280	0.1267(1)	—
Bi −(xBi, xBi, zBi)	xBi	0.2501	—	1/4	0.2497	—	1/4	0.2501	—	1/4
	zBi	0.1415	—	0.14829(5)	0.1347	—	0.14020(4)	0.1264	—	0.12733(9)
Ch1 (xCh1, xCh1, zCh1)	xCh1	0.2512	1/4	1/4	0.2510	1/4	1/4	0.2500	1/4	1/4
	zCh1	0.6567	0.6623(1)	0.6710(2)	0.6684	0.6698(1)	0.6758(1)	0.6771	0.6754(1)	0.6810(1)
Ch2 −(xCh2, xCh2, zCh2)	xCh2	0.2505	1/4	1/4	0.2507	1/4	1/4	0.2499	1/4	1/4
	zCh2	0.6722	0.6623(1)	0.6710(2)	0.6768	0.6698(1)	0.6758(1)	0.6772	0.6754(1)	0.6810(1)

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The terms Δa and Δc represent the percentages of the differences between the calculated and experimental a and c, respectively. The calculated a and c are increased by the Ch substitution, as also observed in the experimental for both (LaO)CuCh and (BiO)CuCh systems. This increase is due to the different effective ionic radii of S²⁻, Se²⁻, and Te²⁻, i.e., 1.84, 1.98, and 2.21 Å.⁵⁹ Furthermore, the previous experimental results show that both a and c are dependent on La and Bi, summarized in Fig. 2. The calculated results show that a is smaller than that of (LaO)CuCh and larger than that of (BiO)CuCh systems. On the other hand, the calculated c is larger than that of (LaO)CuCh and larger than that of (BiO)CuCh systems. However, (La_0.5Bi_0.5O)CuS shows that both a and c are larger than that of the experiments. This result indicates that the co-existence of La and Bi significantly influences both a and c. Moreover, in each (La_0.5Bi_0.5O)CuS and (La_0.5Bi_0.5O)CuTe systems, the calculated cell volumes (V_cell) are between those of both (LaO)CuCh and (BiO)CuCh (Ch = S, Te) systems, while V_cell of (La_0.5Bi_0.5O)CuSe system is larger than those of both systems.

Fig. 2 Trend of lattice parameters of for (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems different Ch from calculation (Calc) and experiments of (LaO)CuCh (Exp1) and (BiO)CuCh (Exp2).

Each system reveals the structural symmetry distortion, indicated by the fact that the change of atomic positions is no longer only possessed by both z_La and z_Ch. Instead, all the atoms shift their coordinate components (x, y, z) from the experimental coordinates. The atomic positions of Ok and Cui slightly shift from 2a and 2b sites, respectively, within the P4/nmm space group. In (La_0.5Bi_0.5O)CuS and (La_0.5Bi_0.5O)CuSe systems, both x_Cu and y_Cu are lower than 1/4, while (La_0.5Bi_0.5O)CuS system shows the opposite result. Moreover, (La_0.5Bi_0.5O)CuS system shows that z_Cu is higher than 1/2, which is in contrast with that of the other systems. Regarding Ok atom, for all the systems, x_O and y_O are slightly higher than 1/4. (La_0.5Bi_0.5O)CuS shows that z_O is slightly higher (lower) than 1/2, while (La_0.5Bi_0.5O)CuTe system shows that z_O is slightly lower than 1/2. On the other hand, (La_0.5Bi_0.5O)CuSe system does not show any z_O shift.

The calculation shows that the atomic positions La, Bi, and Chj shift from their 2c sites. x_La and x_Bi are lower than 1/4, except x_Bi for (La_0.5Bi_0.5O)CuS and (La_0.5Bi_0.5O)CuTe systems. On the other hand, x_Ch1 and x_Ch2 are higher than 1/4, except x_Te2. Furthermore, z_La is higher than that of (LaO)CuCh, while z_Bi is lower than that of (BiO)CuCh systems. For (La_0.5Bi_0.5O)CuS and (La_0.5Bi_0.5O)CuSe systems, z_Ch1 is lower than that of both (LaO)CuCh and (BiO)CuCh systems, while z_Ch2 shows the opposite result. These results provide LSD in CuiCh1₂Ch2₂ and OkLa₂Bi₂ tetrahedra.

The LSD parameters^60,61 are to describe the LSD in CuiCh1₂Ch2₂ and OkLa₂Bi₂ tetrahedra. First, the mean quadratic elongation (λ_tet) is expressed as

where l₀ is A–X bond length for an ideal AX₄ tetrahedron with the same volume with that of the distorted tetrahedron and l_i is A–X bond lengths. The bond-angle variance (θ_tet²) as the second parameter is expressed aswhere θ_i is the X–A–X bond angles.⁶⁰ The value of 109.4712° is the bond angle in the ideal tetrahedron.⁶²

Table 3 summarizes the average bond length (l_av) and the LSD parameters of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems. For all the systems, the Ch substitution increases l_av, λ_tet, and θ_tet² for both calculated and experimental results.³⁸ The calculated l_av of both CuiCh1₂Ch2₂ and OkLa₂Bi₂ tetrahedra are higher than that of both (LaO)CuCh and (BiO)CuCh systems, except l_av of OkLa₂Bi₂ tetrahedra in (La_0.5Bi_0.5O)CuTe system, which is lower than that of (LaO)CuCh system. Furthermore, both λ_tet and θ_tet² of CuiCh1₂Ch2₂ tetrahedra are higher than that of (LaO)CuCh but lower than that of (BiO)CuChsystems. In contrast, both λ_tet and θ_tet² of OkLa₂Bi₂ tetrahedra are lower than that of (LaO)CuCh but higher than that of (BiO)CuCh systems. This result shows the co-existence of La and Bi ions significantly influences the local-symmetry distortion, compared to those of both (LaO)CuCh and (BiO)CuCh systems. For comparing the LSD among the systems, we summarize the LSD parameters from the calculation in Fig. 3. We find that l_av of CuiCh1₂Ch2₂ tetrahedra are higher than that of OkLa₂Bi₂ tetrahedra. Intriguingly, the increases of l_av of both CuiCh1₂Ch2₂ and OkLa₂Bi₂ tetrahedra are almost linear with respect to the Ch substitution, where CuiCh1₂Ch2₂ tetrahedra show the larger l_av gradient. On the other hand, λ_tet and θ_tet² of OkLa₂Bi₂ are higher than that of CuiCh1₂Ch2₂ tetrahedra. Concerning the Ch substitution, λ_tet and θ_tet² increments of OkLa₂Bi₂ are also higher than that of CuiCh1₂Ch2₂ tetrahedra. This result indicates that the LSD of OkLa₂Bi₂ is more sensitive to the Ch substitution than that of CuiCh1₂Ch2₂ tetrahedra. Notably, the LSD of both tetrahedra is induced by the aspiration of the insulating and conducting layers to fit each other on the interface between them. Furthermore, the LSD of CuiCh1₂Ch2₂ tetrahedra cannot be provoked by the Jahn–Teller (JT) effect which the fully-occupied Cu 3d orbital cannot possess. We suggest that this LSD is induced by the pseudo-JT effect (PJTE)⁶³ in CuiCh1₂Ch2₂ tetrahedra, which will be discussed later.

Table 3 Average bond length (l_av) and local-symmetry distortion parameters (mean quadratic elongation (λ_tet), bond-angle variance (θ_tet²)) of CuiCh1₂Ch2₂ and OkLa₂Bi₂ tetrahedra in (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems (Calc) compared with the previous experimental results denoted by Exp₁ and Exp₂ for (LaO)CuCh and (BiO)CuCh,³⁸ respectively

Tetrahedra	lav (Å)			λtet			θtet^2 (°^2)
	Calc	Exp1	Exp2	Calc	Exp1	Exp2	Calc	Exp1	Exp2
(La0.5Bi0.5O)CuS
CuiS12S22	2.4362	2.4291	2.4259	1.0011	1.0002	1.0021	4.0014	0.7452	8.2968
OkLa2Bi2	2.3619	2.3601	2.3138	1.0049	1.0058	1.0024	18.9186	21.9534	9.4120
(La0.5Bi0.5O)CuSe
CuiSe12Se22	2.5403	2.5235	2.5145	1.0026	1.0007	1.0068	10.4807	2.6446	27.7188
OkLa2Bi2	2.3770	2.3760	2.3293	1.0081	1.0106	1.0047	30.6467	39.6827	17.9075
(La0.5Bi0.5O)CuTe
CuiTe12Te22	2.6656	2.6563	2.6560	1.0084	1.0049	1.0164	33.9264	19.5995	67.0207
OkLa2Bi2	2.3967	2.4024	2.3565	1.0164	1.0209	1.0116	60.4193	76.1717	43.0506

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Fig. 3 CuiCh1₂Ch2₂ (i = 1, 2) (top left panel) and OkLa₂Bi₂ (k = 1, 2) tetrahedra (bottom left panel) in (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems. The right panels present average bond length and local-symmetry distortion parameters (mean quadratic elongation and bond-angle variance) of both tetrahedra. Filled and unfilled shapes (circle, square, and triangle) denote those of CuiCh1₂Ch2₂ and OkLa₂Bi₂ tetrahedra, respectively.

3.2. Band structures

The left panels of Fig. 4 present the band structures of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems (range: −2.8 ≤ (E − E_F) ≤ 2.8 eV), zoomed in the right panels (range: −1.0 ≤ (E − E_F) ≤ 1.0 eV). E_F is the Fermi energy level. We find that all the systems are semiconductors, indicated by the presence of E_g. The Ch substitution decreases E_g. The band structures pattern is also modified by the Ch substitution. Fig. 4(d) and (e) show that (La_0.5Bi_0.5O)CuS and (La_0.5Bi_0.5O)CuSe systems have the indirect E_g of 0.529 and 0.256 eV (Γ → 0.4Δ), respectively. The term 0.4Δ denotes the path connecting 0.4Γ to Z points. These E_g are lower than that of both (LaO)CuCh (1.67 and 1.44 eV for Ch = S and Se, respectively)²⁷ and (BiO)CuCh systems (0.68 and 0.40 eV for Ch = S and Se, respectively)⁶⁴ within the GGA. Furthermore, (La_0.5Bi_0.5O)CuTe system exhibits the indirect E_g of 0.094 eV (Z → 0.4Δ), which is lower than that of (LaO)CuTe system²⁷ and shows the different behaviors with that of the metallic (BiO)CuTe system.⁶⁴ However, this E_g is close to that of (LaO)CuTe system by including the on-site Coulomb repulsion (U) and spin–orbit coupling (SOC) corrections.⁶⁵ We suggest that the decrease E_g corresponds to the increase of the lattice parameters as Ch is substituted from S to Te. The increase of the lattice parameters enlengthens the interatomic distances, leaving binding forces valence electrons and the corresponding parent ions reduced. Thus, the valence electrons are easier to move freely and induce the increase of n and σ. This suggestion assumes that E_g is roughly inversely proportional to n.⁶⁶ Hence, the decrease of E_g may indirectly be correlated with the ionic radii of Ch²⁻ ions.

Fig. 4 Band structures of (a) (La_0.5Bi_0.5O)CuS, (b) (La_0.5Bi_0.5O)CuSe, and (c) (La_0.5Bi_0.5O)CuTe systems. (d–f) The right panels show zoomed band structures in the range of −1.0 < E_F < 1.0 eV.

Experimental E_g of all the systems might be higher than that of the present work because of the limitation of the GGA, usually underestimating E_g in the exact Kohn–Sham band structures.⁶⁷ Furthermore, including U in the calculation might also provide a closer E_g to that of the possible experimental result. However, U is not suitable to be included in a closed-shell system, where its valence orbitals are in the full occupation or empty.⁶⁸ Here, (La_0.5Bi_0.5O)CuCh systems are closed-shell systems. The ionic electronic configurations in (La_0.5Bi_0.5O)CuCh systems are La³⁺: [Xe], Bi³⁺: [Xe] 4f¹⁴5d¹⁰6s², O²⁻: [He] 2s²2p⁶, Cu⁺: [Ar] 3d¹⁰, S²⁻: [Ne] 3s²3p⁶, Se²⁻: [Ar] 3d¹⁰4s²4p⁶, and Te²⁻: [Kr] 4d¹⁰5s²5p⁶.⁶⁹ Also, the exchange–correlation term in Cu 3d orbital cannot be fully described by U.^65,70 The use of hybrid-functional^71–75 or GW approximations⁷⁶ might induce the wider E_g than that of the GGA. However, both of them usually overestimate E_g of semiconductors.^77–79 Furthermore, the Hartree–Fock (HF) exchange in the hybrid-functional approximations can lead to the d-element exchange splitting overestimation.^73,80 These explanation encourages us to keep the GGA method without U correction, thus, indicates that the calculated properties are sufficient to predict experimental electronic properties.

The valence band (VB) structures of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) show the tuning of heavy hole (HH), light hole (LH), and split-off hole (SOH) states due to the Ch substitution. We are interested in the k-path of R–Z–Γ–M to observe this tuning since this path is near the E_g transition. Along R–Z path, HH and LH states are separated, followed by SOH. The energy separation between HH and LH states is increased by the Ch substitution, while the energy level of SOH state is pushed down. The increasing separation between HH and LH states is shown by the decrease and increase of steepness of HH and LH states, respectively. Along Z–Γ path, the HH and LH coincide from 0.8Δ to 0.2Δ points. The SOH state shows a valley in the middle of this path, as its energy level is also pushed down by the Ch substitution. Along Γ–M path, the HH and LH states are separated with the lower separation that that of R–Z path. However, this separation is not sensitive to the Ch substitution. On the other hand, the energy level of the SOH state is also sensitively pushed down. We are interested in the shifts of HH, LH, and SOH states at Z and Γ points. By substituting Ch from S to Se, HH, LH, and SOH states show shifts of 137, 122, and −99 meV, respectively, at Z point. At Γ points, HH, LH, and SOH states show shifts of 131, 124, and −88 meV, respectively. By substituting Ch from Se to Te, HH, LH, and SOH states show shifts of 33, −12, and −279 meV, respectively, at Z point. At Γ points, HH, LH, and SOH states show shifts of 0, 3, and −272 meV, respectively. It is indicated that the energy levels of HH and LH states are more sensitive to the Ch substitution from S to Se than that of the SOH state. On the other hand, the energy level of SOH is sensitive to the Ch substitution from Se to Te, while the energy levels of HH and LH are in contrast. This result leads to a shift of split-off energy (Δ_l) (l = 1, 2) of each system, defined as the energy separation between the HH and SOH states. Table 4 presents the split-off energy (Δ_l, l = 1, 2) of the systems. The term Δ₁ and Δ₂ are located at Z and Γ points, respectively. The difference between Δ₁ and Δ₂ are defined as δ₁₂. For all the systems, we find the result of Δ₁ > Δ₂, leading to the positive δ₁₂. Interestingly, the Ch substitution increases both Δ_l and δ₁₂. This result shows the significant role of the Ch substitution in tuning the band structures.

Table 4 Calculated split-off energy (Δ_l) (l = 1, 2) of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems

System	Split-off energy (Δl) (in meV)		δ12 = Δ1 − Δ2
	Δ1 (Z point)	Δ2 (Γ point)
(La0.5Bi0.5O)CuS	350	349	1
(La0.5Bi0.5O)CuSe	586	569	17
(La0.5Bi0.5O)CuTe	897	841	56

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3.3. Density of states

Fig. 5 presents the TDOS of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems (range: −8.5 ≤ (E − E_F) ≤ 5.0 eV). The TDOS shows the decrease of VB width due to the Ch substitution. We find the VB widths of 6.17, 6.00, and 5.98 eV in (La_0.5Bi_0.5O)CuS, (La_0.5Bi_0.5O)CuSe, and (La_0.5Bi_0.5O)CuTe systems, respectively. Hence, the Ch substitution slightly enhances the energy localization of VB. The VB can be divided into four levels, i.e., lower bonding, upper bonding, nonbonding, and antibonding levels, as summarized in Table 5. Theoretically, a VB consists of bonding, nonbonding, and antibonding levels. In this work, the four divisions are only to differ between the two peaks of bonding levels. The Ch substitution decreases the lower bonding level and nonbonding level widths but increases the antibonding level width. On the other hand, regarding the upper bonding level, (La_0.5Bi_0.5O)CuS and (La_0.5Bi_0.5O)CuSe systems show the lowest and highest level widths, respectively. Furthermore, the Ch substitution decreases the conduction band (CB) width. We find the CB widths of 4.60, 4.34, and 3.91 eV in (La_0.5Bi_0.5O)CuS, (La_0.5Bi_0.5O)CuSe, and (La_0.5Bi_0.5O)CuTe systems, respectively, indicating the enhancement of energy localization of CB.

Fig. 5 Total density of states (TDOS) of (a) (La_0.5Bi_0.5O)CuS, (b) (La_0.5Bi_0.5O)CuSe, and (c) (La_0.5Bi_0.5O)CuTe systems. Projected density of states (PDOS) of.O 2p (blue) and Bi 6p states (violet) are also presented.

Table 5 Ranges of divisions in valence band structures of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems

System	Division level (level width) (in eV)
	Lower bonding	Upper bonding	Nonbonding	Antibonding
(La0.5Bi0.5O)CuS	−6.28 to −4.58 (1.70)	−4.58 to −3.16 (1.42)	−3.16 to −1.42 (1.74)	−1.42 to −0.21 (1.21)
(La0.5Bi0.5O)CuSe	−6.09 to −4.50 (1.59)	−4.50 to −2.59 (1.91)	−2.59 to −1.35 (1.24)	−1.35 to −0.09 (1.26)
(La0.5Bi0.5O)CuTe	−6.00 to −4.45 (1.55)	−4.45 to −2.67 (1.78)	−2.67 to −1.66 (1.01)	−1.66 to −0.01 (1.65)

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Fig. 5 also presents the PDOS of O 2p and Bi 6p states (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems. O 2p states of O1 and O2 have the same DOS shape, thus, O 2p states are mentioned without assigning k. We calculate DOS centroids (E_centroid) for analyzing the PDOS using the expression^81–83

where D(E) is the DOS as the function of energy (E). (La_0.5Bi_0.5O)CuS, (La_0.5Bi_0.5O)CuSe, and (La_0.5Bi_0.5O)CuTe systems show the DOS centroids of deep O 2p states of −3.76, −3.73, and −3.95 eV, respectively, as well as the upper limits of high O 2p peaks at −2.54, −2.61, and −2.73 eV, respectively. The upper limits are between that of (LaO)CuCh²⁷ and (BiO)CuCh systems,⁶⁴ implying that the co-existence of La and Bi influences the energy level depth of O 2p states. Notably, O 2p states are fully occupied, while La 5d, La 6s, and Bi 6p states are empty in the ionic bonding scheme. However, we find the low-DOS Bi 6p states are shown in the VB, indicating the strong hybridization of O 2p and Bi 6p states. Moreover, the empty La 5d and La 6s are indicated by the absence of both states near E_F. The deep energy level of O 2p states indicates the insulating behavior of [LaBiO1O2] layers, in which the electrons are stable and difficult to be excited to CB. These insulating layers lead to two-dimensional electron confinement in the conducting [Cu₂Ch1Ch2] layers. This confinement elucidates that (La_0.5Bi_0.5O)CuCh can be inferred as natural superlattice systems, which may provide the thermoelectricity applications.^15,16

Regarding the thermoelectricity, from eqn (2), we predict S using the term −(dD(E)/dE) calculated at E ∼ E_F. In the present work, the term −(dD(E)/dE) corresponds to hole as carriers for E < E_F. The minus (−) sign is used since E below E_F is converted to binding energy, which is represented with the plus sign, as previously shown in the photoemission spectra.⁶⁴ Furthermore, we also calculate n(E) expressed as

n(E) = D(E)f(E) (a.u.) (7)

where f(E) is the Fermi–Dirac distribution function.⁸⁴ At the ground-state limit, we have f(E) = 1 for E < E_F. Fig. 6 presents |dD(E)/dE| and n(E) of states (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems in a short energy range (range: −0.2 ≤ (E − E_F) ≤ 0 eV). Near E_F, we find −(dD(E)/dE) of 0.21, 17.96, 27.60 eV⁻² in (La_0.5Bi_0.5O)CuS, (La_0.5Bi_0.5O)CuSe, and (La_0.5Bi_0.5O)CuTe systems, respectively. We suggest that the higher S of (La_0.5Bi_0.5O)CuTe than that of (La_0.5Bi_0.5O)CuSe might provide the higher thermoelectric power. This result is in contrast to that of our previous report that S of (BiO)CuTe is lower than that of (BiO)CuSe systems.⁶⁴ However, the larger ZT of (BiO)CuTe provides the higher thermoelectric power due to the metallic behavior, the higher σ, and the lower thermal conductivity (κ) than those of (BiO)CuSe system.^6,15,64 From Fig. 6(b), we show that the Ch substitution enhances n(E) of holes as the carriers, which may lead to the increasing σ(E). The term σ is correlated with n(E) and μ(E) with the expression σ(E) = n(E)μ(E)q. We have also proven that the decrease of E_g due to the Ch substitution is proportionally related to the increase of n.⁶⁶ The term κ will be presented elsewhere in a future publication. Notably, experimental investigations are opened for clarifying our results.

Fig. 6 (a) First derivative of total density of states −(dD(E)/dE) and (b) carriers concentration n(E) of (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems as functions of energy (E).

Fig. 7 presents PDOS of Cui 4s, sub-Chj np (p_x, p_y, p_z), and sub-Cui 3d states in (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) systems. This figure shows the details of orbital contributions to the lower bonding, upper bonding, nonbonding, and antibonding levels in the VB. Notably, the degeneracy-lifted Chj np and Cui 3d orbitals may be induced by the PJTE⁶³ in the fully-occupied Cui 3d orbital, related to the LSD in CuiCh1₂Ch2₂ tetrahedra. Notably, the tetrahedral-type crystal would allow the splitting of d orbital into 3-fold degenerate Cu 3d-t_2g (d_zx, d_zy, d_xy) and 2-fold degenerate Cu 3d-e_g states (d_x²−y², d_z²). In the present work, each Cu 3d-t_2g and Cu 3d-e_g states split into the different energy levels. Even, d_zx and d_zy states have the different PDOS profile, implying that Cu 3d orbital no longer degenerates. Hence, the PJTE induces the LSD and totally lifts the degeneracy of Cui 3d orbital. We find that Chj np_x/p_y states mainly contribute S and n(E), followed by Cu 3d_zx and Cu d_zy states.

Fig. 7 Projected density of states (PDOS) of Cui 4s, sub-Chj np, and sub-Cui 3d states (i = 1, 2; j = 1, 2) in (a and b) (La_0.5Bi_0.5O)CuS, (c and d) (La_0.5Bi_0.5O)CuSe, and (e and f) (La_0.5Bi_0.5O)CuTe systems. Notation d_zx(d_zy) is used for Cu1(Cu2) since the PDOS of d_zx and d_zy are the same for Cu1 and Cu2, respectively. This purpose is also used for the notation d_zy(d_zx).

The lower bonding level is contributed by Cui 4s and Chj np states. Based on the theoretical picture, Cu⁺ 4s orbital should be empty. However, top panels for all the systems show the presence of Cui 4s (PDOS of Cu1 4s = PDOS of Cu2 4s) states in the VB. This result can be induced by the hybridization between Cui 4s and Chj np orbitals. Furthermore, the energy level of this hybridization slightly increases due to the Ch substitution, indicated by the increase of the energy levels of both orbitals. Furthermore, we find that the DOS profiles of Ch1 np and Ch2 np states are different. The different profiles are induced by structural symmetry distortion and the fact that Ch1 and Ch2 are close to the different La and Bi layers, leading to different chemical bonding between Bi–Ch1 and La–Ch2 bonds. In the lower bonding level, the energy levels of Ch2 np states are higher than that of Ch1 np states. We find the two highest peaks of Ch1 np_z and Ch2 np_z states in all the systems, alongside Se2 4p_x/p_y peak in (La_0.5Bi_0.5O)CuSe system. This result indicates that the hybridization between Cui 4s and Chj np along c-axis direction is stronger than that of ab-plane direction.

The upper bonding level is contributed by Cui 3d and Chj np states. In (La_0.5Bi_0.5O)CuS system, S1 3p_x/p_y and S2 3p_x/p_y peaks, located at around −4.0 and −4.1 eV, respectively, are the highest peaks among the sub-Chj np states, as presented in Fig. 7(a). At the same energy levels, we find the degeneracy-lifted Cu13d_zx and Cu13d_zy peaks, as well as the degeneracy-lifted Cu23d_zx and Cu23d_zy peaks, as shown in Fig. 7(b). This result implies that the upper bonding is more pronounced along ab-plane direction. However, in (La_0.5Bi_0.5O)CuSe system, Se1 4p_z peak, located at around −3.4, is the highest peak among the sub-Chj np states, followed by Se2 4p_x/p_y located at −3.8 eV, as depicted in Fig. 7(c). From Fig. 7(d), at both −3.4 and −3.8 eV, there appear Cui3d_z² and Cu13d_zx (Cu23d_zy) states, respectively, indicating the slightly more pronounced upper bonding along c-axis direction. On the other hand, in (La_0.5Bi_0.5O)CuTe system, Te1 5p_z peak at −3.4 eV is the highest peak among the sub-Chj np states, as shown in Fig. 7(e). Fig. 7(f) shows Cui3d_x²−y² and Cu13d_zy (Cu23d_zx) peaks at the same energy level with that of Te1 5p_z states. This result indicates that Te1 5p_z states experience the strongest hybridization with Cui 3d states compared to the other sub-Tej np states. We highlight for all the systems that Cui 3d-t_2g states strongly hybridize with Chj np states and also show the larger contribution in the upper bonding level than that of Cui 3d-e_g states.

The nonbonding level is mainly contributed by the localized Cui 3d-e_g states (Cui3d_x²−y² and Cui3d_z²) based on Fig. 7. As the state with the highest peak, Cui3d_z² states are localized at −2.1, −2.4, and −2.1 eV in (La_0.5Bi_0.5O)CuS, (La_0.5Bi_0.5O)CuSe, and (La_0.5Bi_0.5O)CuTe systems, respectively. From Fig. 7(d), (La_0.5Bi_0.5O)CuSe system shows the highest peak of Cui3d_x²−y² states among all the systems. However, the nonbonding level shows the presence of Cu13d_zx (Cu23d_zy) and Cu13d_zy (Cu23d_zx), indicating that Cui 3d-t_2g states partially hybridize with Chj np states. This result is different from the previous suggestion that Cu and Ch ions are bound either along zx, zy, or xy planes.³⁸ For all the systems, Ch2 np_z also slightly contribute to the nonbonding level, followed by Ch1 np_z states. Additionally, the contribution of Ch1 np_z states is increased by the Ch substitution.

The antibonding level is contributed by Cui 3d and Chj np states. Based on the bottom panels of Fig. 7, all the systems show the highest peaks of Cui3d_x²−y² states, located at around −1.2, −1.4, and 1.1 eV in (La_0.5Bi_0.5O)CuS, (La_0.5Bi_0.5O)CuSe, and (La_0.5Bi_0.5O)CuTe systems, respectively. This highest peaks are followed by Cui3d_z² peaks located at the close energy levels to those of Cui3d_x²−y² states. Regarding Chj, all the systems show the highest peaks of Ch1 np_z and Ch2 np_z states, located at around −0.9 eV based on the top panels of Fig. 7. In (La_0.5Bi_0.5O)CuS system, we find two high peaks of S1 3p_x/p_y and S2 3p_x/p_y states, which are located at −0.4 and −1.2 eV, respectively. In (La_0.5Bi_0.5O)CuSe and (La_0.5Bi_0.5O)CuTe systems, the highest Se1 4p_x/p_y (Te1 5p_x/p_y) and Se2 4p_x/p_y (Te2 5p_x/p_y) peaks are located at −0.3 (−0.1) and −1.1 (−1.2) eV, respectively. This result indicates that the antibonding is more pronounced along ab-plane direction. We also highlight for all the systems that Cui 3d-t_2g states strongly hybridize with Chj np states and also show the larger contribution in the antibonding level than that of Cui 3d-e_g states.

4. Conclusions

The structural and electronic properties of the layered oxychalcogenides (La_0.5Bi_0.5O)CuCh (Ch = S, Se, Te) have been investigated based on the first principles. From the structural properties, the LSDs in CuiCh1₂Ch2₂ and OkLa₂Bi₂ tetrahedra are increased by the Ch substitution, in which the LSD in OkLa₂Bi₂ is stronger than that of CuCh₄ tetrahedra. The possible PJTE in the fully-occupied Cui 3d orbital is suggested to be responsible for inducing the LSD in CuiCh1₂Ch2₂ tetrahedra and to lift the degeneracy level of t_2g and e_g states. From the electronic properties, all the systems are semiconductors. (La_0.5Bi_0.5O)CuS and (La_0.5Bi_0.5O)CuSe exhibit the indirect E_g (Γ → 0.4Δ) of 0.529 and 0.256 eV, respectively. On the other hand, (La_0.5Bi_0.5O)CuTe exhibits the indirect E_g (Z → 0.4Δ) of 0.094 eV. The Ch substitution also increases the split-off energies at Z and Γ points. In the valence band, O 2p states are located at the deep energy levels, leading to the electron-confinement between the insulating [LaBiO₂]²⁺ layers. This result is crucial for thermoelectricity, where (La_0.5Bi_0.5O)CuTe may provide the largest thermoelectricity by comparing S and n(E), mainly contributed by Te 5p_x/p_y, Cu 3d_zx, and Cu 3d_zy states. Alongside being located at the bonding and antibonding level, t_2g states are also located at the nonbonding level, leading to the partial hybridization of t_2g and Ch p orbitals. The result provides new insights and finding, which open experimental works.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was supported by the Ministry of Research and Technology (MORT)/The National Agency for Research and Innovation (NARI) of the Republic of Indonesia 2020 research program.

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