Effects of Fe and Ni Doping on the Electronic Structure and Optical Properties of Cu₂ZnSnS₄

Abstract

This study evaluated the electronic structure and optical properties of Fe-doped, Ni-doped, and (Fe,Ni)-co-doped Cu₂ZnSnS₄ through the first-principles pseudopotential plane-wave method based on density functional theory. The results indicated that Fe single-doping and Ni single-doping Cu₂ZnSnS₄ can reduce the charge transfer number of adjacent S atoms, enhancing covalent bonding in Fe–S and Ni–S bonds and reducing the bond length, lattice constants a and c, and unit cell volume v. The formation energies for Fe-doping, Ni-doping, and (Fe,Ni)-co-doping were 1.0 eV, 0.58 eV, and 0.78 eV, respectively. Both Fe and Ni-doping introduced 3d electrons near the Fermi level, resulting in new impurity levels and a gradual decrease in the band gap of Cu₂ZnSnS₄ from 0.16 eV. The conduction band density of Cu₂ZnSnS₄ was primarilycontributed by Sn 5s, Sn 5p, and a portion of S 3p orbital electrons, whereas the valence band density mainly stemmed from Cu 3d, Sn 5p, and S 3p orbital electrons. Fe and Ni-doping also partly contributed to the 3d layer electrons. In the case of (Fe,Ni)-co-doping, the maximum static dielectric constant was 100.49, and the dielectric peak shifted toward the low-energy direction in the presence of both Fe and Ni. Within the visible light range, Fe-doping, Ni-doping, and (Fe,Ni)-co-doping in Cu₂ZnSnS₄ exhibited absorption coefficients greater than 10⁴ cm⁻¹, with the maximum absorption coefficient being 1.6 × 10⁵ cm⁻¹ in the case of (Fe,Ni)-co-doping. In the energy range from 1.5 to 6.3 eV, the reflectivity of Cu₂ZnSnS₄ doped with Fe, Ni, or both was lower than 30%. Notably, a high conductivity peak at 1.9 eV indicated that Cu₂ZnSnS₄ possesses good photoconductivity in the visible range. Fe-doping and Ni-doping resulted in a slight shift of the conductance peak position towardthe low-energy direction, accompanied by an increase in the peak value.

1. Introduction

The increasing depletion of fossil and other energy sources and the resulting energy crisis pose severe challenges to manufacturing industriesand daily life. Solar energy is considered an effective solution to energy scarcity [1]. Solar energy is converted into electricity primarily using solar cells, which are conventionally silicon-based [2]. Silicon-based solar cells are primarily used in solar cell arrays, which require large surface areas and ample solar radiation [3]. However, with the improving living standards, the demand for flexible and wearable solar cells has emerged, leading to the development of thin-film solar cells [4].Among various semiconductor materials, Cu₂ZnSnS₄ (CZTS) is considered the most promising material for thin-film solar cells [5]. This is attributed to its band gap falling between 1.4 and 1.6 eV and its absorption coefficient exceeding 10⁴ cm⁻¹, making it highly suitable as an absorption layer insolar cells [6]. Moreover, the elements constituting Cu₂ZnSnS₄ are non-toxic, environmentally friendly, and abundant in the Earth’s crust, making it a cost-effective and sustainable materialfor solar cells. Thus far, the highest conversion efficiency achievedby Cu₂ZnSnS₄ thin-film solar cells has been 12.6% [7], which is considerably lower than the theoretical conversion efficiency of 32.4% [8]. The primary factors affecting the conversion efficiency of Cu₂ZnSnS₄ thin-film solar cells are the open circuit voltage (Voc) and low fill factor (FF) [9,10]. Cu₂ZnSnS₄ system exhibits a narrow phase-stability region, making it susceptible to defects due to atomic loss or substitution [11]. For example, because of the similarity inion radii between Zn and Cu, shallow energy level defects, such as Cu_Zn and Zn_Cu substitution defects, can easily form [12]. In addition, deep-level defects, such as Sn_Zn substitution defects (SnZn) and sulfur vacancy defects (V_S), can form within the Cu₂ZnSnS₄ system [13,14,15]. Furthermore, the system is susceptible to substitution defects, such as Zn_Sn, and vacancy defects, such as V_Cu, V_Zn, and V_Sn [16]. Studies have demonstrated that deep energy level defects or defect pairs in Cu₂ZnSnS₄ systems lead to the generation of tail states [17,18]. At low temperatures, tail states can capture photo-generated carriers, resulting innon-radiative recombination, which reduces the open-circuit voltage and affects the conversion efficiency of solar cells. In the case of Cu₂ZnSnS₄ thin-film solar cells, inhibiting the formation of deep-energy-level defects, enhancing crystal quality, and inhibiting tail states are effective approaches to improve the conversion efficiency. Previous research [19] has revealed that metal substitution doping can alter the phase structure of Cu₂ZnSnS₄, thereby serving as a defect passivation method. For example, various studies have incorporated metals, such as Li, Na, K, Ag, Cd, Mn, and Al, into Cu₂ZnSnS₄, yielding significant results [20,21,22,23,24,25]. However, studies on the elemental doping of Cu₂ZnSnS₄ have primarily focused on alkali metals, with limited reports on Fe and Ni-doping. Doping semiconductor materials with Fe and Ni can demonstrably enhance electrocatalytic performance, leading to considerable improvements in light absorption [26,27]. Therefore, this study analyzed the electronic structure and optical properties of Cu₂ZnSnS₄ doped with Fe, Ni, and their co-doping (Fe,Ni) through the pseudopotential plane-wave method based on density functional theory (DFT). The effects of Fe and Ni-doping on the structure, state density, and optical properties of Cu₂ZnSnS₄ bands were analyzed.

2. Theoretical Models and Calculation Methods

We used Cu₂ZnSnS₄ unit cells with a kesterite structure with the space group being $I\overline{4}(No.82)$. Each unit cell consisted of 4 Cu atoms, 2 Zn atoms, 2 Sn atoms, and 8 S atoms, with lattice constants of a = 0.5428 nm and c = 1.0864 nm [28]. In the calculations for single-doping and co-doping, 2 × 1 ×1 superunit cells (a total of 32 atoms) were utilized. In Fe-doping, the Zn atom at the Zn 1 position of the superunit cell was substituted with an Fe atom. In Ni-doping, the Zn atom at the Zn 1 position was substituted by a Ni atom. In co-doping, the Zn atom at the Zn 1 position of the superunit cell and the Cu atom at the Cu 1 position were substituted by Fe and Ni, respectively. The doping model of the Cu₂ZnSnS₄ supercell is depicted in Figure 1.

The pseudopotential plane-wave method based on DFT [29,30] was adopted for calculations conducted using the CASTEP software package [31] in the Materials Studio [32] simulation platform. The Perdew–Burke–Ernzerhof (PBE) functional with generalized gradient approximation (GGA) [33] was employed to determinethe exchange correlation energy between electrons. Furthermore, the interactions between real ionic and electronic states were treated usingultra-soft pseudopotentials [34]. The plane-wave truncation energy was set to 380 eV, and the self-consistent convergence accuracy was set at 5.0×10⁻⁷ eV/atom. The Brillouin zone integrals were divided using Monkhorst–Pack’s 4 × 4 × 4 scheme.

To ensure the convergence of the calculation results, a k-point convergence test was conducted within the range from 1 × 1 × 1 to 7 × 7 × 7. The total energy began to converge when the k-point was sampled as 4 × 4 × 4. Therefore, the k-point selected for this study ensured convergence. The results of the k-point convergence test are presented in Figure 2.

To assess the feasibility of atomic doping, the doping energies of Fe and Ni atoms were calculated individually, as well as for their co-doping in Cu₂ZnSnS₄. The doping formation energy was calculated as follows [35,36]:

$$E{(Fe\to Zn)}_{form}=E{(Fe)}_{doped}-E_{pure}+{\mu }_{Zn}-{\mu }_{Fe}$$

(1)

$$E{(Ni\to Zn)}_{form}=E{(Ni)}_{doped}-E_{pure}+{\mu }_{Zn}-{\mu }_{Ni}$$

(2)

$$\begin{gathered} E{(Fe\to Zn,Ni\to Cu)}_{form}=E{(Fe,Ni)}_{doped}-E_{pure}+({\mu }_{Zn}-{\mu }_{Fe})+({\mu }_{Cu}-{\mu }_{Ni}) \\ E{(Fe\to Zn)}_{form},E{(Ni\to Zn)}_{form},E{(Fe\to Zn,Ni\to Cu)}_{form} \end{gathered}$$

(3)

representing the doping formation energies of Fe-doping, Ni-doping, and (Fe,Ni)-co-doping Cu₂ZnSnS₄, respectively.$E{(Fe)}_{doped}$, $E{(Ni)}_{doped}$, $E{(Fe,Ni)}_{doped}$ represent the energies of Fe-doping, Ni-doping, and (Fe,Ni)-co-doping Cu₂ZnSnS₄ after optimization, respectively. E_pure denotes the total energy of the undoped system ofCu₂ZnSnS₄. μ_Zn, μ_Fe, μ_Ni, and μ_Cu denote the chemical potential of the Zn atom, Fe atom, Ni atom, and Cu atom, respectively.

3. Results and Discussion

3.1. Geometric Structure Optimization

Table 1. Lattice constants and doping formation energy of Fe and Ni-doping in Cu₂ZnSnS₄.

Sample	a/Å	a%	c/Å	c%	v/Å3	Formation Energy/eV
Un-doping Cu2ZnSnS4(experiment) [33]	5.4270	—	10.8710	—	—	—
Un-doping Cu2ZnSnS4(caculated) [34]	5.4710	—	10.9440	—	—	—
Geometry optimization Cu2ZnSnS4	5.4690	0.77%	10.9460	0.69%	655.0330	—
Fe-doping Cu2ZnSnS4	5.4415	0.27%	10.9194	0.45%	647.9225	1.00
Ni-doping Cu2ZnSnS4	5.4460	0.35%	10.9085	0.34%	647.0102	0.58
(Fe,Ni)-co-doping Cu2ZnSnS4	5.3665	−1.11%	11.1363	2.44%	652.0260	0.78

presents the lattice constants and doping formation energy of undoped and doped Cu₂ZnSnS₄. Thelattice constants a and c were compared with experimental values. As indicated by the data in Table 1, the lattice constants a = 5.4690 Å and c = 10.9460 Å obtained from the geometric structure optimization of Cu₂ZnSnS₄ are consistent with both experimental and theoretical calculations [37,38]. Both Fe and Ni doping slightly reduced the lattice constants and cell volume v of Cu₂ZnSnS₄. Because the ionic radii of Ni²⁺(0.69 Å) and Fe³⁺(0.64 Å) are smaller than that of Zn²⁺(0.74 Å) [39,40], the atomic spacing decreased upon substituting Zn atoms with Fe and Ni atoms, resulting in a decrease in lattice constants and the unit cell volume.

After (Fe,Ni)-co-doping, the lattice constant a of Cu₂ZnSnS₄ decreased, while the lattice constant c and cell volume v increased slightly compared to those with single-doping.

As mentioned in Table 1, the formation energy of Fe-doping was 1.0 eV, whereas the formation energy of Ni-doping was 0.58 eV. Ni atoms integrated more easily into the Cu₂ZnSnS₄ lattice than Fe atoms. The co-doping formation energy of Fe and Ni atoms was 0.78 eV, which was lower than the formation energy of Fe-atom-doping. Under all three doping conditions, the doping formation energy was greater than 0 eV, indicating that Fe and Ni-doping defect states cannot form spontaneously, and defect states in Cu₂ZnSnS₄ can be controlled through co-doping.

The external electron arrangement of Fe is 3d⁶4s², while that of Ni is 3d⁸4s². The 3d state of Ni exhibits a denser and wider energy level than the 3d state of Fe, facilitating the capture of electrons. Upon substituting Zn, Ni tends to undergo acceptor doping [41], resulting in a lower doping formation energy. Therefore, Ni is more readily doped intoCu₂ZnSnS₄ than Fe. In co-doping, Fe substituted Cu. With the 3d¹⁰4s¹ electronic arrangement outside the nucleus of Cu, the 4s layer can accept electrons. In this scenario, Fe tends to undergo donor doping [41], leading to a higher doping formation energy. Thus, inco-doping, both acceptor doping and donor doping co-occur, resulting in an intermediate doping formation energy.

3.2. Electronic Structure

3.2.1. Energy Band Structure

The high symmetry points of Cu₂ZnSnS₄ are G, F, Q, and Z. The coordinates of these high symmetry points are listed in

Table 2. Coordinates of high symmetric points.

High Symmetry Point	x	y	z
G	0.000	0.000	0.000
F	0.000	0.500	0.000
Q	0.000	0.500	0.500
Z	0.000	0.000	0.500
G	0.000	0.000	0.000

.

Figure 3 illustrates the band structure of Fe-doping and Ni-dopingin Cu₂ZnSnS₄. Figure 3a presents the band structure of undoped Cu₂ZnSnS₄, with the minimum band gap occurring at the high symmetry point G. The value ofthe undoped band gap was 0.16 eV, consistent with the findings of Zhao [42]. The band gap values for Fe-doped and Ni-doped Cu₂ZnSnS₄ were consistent with experimental values reported in the literature [43,44], indicating a decrease in the band gap values of Cu₂ZnSnS₄ after Fe and Ni-doping. The generalized gradient approximation (GGA) functional is a common functional used to calculate semiconductor materials, and underestimating band gap is a feature of this functional. Zhao [42] found that the band gap calculated using the GGA functional was about 1 eV lower than the experimental value.The calculated results were lower than the experimental values primarily because the DFT theoretical framework does not consider the discontinuity of the exchange correlation potential and underestimates the interaction between excited state electrons in the multi-particle system. However, this discrepancy did not affect subsequent calculations and analysis [45,46].

Figure 3b displays the energy band structure of Fe-doped Cu₂ZnSnS₄, Figure 3c shows the band structure of Ni-doping in Cu₂ZnSnS₄, and Figure 3d shows the band structure of (Fe,Ni)-co-doped Cu₂ZnSnS₄. It can be seen from the figure that there is almost no band gap after Fe and Ni-doping. The valence band of Cu₂ZnSnS₄ is mainly composed of the hybridization of Cu/Zn 3d states and S 3p states, while the conduction band is mainly composed of Sn 5s states and S 3p states. Both Fe and Ni have partially filled 3d orbitals, and these partially filled 3d orbitals have a stronger effect on the hybridization of orbital electrons. When Fe and Ni ions are doped, the 3d states of Fe and Ni are hybridized with the 3p states of S, which results in a narrower band gap [47]. In addition, after Fe or Ni-doping, the partially filled 3d orbit reduces the s-p repulsion between Sn and S and reduces the energy of the conduction band minimum(CBM) state, thus reducing the band gap [44]. After (Fe,Ni)-co-doping, more partially filled 3d orbitals are provided, and the 3d states of Fe and Ni are hybridized more strongly with the 3p orbitals of S, the valence band moves down more, and the band gap is smaller. Considering the above factors, Cu₂ZnSnS₄ doped with Fe and Ni does not show a band gap. Of course, this is only the result obtained by using the GGA functional calculation, but we believe that the actual experiment has a band gap, and our calculation results can provide some new ideas for the regulating band gap of Cu₂ZnSnS₄.

3.2.2. Electronic Density of States

Figure 4 presents the total electronic density of states and the partial wave density of states for each sublayer of Fe-doping and Ni-doping Cu₂ZnSnS₄. Figure 4a illustrates the total electronic density of states and partial wave density of states for undoped Cu₂ZnSnS₄. The density of states primarily resulted from the 3d layer electrons of Cu, Zn, and S. Additionally, a few 5s and 5p layer electrons of Sn contributed to the density of states of Cu₂ZnSnS₄. The energy range from −14 to −12.4 eV can be primarily attributed to the 3s layer electrons of S and the 5s and 5p layer electrons of Sn. The energy range from −8.2 to −5.0 eV mainly comprises the 3s layer electrons of Zn, the 5s electrons of Sn, and the 3p layer electrons of S. The energy range from −5.0 to −0.21 eV is primarily influenced by the 3d layer electrons of Cu, the 5p layer electrons of Sn, and the 3p layer electrons of S. Lastly, the energy range from 0.6 to 3 eV is primarily associated with the electrons in the 3p layer of S and the 5s and 5p layers of Sn.

As illustrated in Figure 4b–d, all of Fe-doped, Ni-doped, and (Fe,Ni)-co-doped Cu₂ZnSnS₄ result in an increase in the electron state density around 0 eV. (Fe,Ni)-co-doping resulted in the highest increase of 12.9. This increase can be attributed to the 3d electrons provided by Fe-doping or Ni-doping at approximately 0 eV. After Fe-doping, Ni-doping, or (Fe,Ni)-co-doping, the peaks of density at −12.98 eV in the lower valence band, −6.8 eV in the middle band, and −3.7 eV and−1.7 eV in the upper valence band all shifted toward lower energylevels, with an average deviation of 0.35 eV in the density of the valence band. The peaks at 1.19 eV and 2.78 eV in the conduction band also shifted toward the low-energy region, leading to an average deviation of 0.41 eV of the density ofthe conduction zone. These shifts in peak positions indicate that Fe-doping and Ni-doping encourage electrons in the valence band and conduction band of Cu₂ZnSnS₄ to occupy low-energy orbits. Moreover, the downward shift of the orbital energy level in the conduction band was greater than that in the valence band, causing the Fermi energy level to be embedded in the valence band.

3.3. Mulliken Population Analysis

Table 3. Mulliken population analysis of atoms adjacent to Fe Ni impurity atoms.

Sample	Atom	s	p	d	Total	Charge/e
Cu2ZnSnS4	Zn 1	0.42	0.94	9.98	11.34	0.66
	S 1, S 2, S 3, S 4	1.84	4.54	0	6.37	−0.37
	Cu 1	0.6	0.64	9.81	11.06	−0.06
	S 5, S 6, S 7, S 8	1.84	4.54	0	6.37	−0.37
Fe-doping Cu2ZnSnS4	Fe 1	0.4	0.62	6.94	7.96	0.04
	S 1, S 2	1.83	4.41	0	6.24	−0.24
	S 3, S 4	1.83	4.43	0	6.26	−0.26
Ni-doping Cu2ZnSnS4	Ni 1	0.5	0.69	8.84	10.03	−0.03
	S 1, S 2	1.83	4.45	0	6.29	−0.29
	S 3, S 4	1.83	4.45	0	6.28	−0.28
(Fe,Ni)-co-doping Cu2ZnSnS4	Fe 1	0.41	0.62	6.91	7.94	0.06
	S 1, S 2, S 3	1.84	4.42	0	6.26	−0.26
	S 4	1.81	4.43	0	6.26	−0.26
	Ni 2	0.48	0.66	8.91	10.05	−0.05
	S 5, S 6	1.83	4.49	0	6.32	−0.32
	S 7, S 8	1.84	4.49	0	6.34	−0.34

presents the Mulliken population analysis results for atoms adjacent to Fe and Ni impurity atoms, and

Table 4. Mulliken population analysis of bonds adjacent to Fe Ni impurity atoms.

Sample	Bond	Population	Length (Å)
Cu2ZnSnS4	S 1—Zn 1, S 2 —Zn 1	0.40	2.3659
	S 3—Zn 1, S 4—Zn 1	0.41	2.3653
Fe-doping Cu2ZnSnS4	S 1 Fe 1	0.64	2.1321
	S 2—Fe 1	0.64	2.1322
	S 3—Fe 1	0.60	2.1598
	S 4—Fe 1	0.60	2.1597
Ni-doping Cu2ZnSnS4	S 3—Ni 1	0.49	2.2298
	S 4—Ni 1	0.49	2.2299
	S 1—Ni 1, S 2—Ni 1	0.50	2.2341
(Fe,Ni)-co-doping Cu2ZnSnS4	S 1—Fe 1	0.64	2.1451
	S 2—Fe 1	0.64	2.1433
	S 3—Fe 1	0.58	2.1666
	S 4—Fe 1	0.58	2.1679
	S 5—Ni 2	0.47	2.2055
	S 6—Ni 2	0.47	2.2038
	S 7—Ni 2	0.48	2.2778
	S 8—Ni 2	0.48	2.2794

displays the Mulliken population analysis results forbonds adjacent to Fe and Ni impurity atoms. The S 1, S 2, S 3, and S 4 atoms were adjacent to the Fe 1 and Ni 1 impurity atoms, whereas the S 5, S 6, S 7, and S 8 atoms were adjacent to the Ni 2 impurity atoms. As indicated by the data in Table 3, upon replacing Zn 1 with Fe 1, the charge transfer of the S atoms adjacent to Fe 1 increased from −0.37 e to −0.24 e and −0.26 e, suggesting a weakened charge transfer due to Fe-doping. This effect can be attributed to the smallerionic radius of Fe compared to Zn, which results in the stronger binding of charges. Conversely, upon replacing Zn 1 with Ni 1, the Ni atoms acquire a slight charge of −0.03 e because the 3d shell of Ni was not completely filled with electrons, making it vulnerable to capturing charges from adjacent atoms. Simultaneously, the average charge transfer of the S atoms adjacent to Ni 1 decreased by 0.09 e, which was influenced by the stronger binding capacity of Ni due to its smaller ionic radius compared with Zn.

After (Fe,Ni)-co-doping, the charge transfer of the S atoms adjacent to Fe 1 was consistent with that observed in single-doping scenarios. However, the charge transfer of S atoms adjacent to Ni 2 changed significantly, with an average increase of 0.05 e compared to single-doping. This change can be attributed to the use of Ni 2 to substitute for Cu 1 in co-doping. The smaller ionic radius of Ni resulted in a stronger binding capacity.

As indicated by the data in Table 4, both Fe-single-doping and Ni-single-doping, as well as (Fe,Ni)-co-doping, increase the number of Fe-S and Ni-S bonds while reducing their bond lengths.

This effect can be attributed to the smaller ionic radius of Fe and Ni compared with Zn and Cu, which leads to lattice distortion in Cu₂ZnSnS₄ after doping and an enhanced electrostatic effect. The average population of S atoms adjacent to Fe and Ni after co-doping was 0.54, which was smaller than the average population of 0.56 observed after Fe-doping and Ni-doping. Furthermore, the average bond length of S atoms adjacent to Fe and Ni after co-doping was 2.2 Å, which was slightly longer than the average bond length of 2.19 Å observed after Fe-doping and Ni-doping. Hence, (Fe,Ni)-co-doping weakened the covalent bond in Cu₂ZnSnS₄ while increasing the bond length. Consequently, the lattice constant in the c-axis direction was distorted, and the cell volume increased slightly.

3.4. Optical Properties

This study investigated the effects of Fe and Ni-doping on the optical properties of Cu₂ZnSnS₄, including the complex dielectric function, absorption coefficient, reflectivity, and complex conductivity. The macroscopic optical properties of solids are typically described usingthe complex dielectric function $\epsilon (\omega )={\epsilon }_1(\omega )+i{\epsilon }_2(\omega )$. Optical constants, such as the complex dielectric function, absorption coefficient, reflectivity, and complex conductivity, were derived using the Kramer–Kronig (KK) transformation [45].

3.4.1. Complex Dielectric Function

The dielectric function is generally represented as a complex number, with the imaginary part providing valuable information about electronic transitions and band structures [48]. Figure 5 illustrates the complex dielectric function of Fe-doping and Ni-doping Cu₂ZnSnS₄, where Figure 5a displays the real part and Figure 5b shows the imaginary part. As illustrated in Figure 5a, the static dielectric constant of undoped Cu₂ZnSnS₄, denoted as ${\epsilon }_1(0)=10.54$, was consistent with the findings in the literature [49]. Both Fe-single-doping and Ni-single-doping, as well as (Fe,Ni)-co-doping, led to an increase in the value of the static dielectric constant, ${\epsilon }_1(0)$. After co-doping, the static dielectric constant reached its maximum value of 100.49, which aligned with the results of the population analysis. Fe-doping and Ni-doping in Cu₂ZnSnS₄ introduce additional 3d electrons near the Fermi level. After doping, the covalent bond effect strengthened, leading to an intensified binding effect of the atomic nucleus charge, thus increasing the static dielectric constant. Figure 5b illustrates that the imaginary part, denoted as ε”(ω), of the intrinsic Cu₂ZnSnS₄ complex dielectric function exhibited three distinct dielectric peaks at 1.39 eV, 3.84 eV, and 6.04 eV. In the density of states plot, the dielectric peak at 1.39 eV corresponded to the Cu-3d to Sn-5s orbital electron transition, the 3.84 eV peak corresponded to the Cu-3d to S-3p orbital electron transition, and the 6.04 eV peak corresponded to the Cu-3d to Sn-5p orbital electron transition. In the low-energy range of 0 to 2.5 eV, the Cu₂ZnSnS₄ dielectric peak shifted toward lower energies due to Fe-doping and Ni-doping in Cu₂ZnSnS₄. This shift occurred because Fe-doping and Ni-doping reduced the Cu₂ZnSnS₄ band gap, resulting in a redshift of the absorption peak. In the energy range of 2.5 to 10 eV, the dielectric peaks of Fe-doping and Ni-doping Cu₂ZnSnS₄ closely aligned with the intrinsic dielectric peak of Cu₂ZnSnS₄. These findings indicated that the dielectric properties of Cu₂ZnSnS₄ in the visible light range can be effectively controlled through Fe-doping, Ni-doping, or (Fe,Ni)-co-doping.

3.4.2. Absorption and Reflection Spectra

Figure 6 illustrates the absorption coefficient and reflection spectrum of Fe-doping and Ni-doping Cu₂ZnSnS₄. As illustrated in Figure 6a, the absorption spectrum of Cu₂ZnSnS₄ can be divided into three regions: the visible light region spanning from 0.16 eV to 3.2 eV, the ultraviolet light absorption region ranging from 3.2 eV to 11 eV, and the high-energy absorption region beyond 11 eV. The absorption edge of Cu₂ZnSnS₄ was observed at 0.16 eV, corresponding to the calculated band gap. Fe-doping and Ni-doping Cu₂ZnSnS₄ exhibited a slight red shift in the absorption edge, which can be attributed to the reduction in the band gap following doping. In the energy range of 0.16 eV to 6.9 eV, the absorption coefficient gradually increased with the incident light energy and reached a maximum value of 1.65 × 10⁵ cm⁻¹ at 6.9 eV. Beyond 6.9 eV, the absorption coefficient began to decrease and remained below 10⁴ cm⁻¹ after 11 eV. Notably, a significant absorption peak appearedat 1.9 eV with an absorption coefficient of 3.6 × 10⁴ cm⁻¹, indicating strong light absorption by Cu₂ZnSnS₄ in the visible light region [50]. The absorption coefficients of Fe-doped and Ni-doped Cu₂ZnSnS₄ in the visible light range all exceed 10⁴ cm⁻¹. Among the three doping conditions, (Fe,Ni)-co-doping resulted in the highest absorption coefficient, followed by Fe-single-doping, while Ni-single-doping resulted in the lowest absorption coefficient, in line with the changes in the band gap resulting from Fe-doping and Ni-doping Cu₂ZnSnS₄. As illustrated in Figure 6b, Cu₂ZnSnS₄ primarily reflected light in the energy range of 7.4 eV to 9.4 eV, with reflectivity below 30% in the range of 1.5 eV to 6.3 eV. This indicated minimal reflection loss in the visible light range, thus favoring light absorption by Cu₂ZnSnS₄. In the visible light range, the reflectivity of Fe-doping and Ni-doping Cu₂ZnSnS₄ exhibited an increasing trend. Notably, (Fe,Ni)-co-doping resulted in the highest reflectivity, followed by Fe-single-doping, while Ni-single-doping yielded the lowest reflectivity. Thus, the absorption coefficient and reflectivity of Cu₂ZnSnS₄ can be effectively controlled through Fe-doping, Ni-doping, or (Fe,Ni)-co-doping.

3.4.3. Complex Conductivity

Figure 7 displays the complex conductivity of Fe-doped and Ni-doped Cu₂ZnSnS₄. As illustrated in Figure 7a, the conductivity decreased to nearly zero beyond an energy of 11.3 eV. In the energy range of 0 eV to 6.2 eV, three prominent peaks appeared, corresponding to the positions of the light absorption peaks. The primary peak observed at 1.9 eV indicated that Cu₂ZnSnS₄ possesses strong photoconductivity in the visible light range. Fe-doping and Ni-doping resulted in a slight shift of the peak position toward lower energies, accompanied by an increase in the peak magnitude. Among the three doping conditions, (Fe,Ni)-co-doping resulted in the most significant increase in the peak, followed by Fe-doping, while Ni-doping resulted in the smallest increase. These observations were consistent with the band gap changes in Cu₂ZnSnS₄ under the three doping conditions.

4. Conclusions

In this study, the electronic structure and optical properties of Fe-doped, Ni-doped, and (Fe,Ni)-co-doped Cu₂ZnSnS₄ were calculated and analyzed using first-principles methods. The results indicated that Fe-doping and Ni-doping in Cu₂ZnSnS₄ weakened the charge transfer of adjacent S atoms, thereby enhancing the covalent bonding of Fe–S and Ni–S bonds, shortening bond lengths, and decreasing lattice constants a and c and the unit cell volume v. Fe-doping exhibited the highest formation energy, whileNi-doping had the lowest formation energy, with (Fe,Ni)-co-doping falling in the intermediaterange. Both Fe and Ni-doping introduced 3d electrons near the Fermi level, resulting in an upward shift ofthe valence band and a downward shift of the conduction band, leading to a decrease in the Cu₂ZnSnS₄ band gap from 0.16 eV. (Fe,Ni)-co-doping had the most pronounced effect on the band gap. Both Fe and Ni-doping, as well as (Fe,Ni)-co-doping, increased the static dielectric constant of Cu₂ZnSnS₄, causing the dielectric peak to shift toward lower energy levels. In the visible light range, Fe-doping, Ni-doping, and (Fe,Ni)-co-doping resulted in increased light absorption with higher incident light energies, surpassing an absorption coefficient of 10⁴ cm⁻¹. Notably, Cu₂ZnSnS₄ exhibited strong light absorption at 1.9 eV, with the highest absorption coefficient observed in the case of (Fe,Ni)-co-doping. Within the energy range of 1.5 eV to 6.3 eV, the reflectivity of Cu₂ZnSnS₄ doped with Fe, Ni, or both elements remained below 30%. Thus, Cu₂ZnSnS₄ possesses favorable photoconductivity in the visible light range. Furthermore, the introduction of Fe and Ni dopants resulted in a slight shift of the conductivity peak toward lower energy levels, accompanied by an overall increase in conductivity.