Investigation on the Cu-Dopant-Induced Modulation Effect on the Optoelectronic Efficiency and the Stability of CsPbBr₃ Perovskites

Abstract

This study explores the use of Cu dopant to improve the optoelectronic properties and stability of CsPbX₃ perovskites for blue-light-emitting diode material. The addition of Cu causes the metal octahedron of orthorhombic CsPbBr₃ to shrink, which relaxes the lattice strain from the distortion and twisting of the [PbX₆] octahedron and reduces energy from Jahn–Teller effects. A crystal orbital Hamilton population (COHP) analysis reveals that the Cu-Br bond in the [CuX₆] octahedron has a higher integrated projected COHP (IpCOHP), and the strong hybridization between the Cu-3d and Br-4p bond enhances the bond interaction and the whole crystalline lattice. The addition of Cu dopants in CsPbBr₃ perovskites results in a stronger framework that suppresses intrinsic defects like Br vacancies, leading to enhanced photoluminescence (PL) performance. Additionally, the Cu-3d orbitals contribute to the valence band and increase the band gap, resulting in a blue shift of the luminescence from Cu-doped CsPbBr₃. These findings indicate that Cu dopants significantly improve the luminescence efficiency and the stability of CsPbBr₃ perovskites, making them suitable for blue light LED applications.

1. Introduction

In recent years, halide perovskites, including MAPbI₃ and MAPbBr₃, have emerged as strong contenders for high-performance solar cells. Nawishta et al. have successfully grown single-layer and multilayer MAPbIBr₂ thin films, which show sharper absorption peaks in the visible region, suggesting their potential for application in optoelectronic and photovoltaic devices [1,2,3,4,5]. Among these, all-inorganic perovskites like CsPbX₃ have garnered significant attention for their exceptional stability and optoelectronic properties. Lots of studies highlight the potential use of inorganic halide perovskites as luminescent materials. The band gaps of these materials can be adjusted to cover the entire visible region. Additionally, CsPbX₃ perovskites exhibit a narrow emission line width of 12–42 nm and a high photoluminescence quantum yield (PLQY) of 50–90%. Notably, CsPbBr₃ emits green light [6] and CsPbI₃ emits red light [7], both with a luminous quantum yield of over 90%. As is well-known, the blue luminescence is the most important in applications of the LED, but the all-inorganic CsPbX₃ perovskites are frustrated in this field [8,9,10,11,12,13,14].

Numerous methods have been utilized to enhance the blue luminescence efficiency of CsPbX₃ perovskites. One such method involves doping Cl anions in the Br-halide perovskites, resulting in mixed-anion halide perovskites that emit blue light. This was demonstrated by Loredana et al. in 2015 [15,16]. However, the presence of these mixed anions causes lattice mismatch, which can lead to a deterioration in the crystalline structure and limit the PLQY of the blue luminescence to less than 40%. To address this issue, some reports have explored the size effect of perovskites. For example, Wang et al. fabricated CsPbBr₃ perovskite quantum dots that emit light with a shorter wavelength [9]. Despite their potential in optoelectronic applications, perovskites have been limited by their thermal instability. Fortunately, recent research has shown that metallic impurity doping can effectively enhance their optoelectronic properties, including PLQY and thermal stability. For instance, the addition of Sn into CsPbBr₃ perovskites has been found to significantly increase the PLQY from 45% to an impressive 83% in CsPb_1−xSn_xBr₃ [17,18]. Shen et al. successfully created a stable CsPb_0.64Zn_0.36I₃ crystal with a high PLQY of 98.5% through Zn doping. Furthermore, researchers have made significant advancements in the field of Cu doping in perovskite materials. This is attributed to the similarity in oxidation states between Cu and Pb, with Cu exhibiting a considerably smaller atomic radius than Pb. Additionally, the electronegativity disparity between Cu and Br surpasses that of Pb and Br. As a result, numerous studies have been conducted to explore the effects of Cu doping on the optoelectronic properties of semiconductor materials. The brightness of the light-emitting diodes (LEDs) made from Cu-doped CsPbI₃ perovskites is high, measuring at 1270 cd/m². Additionally, the red luminescence of this device can remain stable in air for up to 35 days [19]. Yu et al. discovered that the bandgap of Cs₂AgSbCl₆ double perovskites can be significantly altered through the use of Cu dopants [20]. Cu doping can alter the electronic interaction within CsPbBr₃ perovskites [21], resulting in an increased bandgap that facilitates the blue light emission. Bi et al. have experimentally demonstrated that substituting Cu for Pb in CsPbX₃ perovskites enhances the PLQY from 23% to an impressive value of 80%. Furthermore, this high PLQY can be sustained for 30 days under 60% relative humidity [22,23].

The remarkable optoelectronic properties exhibited by Cu-doped CsPbBr₃ perovskites have been attributed to the suppression of intrinsic defects. However, the mechanism behind this phenomenon and its impact on the photoluminescence quantum yield and stability require further exploration. Previous studies have also indicated that CsPbBr₃ may undergo a phase transition from orthorhombic to cubic when exposed to visible light or fabricated in nano scales [24]. This paper aims to investigate the impact of Cu dopant on the CsPbBr₃ perovskite lattice and determine if different phases alter its influence. Through an analysis of defect formation energies, geometric distortions, bonding interactions, and electronic structures, we have found that Cu dopant strengthens the bonding interactions between cation and anion ions in the CsPbBr₃ crystal, reducing native defects and increasing co-ordinated numbers of the metallic octahedral. This is helpful in promoting the PLQY and the stability of the lattice as a whole. Our research offers a more extensive theoretical foundation for achieving high-quality all-inorganic CsPbX₃ perovskites that emit blue light.

2. Calculation Methods

The theoretical simulations and analyses in this paper are performed via density functional theory, which is implemented in the Vienna ab initio simulation package (VASP) [25,26]. We use the generalized gradient approximation (GGA) function and Perdew–Burke–Ernzerhof (PBE) model to deal with the exchange and correlation of electrons [27]. Meanwhile, we use the Heyd–Scuseria–Ernzerh of hybridized function (HSE06) with the shielding parameter 0.25 to obtain a more accurate bandgap [28]. The projector-enhanced wave (PAW) method is used to deal with the interaction between electrons and ions [29]. The cutoff energy, the convergence accuracy, and the residual force are set to 400 eV, 1 × 10⁻⁴ eV per atom, and 0.01 eV, respectively. In addition, we use a 2 × 4 × 4 Monkhorst–Pack mesh to integrate in Brillouin zone. The crystal orbital Hamilton population (COHP) [30,31] calculations are carried out by LOBSTER program, in which the chemical bonds involved are: (1) 4s, 4p, and 3d for Cu; (2) 4s and 4p for Br; and (3) 6s, 6p, and 5d for Pb, respectively.

3. Results and Discussion

3.1. Geometric Properties

The physical properties of solid materials are determined by their geometric structures, which can be affected by intrinsic defects or external dopants. Understanding the optoelectronic properties of CsPbBr₃ perovskites requires a thorough examination of these geometric variations. At room temperature, CsPbBr₃ crystallizes in the orthorhombic phase with the space group Pnma, as depicted in Figure 1. The perovskites consist of [PbBr₆] metal octahedra, with Cs ions occupying the vacancies between these octahedra due to their larger radii. The relaxed lattice parameters of the CsPbBr₃ supercell are 16.53 Å, 8.50 Å, and 11.92 Å, respectively. Perovskites are commonly synthesized with intrinsic defects, which can reduce the PLQY by acting as non-radiative recombination centers. However, these defects also play a major role in the decomposition of perovskite materials when exposed to air, due to their strong affinity for water and oxygen molecules. This can lead to a decrease in stability for perovskite materials [32]. The paper focuses on investigating the intrinsic defects in CsPbBr₃, namely, Cs vacancy (V_Cs), Pb vacancy (V_Pb), and Br vacancy (V_Br). The configuration of the CsPbBr₃ supercell with V_Br is depicted in Figure 1c. The formation energy is used to determine the likelihood of defect formation, which is calculated using Equation (1).

$${ E}_f={ E}_{df}-E_{ini}+{\sum }_i{n}_i{\mu }_i-{\sum }_j{n}_j{\mu }_j$$

(1)

where $E_{ini}$ represents the total energy of the defect-free supercell, $E_{df}$ represents the total energy of the defect-containing system. ${\mu }_i$ and ${\mu }_j$ are the chemical potentials of the elements involved in the formation of defects, in which the chemical potentials of the metal cations are obtained from the bulk materials, while the chemical potential of the Br atom is obtained from the gaseous material. For example, if we calculate the defect formation energy of CsPbBr₃ with a defect complex composited by the Cu-substitutional Pb (Cu_Pb) and a Br vacancy (Cu_PbV_Br), then $E_f$ = $E_{df}$ − $E_{ini}$+ ${\mu }_{Br}+{\mu }_{Pb}-{\mu }_{Cu}$. The calculated defect formation energies of various defects are listed in

Table 1. Formation energies (E_f) of various defects in CsPbBr₃ and CsPb_0.875Cu_0.125Br₃ systems.

Defects	VCs	VPb	VBr	CuPbVCs	CuPbVPb	CuPbVBr
Ef (eV)	4.26	3.74	2.90	6.69	5.69	2.92

.

One of the intrinsic defects in CsPbBr₃ materials is the V_Br, which has the lowest formation energy among the defects. On the other hand, the value of V_Cs is the highest among the defects. This means that, in the CsPbBr₃ supercell, V_Cs is the most difficult defect to form, while V_Br is the easiest defect to form. Then, V_Br vacancies are believed to be responsible for the deterioration of the PLQY in the pristine CsPbBr₃ perovskites. These results are consistent with previous reports [15]. Therefore, these vacancies should be suppressed to regulate the stability and the optoelectronic properties of perovskites [33]. Previous reports have suggested that the Cu substitutional defect strongly affects the geometric structure of CsPbBr₃ perovskites. To investigate this effect, we constructed a CsPb_0.875Cu_0.125Br₃ system by replacing a Pb atom with a Cu dopant in the original CsPbBr₃ supercell. The introduction of the Cu dopant resulted in a reduction of the lattice parameters of CsPbBr₃ to a = 16.35 Å, b = 8.41 Å, and c = 11.79 Å, due to the smaller radius of the Cu ion. According to the X-ray diffraction (XRD) pattern analysis in Figure 2 provided by Bi et al. [23], it is evident that the diffraction peaks shift towards higher angles (increased 2θ values), and the positions of peaks at larger 2θ values also increase. This observation suggests a decrease in the interplanar spacing of the crystal, providing experimental confirmation of the conclusion that the lattice constant is reduced. Interestingly, the Cu dopant can also alter the distribution of intrinsic defects. As shown in Table 1, the formation energies of intrinsic vacancies in CsPbBr₃ increases obviously after Cu doping, indicating that the formation of intrinsic defects becomes more difficult after Cu doping, compared with the undoped system. From an alternative standpoint, the reduction in the diameter of the dopant ions leads to the relaxation of lattice stress caused by distortion and compression between adjacent lattices. As a result, this relaxation of lattice stress may also reduce the dislocation density within the crystal, ultimately promoting greater stability of the CsPbBr₃ perovskite structure.

To gain a better understanding of the effect induced by Cu dopant on CsPbBr₃ perovskites, we focus on studying the geometric changes caused by the dopant. According to the commonly held view, the stability of a perovskite can be evaluated based on the tolerance factor t, which is defined in Equation (2).

$$t=\frac{R_A+R_X}{\surd 2(R_B+R_X)}$$

(2)

Among them, R_A, R_B, and R_X are the radii of composition ions in ABX₃ perovskites. The radii used in this work are shown in

Table 2. Crystal radii (CR) [34] and the co-ordination numbers (CN) of ions in CsPbBr₃ systems.

Ion	Cu2+	Cs1+	Br1−	Pb2+
CN	6	12	6	6
CR(pm)	87	202	182	133

.

According to theoretical analysis, perovskites can exist steadily within the range of 0.77–1.10 for the value of t. As t approaches 1, the stability of the perovskite structure is enhanced. From Table 2 and Formula (2), it can be observed that the tolerance factor of CsPbBr₃ is 0.86, which deviates from the ideal value of 1. This deviation is one of the reasons why CsPbBr₃ tends to crystallize in the orthorhombic phase under normal conditions, resulting in a distorted perovskite structure. By calculating t using the radius of the Cu²⁺ ion instead of the original Pb²⁺ ion, we arrive at a value of 1.01, which is almost ideal for perovskites. This indicates that the metal–halogen octahedra frameworks in the CsPbBr₃ lattice are strengthened after Cu doping. The more stable perovskite structure confirms our earlier findings on the formation energies, which suggest that the CsPbBr₃ lattice is less prone to intrinsic defects due to its increased resistance to destruction.

To gain a better understanding of the results, we conducted extensive simulations on the localized structures and bonding interactions for the CsPbBr₃ lattice before and after Cu doping. The results from Figure 2 indicate that the Pb-Br bond lengths in the [PbBr₆] metal octahedron of the original CsPbBr₃ lattice are approximately 3.03 Å prior to Cu doping. Upon substitution of Pb with Cu dopant, the 3.03 Å Cu-Br bond lengths in the [CuX₆] octahedron reduce to 2.86 Å, while the 3.04 Å Cu-Br bond lengths decrease to 2.40 Å, resulting in the shrinkage of the octahedron and the elongating of the octahedron. In accordance with rigorous academic conventions, it is imperative to consider not only the beneficial impacts arising from doping-induced distortions but also their potential drawbacks. When examining the reduction in Cu-Br bond length, it becomes evident that the bromine atom involved in forming the Cu-Br bond experiences elongation due to its proximity to the surrounding lead bromide octahedra. However, it is important to note that the degree of deformation along this axis is not particularly substantial, and it is limited to the nearest neighboring Pb-Br octahedra, thereby restricting its impact on the formation energy of bromine vacancy defects.

The compact lattice resulting from the contraction of the bond length of the [CuX₆] octahedron makes it difficult to lose compositional atoms, thus increasing the formation energy of the V_Br defect. Additionally, the distortion of the metal octahedron due to the Jahn–Teller effect results in an energy gain and reduces the energy of the entire lattice system, which will be further discussed in subsequent sections. Furthermore, the shrinkage of the metal octahedral cage reduces the lattice strain caused by the rotation and twisting of the [PbBr₆] octahedron in the pristine CsPbBr₃ lattice. The stability of CsPbBr₃ perovskites is enhanced by three factors. Additionally, we observed that lattice distortion only occurs in the [PbX₆] metal octahedra closing to the [CuX₆] octahedron, while the Pb-Br bonds further away from the [CuX₆] octahedron remain relatively unchanged. This indicates that Cu dopant only induces a short-range interaction in CsPbBr₃.

3.2. Electronic Properties

The crystal orbital Hamilton population (COHP) analyses provide a direct measure of the bonding strength in CsPbBr₃ systems. As presented in

Table 3. The lengths (Å) and the IpCOHP (eV per cell) for the metal-Br bonds in CsPbBr₃ and CsPb_0.875Cu_0.125Br₃ systems, respectively.

System	Bond	Bond Length	−IpCOHP
CsPbBr3	Pb-Br	3.03	1.63
CsPb0.875Cu0.125Br3	Cu-Br	2.40	5.04
CsPb0.875Cu0.125Br3	Pb-Br	2.97	1.80

, the integrated projected COHP (IpCOHP) for the Pb-Br bonds are 1.63 eV before Cu doping and 1.80 eV after Cu doping, respectively. This indicates that Cu doping strengthens the bond in the nearest neighboring [PbBr₆] octahedron. The Cu-Br bond within the [CuBr₆] octahedron has a significantly higher IpCOHP value of 5.04 eV. This finding agrees with our aforementioned conclusions, which indicate that the reduction of the metal-Br bonds and the shrinkage of the metal octahedra contribute to the strengthening of the lattice. This statement suggests that, by preventing the breaking of bonds, the formation of intrinsic defects can be suppressed. According to Figure 3, the bonding energy peak of the Cu-Br bond is approximately −13 eV, which is significantly lower than that of the Pb-Br bond. This reduction in energy of the system contributes to the stability of the crystal. The study shows that the Pb-Br bond is primarily formed by the interaction of Pb-6p and Br-4p orbitals, while the Cu-Br bond is formed by the interaction of Cu-3d and Br-4p orbitals. The bonding energy between Cu-3d and Br-4p is lower than that between Pb-6p and Br-4p orbitals, but the bonding strength of the former is much higher than the latter. This suggests that the strong hybridization resulting from Cu-3d orbitals enhances the bonding interaction between Cu-3d/Br-4p bonds, thereby reducing the total energy of the supercell system.

Our analysis of the bonding interactions and geometric structures is in agreement with the findings on formation energies. Specifically, the introduction of Cu doping results in a more compact CsPbBr₃ lattice with strengthened bonds, reducing the likelihood of intrinsic defects forming. This increases in the co-ordination number of cations and improved lattice order, which aligns with previous experimental observations [23].

To investigate the effect of copper doping on the optoelectronic properties of the CsPbBr₃ system, we also calculated the band structure and the density of states (DOS) using the hybrid density functional (HSE) method to obtain more precise results. As shown in Figure 4a,b, the undoped CsPbBr₃ system has a bandgap of 2.38 eV. After copper doping, the band gap increases to 2.91 eV. This blue shift of the bandgap is consistent with experimental observations and meets the original goal of extending the luminescence of CsPbBr₃ to blue light. The blue shift can provide an effective idea for us to find complementary blue-emitting LED materials. From the plotted density of states (PDOS) plots in Figure 4c,d, it can be seen that the contribution of Cs ions to the band edge is negligible, which has little effect on the electron transport. In the undoped CsPbBr₃ system, the valence band maximum (VBM) is mainly dominated by Br-4p orbitals, while the conduction band minimum (CBM) is mainly contributed by Pb-6p orbitals. After doping copper, the VBM of the CsPb_0.875Cu_0.125Br₃ system is strongly influenced by the Cu-3d orbital—i.e., Cu-3d is strongly hybridized with Br-4p—while the CBM continues to be controlled by the Pb-6p orbital, leading to the increase of the bandgap accordingly. That is to say, the Cu-3d orbital mainly changes the energy band structure and enlarges the band gap, which is consistent with the COHP analysis we mentioned earlier.

In order to understand the interaction of Cu-3d orbitals in the CsPb_0.875Cu_0.125Br₃ lattice, we take the orbital angular momentum I into account. The 3d orbit of Cu is composed of d_xy, d_xz, d_yz, d_x²−y², and d_z². Ideally, these five orbitals are degenerate. But, as discussed above, when Cu substitutes the Pb position to form the Cu_Pb defect in CsPbBr₃ perovskites, the [CuX₆] octahedron shrinks and changes into an elongated octahedron, and the five-fold degenerate 3d orbit of Cu then splits into the e_g doublet states and t_2g triplet states. This lowers the total energy of CsPbBr₃ systems and is beneficial to their stability.

The analysis in Figure S3 (see Supplementary Materials) shows that the refractive index of the perovskite material increases after doping with Cu. This indicates that the interaction of the material with light is enhanced, resulting in a decrease in the propagation velocity of light within the doped perovskite material. As a result, the material may become more opaque, particularly for certain wavelengths of light. This reduction in transparency can impact the propagation and utilization of light within the material. In addition, the increase in refractive index enhances the scattering of astigmatism, leading to a decrease in the optical uniformity of the material. This results in a more complex path of light propagation within the material, which ultimately affects its optical properties. The deterioration of these properties may have a negative impact on the optoelectronic conversion efficiency, causing an increase in light loss and a reduction in photoelectric efficiency. However, it is important to note that the range of change in the refractive index is relatively small, thus limiting its impact on optical performance. Through the calculation of defect propagation energy after doping, we have observed a significant reduction in defects. This indicates that doping Cu remains a crucial factor for enhancing photoelectric performance, resulting in effective and remarkable improvement.

As previously reported, CsPbBr₃ can exist in the cubic phase under certain conditions. Therefore, it is important to consider whether Cu doping could affect the optoelectronic properties of cubic CsPbBr₃. In this study, we thoroughly investigate the effects of Cu doping on the geometric structure and, thus, the stability of CsPbBr₃ systems, including the distribution of intrinsic defects and bonding interactions. The undoped and Cu-doped CsPbBr₃ supercells in the cubic phase are shown in Figure 5; we can see that, after doping, the metal octahedron and the whole lattice also shrink, and the bonding interactions are strengthened, which are illustrated in Figure S1 in the Supplementary Materials. This means that, after Cu doping, the original lattice becomes stronger than before and the intrinsic vacancies are suppressed, acquiring a more stable perovskite structure and the enhancement of PLQY. These findings are similar to that in the orthorhombic phase CsPbBr₃. However, as shown in Figure S2 in the Supplementary Materials, the cubic phase CsPbBr₃ exhibits an indirect band structure after Cu doping, and the band gap decreases from 2.41 eV to 2.37 eV, which is unfavorable for blue light emitting.

4. Conclusions

In this study, we conducted a series of theoretical simulations and find that the introduction of Cu dopants results in a contraction of the metal octahedron and the formation of a more compact lattice in the orthorhombic CsPbBr₃ materials. Meanwhile, the shrinkage of the metal octahedron relaxes the lattice strain originating from the rotation and the twisting of the [PbBr₆] octahedron in the pristine orthorhombic CsPbBr₃ lattice. Owing to the Jahn–Teller effect, the [CuX₆] octahedron distorts to an elongated octahedron to reduce the energy of whole lattice systems. All these factors turn CsPbBr₃ perovskites into a more stable state, indicating that the frameworks of this Cu-doped CsPbBr₃ become more difficult to break, thus suppressing the intrinsic defect, e.g., Br vacancy. This is believed to be the main contribution to promoting photoluminescence performances. The stronger lattice of Cu-doped CsPbBr₃ materials is further confirmed via the COHP analyses, from which we find that the Cu-Br bond in the [CuX₆] octahedron possesses a much higher IpCOHP with the value of 5.04 eV, and the IpCOHP of Pb-Br bond increases from the initial 1.63 eV to 1.80 eV as well. As illustrated in the COHP diagram, the strong hybridization between Cu-3d/Br-4p bonds enhances the bonding interaction and reduces the total energy of the CsPbBr₃ system. In addition, after Cu doping, the band gap of CsPbBr₃ increases from 2.38 eV to 2.91 eV, resulting from the manifest contribution of Cu-3d orbitals to the valence band. This makes the luminescence of the CsPbBr₃ blue shift, benefiting the blue light emitting of perovskites. Finally, through systematic first-principles calculations, we investigated the influence of Cu doping on the geometric structure, electronic properties, and the bonding interactions of the perovskite crystal. Subsequently we acquire a deep understanding of how Cu dopants enhance the optoelectronic properties and the stability of CsPbBr₃ perovskite, which is not reported previously. Therefore, our investigations can help us to modify the physical properties of perovskites by Cu dopant or other transition metals, which could put forward their practical applicability.