Theoretical study of the influence of doped niobium on the electronic properties of CsPbBr₃

Abstract

In the family of inorganic perovskite solar cells (PSCs), CsPbBr₃ has attracted widespread attention due to its excellent stability under high humidity and high temperature conditions. However, power conversion efficiency (PCE) improvement of CsPbBr₃-based PSCs is markedly limited by the large optical absorption loss coming from the wide band gap and serious charge recombination at interfaces and/or within the perovskite film. In this work, using density functional theory calculations, we systemically studied the electronic properties of niobium (Nb)-doped CsPbBr₃ with different concentration ratios. As a result, it is found that doped CsPbBr₃ compounds are metallic at high Nb doping concentration but semiconducting at low Nb doping concentration. The calculated electronic density of states shows that the conduction band is predominantly constructed of doped Nb. These characteristics make them very suitable for solar cell and energy storage applications.

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1. Introduction

Organic–inorganic hybrid perovskite solar cells (PSCs) have favourable properties including appropriate band gap, high absorption coefficient, low cost and easy fabrication process, and show great potential for photovoltaic devices.^1–6 Their power conversion efficiency (PCE) has been increased dramatically from 3.8% to a certified 25.5% by various strategies such as composition engineering, interface engineering, construction engineering, and preparation techniques.^7–14 Although the rapid increase of PCE has been realized, the intrinsic stability of hybrid perovskites under high humidity and high temperature is still a key issue for meeting the commercial requirements.^15,16

To reduce the instability issues, the use of all-inorganic cesium lead halides (CsPbX₃), which contain inorganic cesium (Cs) rather than organic cations as in organic–inorganic perovskites, has been demonstrated to be an effective strategy for improving the stability of PSCs.^17–19 Thus, currently, CsPbX₃ has attracted much attention. It is divided into different components by tuning the halide anions, mainly focusing on CsPbI₃,^20,21 CsPbI₂Br,^22,23 CsPbIBr₂,^24,25 and CsPbBr₃.^26,27 From the family of all-inorganic PSCs, CsPbBr₃ exhibits superior stability under high humidity and high temperature conditions, which is significant to the practical application of PSC devices. However, the PCE is limited by large optical absorption loss and serious charge recombination. At present, the best PCE of CsPbBr₃-based PSCs is just around 11%.²⁸ Therefore, it is urgent to know how to improve the PCE and reduce the cost of CsPbBr₃ PSCs.

To date, several strategies have been applied to enhance the PCE and simultaneously prolong the thermal stability of inorganic PSCs. For example, Chu and co-workers fabricated an amorphous Nb₂O₅ film as the ETL of inorganic planar CsPbBr₃ by the magnetron sputtering method, and 5.74% PCE was obtained due to the suitable surface work function and high transmittance of amorphous Nb₂O₅ and low charge recombination at the amorphous Nb₂O₅/CsPbBr₃ interface.²⁹ Yu et al. demonstrated an interesting method by face-down liquid-space restriction to prepare high-quality CsPbBr₃ perovskite films on compact TiO₂ layers. This novel method can obtain uniform, smooth and high-quality perovskite films, which greatly increased the PCE and V_oc in planar all-inorganic CsPbBr₃ PSCs.³⁰ Zhong et al. developed a one-step solution-processing method to fabricate CsPbBr₃ films using precursor engineering and applied it for a CsPbBr₃-based device. A PCE of 7.37% has been achieved with high stability over 1500 h under an ambient atmosphere with 30–35% relative humidity.³¹ Liao et al. developed a modified multistep spin-coating strategy for CsPbBr₃ film preparation, and the optimized PCE was improved to 8.12%. This might be mainly attributed to the high crystallinity and reduced density of trap states of the CsPbBr₃ film.³² They also selected a novel antisolvent-washing strategy for highly efficient carbon-based CsPbBr₃ PSCs, increasing the PCE to 8.55%.³³ Tang et al. reported a Lewis-base polymer, polyvinyl acetate (PVAc), to modify the CsPbBr₃ film. A maximum PCE of up to 9.53% with an excellent V_oc of 1.553 V was achieved for the CsPbBr₃-based PSC.³⁴ Yang et al. applied a vapor-assisted solution technique to prepare a uniform and pure CsPbBr₃ film. The optimized CsPbBr₃ PSC showed a PCE of 10.45% and outstanding stability for over 90 days under harsh conditions (80% RH, 85 °C).³⁵ Qi et al. proposed a phase transition-induced method to produce high-quality CsPbBr₃ thin films. A PCE of 10.91% was obtained for n–i–p structured PSCs with metal electrodes, and the carbon electrode-based devices exhibited excellent long-term stability and retained 80% of the initial efficiency in ambient air for more than 2000 h without any encapsulation.²⁸

Although there are many ways to improve the efficiency of the device, few studies were reported to fundamentally improve the absorption capacity of this kind of material, and the current efficiency is far from its ultimate efficiency. Theoretical calculations are an effective method to design materials and study the mechanism.^36–40

In this study, we systematically study the electronic properties of niobium (Nb)-doped CsPbBr₃ with different concentration ratios using first-principles calculations. This work will provide a good theoretical basis for understanding the structure and electronic properties of these compounds. Through the analysis of these results, we propose that Nb-doped CsPbBr₃ may be a promising solar cell absorber with good band gap and light absorption properties, which provides a feasible method for improving the efficiency of the device.

2. DFT calculation details

The Vienna Ab initio Simulation Package (VASP) based on the plane-wave pseudopotential technique was employed, using the Perdew–Burke–Ernzerhof (PBE) functional for the exchange-correlation interaction and the projector augmented wave (PAW) pseudopotential for the ion–electron interaction.^41–44 A kinetic energy cutoff of 350 eV was chosen to ensure good convergence of the total energy and stress. The well-tested Monkhorst–Pack k grid of a uniform spacing of 0.02 Å⁻¹ was adopted to sample the first Brillouin zone. All the structures were fully relaxed using the conjugate gradient algorithm until the force on each atom was less than 0.001 eV Å⁻¹ and the energy was converged to 10⁻⁴ eV.

We calculate the doping energy (E_doping) of five kinds of supercell structures doped with CsPbBr₃ at different Nb concentrations, and the formula of E_doping is given by

E_doping = E_dop + E_Pb − E_pure − E_Nb (1)

where E_dop is the total energy of the system after CsPbBr₃ is doped with Nb atoms, E_pure is the total energy of the pure undoped CsPbBr₃ system, and E_Pb and E_Nb are the energy of single atoms of Pb and Nb, respectively. Visualization of k-point paths in the 1st Brillouin zone is shown in Fig. 1.

Fig. 1 Visualization of k-point paths in the 1st Brillouin zone; g₁, g₂, and g₃ are vectors for the reciprocal lattice.

3. Results and discussion

In order to explore the effect of Nb doping of CsPbBr₃ on its absorption capacity, we doped Nb into CsPbBr₃ by expanding cells, that is, doping one Nb atom in each supercell, as shown in Fig. 2. We constructed Nb-doped CsPbBr₃ with 50%, 25%, 12.5%, 6.25%, and 3.125% concentration ratios, and the corresponding supercells and chemical formulae are shown in Table 1. The original CsPbBr₃ structure of five different supercells and the crystal structure after doping with different Nb concentrations are shown in Fig. 3.

Fig. 2 Schematic diagram of the crystal structure of Nb-doped CsPbBr₃.

Table 1 Supercells and chemical formulae of different concentration ratios of Nb doped in CsPbBr₃

Supercell	Chemical formula	Doping concentration
2 × 1 × 1	Br6NbCs2Pb	50%
2 × 2 × 1	Br12NbCs4Pb3	25%
2 × 2 × 2	Br24NbCs8Pb7	12.5%
2 × 2 × 4	Br48NbCs16Pb15	6.25%
2 × 4 × 4	Br96NbCs32Pb31	3.125%

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Fig. 3 Schematic diagrams of the pristine and Nb-doped CsPbBr₃ crystal structures with different concentration ratios.

The raw data used to calculate the doping energy are shown in Table 2. According to formula (1), we calculated the doping energies of Nb atoms doped in five supercell structures. The detailed calculation results are shown in Table 3. The results show that as the doping concentration increases, the doping energy gradually increases. When the doping concentration of Nb reaches 12.5%, the doping energy reaches the maximum value of −2.77 eV. However, when the doping concentration of Nb atoms is increased, the doping energy will gradually decrease.

Table 2 The raw data for calculating the doping energy

Structures	Pristine (eV)	Doped (eV)
2 × 1 × 1 supercell	−31.7945	−35.2799
2 × 2 × 1 supercell	−63.5882	−66.9168
2 × 2 × 2 supercell	−127.177	−130.491
2 × 2 × 4 supercell	−254.354	−257.757
2 × 4 × 4 supercell	−508.72	−512.19
Pb atom	−0.095720351
Nb atom	−0.64194424

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Table 3 Band gaps and doping energy of different concentration ratios of Nb doped in CsPbBr₃

Supercell	Chemical formula	Doping concentration	k-points	Gap (eV)	Doping energy (eV)
2 × 1 × 1	Cs2Pb2Br6	0	4 × 8 × 8	2.51	—
2 × 1 × 1	Cs2PbNbBr6	50%	4 × 8 × 8	0 (metallic)	−2.94
2 × 2 × 1	Cs4Pb3NbBr12	25%	4 × 4 × 8	0 (metallic)	−2.78
2 × 2 × 2	Cs8Pb7NbBr24	12.5%	4 × 4 × 2	1.94	−2.77
2 × 2 × 4	Cs16Pb15NbBr48	6.25%	4 × 4 × 2	1.89	−2.87
2 × 4 × 4	Cs32Pb31NbBr96	3.125%	4 × 2 × 2	1.84	−2.92

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The optimization results of lattice parameters for these pristine and differently Nb doped CsPbBr₃ are shown in Table 4. Since Nb is significantly smaller than the atomic radius of Pb, when Nb is doped to replace the Pb atom in CsPbBr₃, the lattice constant will be significantly reduced.

Table 4 Comparison of calculated lattice parameters of pristine and Nb-doped CsPbBr₃

Lattice parameters	Supercells
	2 × 1 × 1		2 × 2 × 1		2 × 2 × 2		2 × 2 × 4		2 × 4 × 4
	Pristine	50% Nb doped	Pristine	25% Nb doped	Pristine	12.5% Nb doped	Pristine	6.25% Nb doped	Pristine	3.125% Nb doped
a (Å)	12.001	11.426	11.986	11.758	11.986	11.881	11.982	11.936	11.980	11.956
b (Å)	6.005	5.713	11.986	11.758	11.986	11.881	11.982	11.936	23.960	23.908
c (Å)	6.005	5.713	5.993	5.8796	11.986	11.881	23.964	23.873	23.960	23.908

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Based on the relaxed structures, we studied the electronic properties of these compounds, including the band structures and density of states, which will be discussed below. Fig. 4 shows the band structures of the undoped system calculated by the PBE method and the Nb-doped system with different concentrations. Through comparison, it is found that the Fermi level of CsPbBr₃ after doping with Nb is closer to the conduction band. As shown in Fig. 4a, the energy band of CsPbBr₃ undoped with Nb shows a direct band gap. The highest point of the valence band (VBM) and the lowest point of the conduction band (CBM) are located at point R in the first Brillouin zone, respectively. Moreover, all undoped structures have the same band gap. When the doping concentration of Nb is 50% or 25%, both structures show the properties of metals, as shown in Fig. 4b and c. Furthermore, when the doping concentration of Nb is 12.5%, 6.25% or 3.125%, the Fermi level is closer to the conduction band, which indicates an n-type semiconductor. There is a direct band gap at the Γ point, and the forbidden band widths are 1.94 eV, 1.89 eV, and 1.84 eV, which correspond to Fig. 4d, e and f, respectively.

Fig. 4 (a) Band structures of the CsPbBr₃ supercell of 2 × 1 × 1. Band structures of different Nb doping concentration ratios of (b) 50%, (c) 25%, (d) 12.5%, (e) 6.25%, and (f) 3.125% corresponding to different pristine CsPbBr₃ supercells. The red bands are those of Nb.

The properties of the electronic band gap energy of different concentration ratios of Nb doping in CsPbBr₃ are further explained by the density of states. The density of states (DOS) explains the properties of these materials, as shown in Fig. 5. It can be clearly seen that the materials in Fig. 5a and b have crossed the Fermi level, which proves that when the doping concentration of Nb in CsPbBr₃ is 50% or 25%, the material becomes a metallic conductor. In Fig. 5c–e, none of them cross the Fermi level, which proves that these materials are semiconductors.

Fig. 5 Density of states (DOS) of Nb-doped CsPbBr₃ with different concentration ratios. (a) 50%, (b) 25%, (c) 12.5%, (d) 6.25%, and (e) 3.125%.

4. Conclusion

In summary, CsPbBr₃ is an excellent material for improving the stability of PSCs. Doping Nb into the material is considered to be an effective method to improve the PCE. Through DFT calculations, we systematically studied the electronic properties of CsPbBr₃ doped with different Nb concentration ratios, including the band structure and density of states. The results show that when the doping concentration of Nb is 3.125%, 6.25% or 12.5%, all three compounds have semiconductor properties, the band gaps are direct, and the basic band gaps occur at Γ symmetry points. As the doping concentration increases, the band gap width gradually increases. When the doping concentration of Nb is too high (25%, 50%), the compounds are all metallic conductors, which do not have the properties of semiconductors. From this work, we can expect that the performance of PCE and long-term stability of doped CsPbBr₃ at a certain Nb concentration will be greatly improved.

Conflicts of interest

The authors declare no competing interests.

Acknowledgements

Support of the National Natural Science Foundation of China (21902021, 21908017, 51972293, and 51772039), the Open Foundation of Key Laboratory of Industrial Ecology and Environmental Engineering, MOE(KLIEEE-20-01), the Fundamental Research Funds for the Central Universities (DUT20RC(4)020, DUT20RC(4)018, and DUT20LAB304), and the Supercomputing Center of Dalian University of Technology for this work is gratefully acknowledged.

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