Introduction

Traditional energy generation from fossil fuels has a negative effect on the environment1. Using renewable energy sources instead of fossil fuels is an important issue to overcome this problem in worldwide2,3. Solar cells are the most important renewable source that can convert sunlight to electricity4,5,6,7,8,9,10,11. Silicon solar cell technology is applicable for industrial applications due to long-term stability and high-power conversion efficiency (PCE)12,13. High melting point temperature (1400 °C) and needing for expensive instruments for the fabrication of Si solar cells are the biggest challenge for the production of low-cost solar cells14,15. Researchers are working on, low-temperature and easy fabrication of third-generation of solar cells. The most known and important of these types of solar cells are perovskites due to their suitable properties and efficiency achievement above 25% in a short time (nearly one decade)16. Recently perovskite quantum dots (PQDs) are received great attention17. Mainly \(a\)-CsPbI3 material has been used as an absorber layer in PQDs due to its ideal bandgap of 1.73 eV18,19. Suitable properties such as narrow photoluminescence (PL), high carrier mobility, tunable absorbance, and great defect tolerance enable low non-radiative recombination despite huge defect density18. Good crystallinity and morphological control are not necessary simultaneously for the film deposition of colloidal CsPbI3 QDs and this feature makes them suitable for fabrication of large-scale devices via printing techniques18. Achievement to the efficiency of 16% for CsPbI3 QD solar cells (more than PbS QDs) shows their high potential for next-generation QD solar cells20. Hence the focus of this work is the work on simulation of CsPbI3 QDs solar cells. Yuan et al.21 have fabricated CsPbI3 perovskite quantum dot (QD) solar cells by using a series of dopant-free polymeric hole-transporting materials (HTMs) and they have improved charge extraction at QD/polymer interfaces and increased the efficiency to 13%. Mehrabian et al.22 have simulated perovskite quantum dot solar cells with three different absorber layers of CsPbI3, FAPbI3, and CsPbI3/ FAPbI3, and they optimized their cell by defining the bilayer of the CsPbI3/FAPbI3 structure by optimization of band gap and they achieved the PCE of 18.55%. In this research, we have simulated the CsPbI3 perovskite quantum dot, and compared it to experimental results, at the following, we have investigated the electro-optical properties of CsPbI3 CQD on solar cell performance.

Results and discussion

Numerical simulation and validation

SCAPS-1D (SCAPS 3306) was used for the simulations. This package solves the Poisson equation (Eq. (1)), and the continuity equation for holes and electrons (Eqs. (2) and (3)) by coupling with Shockley–Read–Hall (SRH) recombination statistics (related to defects in bulk and interfaces) (Eqs. (5) and (6))23,24,25,26,27,28,29,30.

$$\frac{{d}^{2}}{{dx}^{2}}\Phi \left(x\right)=\frac{q}{{\varepsilon }_{0}{\varepsilon }_{r}}\left(p\left(x\right)-n\left(x\right)+{N}_{D}-{N}_{A}+{n}_{t}^{+}-{n}_{t}^{-}\right)$$
(1)
$$-\left(\frac{1}{q}\right)\frac{{\partial J}_{p}}{\partial x}-{U}_{p}+G=\frac{\partial p}{\partial t}$$
(2)
$$\left(\frac{1}{q}\right)\frac{{\partial J}_{n}}{\partial x}-{U}_{n}+G=\frac{\partial n}{\partial t}$$
(3)
$${U}_{n}={U}_{p}={R}_{Bulk,SRH}+{R}_{Surface, SRH}$$
(4)
$${R}_{Bulk,SRH}=\frac{np-{n}_{i}^{2}}{{\tau }_{p}\left(n+{n}_{t}\right)+{\tau }_{n}(p+{p}_{t})}$$
(5)
$${R}_{Surface,SRH}=\frac{np-{n}_{i}^{2}}{\left(n+{n}_{ts}\right)/{S}_{n}+(p+{p}_{t})/{S}_{p}}$$
(6)

In Eq. (1), parameter \(\Phi \) is the electrostatic potential, q is the electrical charge, εr and ε0 are the relative and the vacuum permittivity, p and n are hole and electron concentrations, ND and NA are charge impurities of donor and acceptor type, \({n}_{t}^{+}\) and \({n}_{t}^{-}\) are hole and electron trap concentrations, respectively. In Eqs. (2) and (3); Jn and Jp are the electron and hole current densities. G is the generation rate. τn/τp, Rsurface, Sn/Sp , ni, nt/pt , and nts/pts are the electron/hole lifetime, surface recombination rate, surface recombination velocity of the electrons/holes, the intrinsic carrier concentration, the bulk electron/hole concentration of the trap states, and surface trap state concentration, respectively. Figure 1a shows the structure of CsPbI3 CQDs. The input data for the simulation is provided in Table 1, and simulation-experiment J-V comparison was shown in Fig. 1b.

Figure 1
figure 1

(a) Schematic of Perovskite quantum dot solar cells and (b) J-V characteristics of Perovskite quantum dot solar cells simulation and experiment.

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Table 1 Input electro-optical parameters for the simulation.
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The interfaces properties data are available in SI.

Experiment details

The SnO2 nanoparticle solution was deposited on ITO with spin-coating method at 120 °C for 30 min. PCBM CB solution (5 mg/mL) was spin-coated with speed of 5000 rpm for 30 s. In the following, a dissolved solution of 1.2 M CsI, 0.6 M PbI2, and 0.6 M PbBr2 in DMSO was used for precursor solution, and then spin-coated at 1500 rpm and 4500 rpm for 15 s and 45 s, respectively. As an HTL layer, PTB7 solution (10 mg/mL in chlorobenzene) was spin-coated on CSPbI3 CQDs. Finally, MoO3 (10 nm) and Ag (nm) electrodes were deposited via thermal evaporation34.

Tuning properties of CsPbI3 CQDs (absorber layer)

Effect of band gap

Here, we have studied the effect of band gap of CsPbI3 CQDs. By increasing the band gap to value of 1.4 eV, the efficiency will increase to 21%. While, for band gap more than 1.4 eV, Voc is increased to 1.2 V but the efficiency and Jsc is decreased and continued to reach 1%, and 3 mA/cm2, respectively, for band gap of 2.5 eV (Fig. 2).

Figure 2
figure 2

Effect of band gap of CsPbI3 CQDs on J-V parameters.

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By varying the band gap, absorption coefficient also varied due to equation \((A+B/hv)\sqrt{(Eg-hv)}\). For understanding the behavior of band gap effect on performance, we plotted the band structure and electron Fermi level (Figs. 3 and 4) for two cases of high (Eg = 1.4 eV) and low efficiency (Eg = 2.5 eV). The valence band offset (VBO) between absorber and HTL is increased for the case of Eg = 1.5 eV that create a spike against hole transport (Fig. 3) and increase the recombination and leads to Jsc, FF, and efficiency decrement. The higher Voc for the case of Eg = 1.5 eV, is due to electron fermi level increment.

Figure 3
figure 3

Band structure for band gap of (a) 1.4 eV, and (b) 2.5 eV. Graphs taken at V = 0 V at light condition.

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Figure 4
figure 4

Electron Fermi level for band gap of (a) 1.4 eV, and (b) 2.5 eV. Graphs taken at V = 0 V at light condition.

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Effect of electron affinity

Here, we have modified the electron affinity of absorber layer from 2.7 to 4.5 eV (Fig. 5).

Figure 5
figure 5

Effect of electron affinity of CsPbI3 CQDs on J-V parameters.

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In electron affinity of 2.7 eV and 3.9 eV we have the lowest (0.81%) and highest efficiency (15.48%), respectively. By investigation of band structure, we found that the conduction band offset (CBO) between absorber and buffer in case of 3.9 eV, is in cliff form that help the electrons move easily and speedy (Fig. 6). For the case of 2.7 eV, the electrons in conduction band see a barrier and they are stuck which result in high recombination.

Figure 6
figure 6

Band structure for electron affinity of (a) 2.7 eV, and (b) 3.9 eV. Graphs taken at V = 0 V at light condition.

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Effect of electron–hole mobility

Here, the effect of electron and hole mobility on performance are investigated. Electron mobility has low effect on performance (Fig. 7) and it because of the impurity of absorber layer that in p-type semiconductor hole mobility is important. Here, hole mobility has significant impact on J-V characteristics (Fig. 8). By increasing the hole mobility from 10−3 cm2V−1s−1 to 103 cm2V−1s−1 the efficiency is increased from 3.84% to 15.20%.

Figure 7
figure 7

Effect of electron mobility of CsPbI3 CQDs on J-V parameters.

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Figure 8
figure 8

Effect of hole mobility of CsPbI3 CQDs on J-V parameters.

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The recombination rate for the hole mobility of 10−3 cm2V−1s−1 and 103 cm2V−1s−1 is plotted in Fig. 9.

Figure 9
figure 9

Recombination rate for the hole mobility of (a) 10−3 cm2V−1s−1 and (b) 103 cm2V−1s−1. Graphs taken at V = 0 V at light condition.

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For low values of hole mobility, the recombination rate in perovskite layer is increased severely. Here, for fabrication of QD solar cells with high efficiency we need an absorber layer with high mobility.

Effect of acceptor density

We modified the doping of absorber layer, acceptor density, by increasing the density of absorber, efficiency, FF and Voc are increased but Jsc decreases (Fig. 10).

Figure 10
figure 10

Effect of acceptor density of the absorber of CsPbI3 CQDs on J–V parameters.

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As can be seen in Fig. 11, level of electron fermi is enhanced due to higher doping density that helps the electric field in the absorber layer and efficiency increment.

Figure 11
figure 11

Electron Fermi level for Na = (a) 1013 cm−3, and (b) 1019 cm−3. Graphs taken at V = 0 V at light condition.

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Effect of defect density

The defects formation are the most important factors to have high or low efficiency. Here, we have changed defects density from the low (1010 cm−3) to high values (1020 cm−3) (Fig. 12). The high population of defects are detrimental for the device that can reduce the efficiency from 0.12% to 16.49%. It means the high defect density can cause the solar cell device does not work efficiently.

Figure 12
figure 12

Effect of defect density of the absorber of CsPbI3 CQDs on J–V parameters.

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The higher defect density will increase the recombination rate at perovskite layer (Fig. 13).

Figure 13
figure 13

Recombination rate for the defect density of (a) 1010 cm−3 and (b) 1020 cm−3. Graphs taken at V = 0 V at light condition.

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Effect of defect energy and types

Defect energy is important parameter which shows the types of defects in the QD perovskite layer. The defects with energy between 0.4 eV to 1.4 eV are harmful for device due to poor efficiency (Fig. 14).

Figure 14
figure 14

Effect of defect energy of the CsPbI3 CQDs on J–V parameters.

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This behavior is because of recombination rate enhancement.

For defect types we have consider 3 cases,

  1. I.

    \({\sigma }_{n}={\sigma }_{p}\)

    \({\sigma }_{n}={10}^{-15}\) cm2, \({\sigma }_{p}={10}^{-15}\) cm2, and Nt = 1015 cm−3 are considered for the below figures.

  2. II.

    \({\sigma }_{n}>{\sigma }_{p}\)

    \({\sigma }_{n}={10}^{-14}\) cm2, \({\sigma }_{p}={10}^{-15}\) cm2, and Nt = 1015 cm−3 are considered for the below figures.

  3. III.

    \({\sigma }_{n}<{\sigma }_{p}\)

    \({\sigma }_{n}={10}^{-15}\) cm2, \({\sigma }_{p}={10}^{-14}\) cm2, and Nt = 1015 cm−3 are considered for the below figures.

As we see in 3 cases of I, II, and III (Figs. 15, 16, and 17), there is no significant effect on J-V parameters on 3 types of defects. However, in real situation it is important due to different density of defect (also we show this in previous section), but here we assume the same density for 3 cases of defect type.

Figure 15
figure 15

Effect of defect types of the CsPbI3 CQDs on J–V parameters.

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Figure 16
figure 16

Effect of defect types of the CsPbI3 CQDs on J–V parameters.

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Figure 17
figure 17

Effect of defect types of the CsPbI3 CQDs on J–V parameters.

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Effect of thickness

The effect of thickness is investigated on J-V characteristics (Fig. 18). By increasing the thickness from 10 to 200 nm, the efficiency is enhanced drastically, and for the thickness higher than 200 nm, the efficiency will drop slowly. The thickness between 100 and 350 nm seems suitable for choosing CPQDs solar cells.

Figure 18
figure 18

Effect of thicknes of CsPbI3 CQDs on J–V parameters.

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Optimized case

Finally, we optimized the cell by definition of new ETL, HTL and optimum electro-optical parameters for HTL/absorber, Buffer/absorber and absorber layer. The efficiency is enhanced from 14.85% to 29.88% (Fig. 19). This improvement eager the researcher to work on CQD Perovskite solar cell for industrial and marketing application in near future.

Figure 19
figure 19

The J-V characteristics comparison between optimized, simulation and experiment case.

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Conclusion

This study addressed the comprehensive investigation of absorber layer properties in CsPbI3 perovskite quantum dots (CPQDs) solar cells. For the achievement of highly efficient CPQDs solar cells, it is important to choose absorber layer materials with a band gap of 1 − 1.7 eV, an electron affinity of 3.7–4 eV, and electron mobility (\({\mu }_{e}\)) of 10−2–103 cm2/V.s, hole mobility (\({\mu }_{h}\)) of 101–103 cm2/V.s, acceptor density (Na) of 1013–1019 cm-3, defect properties such as defect density of 1010–1013 cm−3, and Defect energy of 0 − 1.76 eV. For modifying the CsPbI3 properties, the material ratio, deposition processes such as temperature and time of deposition, different treatments, adding nanoparticles such as graphene, and using stacked deposition with different sandwich materials are the ways that we have proposed for the modification. The optimum efficiency of 29.88% was achieved for the CPQD solar cell in this research. These results are very promising and eager the researcher work on our proposed model to achieve highly efficient CPQD solar cells.