A study on numerical simulation optimization of perovskite solar cell based on CuI and C60

The feasibility of CuI and C60 as hole transport layer and electron transport layer in the perovskite solar cell is tested by using the software Solar Cell Capacitance Simulator (SCAPS). It is found that the thicknesses of the absorption layer, electron transport layer and hole transport layer, and the Interface Density of Defect State of their interface have a key influence on the efficiency of the perovskite solar cells. After optimization, the efficiency was as twice as that before, 22.70% to 11.62%, and the fill factor can still be at a high value, 76%.


Introduction
Perovskite materials have the advantages of good light absorption, good charge transfer rate, and high photoelectric conversion efficiency.Solar cells made of perovskite (Perovskite Solar Cells, PSC) belong to the third generation of solar cells.2009, Mi-Yasaka et al prepared the first perovskite solar cell [1], the two perovskite materials, CH 3 NH 3 PbBr 3 and CH 3 NH 3 PbI 3 , are mainly used as absorber layers.Although its photoelectric conversion efficiency is only 3.8%, it has attracted wide attention in the photovoltaic research field.In recent years, with the effort of researchers, the power conversion efficiency (PCE) of perovskite solar cells has been continuously improved [2][3][4][5][6].At present, the power conversion efficiency of perovskite solar cells has reached over 20% [7].It shows that perovskite solar cell has good development prospects in the field of clean energy.
There are roughly two kinds of structure of perovskite solar cell, upright (n-i-p) structure and inverted (p-in) structure.The planar PSC has a simple structure, which has few interface defects and an almost 100% internal quantum efficiency [8].Take the inverted planar perovskite battery as an example, the battery structure from bottom to top is glass, transparent electrode (ITO or FTO), electron transport layer (ETL), perovskite layer (Perovskite), hole transport layer (HTL), and metal electrode.In the perovskite battery structure, due to the energy gap between the perovskite absorption layer, electron transport layer, and hole transport layer, and photogenerated electron-hole pairs will be dissociated and injected into ETL and HTL, then pass through their respective electrodes collect electrons and holes to generate photo-generated current and photo-generated voltage.Of course, there will inevitably be losses in the carrier transport process, such as the recombination of holes and electrons between two adjacent layers, the capture and annihilation of carriers by surface and interface defects, which have negative impacts on the optoelectronic performance of the device.Therefore, how to increase the yield of electron-hole pairs but reduce the recombination loss needs to be considered in terms of improving the crystal quality of the perovskite layer, optimizing the surface and interface of the device, and reducing defects.
In perovskite battery devices, 9,9-bifluorene (spiro-OMeTAD) and TiO 2 are often used as hole and electron transport layer materials, respectively.For spiro-OMeTAD, due to the high cost of preparation and the complexity of the process, which limited its large-scale commercial application.Also, TiO 2 is widely used as ETL due to its high thermal stability, suitable band arrangement, and low cost [9], But, TiO 2 has a high density of defect states, lag in its efficiency in the device, low electron mobility, high catalytic activity, unfavorable charge recombination and agglomeration [10,11], Simultaneously, ultraviolet light can transmit titanium dioxide that causes degradation of the perovskite layer [10].Therefore, it is significant to look for alternative materials for the ETL and HTL layer of perovskite solar cells.
CuI has excellent performance of wide bandgap and hole mobility, which is an excellent inorganic P-type material of HTL, when doping with poly-triarylamine (PTAA) [11], the PCE of perovskite solar cells can exceed 20%.Compared with spiro-OMeTAD, CuI has a lower valence band, which is favorable for hole transport.For lowering manufacturing costs of lead-free perovskite solar cells.C60 has high and adjustable LUMO energy levels, which match well with the energy band of perovskite and can be prepared in a solvent that does not react with perovskite.And it improves the extraction of electric charge, alleviates the hysteresis effect of the battery, which makes the battery show high efficiency and high stability at the same time.Their advantage over TiO 2 is that they can be prepared at low temperatures.Thus, CuI as HTL layer and C60 as ETL layer are potentially quality to take place of spiro-OMeTAD and TiO 2 in perovskite solar cell.However, there are few related research based on CuI and C60 of perovskite solar cells about cell structure parameters, especially each layer's thickness influence, the interface density of defect state, and so on.
In perovskite solar cells, the perovskite absorber layer plays a crucial role in the overall performance of the battery by absorbing light and accelerating the carrier migration rate.The thickness of the perovskite layer is one of the important parameters, which can influence the generation and migration of charge carriers, thereby influencing the performance of PSC.If it is not thick enough, it would not absorb enough light.While the charge carriers from ETL to HTL, or from HTL to ETL, must go through the perovskite absorber layer, if it is too thick, the process of charge carriers reaching ETL or HTL will be severely limited.For the thickness of HTL and ETL, they provide superior channels for holes and electrons to reach external circuits by blocking electrons and holes.Therefore, the thickness of HTL and ETL is also an important factor in the battery's performance.In terms of interfacial density of defect state, if too high, it will lead to both low diffusion length and a low lifetime of charge carriers, thereby causing a high recombination rate of the perovskite absorber layer, which means low carrier mobility, at last affects the overall performance of the battery.
In this paper, CuI as the hole transport layer and C60 as the electron transport layer, using the solar cell simulation software SCAPS model, simulate and optimize the perovskite solar cell structure.Using the combination of inorganic materials and organic materials to fabricate perovskite solar cells while replacing spiro-OMeTAD to reduce fabrication costs.Numerical simulation experiments reduce the consumption of physical experiments, and it will be more efficient to conduct experiments after determining the appropriate structure.The open-circuit voltage (Voc), the short-circuit current density (Jsc), the fill factor (FF), and the power conversion efficiency (PCE) are analyzed as performance evaluation indicators to study the influence of the thickness of the absorber layer, electron transport layer and hole transport layer on the performance of perovskite solar cell.Also, the interface density of the defect state and working temperature are discussed here.

Simulation method and process
The SCAPS3310 software involves those following coupled equations for semiconductors, where appropriate boundary conditions are considered for interfaces and contacts of the device: where Jn and Jp are given by And ε is the permittivity of semiconductors, j is the electrostatic potential, q is the elementary charge, T is the operating temperature, D p and D n are the diffusion coefficients of holes and electrons, and p and n are the concentrations of holes and electrons, respectively.G p and G n are the hole generation rate and electron generation rate, respectively, N A and N D are the doping concentration of holes and electrons, J p and J n are the current densities of holes and electrons, μ p and μ n are the hole migration rates, electron migration rate.R n and R p respectively represent the electron recombination rate and hole recombination rate, under steady-state conditions.Those parameters such as doping concentration and migration rate are calculated by simulation experiments and put into formulas (1)-( 4) to calculate the appropriate density of defect states.They affect the carrier lifetime of electrons and holes (τ n , τ p ), and the interface recombination rate is related: where σ n and σ p are the electron and hole capture cross-sections, respectively.And V th , N t , n r are thermal velocity, the total defect density (occupied and unoccupied), the occupied defects.The thermal velocity of the interfacial layer can be expressed as V 1R , and the total interfacial defect density can be expressed as N IR .Here, the carrier lifetime decreases as the defect density increases, and therefore the carrier diffusion length (L) also decreases, adversely affecting the photovoltaic performance of perovskite solar cells.Defect recombination current (J O ) depends on the diffusion length » J q and the open-circuit voltage (Voc), ( ) The concentration of holes (N A ) and electrons (N D ) are key parameters in material effects, they are the same called the built-in potential (V bi ), which is related to temperature, ( ) Shockley-Read-Hall (SRH) reorganization provides more insight into defect density in the performance of perovskite solar cells, Where V th is the electron thermal velocity, ni is the intrinsic number density; p 1 and n 1 are the holes and electron concentration in the trap centers, and N T is the defect density (per volume) [12].

Experimental results
In SCAPS3310, the heterostructure of perovskite solar cells can be designed with seven different semiconductors cell layers and can be simulated and executed on the device under the required incident spectrum [13].The structure of the perovskite solar cell is ITO/C60/Perovskite/CuI/Ag in this study.Where, C60 and CuI are used as electron transport layers and the hole transport layer respectively; Because carriers will recombine at the battery layer interface during the migration process, interface layers labeled as L1 and L2 were applied at ETL/ perovskite and perovskite/HTL interfaces, respectively.ITO and Ag are used as front electrodes and metal back electrodes, respectively, and their work function is set to 4.1 and 4.7 eV, respectively [14].The battery parameter configuration of each layer is shown in table 1 [15][16][17].In addition, the thermal velocity of electrons and holes of each layer of material is set to 10 7 cm s −1 [17].Light reflectivity at the surface and interface is considered here.The defect energy level is in the central band gap and has a Gaussian distribution and an energy of 0.1 eV.The simulation is performed under AM 1.5 G spectrum and working temperature of 300 K, and resistance is assumed to be 2.00 Ω•cm 2 .

Effect of perovskite absorption layer
As shown in figure 2, the performance parameters of PSC (Jsc, Voc, FF, and PCE) vary with the thickness of the perovskite layer.See the 20 nm thick ETL and HTL curve (figure 2, triangle), short-circuit current density (Jsc), open-circuit voltage (Voc) and power conversion efficiency (PCE) all monotonically increases with the thickness of the absorber layer, while fill factor (FF) monotonically decreases.It can also be seen from the figure that after the thickness of the perovskite layer exceeds 500 nm, those changes of Jsc, Voc, and PCE tend to be gentle, and the difference between 800-1000 nm is very small.10 nm ETL−50 nm HTL ones were further examined.As shown in figure 2 (circle), they obey the same trend, which tells the rules are consistent.Therefore, without considering the density of the defect state, ensuring FF>70%, the thickness of the selected absorber layer should be roughly greater than 700 nm.The continuous drop in FF is caused by a drop in the maximum output power.After configuring a suitable interfacial defect state density and thickness of HTL and ETL, it can be seen that Voc increases, resulting in a higher FF of 10 nm ETL -50 nm HTL than that of 20 nm ETL -20 nm HTL and a slow decline.

Effect of HTL and ETL
As shown in figure 3, see the blue triangles, they represent the variation of Jsc, Voc, FF, and PCE with ETL thinness and absorber layer thickness is 700 nm and HTL is 20 nm.We can see that Jsc and PCE decrease monotonically with the thickness of ETL, but change slowly between 10 and 50 nm.However, Voc and FF did not change significantly with the thickness of ETL.The blue square ones tell the influence of HTL, at the same conditions except the ETL fixed 20 nm.It can see that after HTL thickness exceeds 50 nm, it will influence the performance slightly, not obvious.Similarly, the extra thickness of the absorber layer, 500 nm(red) and 900  The battery performance (Jsc, Voc, FF, and PCE) changes with the thickness of the perovskite layer.'20 nm' means that the thickness of ETL and HTL are both 20 nm, and '10, 50 nm' means that the thickness of ETL is 10 nm and thickness of HTL is 50 nm.nm(green), for both ETL (triangles, HTL fixed 50 nm) and HTL (square, ETL fixed 10 nm) are examined to verify the trend.it can see that the trend is consistent the same.

Effect of interface density of defect state
In the simulation settings, the defect of the two interfaces of and L2 varies from 10 6 to 10 16 cm −3 at the same time.If it is too large, the carriers at the interface are recombined too much, and the carriers entering the absorption layer for recombination are reduced, resulting in the inability of holes and electrons transporting through the absorption layer, affecting the open-circuit voltage, and thus affecting battery performance.Figure 4(a) shows the J-V characteristic curves of different interface defect state densities of L1 and L2 when the thicknesses of the perovskite absorber layer, ETL and HTL are 900 nm, 10 nm, and 50 nm, respectively.It can see that higher defect densities generate more defects and recombination centers, leading to a decrease in cell performance.In addition, when the interfacial density of the defect state is smaller than 10 9 cm −3 , the J-V characteristic curves remain almost unchanged.Therefore, on one hand, it is limited to improve the battery performance by reducing the interface density of the defect state when it is less than 10 9 cm −3 .On the other hand, for current technology, it is difficult to make it smaller than 10 9 cm −3 , even if it is, the filling factor will become small and extremely unstable.Therefore, it is reasonable to set the interfacial density of the defect state of L1 and L2 to 10 9 cm −3 .
But for the interface density of defect state influence, we only discuss one case that the absorption, ETL and HTL layer is 900 nm, 10 nm, and 50 nm respectively, and change the density of defect state of both L1 and L2 at Figure 3. Variation of cell performance (Jsc, Voc, FF, and PCE) with changes in ETL and HTL thickness, '500 nm' means the thickness of perovskite absorber layer thickness is 500nm, '700 nm' means the perovskite absorber layer thickness is 700 nm, '900 nm' means the thickness of the perovskite absorber layer is 900nm.
Figure 4.The effect of the density of defect states of L1 and L2 on the J-V characteristic curve.(a) perovskite absorber layer thickness is 900 nm, HTL thickness is 50 nm, and ETL thickness is 10 nm.(b) perovskite absorber layer thickness is 700 nm, HTL thickness is 50 nm, and ETL thickness is 10 nm. the same time.When the thickness of the absorber, ETL, and HTL layer changes, we can get the same conclusions as in figure 4(b).when the absorber layer thickness is changed to 700 nm, 10 9 cm −3 is also the best choice.In addition, it is found that, by calculation, the interface density of defect state of L2 layer alone has little effect on the performance of PSC, while the density of defect state of L1 layer alone or both L1 and L2 together has almost the same effect on the performance of perovskite solar cell.Therefore, in this work, we choose to change the interface density of the defect state of both the L1 and L2 layers at the same time.
In summary, satisfying FF>70%, within the calculation range, the larger the thickness of the absorber layer, the higher the power conversion efficiency is.When HTL thickness is more than 50 nm, it has little effect on perovskite solar cells.The smaller the ETL thickness, the higher power conversion efficiency is.If technical allows, the smaller surface density of defect state, the higher power conversion efficiency can be got.But, further reduction, below 10 9 , has very little improvement.Therefore, we can get the best-optimized performance by setting the parameters, the thickness of the absorber layer, HTL, ETL, and interface density of defect state of the L1/L2 layer to 900 nm, 50 nm, 10 nm, and 10 9 cm −3 respectively.As in figure 5, the J-V characteristic curves of the perovskite solar cell, before and after optimization, are compared.We can see that the performance of the optimized solar cell is significantly improved.Its parameters are: Voc= 1.14V, Jsc=26.06mA cm −2 , FF=76.12%,PCE=22.70%.Compared with the efficiency before optimization, PCE is double improved.

Conclusion
C60 and CuI as electron and hole transport layer, respectively, the perovskite solar cell simulation was carried out with the software SCAPS.The perovskite solar cell, as the power conversion efficiency for the solar cell having a positive correlation with the thicker perovskite absorber layer, negative correlation with ETL thickness and the surface density of defect state of L1 and L2 layers, irrelevant with, when over 50 nm, HTL, can be optimized.The optimized power conversion efficiency of perovskite solar cells is twice that before optimization, and the fill factor can still maintain 76%.Therefore, the structure ITO/C60/Perovskite/CuI/Ag of solar cells has practical potential.Additionally, it is temperature stable.

Figure 1 .
Figure 1.Pseudocode of experimental process (description in MATLAB language).

Figure 2 .
Figure2.The battery performance (Jsc, Voc, FF, and PCE) changes with the thickness of the perovskite layer.'20 nm' means that the thickness of ETL and HTL are both 20 nm, and '10, 50 nm' means that the thickness of ETL is 10 nm and thickness of HTL is 50 nm.

Table 1 .
Parameters of each battery layer.