Modeling of Abnormal Hysteresis in CsPbBr₃ based Perovskite Solar Cells

^*B GopalKrishna, Sanjay Tiwari

Photonics Research Laboratory, School of Studies in Electronics & Photonics

Pt. Ravishankar Shukla University, Raipur, India

Corresponding Author Email: krishna_burra85@yahoo.com

[Received: 27 December 2020; Revised: 18 March 2021; Accepted: 22 March 2021]

Abstract: Perovskite solar cells are emerging photovoltaic devices with PCE of above 25%.  Perovskite are suitable light absorber materials in solar cells with excellent properties like appropriate band gap energy, long carrier lifetime and diffusion length, and high extinction coefficient. Simulation study is an important technique to understand working mechanisms of perovskites solar cells. The study would help develop efficient, stable PSCs experimentally.  In this study, modeling of perovskite solar cell was carried out through Setfos software.  The optimization of different parameters of layer structure of solar cell would help to achieve maximum light absorption in the perovskite layer of solar cell.  Simulation study is based drift-diffusion model to study the different parameters of perovskite solar cell. Hysteresis is one of the factors in the perovskite solar cell which may influence the device performance.  The measurement of abnormal hysteresis can be done by current-voltage curve during backward scan during simulation study. In backward scan, the measurement starts from biasing voltage higher than open circuit voltage and sweep to voltage below zero. The numerical simulation used to study the various parameters like open circuit voltage, short circuit current, fill factor, power conversion efficiency and hysteresis. The simulation results would help to understand the photophysics of solar cell physics which would help to fabricate highly efficient and stable perovskite solar cells experimentally.

Keywords- Perovskite solar cells, Transient photo-current, Hysteresis, Efficiency, Setfos software.

Introduction

Perovskite solar cells have achieved a reported efficiency of over 25% in recent years and can be future solar technology for energy generation for human race. Perovskite materials are semiconductors with properties like tunable band gap, efficient light absorption and high charge mobility for fabricating efficient solar cells. The performance of perovskite depends on its structural order which is temperature dependent even in typical solar cell operating conditions. Perovskite/silicon, perovskite/CIGS, and perovskite/perovskite tandem solar cells are the next PV technologies for fabricating highly efficient PV devices.  Perovskite/silicon tandem solar cells have reported to achieve a record efficiency of 26.7%. The power conversion efficiency of perovskite/silicon tandem solar cells could reach beyond 30% (Quiroz et al., 2018; Altazin et al. 2018). The physics and operational mechanism of perovskite solar cells are very difficult to understand by simple analytical formulations. Numerical study of the operational mechanism gives deeper knowledge of the underlying device physics of PSCs.Drift diffusion model can be helpful to simulate different solar cell parameters such as voltage, current, carrier density, and charge recombination. The simulation of PSC will provide the J-V curve characteristics to know the evolution of hysteresis in the device. The phenomena of hysteresis are assumed to occur due to internal capacitance and polarization inperovskite solar cell. The hysteresis caused by internal capacitance and polarization of perovskite solar cell can be studied under fast and slow scanning rates respectively. In this simulation study, the scanning rate was being kept at slow process.There are different device simulations modelswhich are used to study parameters like open-circuit voltage, photocurrents, series resistance, shunt resistance and fill factor(Snaith et al.,2014).Many models based on mobile ions neglect RC effects which are important to understand transient or frequency-domain experiments and used for solar cell simulation to get errors in results. Therefore, simulation model should include series resistance, frequency and transientparametersto get a better knowledge of influence of mobile ions in layer structure of perovskite solar cell. In this study, we present various parameter measurements of a planar CsPbBr₃ perovskite solar cellthrough simulations using drift-diffusion model. The simulation model incorporating mobile ions and charge traps gives the good information about the dependence of the open-circuit voltage on the light intensityand photocurrent. The underlying device physics of PSC can be described properly by the device model including inert mobile ions and traps(Krishna et al., 2020). The parameter analysis of PSC by simulation is importance to determine which factors limit the device performance and will be taken care of during development of PSC(Snaith et al.,2014; Perez et al. 2014).

In this research, numerical simulation of CsPbBr₃ perovskite solar cell using Setfos software will be done to optimize the different parameters like layer thickness, hysteresis and other factors for getting better device performance.

Methodology

The numerical modeling was done by using simulation software Setfos 5.0 from Fluxim. Different parameters used for simulation as shown in Table 1.The CsPbBr₃ perovskite solar cell structure has a p-i-n architecture as shown in Figure 1. Perovskite solar cell  structure consists of CsPbBr₃ perovskite as light absorbing layer, TiO₂ as electron transporting layer (ETL), Spiro-OMeTAD as hole transporting layer (HTL). The architecture of perovskite solar cell is FTO/TiO₂ /CsPbBr₃ / Spiro-OMeTAD / Au. The layer thicknesses of TiO₂, Spiro-OMeTAD, perovskite were taken such as 80 nm, 100 nm and 450 nm respectively.

Figure 1. Structure of the CsPbBr₃ based Perovskite Solar Cell

When reversed biased voltage is applied to the PSC, the properties of the device changes due to  the   development of smaller value of electric current in the device. The phenomena can be measured by I-V curve. In backward scan, the measurement starts from biasing voltage higher than open circuit voltage and sweep to voltage below zero. The numerical simulation used to study the hysteresis which gives the proper understanding of charge transport.

The efficiency of the solar cell can be influenced by charge carrier doping because it leads to extra charge inside the bulk which may produce screening effect. In case of high doping density,the screening effect influences the electric field whichhinders the charge extraction. This would lead to decrease in photocurrent. In case of low doping density, the short-circuit current is decreased and fill-factor is increased (Tress et al.,2015; Walsh et al., 2015).

In PSC device, the photon-to-charge conversion efficiency may be reduced due to reduced light absorption or hindered exciton dissociation. Exciton dissociation is hindered due to the roughness in phase-mixing in perovskite solar cell. The different parameters for the materials used in the solar cell for simulation were summarized in Table 1.

Table 1 Showing the Parameters of the light absorption material, ETM and HTM used of the PSC

Results

The J-V characteristics of perovskite solar cell structure measured under reverse voltage. The simulated values of  open-circuit voltage V_OC, short-circuit current J_sc, fill factor FF, EQE and PCE, are 0.62 V, 15.6 mA/cm² , 0.79, 80% and 18 %, respectively as shown in Figure 3, 4 and 5.  There is a strong influence of bandgap and electron affinity of HTL and ETL on open circuit voltage Voc. There is an increase in open circuit voltage Voc with increase in band gap of HTM because there is a decrease in valance band energy of HTM. The value of open circuit voltage Voc remains constant with increase in band gap of ETM because there is no change in the conduction band energy of ETM. There is an increase in open circuit voltage Voc with increase in electron affinity of HTM because there is a decrease in valance band energy of HTM. There is a decrease in open circuit voltage Voc with increase in electron affinity of ETM because there is a decrease in conduction band energy of ETM. There is a increase in short circuit current J_sc due to easy transport of holes to the anode(Eames et al., 2015; Lee et al. 2017).

Transient opto-electrical measurements were performed to analyze the current-voltage characteristics of CsPbBr₃ solar cells (PSCs) through Setfos software. The current voltage curves were measured at constant voltage under slow scan-rate. The simulation was based on drift-diffusion having different distributions of ions get IV curves.The dynamic response measurements and numerical simulations gave the required information of working mechanisms and characterization of perovskite solar cells in terms of J-V curve hysteresis and EQE as shown in Figure 2 and 3.

Figure 2. Current-voltage characteristics for hysteresis effect

Figure 3. EQE measurement of the PSC investigated

Under fast scanning rate, there is negligible change in the polarization density of perovskite material in the I-V curve. The scanning process is forward scan plus a backward scan.  In this study, the scanning rate was slow to measure the hysteresis effect in the PSC. The measurement is done until a steady state was reached. Therefore, the effect of hysteresis changes with different scanning rates and thickness. Hysteresis effect could be observed when scanning rate equals to the changing rate of the polarization. There was no hysteresis effect observed when the same voltage is applied between forward and backward scan.

The IV curve shape of a perovskite solar cell depended on voltage ramp speed and direction. The hysteresis curve have been observed at the time of simulation, but would remain a subject of intense debate. The hysteresis curvewas occurred on the same time scale as the voltage ramps used and as related to slow processes.The hysteresis observed in the architecture of PSC was small for optimized thickness of 450 nm for perovskite layer and PCE was about 18%  as shown in figure 2 and 4.

Figure 4. Power conversion efficiency of the Perovskite Solar Cell

The shape of the IV curve depends on the slope speed and direction. The IV curve hysteresis measured with a slow sinusoidal voltage with step time of 2 x 10^-04sec.The hysteresis measurement was performed under illumination with AM1.5. External quantum efficiency (EQE) of the PSC was about 0.8 as shown in Figure 3.

Effect of front and back electrode on Solar Cell Performance

The front and back contact of the perovskite solar cell are FTO and gold respectively. The device performance would be improved by using FTO as front contact. The workfunction of gold is 5.3 eV due to which it is a better element  to be used as a back contact. The performance of the perovskite is enhanced with FTO as front contact and gold as back electrode under illumination condition(G. Richardson et al., 2016; Courtier et al., 2018). The photovoltaic response and stability of device can be improved by using textured  FTO surface which would influence the light absorption by perovskite layer as compared to the unetched substrate because there would be an improvement in the scattered light in the perovskite layer. Back contact gold make good chemical bond with itself and other materials, highly stable at high temperatures, corrosion resistive during the fabrication of   metal electrode for perovskite solar cells. The device performance would improve with the use of gold as back contact. FTO and gold are front and back contacts in this simulation study(Reenen et al. 2015).

Effect of Thickness of perovskite layer

The thickness of perovskite plays an important part in the enhancement of the device performance because there is a decrease in the light absorption with decrease in perovskite thickness. This would result in low power conversion efficiency of the device(Tiwari et al., 2017). The optimization of absorber layer thickness is necessary to improve power conversion efficiency of the device(Tiwari et al., 2018). The optimized layer thickness of perovskite, TiO₂ and Spiro-OMeTAD were as 450 nm, 80 nm and 100 nm respectively.

Figure 5. Current-Voltage Curve for different thickness of perovskite layer

Hysteresis phenomenon

Ferroelectricity, ion migration, charge trapping and capacitive effects are major factors for hysteresis in perovskite solar cells. The scanning rate or electric poling under electric field is also the major factors for hysteresis. The ferroelectric effects dominate the other effects, then there is a delay in the ferroelectric domains alignment. This delay in ferroelectric domains alignment influence hysteresis phenomenon. When ion migration or charge trapping effects dominates other effects, then there is a delay in charge extraction or related recombination processes. This delay in charge extraction or related recombination processes influences hysteresis phenomenon. The cationic displacement in the perovskite would induce lattice or structural distortion due to defect concentrations. The low defect concentrations may eliminate hysteresis and enhance perovskite stability. The reduced dipole moment of cations and trap or defect states or improved processing techniques would eliminate hysteresis phenomenon. Hysteresis free solar cell could be possible by selecting proper charge selective contact materials which decrease electrode polarization at the interfaces of electrode and layer structure and enhance charge carrier transport characteristics. The decrease in charge accumulation would decrease hysteresis.  The study of hysteresis phenomena is very important to determine the accurate value of power conversion efficiency of solar cell(Elumalai et al. 2016). Therefore, ferroelectricity, ion migration, charge trapping and capacitive effects are the important factors which influence net resultant I-V response of the solar cell. The proper understanding of device operation is possible by convincingly explaining hysteresis phenomenon. The use of sophisticated characterization techniques is important to measure the hysteresis experimentally in perovskite solar cells.

Optical properties of perovskite layer

The performance of the perovskite solar cell can be determined by the light absorption property of perovskite layer and photogenerated charge carriers. It is seen that the absorption of light of particular radiation depends upon the volumetric ratio of CsPbBr₃. The increase in volumetric ratio of CsPbBr₃ would increase the absorption edge of the perovskite. The varying volume of ABX₃ leads to shift in the absorption edge in the absorption spectra. The amount of wavelength of particular light penetrated into perovskite material depends on the absorption coefficient of the perovskite (Tiwari et al., 2018). The equation for absorption coefficient is given as

                                 (1)

where A and t are absorbance and thickness of perovskite film respectively.

The lower value of absorption coefficient of perovskite film means poor absorption of light. The absorption coefficient of semiconductor materials has a sharp edge due the light does not excite the electron from valence band to conduction band below its energy band gap(Yakhmi et al., 2018).

Optical parameters like refractive index (n) and extinction coefficient (k)  can be calculated by the equations

                  (2)

                                                               (3)

Where n, R, k, α  and λ are  the refractive index, reflectance, extinction coefficient, absorption coefficient, wavelength respectively. The relationship between parameters like dielectric constant, refractive index and extinction coefficient is given by

                                                      (4)

                                                             (5)

The real and imaginary parts of dielectric constants are represented by respectively.

The phenomena of screening effect of different charge carriers and CsPbBr₃ molecular dipoles depend on the values of dielectric constant of the perovskite material. Uncombined state of CsPbBr₃ perovskite has less imaginary dielectric values. The potential barrier of charge would be decreased to pull down the scattering of free carriers due to higher values of dielectric constants.  Recombination models are suggested to understand the electronic structure, lifetime and mobility of CsPbBr₃perovskite. These models include parameters like dielectric constant, effective mass, band bonding character, and band dispersion to understand the J-V characteristics and hysteresis. From the Drude free electron model, the dependence of real and imaginary parts of the dielectric constants on the wavelength can be related with the equation

                        (6)

                                                (7)

Here ,N ,,e,, c and are  high frequency dielectric constant, optical carrier concentration in the conduction band, relaxation time, electronic charge, permittivity of free space, velocity of light and effective mass of free carrier respectively.

The optical conductivity is the optical excitation without any external electric field in the perovskite material as shown by equation below.

Optical conductivity                                       (8)

The increase in photon energy would increase the optical conductivity of the perovskite material.  

Conclusions

In this paper, CsPbBr₃ perovskite solar cell was simulated at STC conditions. The simulation study would help in selecting proper materials for the HTL and ETL to have high FF and PCE for fabrication of the solar cell. IV characteristics of CsPbBr₃ solar cells were done to find the PCE, EQE and hysteresis effects through simulation.Drift-diffusion model used to understand the influence of mobile ions and optical parameters on IV curve.The simulation results showed that hysteresis effect would be evident by studying I-V curve. The phenomena might be caused due to internal polarization and capacitance in perovskite solar cell. The causes for hysteresis must be studied experimentally. Hysteresis effect can be studied by understanding the conductance at the interfacial ETM/perovskite layer and HTM/perovskite layer and measuring I-V curve. It is possible that the polarization lags behind the voltage which causes hysteresis effect. In future, the numerical model with ion migration will allow simulating full transient experiments. In this way a complete model could be presented to describe charge transport in perovskite solar cells from microseconds to minutes after excitation.

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