Accelerating defect analysis of solar cells via machine learning of the modulated transient photovoltage

Abstract

Fast and non-destructive analysis of material defect is a crucial demand for semiconductor devices. Herein, we are devoted to exploring a solar-cell defect analysis method based on machine learning of the modulated transient photovoltage (m-TPV) measurement. The perturbation photovoltage generation and decay mechanism of the solar cell is firstly clarified for this study. High-throughput electrical transient simulations are further carried out to establish a database containing millions of m-TPV curves. This database is subsequently used to train an artificial neural network to correlate the m-TPV and defect properties of the perovskite solar cell. A Back Propagation neural network has been screened out and applied to provide a multiple parameter defect analysis of the cell. This analysis reveals that in a practical solar cell, compared to the defect density, the charge capturing cross-section plays a more critical role in influencing the charge recombination properties. We believe this defect analysis approach will play a more important and diverse role for solar cell studies.

Graphical abstract

1. Introduction

Electronic defect is one of the most fundamental and important physical properties of a semiconductor material, which determines both the carrier doping and the charge non-radiative recombination characteristics of an optoelectronic device [1], [2], [3]. Fast and non-destructive characterization analysis of the material defect has become a crucial demand. Currently, this characterization is realized mainly based on optical or electrical methods, such as photoluminescence [4], photoconductance [5], and electroluminescence [6]. Optical or electrical decay lifetime derived from transient measurement is a characteristic parameter that can be directly correlated to the defect-assisted charge recombination dynamics and thus is usually used to reflect the material quality [4,7].

Among the transient technologies, the photovoltage decay induced by a perturbation pulsed light excitation is an important candidate because it can measure the charge dynamics of a complete device [7,8]. This method has been widely applied for solar cell studies, and a variety of analysis approaches based on characteristic time parameters has been proposed [9], [10], [11], [12], [13]. For instance, photovoltage rise time has been used as a tool to reflect electron transport in solar cells [14,15]. Another more frequently used parameter is the photovoltage decay lifetime [16], [17], [18], [19], [20]. However, in most literature, the decay lifetime is simply used for qualitative comparisons between different cells while lacking a clear understanding of the charge-carrier mechanism. In these cases, decay lifetime in fact has no exact physics meaning and it can hardly be accurately correlated to the charge recombination rate or defect properties. Therefore, deepening the understanding of the charge-carrier mechanism of the photovoltage decay behavior and extracting more defect information from these electrical signals have emerged as a highly valuable topic in solar cell characterization studies.

Previously, a combination analysis of photovoltage intensity and photo-induced charge has been adopted to determine the chemical capacitance of a cell to extract the band-tail state distribution properties [21]. Nonetheless, the decay dynamics, for example, lifetime, has still not been fully exploited in this analysis process, and additionally, this method has a significant overestimation of the band-tail state [22]. Recently, a new analysis based on the modulated transient photocurrent and carrier diffusion/recombination model has been proposed to estimate the defect density of the photoactive layer in the perovskite, silicon, and Kesterite solar cells [22]. The steady-state modulation conditions introduced have effectively extended the electrical transient technique and offer more opportunities for defect analysis.

Herein, we focus on exploring a defect analysis method based on modulated transient photovoltage (m-TPV) and apply it to the perovskite solar cell as an attempt. We firstly make a time-dependent simulation of charge-carrier dynamics properties of a triple-layer structured perovskite solar cell to obtain a comprehensive understanding on the physics mechanism of the photovoltage generation and decay. It is found that the perturbation photovoltage is generated by the charge accumulation in the charge transporting layers (CTLs) and is subsequently decayed due to the non-radiative charge recombination in the perovskite layer. Afterwards we introduce a machine learning (neural network) approach to correlate the perovskite defect properties and the m-TPV characteristics derived from high-throughput electrical transient simulation. A well-trained Back Propagation neural network (BPNN) is finally used to accelerate the defect analysis of the perovskite solar cell in experiment. The reliability of this method is further supported by a comparison with the result of space-charge limited current (SCLC) measurement. Overall, this work brings an opportunity to understand the physics mechanism of electrical transient and provides an effective analysis route for solar cell defect studies.

2. Results and discussion

2.1. Charge-carrier mechanism of perturbation TPV

In a complete cell, charge-carrier processes are determined by a series of time-dependent charge continuity equations in which multiple physics parameters are coupled together. Herein, we use a COMSOL Multiphysics simulation approach to compute charge-carrier properties of a perovskite solar cell with a triple-layer device configuration [i.e., electron transporting layer (ETL, 30 nm)/perovskite (PVSK, 500 nm)/hole transporting layer (HTL, 180 nm)]. To enhance the simulation accuracy, steady-state physics properties of the cell is obtained as the first step; subsequently a light pulse is introduced to excite the cell and the steady-state properties are used as the initial conditions for the transient calculations. In the simulation, perturbation photovoltage of the cell is directly obtained by coupling an external electric circuit to the cell. Detailed descriptions about model schematic diagram, building steps, parameters, and equations are given in the Supplementary materials (note 1). The ion migration in the perovskite solar cell has not been considered here because we focus more on the fast charge-carrier dynamics process and the ion migration has already been able to be effectively suppressed in experiment. The reliability of the modeling and computing processes has been independently checked numerically (Supplementary material note 1 and Fig. S3) and experimentally (Fig. 1d).

Fig. 1.

Perturbation TPV simulations. (a-b) Time-dependent non-equilibrium electron (∆n) and hole (∆p) distribution in a perovskite solar cell under a light pulse (1 ns, ∼1.5 × 10⁹ cm⁻²) excitation. (c) Changes in quasi-Fermi energy level profiles at different time points after the light excitation. (d) TPV of the cell and its correlation with (top) charge accumulation in the perovskite and in the charge transporting layers (CTL), and (bottom) with the charge transport at the perovskite/CTL interfaces.

Time-dependent non-equilibrium electron (∆n = n - n₀, where n and n₀ are electron concentrations after and before light pulse excitation, respectively) and hole (∆p) distribution in the cell (1 sun and 0 V) after light pulse excitation (1 ns, ∼1.5 × 10⁹ cm⁻²) is shown in Fig. 1a-b. It can be seen that non-equilibrium carriers are firstly generated in the perovskite layer and then gradually transport into the CTLs. Interestingly, carriers in the CTLs exhibit a nonuniform distribution mainly accumulating close to the perovskite/CTL interface. This phenomenon may arise because of the Coulombic attraction between electrons and holes although they have been spatially separated by the built-in electric field and interface selective charge extraction. Evolutions in the quasi-Fermi energy level profile (E_f - E_f0, where E_f and E_f0 are Fermi energy levels of the cell after and before light pulse excitation, respectively) caused by the non-equilibrium carriers are also extracted from the calculation. As in Fig. 1c, initially after light excitation, quasi-Fermi energy level splitting (QFLS=E_fn – E_fp) in the perovskite layer has exhibited a large increase. The QFLS reaches 50 meV in the interface region. It was once considered that this QFLS is the origin for the generation of perturbation photovoltage [21]; however, here we need to emphasize that perturbation photovoltage has still not been generated at this time point although large QFLS has already appeared in the bulk perovskite.

Perturbation photovoltage is in fact originated from the change in the Fermi energy level difference between the ETL and the HTL [∆Ẽ_f = (E_fn^ETL - E_fp^HTL)-(E_fn0^ETL - E_fp0^HTL)] caused by the accumulated carriers. As shown in Fig. 1c, in the early 50 ns, the ∆Ẽ_f continuously increases and reaches a peak value of 23 meV, resulting in a perturbation photovoltage of about 23 mV. At this time point, the (E_f - E_f0) profile in the bulk perovskite is linear to the spatial position and keeps flat in the CTLs. This means that almost no non-equilibrium carriers are retained in the bulk perovskite. After the peak point, the ∆Ẽ_f gradually decreases and ultimately reaches zero. This corresponds to the photovoltage decay process. We have made a reliability verification of the simulation result by comparing the simulated TPV with an experimental result, as in Fig. 1d. These two TPV curves have almost the same rise and decay characteristics.

To have a clearer insight into the photovoltage generation and decay mechanism, a direct comparison between perturbation photovoltage, carrier density and interface carrier transport is made here. It can be seen that the photovoltage exhibits a similar dynamics behavior to that of the non-equilibrium electrons accumulated in the ETL (∆n_ETL). The non-equilibrium hole in the HTL (∆p_HTL) exhibits a slightly slower rise rate because of a larger transport distance but decays synchronously with the ∆n_ETL. This phenomenon means that photovoltage is linearly proportional to the charge accumulated in the CTLs. This is a clear signature of a geometric flat capacitor, where the CTLs are the flat electrode and the perovskite is the dielectric layer [20,23]. Charging and discharging of the CTLs are realized through forward and backward charge transport at the perovskite/CTL interface, respectively, as shown in the bottom of Fig. 1d. The forward current mainly originates from charge extraction of the CTLs while backward current arises from charge recombination in the perovskite layer.

Charge recombination properties of the perovskite during the photovoltage decay process are further studied. Non-radiative and radiative recombination rates of the non-equilibrium carriers are shown in Fig. 2a. It can be seen that the non-radiative recombination rate is about two orders of magnitude higher than the radiative one, indicating that charge decay in the perovskite under is dominated by the defect-assisted non-radiative recombination. The interface region has the highest charge recombination rate of about 10¹⁹ cm⁻³s⁻¹. Changes in the perovskite defect occupation properties are also extracted (∆ρ-∆p+∆n and ∆ρ is the net charge density) and shown in Fig. 2b. It can be seen that defects in the interface region exhibit a more active response to the non-equilibrium carriers. For the bulk perovskite, despite having a relatively low recombination rate and negligible defect occupation variation, defects in the bulk region also have a large contribution to the charge recombination of the cell. Spatial integration of the recombination rate indicates that more than half of carriers are recombined in the bulk region (position: 100–500 nm). Electron and hole flow calculation results shown in Fig. 2c-d reveal that the diffusion mechanism plays a critical role in transferring carriers from CTLs to the bulk perovskite. This finally makes the perovskite have a relatively balanced carrier decay dynamics in varied positions, as the time-dependent carrier profiles shown in Fig. 2e-f. Therefore, it is reasonable to conclude that the carrier decay characteristics of the cell are synergistically influenced by both carrier transport and non-radiative recombination dynamics properties. Multiple physics parameters such as carrier mobility (µ), defect energy level (E_t), defect density (N_t), charge capturing cross-section (σ) and device geometric structure are coupled together in determining the perturbation photovoltage behaviors. In such a situation, how to extract defect properties from the transient photovoltage is a challenge.

Fig. 2.

Charge recombination properties of the perovskite layer during photovoltage decay process. (a) Position-dependent non-radiative and radiative charge recombination rate. (b) Changes of defect occupation properties in the perovskite layer. (c-d) Electron and hole flow properties. (e-f) ∆n and ∆p distribution at different decay time.

2.2. Machine learning of m-TPV

Conventionally, physics parameter extraction is realized by the analytically fitting of experimental results. However, for the TPV dynamics, no reliable analytical physics model has been established until now. Herein we focus more efforts on developing a numerical computing route based on the machine learning (neural network) to realize defect analysis from the perturbation TPV measurements, as schematically shown in Fig. 3. The development in machine learning and neural network algorithm makes it possible in establishing complex correlations between multiple physics parameters and the photovoltage dynamics [24], [25], [26]. The high-throughput simulation can generate a large amount of TPV data for the machine learning. The modulated electrical transient measurement approach (especially the m-TPV) that we have developed [7,9,22,27] can provide a variety of experimental results for the defect parameter extraction.

Fig. 3.

Schematic diagram of defect analysis routes by using experimental TPV measurements. The conventional route is based on the analytical physics model. An alternative route is based on establishing the defect-TPV multiple parameter correlation through the machine learning (neural network).

Training neural network is the key process for the defect analysis from the m-TPV. We firstly use the COMSOL simulation to generate millions of m-TPV curves of perovskite solar cells with varied material parameters to build up a m-TPV database. The carrier transport and recombination parameters of the perovskite (i.e., µ, E_t, N_t, σ) are chosen as the main variable in the following studies because we found that they have more obvious influence on the cell performance and the electrical transient properties. Imitating experimental m-TPV measurements, different working conditions (bias voltage and illumination) of the cell have also been included in the simulation. The data characteristics of these m-TPV curves and the four material parameters are extracted as the input and output layers of the neural network, respectively. These extracted data are further numerically processed to make them suitable for the neural network algorithm. Afterwards, these data are randomly divided into two groups; one is used as the training group to train the neural network and the other one is used as the test group for the reliability validation. In the training process, the organization, number of the neurons and the hidden layer, propagation function and hyperparameter of the neural network have been optimized. Finally, the test-group data is used to evaluate the reliability of the trained neural network. This validation process can also reversely help optimize the neural network. For self-consistency validation, the m-TPV simulation is made based on the extracted defect parameters and further compared with the experimental curves.

Different types of neural networks including BPNN [28,29], Genetic Algorithm-Back Propagation Neural Networks (GA-BP) [30,31], Extreme Learning Machine (ELM) [32], General Regression Neutral Network (GRNN) [33] and Radial Basis Function Neutral Network (RBF) [34,35] have been tried to obtain an optimal result. BPNN is found to have the highest prediction accuracy for all the four material parameters. The optimization also finds that four m-TPV curves measured in varied bias voltage and illumination conditions are required to obtain an accurate prediction of the material parameters.

Performance assessment of the optimal BPNN in predicting the four physics parameters is further made and the results are shown in Fig. 4. The linear regression analysis of both the training- and the test-group data is given in Fig. 4a, b. Both of these two groups have a very high regression coefficient of approaching 1. Under 300 epochs, the mean squared error of both training- and test-group data can be lower than 2 × 10⁻⁴ (Fig. 4c). These results indicate that there is a good correlation between these four physics parameters with the m-TPV characteristics of the perovskite solar cell. For clarity, a direct comparison between the predicted values (criss-cross) of these four physics parameters (μ, N_t, E_t and σ) and the true values (solid circle) is shown in Fig. 4d. The 50 samples exhibited here are randomly selected from the test group. It can be seen that the predicted value is almost coincided with the true value, demonstrating a very high prediction accuracy. The relative error distribution of predicting these four parameters is summarized in Fig. 4e-h. More than 97.5% of the predicted μ has the relative error of ≤ 0.022 (2.2%); more than 99.5% of predicted N_t has the relative error of ≤ 0.020; more than 98.9% of predicted E_t has the relative error of ≤ 0.023; and 98% of predicted σ has the relative error of ≤ 0.015. These results demonstrate that the machine learning route based on neural network and high-throughput simulation can be an effective approach for the defect analysis of solar cells.

Fig. 4.

Performance assessment of the optimal BPNN. Linear regression analysis of (a) training- and (b) test-group data, respectively. (c) Mean squared error of both training- and test-group data under increased epochs. (d) A direct comparison between the predicted physics parameter values (criss-cross) and the true values (solid circle). The 50 samples are randomly selected from test group. (e-h) Relative-error histogram of the predicted μ, N_t, E_t and σ.

2.3. Defect analysis of a perovskite solar cell

The trained neural network is finally applied for the defect analysis of a perovskite solar cell fabricated in experiment. The cell has a device structure of F:SnO₂/TiO₂/PCBA/(FA, Cs)PbI₃/Spiro-OMeTAD/Au. Here, the fullerene derivative PCBA is introduced to suppress the interface defect and corresponding charge recombination in the cell. Current-voltage characteristics of the as-fabricated cell is shown in Fig. 5a, which gives a high efficiency of 23.35%. To change the defect properties, the cell was placed in high humidity for aging. The aged cell exhibited an obviously lower efficiency of 20.13%. Fill factor and open-circuit voltage that closely correlate to the defect properties are the main factors that cause the efficiency degradation (see more information in Supplementary materials note 3).

Fig. 5.

Defect analysis of the perovskite solar cell based on the trained neural network. (a) Current-voltage characteristics of a perovskite solar cell before and after humidity aging process. (b-c) Electron SCLC measurement of the cell before (b) and after (c) the aging process, respectively. (d) m-TPV curves derived from experimental measurement and simulation, respectively. Physics parameters used in the simulation are obtained from defect analysis of the experimental m-TPV curves with the aid of the trained neural network.

We firstly make an evaluation of the perovskite defect using the SCLC method [36,37], as in Fig. 5b-c. The trap filled limit voltage (V_TFL) of the as-fabricated perovskite is obviously smaller than that of the aged one. The averaged N_t of the as-fabricated and the aged perovskite is 4.79 × 10¹⁶ and 1.17 × 10¹⁷ cm⁻³, respectively (Table 1). Although difference in the N_t can be obtained by the SCLC method, this two-fold variation can hardly explain the giant efficiency difference of the cells. m-TPV measurement together with the neural network analysis is thus further exploited to obtain a more detailed analysis of the perovskite defect properties. TPV curves measured at different bias voltage (0 and 0.8 V) and illumination (dark and 1 sun) combined conditions are shown in Fig. 5d. Qualitatively, the aged cell has a much faster photovoltage decay rate. After inputting the m-TPV curves into the trained BPNN, the defect properties are obtained and shown in Table 1. The N_t of the as-fabricated and aged perovskite is 2.39 × 10¹⁶ and 4.56 × 10¹⁶ cm⁻³, respectively, which also exhibits a two-fold difference, similar to the SCLC result. More importantly, the m-TPV method indicates that the σ of the defect has increased by about 10 folds after the aging process. This means that the σ rather than the N_t plays a more dominant role in determining the charge recombination properties of the perovskite solar cell. This finding agrees well with our previous defect studies obtained from temperature-dependent capacitance measurements [38]. We attribute the observed changes in defects and transport parameters to the increase in the distortion of the perovskite soft lattice [39,40]. With these derived defect parameters, we reversely make a simulation of the m-TPV curves of the cell, as shown by the solid lines in Fig. 5d. It can be clearly seen that the simulated curves coincide well with the experimental results, thus demonstrating the reliability of defect analysis using this m-TPV method. We believe this defect analysis method will play a more important and diverse role for solar cell studies by further expanding the m-TPV and neural network database.

Table 1.

Derived physics parameters of the cells with two different methods. m-TPV method refers to that based on experimental m-TPV curves and neural network, and SCLC method refers to that based on analytical fitting of SCLC curves.

Physics properties	Fresh cell		Aged cell
	m-TPV method	SCLC method	m-TPV method	SCLC method
µ (cm2 V−1s−1)	1.24	–	0.67	–
Nt (1016 cm−3)	2.39	4.79 ± 0.74	4.56	11.7 ± 1.59
Et (eV)	0.12	–	0.56	–
σ (cm2)	9.4 × 10−18	–	1.0 × 10−16	–

3. Conclusion

In this work, based on a comprehensive understanding of the generation and decay mechanism of the perturbation photovoltage, we have explored to develop a defect analysis method via the machine learning of the m-TPV experimental measurements. Time-dependent charge-carrier dynamics simulation of the perovskite solar cell reveals that the perturbation photovoltage is generated from the non-equilibrium charge accumulation in the CTLs and is decayed due to the defect-assisted non-radiative charge recombination in the absorber layer. A neural network approach has been exploited to correlate the m-TPV characteristics to the defect properties of the cell. A database containing millions of m-TPV curves derived from high-throughput simulations has been established for the neural network training. Through a synergetic optimization of the network type and the number of required m-TPV curves, neurons and hidden layers, a BPNN has been well trained with high prediction accuracy and ultra-small relative error. This BPNN has been further used to provide a detailed defect analysis of an experimentally fabricated perovskite solar cell, which finds that the σ rather than the N_t plays a more dominant role in determining the charge recombination properties. We believe this defect analysis method will play a more important and diverse role for solar cell studies by further expanding the m-TPV and neural network database.

Author contributions

Y. S. Li, J. Shi and Q. Meng conceived the idea. Y. S. Li conducted device simulation, machine learning programming, data analysis and paper writing. Y. M. Li contributed to the device fabrication, electrical measurement and analysis. J. Shi contributed to supervision, model and data analysis, and paper writing. L. Lou, X. Xu, Y. Cui, J. Wu, and T. Zhang contributed to device simulation. D. Li, Y. Luo, H. Wu, Q. Shen contributed to electrical measurement and discussion. Q. Meng contributed to supervision, discussion and project administration.

Declaration of competing interest

The authors declare that they have no conflicts of interest in this work.

Biographies

Yusheng Li received his BSc (2011) degree in material physics from Jilin University, China and MSc (2015) degree in condensed matter of physics from Institute of Physics, Chinese Academy of Sciences. He is currently a PhD candidate in the University of Electro-Communication, Japan. His research interests include ultrafast photophysics spectroscopy study of perovskite materials and charge carrier dynamics of perovskite solar cell.

Yiming Li received the BS degree from Nankai University in 2015 and the PhD degree in condensed matter physics from the Institute of Physics, Chinese Academy of Sciences (CAS) in 2020. Her research interests focus on charge carrier dynamics and charge loss mechanism in new-generation solar cells.

Jiangjian Shi obtained his BS degree from Southeast University in 2012 and the PhD degree from the Institute of Physics, CAS in 2017. Now, he is an associate professor at the Institute of Physics, CAS. His research interest includes investigation on charge carrier dynamics and defect properties in new-generation solar cells such as the perovskite and the Kesterite thin-film solar cells.

Qingbo Meng(BRID: 09275.00.82652) is currently a full professor of University of Chinese Academy of Sciences (UCAS), Institute of Physics (IOP), CAS. He is the director of Center for Clean Energy, IOP and a director member of Chinese Renewable Energy Society. He received his PhD degree in 1997 from Changchun Institute of Applied Chemistry, CAS. His current research interest focuses on solar energy materials & technologies, including the photoelectrical and the photochemical conversions.