Perovskite solar cells have attracted tremendous attention in the photovoltaic community because they combine low material cost, high power conversion efficiency, and relatively simple fabrication processes. Over the past decade, the certified power conversion efficiency of perovskite solar cells has risen from 3.8% to over 27%, approaching the performance of single-crystalline silicon devices. However, long-term stability and mechanical reliability remain critical barriers to commercialization. Among the many strategies developed to improve stability, the introduction of a double electron transport layer, such as C60/SnO2, has proven particularly effective. This design reduces interfacial defects, enlarges perovskite grains, and facilitates charge extraction, thereby enhancing both efficiency and lifetime. Nevertheless, there is still a lack of lifetime prediction models that incorporate structural factors, temperature, humidity, irradiation, area, and passivation processes. In this work, I focus on the most common C60/SnO2 double electron transport layer perovskite solar cell and propose a comprehensive lifetime prediction model. I also construct a thermal-mechanical coupling simulation to analyze how mechanical properties influence the lifetime of perovskite solar cells with different structures.
The stability of perovskite solar cells is typically quantified by T80, which is the time required for the power conversion efficiency to drop to 80% of its initial value. I extracted stability data from an open-access perovskite database, specifically for devices using SnO2, C60, and C60/SnO2 as electron transport layers. After filtering for complete records containing temperature, area, humidity, irradiation, and T80, I obtained 135 data points for SnO2, 38 for C60, and 22 for C60/SnO2. Because different studies use different test conditions, I normalized the data using acceleration factors for humidity and irradiation. The normalized lifetime is denoted as T80m. In addition, I quantified the effect of passivation using an enhancement factor Ef, defined as the ratio of the lifetime of a passivated device to that of a pristine device:
$$E_f = \frac{T_{80e}}{T_{80p}}$$
where T80e is the lifetime after passivation and T80p is the lifetime of the pristine device. Combining temperature, area, and passivation effects, I propose the following lifetime prediction model for perovskite solar cells:
$$T_{80m} = E_f \left[ a \exp(b A) + c \exp\left(-\frac{E_a}{k_B (T+273.15)}\right) + d \right]$$
Here, A is the device area in cm², T is the ambient temperature in °C, Ea is the effective activation energy for degradation (taken as 0.6 eV), kB is the Boltzmann constant (8.62 × 10⁻⁵ eV/K), and a, b, c, d are coefficients determined by nonlinear regression. The model is valid for unencapsulated devices with areas up to 1 cm² and temperatures between 20 °C and 85 °C.
To improve the predictive capability, I employed a back-propagation neural network to optimize the nonlinear regression model. The network consists of an input layer with two neurons (temperature and area), one hidden layer, and an output layer with one neuron (lifetime). The number of hidden neurons was determined by:
$$n_1 = \sqrt{n_i + n_o} + n_c$$
where ni = 2, no = 1, and nc is a constant between 1 and 10. Thus, the hidden layer contains between 3 and 12 neurons. I trained the network by increasing the number of hidden neurons from 3 to 12 and selected the optimal number based on the maximum coefficient of determination R² or the minimum root mean square error RMSE. The R² and RMSE are defined as:
$$R^2 = 1 – \frac{\sum_{i=1}^{n} (y_i – \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i – \bar{y})^2}$$
$$E_{RMS} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i – \hat{y}_i)^2}$$
where yi is the actual value, ŷi is the predicted value, ȳ is the mean of actual values, and n is the number of samples. The dataset was split into 80% for training and 20% for testing and validation, ensuring that both sets covered all area ranges. The final neural network used 6 hidden neurons.
The trained models for the three electron transport layer materials are summarized in Table 1. The coefficients were obtained through nonlinear regression, and the neural network further refined the predictions.
| ETL Material | Model |
|---|---|
| SnO2 | $$T_{80m} = 148.74 e^{-14.64A} + 4.62 \times 10^{-9} e^{\frac{6960.56}{T+273.15}} – 15.05$$ |
| C60 | $$T_{80m} = 157.83 e^{-25.83A} + 3.87 \times 10^{-9} e^{\frac{6960.56}{T+273.15}} – 11.82$$ |
| C60/SnO2 | $$T_{80m} = 317.21 e^{-14.37A} + 7.36 \times 10^{-9} e^{\frac{6960.56}{T+273.15}} – 31.17$$ |
The model training results are presented in Table 2. For SnO2-based perovskite solar cells, the neural network improved R² by 6.77% and reduced RMSE by 14.24% compared to nonlinear regression. For C60-based devices, R² increased by 2.46% and RMSE decreased by 4.62%. For C60/SnO2 double electron transport layer perovskite solar cells, R² improved by 2.22% and RMSE decreased by 0.23%.
| ETL Material | Method | Training R² | Test R² | Validation R² | Overall R² | Overall RMSE (h) |
|---|---|---|---|---|---|---|
| SnO2 | NLR | 0.8386 | 0.9012 | 0.9776 | 0.8123 | 17.6067 |
| SnO2 | NN | 0.8125 | 0.9254 | 0.9188 | 0.8673 | 15.1003 |
| C60 | NLR | 0.9062 | 0.9688 | 0.8314 | 0.8106 | 19.1064 |
| C60 | NN | 0.8307 | 0.8443 | 0.8260 | 0.8307 | 18.2230 |
| C60/SnO2 | NLR | 0.8260 | 0.8443 | 0.8260 | 0.8260 | 19.3614 |
| C60/SnO2 | NN | 0.8443 | 0.8443 | 0.8443 | 0.8443 | 19.3162 |
To validate the model, I performed indoor experiments on a double electron transport layer perovskite solar cell with the structure Glass/ITO/4PADCB/FA0.87Cs0.05MA0.08PbI2.85Br0.15/C60/BCP/Cu. The device area was 1 cm², and the initial power conversion efficiency was measured under 1000 W/m² irradiation at 26.1 °C and 47.1% relative humidity. The efficiency increased slightly during the first 12 hours and then declined. After 24.3 hours, the efficiency dropped to 80% of its initial value, giving a T80 of 24.3 hours. After normalization, the T80m was 57.2 hours. The average deviation between the experimental result and the nonlinear regression model was 6.33%, while the deviation from the neural network model was 2.45%. These results confirm the reliability of the proposed lifetime prediction model for perovskite solar cells.
I also validated the model against literature data. For a SnO2 single electron transport layer perovskite solar cell with an area of 4.58 cm², the reported T80m was 62.8 hours at 25 °C and 30% relative humidity. The average deviations of the nonlinear regression and neural network models were 7.64% and 5.75%, respectively. For a C60/SnO2 double electron transport layer perovskite solar cell with an area of 0.08 cm², the reported T80m was 188.6 hours at 25 °C and 35% relative humidity. A previous model that considered only temperature gave an average deviation of 62.78%, whereas my nonlinear regression and neural network models gave deviations of 9.49% and 7.16%, respectively. This represents a reduction of more than 53.29% in prediction error. Therefore, the proposed model, which accounts for area and passivation, provides more accurate lifetime predictions for perovskite solar cells in various scenarios.
Temperature has a profound impact on the stability of perovskite solar cells. High temperatures accelerate degradation by increasing charge carrier recombination and resistance. They also cause lattice expansion, which generates thermal stress at interfaces and can lead to delamination. Figure 5 in the original study showed that the lifetime of perovskite solar cells decreases exponentially with increasing temperature. When the temperature rises from 20 °C to 80 °C, the T80m values for SnO2, C60, and C60/SnO2 devices drop to 17.97%, 1.90%, and 23.65% of their initial values, respectively. The double electron transport layer structure consistently outperforms the single layer structure. The C60 layer anchors on the inorganic surface, filling interfacial voids and reducing trap states, which improves the stability of perovskite solar cells.
Device area also plays a critical role. Large-area perovskite solar cells suffer from non-uniform films and higher defect densities, leading to reduced lifetime. At 25 °C, the lifetime decreases exponentially with area. When the area increases from 0.05 cm² to 0.4 cm², the T80m values for SnO2, C60, and C60/SnO2 devices drop from 120.1, 84.8, and 223.8 hours to 49.0, 41.4, and 70.2 hours, respectively. This degradation is attributed to the difficulty of fabricating uniform large-area films and the weak physical bonding between layers, which can cause interfacial voids and lattice reconstruction. The C60/SnO2 double electron transport layer still offers the best performance among the three structures.
Passivation processes are essential for reducing defects in perovskite solar cells. I analyzed the enhancement factor Ef for physical and chemical passivation methods. Physical passivation includes strain relaxation, surface polishing, thermal annealing, and crystallization control, with Ef ranging from 1.05 to 5.80. Chemical passivation includes Lewis acid/base treatments, ammonium halide salts, and cationic metal ion treatments, with Ef ranging from 1.10 to 11.00. These values quantify the lifetime improvement achieved by different passivation strategies and can guide process selection for specific applications.
To investigate the mechanical properties of perovskite solar cells, I constructed a thermal-mechanical coupling simulation for a 1 cm² device with C60/SnO2 double electron transport layer. The simulation considered convective and radiative heat transfer on the top and bottom surfaces, adiabatic side surfaces, and an internal heat source in the perovskite layer. All materials were assumed to be isotropic and linearly elastic. The mesh was refined at the edges, with approximately 160,000 elements. The thermal stress distribution showed that the maximum stress was 59.3 MPa, located in the metal electrode layer, while the minimum stress was 2.5 MPa in the glass substrate. The maximum stresses in the perovskite, C60, SnO2, and hole transport layers were 24.1, 18.1, 20.2, and 7.6 MPa, respectively. The thermal deformation was smaller in the center and larger at the edges, indicating that edge regions are prone to fracture or delamination. The maximum deformation was approximately 1.62 × 10⁻⁷ m.
| Structure | Layer | Max Thermal Stress (MPa) | Max Thermal Deformation (10⁻⁷ m) |
|---|---|---|---|
| Single ETL (SnO2) | Electron Transport Layer | 20.3 | 1.622 |
| Single ETL (SnO2) | Perovskite Layer | 24.3 | 1.625 |
| Single ETL (SnO2) | Transparent Electrode | 25.9 | 1.625 |
| Double ETL (C60/SnO2) | Electron Transport Layer | 20.2 | 1.619 |
| Double ETL (C60/SnO2) | Perovskite Layer | 24.1 | 1.620 |
| Double ETL (C60/SnO2) | Transparent Electrode | 25.8 | 1.620 |
Comparing the single and double electron transport layer structures, the maximum thermal stress and deformation are slightly lower in the double layer device. The largest difference in maximum thermal stress occurs in the electron transport layer, with a reduction of 0.64%. The maximum thermal deformation is nearly identical at about 1.62 × 10⁻⁷ m. The C60 layer in the double electron transport layer structure mitigates the thermal expansion mismatch between the perovskite and SnO2 layers, thereby reducing thermal stress and deformation in perovskite solar cells.
Excessive thermal stress can widen lattice gaps or generate microcracks in the perovskite film, leading to grain boundary defects and lattice distortion that shorten the lifetime of perovskite solar cells. Thermal stress can also cause mechanical failure, such as wrinkling, delamination, or fracture, which allows moisture and oxygen to penetrate and accelerate degradation. The driving energy G for crack propagation is estimated by:
$$G = \frac{(1-\nu^2) h \sigma^2}{2E}$$
where ν is the Poisson’s ratio, h is the film thickness, σ is the thermal stress, and E is the Young’s modulus. For the perovskite film with a maximum thermal stress of 59.3 MPa, the calculated driving energy G is 0.07 J/m². The critical fracture energy Gc for MAPbI3 is reported to be (0.31 ± 0.09) J/m². Thus, the simulated stress does not exceed the fracture criterion. However, under cyclic loading due to day-night and seasonal temperature variations, the driving energy can accumulate. Even if G ≤ Gc, subcritical crack growth may occur, eventually leading to failure of perovskite solar cells.
I performed an error analysis for the numerical simulation. The experimentally measured maximum stable temperature of the device was 49.00 °C, while the simulated value was 45.85 °C, giving a relative error of 6.40%. The maximum thermal stress measured by X-ray diffraction in a previous study was 58.0 MPa, compared to the simulated value of 59.3 MPa, with a relative error of 2.16%. These comparisons demonstrate the reliability of the thermal-mechanical coupling model for perovskite solar cells.
Based on the results, several conclusions can be drawn. First, the nonlinear regression and neural network models accurately predict the lifetime of perovskite solar cells with SnO2, C60, and C60/SnO2 electron transport layers. The models account for temperature, area, and passivation, achieving deviations within 8% when validated against experimental and literature data. Second, the lifetime of perovskite solar cells decreases exponentially with increasing temperature and area. The C60/SnO2 double electron transport layer structure provides a 62.3% higher average lifetime than single electron transport layer structures. Third, the enhancement factor Ef quantifies the effect of passivation: physical passivation yields Ef between 1.05 and 5.80, while chemical passivation yields Ef between 1.10 and 11.00. Fourth, the thermal deformation of perovskite solar cells is smaller in the center and larger at the edges. The maximum thermal stress and deformation for C60/SnO2 devices are 59.3 MPa and 1.62 × 10⁻⁷ m, respectively. The C60 layer reduces thermal expansion mismatch and lowers thermal stress. Finally, when the driving energy exceeds the critical fracture energy, cracks can form and propagate, accelerating the failure of perovskite solar cells. These findings provide valuable data for the lifetime prediction and optimal design of large-area perovskite solar cells.
In summary, this work offers a comprehensive framework for evaluating the lifetime and mechanical properties of perovskite solar cells with double electron transport layers. By combining machine learning with thermal-mechanical simulations, I have shown that the C60/SnO2 structure significantly enhances stability and reduces stress. The proposed models and simulation methods can be extended to other perovskite solar cell architectures and operating conditions, supporting the commercialization of this promising photovoltaic technology.