Predicting trap depth and density in Perovskite solar cells through small-perturbation method

Nada Alati^a, Sandheep Ravishankar^a

^aIMD-3 Photovoltaics, Forschungszentrum Jülich GmbH, Wilhelm-Johnen-Straße, 52428, Jülich

Proceedings of International Conference on Hybrid and Organic Photovoltaics (HOPV26)

Uppsala, Sweden, 2026 May 18th - 20th

Organizers: Gerrit Boschloo, Ellen Moons, Feng Gao and Anders Hagfeldt

Poster, Nada Alati, 222
Publication date: 11th March 2026

Excess non-radiative recombination is one of the key limitations to further performance improvements in perovskite solar cells[1]. Quantifying and identifying the underlying trap states responsible for recombination is therefore essential for controlling device losses. Recent studies have highlighted that shallow traps dominate recombination in perovskite absorbers, influencing carrier dynamics and device performance[2]. While the theory of deep traps and their impact on frequency-domain response has been investigated, the effect of shallow traps in small-perturbation measurements remains insufficiently understood.

We develop a semi-analytical model that links the trap depth and density to the time constants measured from intensity modulated photovoltage spectroscopy (IMVS). Starting from the Shockley–Read–Hall (SRH) recombination formalism, we derive analytical expressions for the decay time, accounting for both bulk recombination channels and the coupling of the recombination with charge carrier re-injection from the electrodes[3]. The model predicts distinct exponential voltage dependences of the decay time constants, characterized by a slope factor θ, whose value depends systematically on trap depth and trap density. By comparing the slope factor with the ideality factor n_{_id}, obtained from the voltage dependence of the recombination rate, we demonstrate that both provide complementary information about the dominant recombination pathway. In the low V_{_OC} range, θ and n_{_id} take distinct values corresponding to shallow and deep trap states under high and low trap density conditions. Numerical drift–diffusion simulations support the analytical results and confirm that information about trap depth and density is encoded in the voltage dependence of the time constants and the ideality factor.

IMVS measurements performed on devices with different band gaps further validate the model predictions. Slope and ideality factors of 1.5 are frequently observed from electrical measurements, indicating the presence of a high density of deep trap states.

References:

[1] Luo, D., Su, R., Zhang, W., Gong, Q. & Zhu, R. Minimizing non-radiative recombination losses in perovskite solar cells. Nature Reviews Materials 5, 44-60 (2019).

[2] Yuan, Y. et al. Shallow defects and variable photoluminescence decay times up to 280 µs in triple-cation perovskites. Nature Materials 23, 391-397 (2024).

[3] Kiermasch, D., Baumann, A., Fischer, M., Dyakonov, V. & Tvingstedt, K. Revisiting lifetimes from transient electrical characterization of thin film solar cells; a capacitive concern evaluated for silicon, organic and perovskite devices. Energy & Environmental Science 11, 629-640 (2018).

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