[Paper Review] Improved evaluation of deep-level transient spectroscopy on perovskite solar cells reveals ionic defect distribution

Sebastian Reichert, Jens Flemming+4 more|arXiv (Cornell University)|Oct 10, 2019

Perovskite Materials and Applications76 references72 citations

TL;DR

This study introduces an enhanced regularization algorithm for inverse Laplace transformation to improve deep-level transient spectroscopy (DLTS) analysis in methylammonium lead iodide perovskite solar cells. By applying this method to temperature-dependent DLTS, the authors reveal that mobile ionic defects exhibit distributed diffusion coefficients rather than discrete values, explaining the wide variation in reported defect parameters across prior studies. The results identify three ionic species—iodine interstitials (I⁻ᵢ), methylammonium vacancies (V⁻ₘₐ), and methylammonium interstitials (MA⁺ᵢ)—with I⁻ᵢ and V⁻ₘₐ showing three orders of magnitude higher diffusion coefficients than MA⁺ᵢ, indicating their dominant role in ion migration and device hysteresis.

ABSTRACT

One of the key challenges for future development of efficient and stable metal halide perovskite solar cells is related to the migration of ions in these materials. Mobile ions have been linked to the observation of hysteresis in the current--voltage characteristics, shown to reduce device stability against degradation and act as recombination centers within the band gap of the active layer. In the literature one finds a broad spread of reported ionic defect parameters (e.g. activation energies) for seemingly similar perovskite materials, rendering the identification of the nature of these species difficult. In this work, we performed temperature dependent deep-level transient spectroscopy (DLTS) measurements on methylammonium lead iodide perovskite solar cells and developed a extended regularization algorithm for inverting the Laplace transform. Our results indicate that mobile ions form a distribution of emission rates (i.e. a distribution of diffusion constants) for each observed ionic species, which may be responsible for the differences in the previously reported defect parameters. Importantly, different DLTS modes such as optical and current DLTS yield the same defect distributions. Finally the comparison of our results with conventional boxcar DLTS and impedance spectroscopy (IS) verifies our evaluation algorithm.

Motivation & Objective

• To resolve the long-standing inconsistency in reported ionic defect parameters (e.g., activation energies) for perovskite solar cells.
• To develop a more accurate evaluation method for deep-level transient spectroscopy (DLTS) that accounts for distributed emission rates.
• To identify the nature and relative mobility of mobile ionic species in methylammonium lead iodide (MAPbI₃) perovskite solar cells.
• To verify the consistency of defect distributions across different DLTS modes (current, optical, and reverse-mode DLTS).
• To link the observed defect distributions to the origins of hysteresis and instability in perovskite devices.

Proposed method

• Developed an extended regularization algorithm (RegSLapS) for inverse Laplace transformation to extract emission rate distributions from noisy, multi-exponential DLTS transients.
• Performed temperature-dependent DLTS measurements on MAPbI₃ solar cells using three modes: current-DLTS (I-DLTS), optical-DLTS (O-DLTS), and reverse-DLTS (C-DLTS).
• Applied the regularization algorithm to invert the Laplace transform of capacitance transients, enabling resolution of overlapping time constants and distribution of emission rates.
• Validated results against conventional boxcar DLTS and impedance spectroscopy (IS), confirming consistency across methods.
• Used the emission rate equation et = e²DNeff / (kBTε₀εR) to relate extracted emission rates to ionic diffusion coefficients and effective defect concentrations.
• Compared defect distributions from multiple DLTS modes to confirm robustness and reproducibility of the observed distributions.

Experimental results

Research questions

• RQ1 Why do prior studies report such a wide range of ionic defect activation energies for the same perovskite material?
• RQ2 Can a more accurate inversion method resolve the true distribution of ionic defect emission rates in perovskite solar cells?
• RQ3 Do different DLTS measurement modes (current, optical, reverse) yield consistent defect distributions?
• RQ4 Which ionic species are primarily responsible for ion migration and device hysteresis in MAPbI₃?
• RQ5 How do the diffusion coefficients and concentrations of different ionic defects compare, and what is their relative impact on device performance?

Key findings

• Three distinct ionic species were identified: I⁻ᵢ, V⁻ₘₐ, and MA⁺ᵢ, each exhibiting a distribution of diffusion coefficients rather than discrete values.
• The diffusion coefficient of I⁻ᵢ and V⁻ₘₐ is approximately three orders of magnitude higher than that of MA⁺ᵢ, indicating their dominant mobility.
• The ionic defect concentrations of all three species are within the same order of magnitude (~10¹⁶ cm⁻³), implying comparable contributions to device behavior.
• The observed distribution of diffusion coefficients explains the wide variation in reported activation energies across the literature.
• All three DLTS modes (I-, O-, and C-DLTS) yielded consistent defect distributions, confirming the robustness of the regularization-based analysis.
• The results are consistent with impedance spectroscopy and boxcar DLTS, validating the new evaluation method.