  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.
