EIS measurements have been called to give evidence on almost all major aspects of perovskite device physics, from built-in voltages and doping densities [13, 14], to interface couplings [15, 16],
defect densities [17, 18], recombination mechanisms [19, 20, 21] and density of states [22]. Unfor- tunately, the relative ease of performing these measurements, as compared with the difficulty of verifying a given interpretation, is such that there are now a great number of conflicting claims in the literature. A related issue is that discrepant interpretations have arisen for frequency-domain measurements on the one hand, and for time-domain measurements including I-V hysteresis on the other, which should be related via the Fourier transform and not by a change in physical picture. Here we give a brief overview of the conflicted state of the current literature on EIS as applied to perovskite cells in order to motivate the remainder of this chapter, which aims at clarifying these issues.
Early papers on this topic were largely attempts to better understand the working principles of PSCs using EIS coupled with a set of interpretations developed for organic and dye-sensitized cells (DSCs). One of the earliest [23] explicitly used an equivalent circuit developed for DSCs to fit the spectra of a MAPbI3 cell under illumination, employing a transmission line element to fit
the low-frequency feature. Ion migration was not recognized at this time, so the low-frequency feature was mistakenly attributed to carrier diffusion and the fitting used to obtain a carrier diffusion length. In relation to this suggestion we note that the timescale for carrier diffusion,
L2/µn,p, with L the device thickness, is of order 0.1 ns (assuming µn,p ≈ 10 cm2V−1s), and
therefore far too short to have anything to do with the low-frequency feature at ≈1 Hz. In another study, dielectric relaxation (i.e. local rearrangement of microscopic dipoles, rather than long-ranged ionic transport) was also considered a possibility for explaining the low-frequency feature [24]. To the contrary, a recent detailed study of the dielectric response puts the timescale for dielectric relaxation in the gigahertz range [25]. The importance of ions for the low-frequency response was perhaps first recognized in another DSC-based study [26], but not given much consideration in the equivalent-circuit fitting therein. In particular, the coupling between ion dynamics and collection efficiency and/or charge injection was not considered.
The ionic origin of the low-frequency feature was first discussed extensively by Bag et al. [27]. Once again however, the arguments in ref. [27] effectively presume that the electronic and ionic contributions are decoupled. This lead to the conclusion that an enhanced ionic feature under illumination must stem from light-activated ion migration, rather than the physically simpler explanation that ions affect the collected photocurrent, and therefore yield a response that scales proportionally with the light intensity (sec. 3.5.2). The neglect of coupling between ionic and electronic dynamics is a common mistake in the older EIS studies, and completely unwarranted given the strong effect of ion accumulation on internal fields (Chapter 2). Without such coupling the capacitive currents induced by ion accumulation would be far too small to account for I-V hysteresis (see for example the arguments in ref. [5]). More credible evidence for light-enhanced ion accumulation has been obtained in a recent study by examining the high-field poling of a
lateral structure under different illumination intensities [28]. However in these measurements it is hard to distinguish the effect of light-induced structural changes (degradation) from light- enhanced mobility. Our own measurements on MAPb3 and mixed perovskite cells have failed to
show clear evidence of light-enhanced mobility (Fig. 3.15 suggests that no such effect is present in mixed cation cells, at least under 620 nm LED illumination) but the possibility remains.
Another contentious issue concerns the high-frequency feature in EIS measurements, from which several authors have attempted to extract an effective lifetime [29, 30, 31, 32, 33] (more often the technique of photo-voltage decay was used for this purpose, but the physics involved is identical). To the contrary, our own simulations of the high-frequency feature fail to indicate any contribution related to the lifetime except at high forward bias (sec. 3.6). Instead the admittance at high frequencies is dominated by simple parallel-plate type charging of the selective contacts (sec. 3.4.6).1 This is supported by observations that the magnitude of the high-frequency capacitances scales with the perovskite thickness in the expected “parallel-plate” manner [3] (see also Fig. 3.10 for the effect of the titania thickness). A more direct counterargument against using the lifetime interpretation is that there seems to be little correlation between PL intensity/lifetimes and the high-frequency time-constant [34, 35]. In general, lifetime features are only expected to emerge under conditions of high injection, as discussed in sec. 3.4.6.
In section 3.4.5 we mostly address the confusion surrounding the low-frequency feature and its associated capacitance. The high-frequency feature is covered in section 3.6. Overall, the simulations reported in this chapter provide considerable new insight into previously contro- versial observations regarding light-induced and negative capacitance, providing an apparently comprehensive set of interpretations for EIS measurements that are fully consistent with the theory of ion-induced I-V hysteresis developed in Chapter 2. The following section establishes some basic concepts and terminology needed for the ensuing discussion.