Mapping of Internal Ionic/Electronic Transient Dynamics in Current–Voltage Operation of Perovskite Solar Cells

Abstract

Metal halide perovskites are mixed ionic‐electronic semiconductors that involve an important and particular phenomenology that negatively affects the performance and stability of next‐generation photovoltaic devices based on such material. The ionic nature of perovskites is shown to undergo not only a simple redistribution of charges but also influences the electronic processes and ultimately the steady‐state device operation. Nevertheless, a comprehensive understanding of the internal contributions of ionic and electronic conductivities to the evolution of current during device performance experiments and to degradation losses in ageing tests is currently missing. Here the ionic‐ and electronic‐based currents are separately shown in photovoltaic perovskites by means of transient experiments, beyond the external measured response. From an advanced mathematical model, the experimental observations attributing the partial transient features to physical effects in perovskites are rationalized. It is revealed that ion‐driven surface recombination effects are a dominant factor in the slowdown of efficiency measurements and in the long‐term degradation of perovskites under operational conditions. This work contributes to tracing a more accurate physical picture of the complex energy landscape of the perovskite‐based solar cells, which will be key to taking steps toward industrialization.

Understanding the mixed ionic‐electronic conductivity in perovskite solar cells is a crucial challenge to prevent degradation mechanisms and ultimately push this technology toward commercialization. This study examines the transient photocurrent responses in state‐of‐art perovskite solar cells for different ageing stages, dissecting the internal evolution of the simultaneous conduction of ionic matter and electronic charges and their respective contribution to degradation losses.

1. Introduction

Solar cells based on perovskites have captured significant attention in the research field during recent years as promising candidates for next‐generation photovoltaic technology.^{[ 1} , ^{2 ]} However, the practical application of these devices is still impeded by a number of fundamental limitations, which are unacceptable in real‐world energy yield.^{[ 3 ]} One of the most important properties of metal halide perovskite materials is their intrinsic coupled ionic‐electronic conductivity,^{[ 4} , ^{5 ]} leading to peculiarities that influence steady‐state operation and device lifetime.^{[ 6 ]} The ability to conduct both ionic matter and electronic charges simultaneously indeed represents an enormous problem for the perovskite's community, contributing to the lack of a universal understanding of ubiquitous electrical responses with anomalous traces, such as current–voltage hysteresis,^{[ 7 ]} negative capacitance effects in impedance spectra^{[ 8} , ^{9 ]} or complex multiscale dynamics of transient responses.^{[ 10 ]} Therefore, extensive research efforts have been focused on controlling this fascinating phenomenology of the mixed ionic‐electronic conductivity in today's star material for photovoltaics using a variety of experimental characterization techniques.^{[ 11} , ¹² , ¹³ , ^{14 ]} This complex physics underlying perovskites, further complicated by the presence of chemical reactions and therefore not included in the usual catalogue of semiconductor photovoltaic models,^{[ 15 ]} continues to pose a unique challenge to the research field.

Among the various (opto)electronic techniques used to characterize metal halide perovskites, Impedance Spectroscopy (IS) stands out as the most recognized within the scientific community^{[ 9} , ¹⁶ , ¹⁷ , ¹⁸ , ^{19 ]} due to its effectiveness in decoupling processes from coherent physical pictures associated with equivalent circuits that lead to a highly intuitive interpretation of the results.^{[ 12 ]} While simple, this approach does not always bear a direct correspondence with latent situations in perovskites, such as when memory effects influence the overall response,^{[ 7} , ^{20 ]} since impedance, by definition, explains the steady‐state device characteristics. The equilibrium behavior alone is not indeed sufficient for extracting all the information about the anomalous mechanisms that determine the physical behavior in perovskite solar cells and that, for example, represents a critical factor in estimating device efficiency from stabilized current responses.^{[ 14 ]} On the other hand, this frequency‐resolved technique also does not allow us to directly delineate the evolution of the internal dynamics that constitute the overall current responses and, ultimately, explain the device physics operating at different voltage conditions from the perspective of the affectation of device performance and stability. To obtain all this information and develop a general energy landscape of the operation in perovskite solar cells, it is necessary to complement the IS technique with alternative methods, such as those based on advanced transient analysis, which, although they are mathematically equivalent when operating under small‐signal conditions, exhibit a greater power to describe non‐equilibrium processes and dissect the ionic and electronic traces of the anomalous responses observed in experiments.

Here, we explore the contributions of partial transient dynamics to the photocurrent in order to provide significant information about the competition between ionic and electronic conductivities in the performance and stability of perovskite solar cells under operational conditions. We define this operation as a “mapping of the ionic‐electronic currents” in order to represent the relative distribution of the internal parts that constitute the external current at different points in time during the ageing process. This is achieved by first describing impedance measurements at the open‐circuit voltage (V _oc) and establishing a general equivalent circuit model to understand the observed spectra during illumination‐induced degradation experiments. Impedance description, complemented by small‐amplitude transient responses at this voltage region, results in an analytically accurate model that allows the study of the separate evolution of ionic and electronic currents at short‐ and long‐term scales. Capacitive ionic currents dominate in pristine conditions and the ion‐delayed electronic response is irrelevant since, in fact, it is indiscernible according to the results. At the early ageing stages, the ionic conductivity slightly decreases, being visible in impedance and time‐domain responses but coupled to the electronic response because both kinetic properties approximately exhibit the same characteristic relaxation times. Nevertheless, we experimentally show that a prolonged illumination leads to a significant decay in the steady‐state power conversion efficiency (PCE) due to the increase in the magnitude and duration of ion‐controlled recombination photocurrents in line with the breaking of strict equality of both time constants (interfacial accumulation processes are now much faster). This work provides key information on the device degradation processes and the critical role played separately by both electronic and ionic responses in the construction of current–voltage behavior, laying the foundation for experimental protocols evaluating the performance of perovskite devices in ageing tests.

2. Results and Discussion

To study the ionic‐electronic dynamic effects on illumination‐induced degradation for perovskites, we investigate the multi‐cation Rb_0.05Cs_0.05FA_0.75MA_{0. 15}Pb_1.05(I_0.95Br_0.05)₃ perovskite composition adding the organic molecule 2‐phosphonopropionic acid (H2pp) to the active layer in a nip‐type structure. The following cell architecture was used: FTO/c‐TiO₂/m‐TiO₂/perovskite/spiro‐OMeTAD/Au, that is, fluorine‐doped tin oxide/compact‐TiO₂/mesoporous‐TiO₂/perovskite/2,2′,7,7′‐tetrakis[N,N‐di(4‐methoxyphenyl)amino]‐9,9′‐spirobifluorene/Au. The cells were exposed to 1 Sun continuous illumination during 300 h in N₂ according to the International Summit on Organic Photovoltaics Stability (ISOS) protocol, ISOS‐L‐1l.^{[ 21 ]} In Figure  1a, the normalized current–voltage curves obtained at sufficiently slow scan speeds to avoid hysteresis effects (≈5 or 1 mV s⁻¹) after different illumination times are exemplified. In these photovoltaic perovskites, the decreasing V _oc over time dominates the degradation process because the short‐circuit current density (j _SC) and fill factor (FF) losses are not significant. Notably, the PCE decreased from 17.04% to 15.22% after roughly 300 h. Representative Nyquist plots of Figure 1 show how the impedance response at V _oc change over time with ageing, from the classical double arc^{[ 22 ]} (Figure 1b) to high‐frequency capacitive features with final semicircles in the form of hooks or curl‐backs^{[ 9} , ²³ , ²⁴ , ^{25 ]} in the fourth quadrant (Figure 1c,d, respectively), at long time scales. In effect, current–voltage curves and impedance responses of Figure 1 similarly exhibit the typical evolution of the characteristic signatures during degradation experiments of photovoltaic perovskites, which guarantee the “universality” of our study from state‐of‐art high‐performance configurations^{[ 26} , ^{27 ]} to low‐efficiency defective cells.^{[ 19} , ²³ , ²⁸ , ^{29 ]}

Figure 1.

a) Representative stabilized current–voltage (j–V) curves at slow scan rates (from 5 to 1 mV s⁻¹) measured on a pristine perovskite solar cell (based on the multi‐cation absorber of nominal formulation Rb_0.05Cs_0.05FA_0.75MA_{0. 15}Pb_1.05(I_0.95Br_0.05)₃ with the H2pp molecule) as well as after continuous illumination for the specified time. Note that the j–V curves are normalized at 0 V. b–d) Impedance spectra as a function of ageing time. Parameters: PCE is the power conversion efficiency, and Z _r and Z _j are the real and imaginary parts of the impedance, respectively.

To quantify, in electrical terms, the impact of mobile ions and electronic charges on the light‐induced performance degradation, we performed small‐amplitude transient chronoamperometric measurements at V _oc conditions during the ageing process. While the specific details are presented in the Experimental Section, we note that the devices are initially held at V _oc for 5 s (intentional pre‐treatment to start from an equilibrium situation), followed by a step transition of 10 mV at the instant t  =  0 (refer to Figure  2a), and finally recording the subsequent transient currents until a new steady state is achieved. The methodology allows us to unmask the multiple faces of representative transient currents in perovskite solar cells efficiency assessment protocols, in the context, for example, of current–voltage measurements^{[ 14} , ³⁰ , ^{31 ]} or maximum power point (MPP) tracking‐recording of stabilized power outputs.^{[ 32} , ^{33 ]} From a preliminary exploration, the experimental results reveal that the movement of charge carriers is significantly affected due to the evolution of transitions in the current density obtained between consecutive voltage stimuli with ageing. Indeed, throughout the light‐induced degradation process of perovskite devices, a variety of qualitatively different time‐domain patterns are obtained, from the classical capacitive decay^{[ 30} , ^{34 ]} (Figure 2b) to the famous negative transient spike^{[ 35 ]} (Figure 2c) and the slow multiscale dynamics shown in Figure 2d,^{[ 10 ]} in correspondence with impedance responses of Figure 1. There is an excellent agreement between the values calculated from the fittings of time transients and impedance data. Overall, the anomalous traces of the transient responses shown in Figure 2 suggest the difficulty of determining the dominant loss mechanism after ageing due to the characteristic ionic‐electronic coupling of metal halide perovskites, but, at the same time, give certain clues. Next, we will dissect these transient current responses to deconvolute the partial contributions of each component.

Figure 2.

a) Voltage excitation ΔV, consisting of a step‐size of 10 mV from V _oc and the ulterior current responses j after different ageing times: b) 0 h (fresh device), c) 120 h, and d) 300 h.

To get further understanding of the conductance properties of the perovskite devices during voltage exploration and light‐induced degradation, we propose an advanced electrical model, representative of charge collection and recombination, that tracks the evolution of the ionic‐electronic processes and the subsequent transformation of impedance and transient responses of Figures 1 and 2, respectively. Analytical descriptions presented in previous works allow the derivation of the equivalent circuit shown in Figure  3a,^{[ 10} , ¹⁴ , ^{36 ]} through a small signal analysis of the relevant equations corresponding to the nonlinear perovskite device model described in detail in the Supporting Information. The equivalent circuit elements have the following values in terms of model parameters:

$$g_{\mathrm{rec}}=\frac{\mathrm{d}{J}_{\mathrm{rec}}\left(V\right)}{\mathrm{d}V}=\frac{q{J}_{\mathrm{rec}0}}{n_{\mathrm{rec}}{k}_{\mathrm{B}}T}{e}^{qV/n_{\mathrm{rec}}{k}_{\mathrm{B}}T}$$ (1)

$$C_{\mathrm{s}}=\frac{\mathrm{d}{Q}_{\mathrm{s}}\left(v_{\mathrm{s}}\right)}{\mathrm{d}{v}_{\mathrm{s}}}=C_{\mathrm{s}0}{e}^{q{v}_{\mathrm{s}}/n_{\mathrm{ion}}{k}_{\mathrm{B}}T}$$ (2)

$$g_{\mathrm{ion}}=\frac{1}{{\tau }_{\mathrm{s}}}\frac{\mathrm{d}{Q}_{\mathrm{s}}\left(v_{\mathrm{s}}\right)}{\mathrm{d}{v}_{\mathrm{s}}}$$ (3)

$$g_{\mathrm{elect}}=\frac{\mathrm{d}{J}_{\mathrm{elect}}\left(V\right)}{\mathrm{d}V}=\frac{q{J}_{\mathrm{elect}0}}{n_{\mathrm{elect}}{k}_{\mathrm{B}}T}{e}^{qV/n_{\mathrm{elect}}{k}_{\mathrm{B}}T}$$ (4)

$$L_{\mathrm{d}}=\frac{{\tau }_{\mathrm{d}}}{g_{\mathrm{elect}}}$$ (5)

where g _rec denotes a fast recombination conductance, C _s is the surface capacitance, g _ion represents the typical ionic conductance mode in metal halide perovskites, g _elect is the slow recombination conductance, and L _d represents the chemical inductor operation^{[ 37 ]} of perovskites, qualitatively equivalent to the famous negative capacitance effects^{[ 9 ]} and originated by delayed ion‐driven interfacial recombination processes. Note that the conductances of electronic nature in the perovskite model, g _rec and g _elect, are defined as differential parameters obtained from the instantaneous current J _rec(V) and the stationary value of J _elect(V) controlled by the time constant τ_d (Equation S3, Supporting Information), respectively. The model also includes a surface charge function, Q _s, dependent on an internal potential v _s also delayed by τ_s (Equation S2, Supporting Information). From these parameters, one can model the RC branch of the equivalent circuit shown in Figure 3a. Here, J _rec0, C _s0, and J _elect0 are constant pre‐factors, q is the elementary charge, k _B is the Boltzmann's constant, T is the absolute temperature, and n _rec, n _ion, and n _elect are ideality factors. For clarity, we specifically indicate that n _ion is an effective ideality factor arising from the exponential dependence of the surface accumulation capacitance.^{[ 15 ]} In this model, j and V are the external current and voltage, related to the internal potential as u  =  V − jR _s due to parasitic series resistance effects. j _ph is the photogenerated current. For simplicity, we will assume hereafter u  =  V because R _s is negligible in relation to the perovskite conductances, as will be seen later.

Figure 3.

a) General electrical equivalent representation of perovskite solar cells, with each part of the circuit intentionally superimposed on the region of the device where the modelled physical phenomenon occurs (bulk: C _g and 1/g _rec; interface: 1/g _ion, C _s, 1/g _elect, and L _d). Internal transient currents generated for the fitting parameters of transient current experiments Δj(t) (Figure 2) and obtained during the degradation of regular perovskite devices: b) dielectric relaxation Δj _c(t), c) instantaneous recombination current Δj _rec(t), c) slow surface charging current Δj _s(t), and d) delayed electronic process Δj _d(t). Note that, in our case, we indicate j(t) and not Δj(t) in the panels because the initial current is zero at V _oc.

Remember that, for IS, we use sinusoidal small perturbations $\widehat{V}$ over a dc steady state $\overline{V}$, measuring subsequently the ulterior responses, $\widehat{j}(t)$ (refer to experiments shown in Figure 1b−d and Equation S4, Supporting Information). In performance assessment protocols, one however biases the device by using pre‐determined constant voltages

$$V=\overline{V}+\mathrm{\Delta }V$$ (6)

and monitors the current density Δj(t) to convert, in a final step, to the power output or the PCE. In Figure 2, we consider $\overline{V}=V_{\mathrm{oc}}$ and ΔV  =  10 mV. By a simple linear expansion of Equation S1 (Supporting Information), we obtain the transient results

$$\mathrm{\Delta }j\left(t\right)=\mathrm{\Delta }{j}_{\mathrm{c}}\left(t\right)+\mathrm{\Delta }{j}_{\mathrm{rec}}\left(t\right)+\mathrm{\Delta }{j}_{\mathrm{s}}\left(t\right)+\mathrm{\Delta }{j}_{\mathrm{d}}\left(t\right)$$ (7)

that indicate that the total measured current is composed of four different channels, as we labeled in the equivalent circuit of Figure 3a. In the previous theory, R _s denotes a series resistance and C _g represents the dielectric geometrical capacitance that, along the immediate recombination conductance g _rec, produce the fast partial currents that govern the resulting response during the initial part of stepwise current–voltage experiments:

$$\mathrm{\Delta }{j}_{\mathrm{c}}\left(t\right)=\frac{\mathrm{\Delta }V}{R_{\mathrm{s}}}{e}^{-\frac{t}{{\tau }_{\mathrm{v}}}}$$ (8)

$$\mathrm{\Delta }{j}_{\mathrm{rec}}\left(t\right)=\mathrm{\Delta }V{g}_{\mathrm{rec}}$$ (9)

where τ_v = R _s C _g, basically constant and voltage‐independent.

The key point of this perovskite device model is the interpretation of the two slow variables represented in Equations S2 and S3 (Supporting Information) as delayed memory‐based channels that describe, respectively, the equilibration of a surface potential v _s and an additional recombination current j _d.^{[ 38} , ^{39 ]} After the physical and mathematical formulation of the dynamical equations for the stimulus of small‐amplitude voltage steps, we hence obtain,

$$\mathrm{\Delta }{v}_{\mathrm{s}}\left(t\right)=\mathrm{\Delta }V\left(1-e^{-\frac{t}{{\tau }_{\mathrm{s}}}}\right)$$ (10)

in which, as Δv _s(t) models the voltage across the interfacial ionic‐electronic capacitance C _s, the corresponding internal current Δj _s(t) that flows through this branch of the circuit can be easily obtained as follows:

$$\mathrm{\Delta }{j}_{\mathrm{s}}\left(t\right)=C_{\mathrm{s}}\frac{\mathrm{d}\left(\mathrm{\Delta }{v}_{\mathrm{s}}\left(t\right)\right)}{\mathrm{d}t}=\mathrm{\Delta }V{g}_{\mathrm{ion}}{e}^{-\frac{t}{{\tau }_{\mathrm{s}}}}$$ (11)

by using Equation (3). This polarization current is indeed necessary to explain the evolution of the transient responses, and the equivalent experimental impedance spectra, with voltage observed here and in literature. As we previously commented on, the charging of the surface charge introduces, under small signal conditions, an interfacial capacitance C _s in series with a resistance 1/g _ion that vanishes in dc conditions and thus exhibits an ionic origin, playing a key role at medium time scales.^{[ 10} , ³⁵ , ³⁶ , ^{38 ]}

Analogously, we get the last internal current, related to ion‐controlled recombination processes, defined by

$$\mathrm{\Delta }{j}_{\mathrm{d}}\left(t\right)=\mathrm{\Delta }V{g}_{\mathrm{elect}}\left(1-e^{-\frac{t}{{\tau }_{\mathrm{d}}}}\right)$$ (12)

and obtained from the linearization of Equation S3 (Supporting Information) by considering zero initial conditions. With all this, it is evident that ionic charges (in electrical terms, g _ion and L _d) modulate the carrier accumulation (C _s) and recombination (g _elect), coupling the processes in the branches of the electrical circuit shown in Figure 3a and making the analysis problem difficult.

This model previously explained how the ionic and electronic conductances interchange the governability in the responses of metal halide perovskite devices in pristine conditions to show positive or negative capacitance features in impedance, classical decays or negative transient spikes in chronoamperometric experiments, and regular or inverted hysteresis in current–voltage curves when ${\tau }_{\mathrm{s}}\sim {\tau }_{\mathrm{d}}$.^{[ 14 ]} However, the continuity property of time constants is not always a reality, and even more so when the devices undergo changes due to degradation mechanisms.

Figure 3b–e shows the graphical representation of the simulated internal transient currents obtained from the fitting parameters of Figures 1 and 2. First, we note that Δj _c(t) is indeed an ultra‐fast dielectric process that represents as C _g blocks the current at the initial instant and charges rapidly, which is evoked by a pseudo‐instantaneous current decay (see Figure 3b).^{[ 40 ]} Logically, the initial value (ΔV/R _s) and relaxation time (τ_v) decrease and increase, respectively, upon ageing as a consequence of the slight enlarge of R _s. Nevertheless, this dielectric phenomenon is invisible and negligible in the overall experimental current, as illustrated in Figure 2, because there are much slower processes governing the response (i.e., τ_v ≪ τ_s,τ_d). We can consider that the ions are immobilized or frozen in this time regime.^{[ 41 ]} On the other hand, Figure 3c shows the evolution of the instantaneous recombination current Δj _rec(t), which models as a part of the Δj(t) is rapidly extracted by the contacts. We found, in this sense, an increase of g _rec, thus representing an important pathway of degradation in the perovskite devices. Finally, Δj _s(t) and Δj _d(t) respectively decrease and increase exponentially (refer to Figure 3d,e). Electrically speaking, it occurs the effects of the capacitor (inductor) that make the current (decrease) increase over time τ_s (τ_d) up to the stationary value. The meaning of the evolution in the transient responses, when representing purely resistive contributions and in terms of speed, is intuitive: Δj _d(∞), as well as τ_s/τ_d, increase and Δj _s(0⁺) decreases with the passage of time due to g _ion and g _elect are getting smaller and larger, respectively. Specifically, the ion conductivity suffers a very steep drop during the degradation process, as illustrated in Figure 3d. It is important to note, in this sense, that we obtain ${\tau }_{\mathrm{s}}\sim {\tau }_{\mathrm{d}}$ for fresh devices and in the early degradation stages; however, the ideal charge coupling, in terms of equality in the slow relaxation times, is broken with the device degradation (τ_d > τ_s), inducing certain characteristic deformations of the ideal spectra and transients for perovskite devices (see Figures 1d and 2d). Although the process of ion‐mediated charge accumulation is also slowed down (τ_s), we find that the increased τ_d is the most important factor contributing to the ion‐induced loss in the slow step of the recombination processes in our perovskite solar cells, predominately affecting the device efficiency parameters (cf. Figure 1a). The total current Δj(t) is subsequently slowing down and, in addition, the steady‐state value to which it tends decreases upon prolonged illumination. We summarize the theory presented and the experimental results obtained in Figure 3 through the band‐bending structure of Figure  4 , inspired by previous schematic representations.^{[ 36} , ³⁸ , ^{42 ]}

Figure 4.

Energy band diagram of the perovskite solar cells in open‐circuit conditions, as previously reported,^{[ 36} , ^{38 ]} with electron‐selective contact at the left and hole‐selective contact at the right side. E _c, E _v: Edges of conduction and valence bands. E _F: Fermi Level. E _Fn, E _Fp: Quasi‐Fermi level of electrons and holes. Here, the colored arrows represent the voltages and currents experimentally obtained as a function of ageing, where the thickness and length of each of them denote the slowness and maximum value, respectively.

Panels a and b of Figure  5 plot both g _ion − g _elect and the characteristic relaxation times obtained from transient measurements carried out at V _oc conditions under different ageing levels. Except in pristine devices, negative capacitance was observed for all the samples, suggesting that the ionic motion decreases dramatically during the degradation process of the devices (see Figure 3d). In electrical terms, we first find that the voltage range in which the transition from positive to negative values of g _ion − g _elect occurs decreases with ageing‐induced losses, as an unequivocal symptom that the ionic conductivity limits the performance of the devices. The change of type of dominant conduction mode is well documented in halide perovskite devices.^{[ 14} , ^{15 ]} As we previously commented on, it raises due to the combination of the large surface capacitance of the perovskite and the delay of recombination current, both due to ionic effects. At low voltage polarization effects, it dominates the accumulated electronic charge, but at higher voltages, the electronic carriers cannot follow the ionic motion and the negative capacitance effect emerges in the experimental data.^{[ 9} , ^{36 ]} In addition to the conductance ratios, all kinetic time constants have been calculated to provide an idea of how the voltage‐dependent electrical processes slow down during the accelerated degradation process (Figure 5b). Apart from the classical voltage‐independent characteristics typically observed in the relaxation times of perovskites,^{[ 9} , ^{39 ]} this analysis allows us to visualize as τ_v remains approximately constant and, τ_s and τ_d increases, abruptly breaking the electrical coupling charge (equality property of time constants)^{[ 43} , ^{44 ]} and demonstrating the largest losses induced by the movement of mobile ions in our perovskite solar cells.

Figure 5.

a) Relation of ionic/electronic conductances, g _ion − g _rec, and (b) relaxation times (τ_v, τ_s, and τ_d) extracted from the transient responses throughout the voltage range V for different ageing states. Note that shunt resistance effects are visualized at low voltages in Figure 5a.

Finally, we propose a basic physical interpretation of the electrical results obtained. From Figures 3 and 5, it can be easily deduced that the pre‐factors of the conductances given by Equations (1), (3), and (4) change abruptly with ageing. First, we have g _rec0 = qJ _rec0/n _rec k _B T and g _elect0 = qJ _elect0/n _elect k _B T, which both increase due to possible decrements of the respective ideality factors and increments of the current pre‐factors. The former option seems the most reasonable origin because of the change in the slopes of Figure 5a, suggesting a transition from Shockley‐Read‐Hall (SRH) recombination to surface recombination, related to ionic migration and due to non‐selective contacts.^{[ 45 ]} The latter alternative, on the other hand, indicates the logical increase of the recombination rate and bulk electron density at equilibrium. On the other hand, we have g _ion0 = C _s0/τ_s, which decreases sharply, suggesting a marked decrease (increase) of C _s0 (τ_s) with degradation. n _ion does not change excessively, which means that a drop in n _elect, together with what is deduced in the conductance prefactors, causes a change in the governability of the responses at long time scales (Figure 5a). The increase in τ_s is well‐known (see Figure 5b). As C _s0 = qQ _s0/n _ion k _B T (Q _s0 is a charge pre‐factor),^{[ 36} , ^{38 ]} a rise in this value indicates an increase of the equilibrium hole density, as a detrimental effect of ion mobility. From here, complementary techniques could be used to further characterize the physical landscape of ionic/electronic interactions in the perovskite devices.^{[ 12} , ^{46 ]}

3. Conclusion

In this work, we investigate the internal currents of perovskite solar cells during transient operation, somehow separating the contribution of ionic and electronic conductivities of the devices. From a practical point of view, our general theory presents a physical explanation for the ageing‐induced degradation in the complex energy landscape of perovskite devices by using an advanced analysis of the current dynamics during device performance assessment protocols based on applying step‐function voltage excitations. We reveal, in electrical terms, the dominant degradation effects in state‐of‐art perovskite devices for different ageing stages. The early degradation losses consist of an abrupt decay of the ionic conductivity. Later, we attribute a tremendous speed up in the ageing to ion‐driven delayed surface recombination processes. Both instability mechanisms significantly decelerate the time‐domain current responses and ultimately deform the impedance spectra (negative capacitance), transient responses (negative spikes), and current–voltage curves (hysteresis), as reported in the literature. The intrinsic ion‐induced losses in perovskites appear to be ultimately more significant in the increased recombination rates than in the charge accumulation mechanisms at the interfaces. Our results contribute to the understanding of ionic‐electronic phenomenology in photovoltaic perovskites, paving the path to rapidly identify and prevent the degradation routes in perovskite‐based devices from time‐resolved experiments.

4. Experimental Section

FTO glass sheets were etched with Zn powder and dilute 4 m HCl. Then, the etched substrates were cleaned in an ultrasonic bath with Hellmanex, acetone, and ethanol for 15 min and finally were immediately dried with dry air. c‐TiO₂ solution was prepared with titanium diisopropoxide bis(acetylacetonate):acetylacetone:ethanol = 0.6:0.4:9 (v:v) and then sprayed onto FTO substrates at 450 °C. m‐TiO₂ paste was prepared with titanium paste:ethanol = 1:6 (w:w), and was spin‐coated to c‐TiO₂ substrates at 5000 rpm for 20 s and then annealed at 450 °C for 30 min. After that, the as‐prepared FTO/c‐TiO₂/m‐TiO₂ substrates were quickly transferred to a N₂‐filled glove box for perovskite and spiro‐OMeTAD deposition. The metal halide perovskite with the nominal formulation Rb_0.05Cs_0.05MA_0.15FA_0.75Pb_1.05(I_0.95Br_0.05)₃ was prepared as follows. Briefly, first 1.5 m stock solution of (1) CsI (DMSO), (2) RbI (DMSO), and (3) PbI₂ (DMSO:DMF = 1:4) were prepared, respectively. Then, 1.5 m (4) (MABr)_0.9(PbI₂) (DMSO:DMF = 1:4), and (5) (FAI)_0.9(PbI₂) (DMSO:DMF = 1:4) were freshly prepared by dissolving MABr or FAI power in solution (3), respectively. After that, the solutions were mixed at a ratio of (4):(5):(1):(2):(3) = 190:950:60:60:60 (v:v) in sequence. 2‐phosphonopropionic acid (H2pp)‐doped perovskite solutions were prepared by simply dissolving H2pp in the perovskite precursor solution to achieve H2pp:perovskite with a 1:500 molar ratio. The perovskite spin coating process was carried out at 2000 rpm for 10 s, and then 6000 rpm for 30 s. Initially, 50 µL perovskite solution was dropped on a 1.5 × 2.5 cm² FTO/c‐TiO₂/m‐TiO₂ substrate. During the second step of spin coating, 100 µL chlorobenzene was dropped at 15 s before ending. The samples were annealed at 100 °C for 1 h on a hot plate for crystallization. The hole transporting layer was prepared by dissolving 0.12 g spiro‐OMeTAD in 1130 µL chlorobenzene and then doped with 47.3 µL TBP and 23.5 µL Li‐TFSI (1.8 m in acetonitrile). The spin coating was conducted at 4000 rpm for 20 s with 50 µL solution. The finished devices were placed inside a dry air box for 12 h to fully oxidize the spiro‐OMeTAD. Finally, 80 nm Au was deposited as the front electrode by thermal evaporation. The evaporation rate was controlled in different stages to limit the damage to the spiro‐OMeTAD layer.

Electrical measurements were carried out with a PGSTAT302N Potentiostat/galvanostat, equipped with an impedance and ultra‐fast sampling module, FRA32M and ADC10M, respectively, from Metrohm AutoLab. Impedance measurements were carried out by configuring the AutoLab to apply sinusoidal signals of 10 mV amplitude from 1 MHz to 1 Hz at V _oc. On the other hand, chronoamperometric experiments were developed, immediately after frequency‐resolved measurements, by applying a constant signal with the value of V _oc and, after a long time, a voltage‐excited step of 10 mV. A sampling rate of 1 MHz was used to record the current responses of RbCsMAFAPbIBr‐based perovskite solar cells. All the experiments at room temperature were carried out under an ambient atmosphere with the dry‐air flow. The reproducibility of the model was checked by conducting experimental measurements in ten samples with the same device configuration.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

H. Balaguera E., Bisquert J., Mapping of Internal Ionic/Electronic Transient Dynamics in Current–Voltage Operation of Perovskite Solar Cells. Small 2024, 21, 2409534. 10.1002/smll.202409534

Data Availability Statement

The data that support the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.14033382, reference number 14033382.