Characterization of ionic–electronic transport and recombination in perovskite solar cells under multi-biasing conditions

Abstract

Perovskite solar cells (PSCs) are among the most promising photovoltaic technologies, offering high efficiencies and low fabrication costs. However, their commercialization remains limited by stability issues and incomplete understanding of the intrinsic mechanisms governing device performance. In particular, slow mobile-ion dynamics can modulate charge recombination and extraction, strongly affecting device operation. Here, we use impedance spectroscopy (IS) to investigate the underlying processes that govern the current–voltage (J–V) response of PSCs under operational conditions. To this end, we combine J–V, Suns-V_oc and IS measurements using a multi-bias approach to analyze p–i–n PSCs under short-circuit (SC) and open-circuit (OC) conditions over a wide range of illumination intensities. Complementarily, drift-diffusion (DD) simulations and equivalent circuit model (ECM) analysis of IS under SC conditions enable extraction of key transport properties, including carrier mobilities, mobile ion concentration, and shunt resistance. The role of mobile ion concentration is analyzed for both regimes. Across the simulated parameter space, the low-frequency dark resistance is determined by the shunt resistance and nearly independent of recombination rates or mobile ion concentration. Therefore, the associated dark low-frequency RC time constant cannot be directly interpreted as a recombination lifetime. Under OC conditions, we further evaluate the coupled effects of ionic motion and energy band offsets on recombination, comparing the ideality factor derived across techniques. This integrated experimental–theoretical framework provides deeper insight into the electronic and ionic processes governing PSC performance.

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Broader context

Perovskite solar cells (PSCs) hold immense promise for next-generation photovoltaic technologies, offering high efficiency and cost-effective manufacturing. However, their widespread deployment is hindered by fundamental challenges related to charge transport, interfacial recombination, and ion migration—factors that significantly affect device stability and performance. Our study presents an advanced characterization approach combining J–V, Suns-V_oc, and impedance spectroscopy (IS) with multi-biasing analysis to disentangle the effects of mobile ions and energetic band offsets at perovskite/contact interfaces in inverted (p–i–n) architectures. By integrating experimental IS data with drift-diffusion (DD) simulations, we provide deeper physical insights into charge carrier dynamics, recombination mechanisms, and interfacial selectivity. Our findings reveal that high energetic band offsets at charge transport layers (CTLs) can limit the fill factor (FF) and open-circuit voltage (V_OC), while ionic accumulation modulates capacitive and recombination behavior. Understanding these complex interdependencies is crucial for overcoming efficiency bottlenecks and enhancing long-term PSC stability, paving the way for the optimization of next-generation tandem and scalable perovskite-based solar technologies.

Introduction

Perovskite solar cells (PSCs) are arguably the emerging photovoltaic (PV) technology of the decade, recently achieving certified power conversion efficiencies (PCEs) of 27.3% and 34.8% for single junction and silicon/perovskite tandem devices, respectively.¹ Their exceptional optoelectronic properties, including high absorption coefficients, long carrier diffusion lengths, defect tolerance, and tunable bandgap (E_g);² combined with low-temperature processability, make them strong candidates for large scale industrialization.^2–4 However, their limited long-term stability remains a challenge.⁵ A major factor underlying this instability is the presence of mobile ions within the perovskite absorber, whose redistribution under electrical bias and illumination modifies the internal electric field and affects charge-carrier dynamics.

Standard photovoltaic characterization methods, including current density–voltage (J–V) and Suns-V_oc measurements, are routinely employed to evaluate device performance and infer recombination mechanisms.^6–9 Their interpretation typically relies on the assumption of fast electronic charge-carrier response under steady-state conditions.^10,11 In PSCs, however, this assumption is frequently invalidated by slow ionic motion. The measured optoelectronic response reflects a convolution of electronic transport and recombination with bias-dependent effective built-in potentials (V_bi),¹² contact instabilities,^13–16 interfacial band offsets^7,17 and electric field screening due to mobile ion redistribution within the perovskite (PK) layer.^18–20 Among these, ionic accumulation at PK/charge transport layer (CTL) interfaces can dynamically reshape recombination pathways, impede charge extraction, and induce J–V hysteresis.²¹ Consequently, the ideality factor derived from J–V or Suns-V_oc measurements alone provides limited insight into underlying losses. Decoupling these coupled electronic and ionic processes requires characterization techniques capable of resolving distinct temporal scales, supported by physical interpretation via drift-diffusion (DD) simulations.^22,23

Impedance spectroscopy (IS) is a powerful method to probe these coupled dynamics in the frequency domain. PSCs exhibit characteristic impedance features spanning multiple decades in frequency, reflecting fast electronic processes in the PK bulk and slower ionic redistribution and interfacial charge accumulation.^24,25 The strong coupling between these processes produces complex spectra, including pronounced low-frequency capacitances and bias-dependent resistive elements. Multiple equivalent electric circuit models (ECMs) have been proposed to interpret these responses,^25–29 mainly depending on the given operating conditions such as voltage bias and light illumination under short-circuit (SC), maximum power point (MPP) or open-circuit (OC) conditions, as well as on device-specific factors including composition and degree of degradation. The use of general ECMs, for the interpretation of IS spectra in PSCs, remains limited. A unified physical understanding of IS in PSCs therefore requires models that incorporate coupled electronic and ionic transport across operating conditions.

Bias-dependent IS offers complementary insight into the dominant device physics. Under SC conditions, the impedance response primarily reflects charge transport and extraction processes.³⁰ Under OC conditions, the IS response is governed by recombination and diffusion-driven mobile ionic redistribution.^20,24,25 This is due to the device operating at zero current flow and near-flat-band conditions in the case of standard one sun illumination (open circuit voltage close to the V_bi). At the MPP, the high nonlinearity in the J–V response, together with the overlap of charge transport-recombination and extraction, complicates the interpretation of IS spectra. Although IS in PSCs has been widely studied under OC^31–33 and, more recently, under SC conditions,³⁰ a unified framework that consistently combines both regimes and enable direct comparison with DD simulations remains limited. In this context, a multi-bias approach is essential to resolve the coupled effects of electric field screening, recombination, and ionic dynamics, which is the focus of this study.

In this work, we present a comprehensive optoelectric characterization methodology for PSCs, combining J–V, Suns-V_oc and IS with a multi-biasing approach to quantitatively resolve coupled electronic–ionic effects in PSCs. Using an inverted (p–i–n) architecture as a case study, IS measurements are performed under SC and OC conditions over a wide range of illumination intensities. To enable a physically grounded interpretation, the experimental spectra are analyzed using ECMs and compared with the ECM fitting of the one-dimensional DD simulations performed with the open source Driftfusion code.³⁴ To the best of our knowledge, this work provides the first study integrating both OC and SC regimes through combined experimental and DD simulations. In particular, we analyze the IS data through the representation of resistive and capacitive elements as a function of short-circuit current density (J_SC) and open-circuit voltage (V_OC). First, DD simulations are used to evaluate the impact of key device parameters, with particular emphasis on mobile ion concentration, and to identify new correlations with high- and low-frequency resistive components. We analyze the effect of field screening and IS response difference between SC and OC conditions. Subsequently, the combined experimental–numerical framework enables extraction of key physical parameters, including carrier mobility (µ_PK), mobile ion concentration (N_ion), and shunt resistance (R_SH) from SC measurements. In addition, ideality factors (n_id) derived from dark J–V and Suns-V_oc analyses are compared with those obtained from OC impedance, establishing a consistent framework for assessing dominant recombination pathways. This approach further enables evaluation of the coupled effects of mobile ions and interfacial energy band offsets at perovskite/CTL interfaces.

Results and discussion

In this work, we analyzed PSCs with an inverted (p–i–n) configuration that were fabricated on FTO/glass substrates with the structure glass/FTO/NiO_x/perovskite/C₆₀/SnO₂/Au, as depicted in Fig. 1(a). First, dynamic light J–V curves were measured under 1 sun equivalent illumination and compared with DD simulations using the one-dimensional Driftfusion code (see the simulated device structure in Fig. 1(b)). For the device performance analysis, we focused on the variation of four key parameters in the PSCs. First, the carrier mobility in the perovskite µ_PK was varied from 0.2 to 20 cm² V⁻¹ s⁻¹, covering the typical range reported in the literature,³⁵ with electron and hole mobilities assumed to be equal for simplicity. Second, the mobile ion concentration N_ion was varied from 10¹⁵ cm⁻³ to 10¹⁹ cm⁻³ (ref. 36 and 37), considering two mobile ion species (cations and anions) present within the perovskite layer. From the J–V simulations, an ionic concentration close to 10¹⁸ cm⁻³ is expected considering the set of fixed device parameters (Fig. 1(c)). Further details regarding device fabrication, parameter selection (Table S1), and simulation methodology are provided in Section S1 of the SI. Third, the energy band offsets and built-in potential (V_bi) are defined as the difference between the anode and cathode work functions ϕ_a–ϕ_c (Fig. 1(b)). Interfacial band misalignment can effectively reduce V_bi impacting the J–V characteristics (see Fig. 3). In the simulations, V_bi is modified by varying the valence band offset ΔV_B at the perovskite/HTL interface and the conduction band offset ΔC_B at the perovskite/ETL interface through adjustment of the electron affinity of the respective CTLs. The CTLs are assumed to be highly doped, with their Fermi level positioned 100 meV from the band edge (conduction band for the ETL and valence band for the HTL, respectively). For simplicity, metal contacts are fixed as ohmic, and their Fermi level is perfectly aligned with the respective CTL Fermi level as an approximation in the DD model (SI section S1). Fourth, bulk recombination is modelled via defect-assisted Shockley–Read–Hall (SRH) processes assuming a single trap level³⁴ characterized by equal electron–hole lifetimes (τ^SRH_PK = τ_e = τ_h) in the PK bulk.

Fig. 1 (a) PSC schematic and corresponding top-view photograph deposited on FTO/glass. (b) Energy levels of the one-dimensional structure, before contact equilibrium, defined in DD simulations. (c) Experimental vs. DD simulated J–V curves, varying N_ion (cm⁻³) = {10¹⁵, 10¹⁷, 10¹⁹} and µ_PK (cm² V⁻¹ s⁻¹) = {0.2, 20}, at τ^SRH_PK = 1 µs and a low V_bi = 0.6 V (ΔV_B = 500 meV and ΔC_B = 300 meV). All J–V scans are simulated and experimentally performed in reverse direction at 30 mV s⁻¹ and under 1 sun equivalent illumination.

After the J–V measurements, the IS response was measured under dark conditions and increasing illumination intensity (Ψ) from 10⁻⁴ to 1 sun (1000 Wm⁻²), in the range of 100–1 MHz under ambient conditions and at a controlled temperature of 25 °C. Measurements were performed under both SC and OC conditions. The results are shown in Fig. 2, as Nyquist plots with real (Z′) vs. (–Z″) imaginary semicircle representation and the corresponding frequency-dependent capacitance Bode plots.

Fig. 2 IS data with increasing Ψ, measured under SC (a and c) and under OC (b and d) bias conditions, presented as: Nyquist plots (a and b), with real Z′ vs. –Z″ imaginary components. Multipliers indicate the required scale-up factor for full magnitude display in measurements towards low Ψ conditions. Bode plots (c and d), with frequency-dependent capacitance. Experimental data (dots) and respective fits (solid lines) to the selected ECM, as the inset depicted in (d).

Impedance spectra were fitted to the selected ECM, as shown in the inset of Fig. 2(d). The model consists of a nested configuration connected in line with a series resistance (R_S), accounting for contact- and transport-related ohmic losses. Two primary Voigt elements, each comprising a resistor (R) in parallel with a capacitive element (C), describe the high-frequency (HF) and low-frequency (LF) responses, with characteristic relaxation times τ = RC. To account for non-ideal capacitive behaviors arising from interfacial inhomogeneities and material disorder, ideal capacitors were replaced by constant phase elements (CPEs), reflecting a distribution of relaxation times rather than a single one.³⁸ The high-frequency semicircle (ω > 1 kHz) is usually attributed to electronic transport-recombination and geometric capacitance effects of the multilayer device stack. A second semicircle at low frequencies (tens Hz to mHz) is ascribed to additional slow ionic–electronic dynamics and its coupling to interfacial charge accumulation and recombination.

The fitted values of the individual R and C elements were analyzed as a function of J_SC and V_OC. To interpret the experimental results, IS spectra were simulated using DD simulations under equivalent bias and illumination conditions, while varying key device parameters, particularly the mobile ion concentration. Under SC conditions and low illumination, the LF semicircle is often not fully closed within the frequency range measured experimentally (until 100 mHz), which may introduce uncertainty in the extraction of the LF components (R_LF and C_LF). Therefore, experimental accuracy is very important when analyzing extrapolated LF parameters. DD simulations were extended to lower frequencies (down to 0.1–1 mHz), enabling a more reliable estimation (see SI Section S4 and Fig. S4.17). However, when comparing simulations and experiments, uncertainties related to extrapolation and parameter correlation should be considered. Both experimental and simulated spectra were fitted using the same ECM, enabling a consistent extraction of circuital elements, and a summary of the fitting parameters, including errors, is provided in the SI (Section S4, Tables S4.1–S4.4).

A shunt resistance R_SH was not explicitly included in the selected ECM, although it is included in the DD simulator. The contribution of R_SH to the resistive components (R_HF and R_LF), which depends on bias and illumination conditions,²⁵ is analyzed in the next sections. Further details on the measurement protocol, the impedance transfer function of the selected ECM (with and without the R_SH element), and discussion of additional RC contributions reported for PSCs are provided in Section S2 of the SI.

Analysis of J–V and Suns-V_oc characterization

Performance parameters extracted from J–V measurements under 1 sun illumination are shown in Fig. 3 and summarized in Table S3.1 of the SI. Experimental results (dot distributions) are compared with DD simulations (plots). Although V_OC values exceeding 1100 mV were achieved, reduced J_SC and FF limited the PCE compared with state-of-the-art inverted PSCs³⁹ (Table S3.2 of the SI). While FF losses are partly attributable to high series resistance (R_s) and/or low shunt resistance (R_SH), reduced J_SC may arise from optical or extraction losses.⁴⁰ DD simulations performed with fixed R_s, R_SH, and photogeneration show that the performance limitations also originate from coupled effects of reduced carrier mobility and increased mobile N_ion, which appears to be governed by band offsets, captured via variations in V_bi.

Fig. 3 Simulated power conversion efficiency (PCE) (a), open-circuit voltage (V_OC) (b), fill factor (FF) (c) and short-circuit current (J_SC) (d), extracted from DD simulated J–V curves assuming τ^SRH_PK = 1 µs and varying V_bi (V) = {0.6, 0.8, 1}, within the ranges of high (solid lines) and low (dashed lines) electron–hole mobility µ_PK. Side comparison with experimental results (black dots) with dashed horizontal lines indicating the median of the measured distributions.

Energy band offsets greater than 300 meV (low V_bi) are detrimental for the PCE, V_OC and FF in PSCs.^13,14,40 However, simulations (Fig. 3(a–c)) reveal enhanced tolerance to such band offsets as N_ion increases from 10¹⁵ to 10¹⁹ cm⁻³, due to ionic screening that lowers interfacial barriers even under forward bias (MPP and OC; SI Section S4, Fig. S4.1 and S4.2), in line with previous reports.^19,20 Yet, as shown in Fig. 3(d), at low µ_PK, high N_ion hinders charge extraction and reduces the J_sc,⁴⁰ evidencing a trade-off between barrier screening and transport constraint. We note that for other device configurations with low doped CTLs and high interface recombination, an increase of the mobile ion concentration leads to a decrease of the PCE.

Experimental dark J–V curves and Suns-V_oc (J_sc–V_OC points) measurements are presented in Fig. 4(a). Dark J–V exhibit three regimes: shunt-dominated leakage at low bias (V < 0.6 V), a recombination-controlled intermediate region, and R_S-limited saturation at high bias (V > 1.1 V), when V_bi is surpassed and the injection of charge is significative. In the recombination regime, the current density (J_d) follows the diode expression:⁴¹

where k_B is the Boltzmann constant, q is the elementary charge, J₀ is the saturation current density pre-factor, n_id is the ideality factor and T is the temperature of the internal diode. The R_s induces V = V_int − J R_S, and the internal voltage, V_int, approximates the quasi-Fermi level splitting (ΔE_F/q).^11,42,43 Therefore, Suns-V_oc measurements directly probe intrinsic recombination, as V_OC = V_int under OC conditions and a sufficiently large R_SH ^8,9 Experimental J_sc–V_OC points in Fig. 4(a) closely reproduce the J_d profile without the R_s saturation effect towards high applied voltages.

Fig. 4 (a) Dark J–V curves in forward (solid) and reverse (dashed) sweep directions at 30 mV s⁻¹, directly compared with Suns-V_oc (J_sc–V_OC) measurements (solid dots) for recombination analysis at the diode-like current (J_d) zone. (b) DD simulated dark J–V curves (reverse scans), varying N_ion (cm⁻³) = {10¹⁷, 10¹⁸, 10¹⁹, at µ_PK = 0.2 cm² V⁻¹ s⁻¹, low V_bi at 0.6 V (ΔV_B = 500 meV and ΔC_B = 300 meV) and R_SH = 10⁸ Ω cm². The n_id values of 1 and 2 were estimated using linear regression fits to eqn (1) and from its local derivative minimum applied to the J–V (n_id (V) inset in (b)).

An ideality factor n_id close to 2 (see SI, Tables S3.3 and S3.4) was obtained experimentally using eqn (1), as shown in Fig. 4(a), which suggests dominant SRH recombination.^8,41,44 In classic recombination theory for p–n junctions, n_id = 1 indicates that the J–V response is dominated by band-to-band recombination in the quasi-neutral regions, while n_id = 2 corresponds to dominant SRH recombination mediated by deep defects in the space charge region. In inverted PSCs, strong interfacial recombination may reduce the apparent n_id towards unity.^7,17 Within the DD framework, modifications of V_bi, via ΔCB (PK/ETL), ΔV_B (PK/HTL), or interfacial N_ion accumulation, directly modulate carrier collection and modify the magnitudes of n_id and J₀.¹² As shown in Fig. 4(b) the diode-regime recombination analysis is highly dependent on N_ion, complicating quantitative extraction of n_id in these devices.

Comparable n_id values were obtained from Suns-V_oc and dark J–V curves (SI, Tables S3.3 and S3.4), whether extracted by linear regression or from the local derivative yielding the minimum n_id(V), as shown in the inset of Fig. 4(b). As Suns-V_oc measurements largely eliminate R_S and R_SH contributions, recombination remains governed by minority carrier concentrations. Under illumination, high N_ion can therefore produce apparent n_id equal and above 2 (SI, Fig. S4.3).

Consistent with the J–V analysis, at a low µ_PK and high band offsets, the tolerance effect at high N_ion cannot fully compensate recombination losses. Simulations show electron–hole concentration imbalances within the PK layer (see SI, Fig. S4.4) for large band offsets ΔV_B and ΔC_B at the PK/HTL and PK/ETL interface, respectively. These coupled interactions between band offsets and mobile ions, and their impact on recombination, are further examined through the comparison between experimental and simulated IS in the following sections.

IS under short-circuit conditions at variable illumination

To further interpret the device behavior, R_HF and R_LF are plotted as a function of J_sc in double-logarithmic representation, as shown in Fig. 5, comparing experimental data with DD simulations varying µ_PK and N_ion. Under SC conditions, the internal electric field, determined by V_bi, can be partially screened by mobile ion accumulation at the PK/CTL interfaces. However, varying V_bi from 0.6 to 1.0 V in the simulations does not produce significant changes in the resistive or capacitive response across the explored ranges of N_ion and τ^SRH_PK. Noticeable deviations arise at low V_bi under transport-limited conditions (i.e. at lower µ_PK) in the PK, as detailed in SI Fig. S4.5.

Fig. 5 R_HF (a–c) and R_LF (d–f), as a function of J_SC under increasing Ψ from 1 × 10⁻⁴ to 1 sun equivalent, extracted from IS fits to the selected ECM (as the inset of Fig. 4(d)). For DD simulations, the ion concentration varies in the range of N_ion = [10¹⁵ − 10¹⁹] cm⁻³, with V_bi = 0.6 V, R_SH = 10⁸ Ω cm² and τ^SRH_PK = 1 µs. Effect of increasing N_ion at high (b and e) vs. low (c and f) electronic mobility, µ_PK (cm² V⁻¹ s⁻¹) = {0.2, 20}, respectively.

In general, R_HF and R_LF exhibit two distinct regimes as a function of J_sc. At low Ψ, both resistances exhibit an apparent plateau reaching a maximum value, denoted here as . At higher Ψ, they decrease linearly with increasing J_sc, consistent with a dominant recombination resistance (R_rec) associated with the enhanced photogenerated carrier density in the PK bulk. Accordingly, despite their different frequency origins (HF and LF), each resistance contribution can be independently described by a parallel combination of an effective and an illumination intensity-dependent R_rec (J_sc), expressed as follows:

Focusing on the plateaus in Fig. 5(a–c), we find that R_HF is affected by an additional resistive contribution (R_ion) coming from the static N_ion distribution, which screens the internal electric field and remains effectively invariant within the HF perturbation range. The effect of mobile ions in the HF response has been often considered negligible in previous studies.^24–26,28 For the PSC architecture investigated here, the combined IS and DD analysis suggests N_ion in the range of 10¹⁸–10¹⁹ cm⁻³. In the case of low mobile ion concentration and ideally no shunt resistance, the plateau would originate from a resistive dark recombination that is in parallel with R_ion. This resistance R_ion is independent of illumination intensity and should be distinguished from the R_rec–LF, which is rather associated with additional modulation of recombination from slow ion motion in the LF range.

DD simulations also show that the slope of the linear R_rec decay, both at HF Fig. 5(b and c) and LF in Fig. 5(e and f), is independent of the selected parameters. Additional simulated IS results (SI, Fig S4.6) explore µ_PK = [0.2–20] cm² V⁻¹ s⁻¹ and τ^SRH_PK from 10 ns to 1 µs, spanning typical recombination rates reported for comparable PSC devices.^20,30,45 The illumination range in which R_rec predominates is strongly governed by µ_PK and τ^SRH_PK in the PK layer. Hence, we find that the best agreement with experimental IS fits is obtained for medium-to-low mobilities of µ_PK = [0.2–2] cm² V⁻¹ s⁻¹ and τ^SRH_PK = 1 µs. A complementary analysis of IS fits, that takes into account the impact of the imbalance of the electron–hole mobilities (µ_e/µ_h) in the PK, can be found in the SI (see section S4, Fig. S4.16). Notably, the same R–J_sc profiles are obtained in DD simulations when varying µ_PK and τ^SRH_PK independently, as long as their product µ_PK·τ^SRH_PK, which determines the diffusion length , remains constant for a given N_ion. This behavior arises from the implementation of the Einstein relation in the DD simulations, which couples mobility and diffusion coefficient. Under dark conditions, where current is dominated by shunt-assisted leakage recombination, both and would be expected to converge toward R_SH, consistent with the J–V analysis. Experimentally, R_HF and R_LF exhibit markedly different magnitudes at the lowest illumination (Ψ =10⁻⁴ sun), as shown in Fig. 5(a) and (d). DD simulations at high µ_PK, in Fig. 5(b) and (e), indicate that R_LF approaches the input R_SH = 10⁸ Ω cm² across all N_ion; whereas R_HF progressively departs from R_SH with increasing N_ion. The pronounced divergence between R_HF and R_LF near dark conditions at 0 V bias suggests that the HF and LF responses are differently influenced by R_SH, mediated by ionic effects in the PK layer, as illustrated by the ECMs in Fig. 6(a) and (b). From the maximum experimental R_LF values, the dark R_SH is estimated to be equal or higher than 10 MΩ cm⁻² (lower R_SH effects on simulated IS are shown in SI Fig. S4.7).

Fig. 6 (a) Extended ECM proposed from the IS analysis of inverted PSCs in this study. It includes resistance dependence on the static N_ion distribution (R_ion) at high frequencies, in parallel with internal diode recombination (R_rec–HF) and parasitic R_SH. At low frequencies, the diode recombination (R_rec–LF) is modulated by mobile ions in the PK. (b) Equivalent structure from the perspective of individual shunt effects at high () and low () frequencies, resulting from a dynamic role of N_ion in the parasitic leakage currents, respectively.

It should be noted that the alternative ECMs proposed in Fig. 6(a and b) are not intended for a direct experimental implementation, as parallel resistive elements are reduced to a single equivalent resistance in the fitting process. Rather, they serve as a conceptual framework to illustrate the distinct physical contributions inherent to the R_HF and R_LF components arising from the multiple “aggregated” ionic and electronic effects identified through DD simulations.

For R_LF, shown in Fig. 5(d–f), increasing N_ion does not impact the plateau, but enhances R_rec–LF at high illumination. DD simulations indicate that internal bulk screening in the perovskite is reached for N_ion ∼ 10¹⁷ cm⁻³ (see SI, Fig. S4.2) enabling ion redistribution under small LF perturbations. Consequently, the interfacial ion layer that contributes an additional R_ion at HF becomes less effective at LF due to ion migration. This is of particular importance because, for all the IS fits in this study, the magnitude of R_LF was always higher than that of R_HF, indicating that the LF contribution dominates the resistive component of the J–V response at J_SC. Similar trends have been reported in DD simulations of inverted PSCs, where N_ion > 10¹⁷ cm⁻³ leads to an overall resistance increase (primarily dominated by R_LF) and a concurrent reduction in the low frequency capacitance.³⁰ Importantly, as shown in Fig. 5, R_LF and R_HF exhibit opposite dependences on mobile ion concentration. An increase in N_ion reduces the HF resistance due to enhanced internal field screening, while it increases the LF resistance by modulating charge accumulation at the interfacial barriers. Complementary C–J_sc profiles are included in the SI (see Fig. S4.8).

Within the wide range of parameters explored in our simulations, the high frequency SC resistance in the dark and under illumination shows a clear dependency on the recombination parameters and the mobile ion concentration, given a sufficiently high shunt resistance. This suggest that, depending on the nature of the coupled capacitance, the high frequency RC response time τ_HF can be considered as a recombination lifetime. However, our analysis also indicates that the low frequency resistance under dark and low illumination SC conditions is governed by the shunt resistance and shows no dependency on the concentration of mobile ions or the recombination parameters (except for high recombination rates). This implies that the RC response time τ_LF associated with the corresponding dark low frequency process cannot be straightforwardly interpreted as a recombination lifetime. Furthermore, this also questions the nature of τ_LF under illumination, whose values typically are in the order of the dark τ_LF. These findings are not only important for our general understanding of the recombination-related features of impedance spectra in PSCs, but they are particularly relevant for perovskite-based indoor photovoltaic and photodetector applications.

IS under open-circuit conditions at variable illumination

The combined protocol of IS measurements under OC conditions, compared with DD-simulations, enables a refined recombination analysis by separating fast HF processes, where ionic profiles remain effectively frozen, from slower LF dynamics governed by ion redistribution. We measured IS under open-circuit conditions (V_app = V_OC) increasing Ψ from 10⁻⁴ up to 1 sun illumination, which corresponds to V_oc ≈ 0.6–1.2 V, as presented in Fig. 2(b) and (d). Lower voltages (V_OC ≤ 0.6 V) were not accessible due to instrumental limitations. At very low Ψ, the OC response is expected to show trends similar to those reported under SC conditions due to the reduction of electron and hole carrier concentrations in the PK bulk.

The resulting R–V_OC plots present two regimes, analogously to the SC case, and are described using eqn (2) and (3). R_HF – V_OC profiles are presented in Fig. 7(a–c) (R_LF – V_OC profiles are included in SI section S4, Fig. S4.12) for which the experimental IS data were fitted with DD simulations. We particularly highlight the impact of energy band offsets at the PK/HTL interface (ΔV_B, in Fig. 1(b)), which modify V_bi, and of the mobile ion concentration on the IS response under OC conditions.

Fig. 7 R_HF (a–c) and C_HF (d–f) under open-circuit conditions for different illumination intensities from 10⁻⁴ up to 1 sun equivalent, obtained from IS fits to the selected ECM (inset in Fig. 2(d)). Comparison of experimental IS measurements in (a) and (d) versus DD simulations in (b and c) and (e and f) varying N_ion and V_bi at τ^SRH_PK = 1 µs. The n_id and m reference values, indicated by dashed lines, were determined using eqn (4) and (5), respectively.

At low V_OC < 0.6 V, R_HF displays a plateau consistent with a high R_SH (∼10⁸ Ω cm²), whose magnitude is modulated by N_ion (see the effect of low R_SH under varying N_ion, in SI, Fig. S4.13). At higher V_OC, once R_S and R_SH contributions are excluded and in the absence of strong injection/extraction barriers (resulting in a strong deviation of V_int from V_app),⁴⁶ R_HF is predominantly governed by diode recombination under flat-band conditions, following the characteristic exponential decay of R_rec:⁸

In line with the approach of Caprioglio et al.,^7,17 we evaluated the impact of ΔV_B on the recombination analysis by extracting n_id from the R_HF–V_OC slope (eqn (4)). Simulated IS fits were compared for moderate band offsets (ΔV_B = ΔC_B of 250 meV) and high band offsets (ΔV_B of 500 meV and ΔC_B of 300 meV) mainly at the PK/HTL interface. The corresponding cases, with V_bi = 0.9 V and 0.6 V, are shown in Fig. 7(b) and (c), respectively.

Comparing experimental data (Fig. 7(a)) with DD simulations (Fig. 7(b and c)) in the R_rec–HF decay regime at increasing V_oc reveals that higher N_ion leads to larger extracted n_id values, consistent with the dark J–V analysis. Experimental n_id (HF) values closer to 2 for representative devices confirm SRH-dominated recombination in the investigated PSCs. At the high N_ion range (10¹⁸–10¹⁹ cm⁻³) identified under SC conditions, the electric field in the PK bulk becomes fully screened. Notably, at medium V_bi and high N_ion, the inflection point of R_HF–V_OC is at V_bi.

In PSCs, the resistance extracted from IS under OC conditions is commonly interpreted as electronic at HF, where ionic motion is effectively frozen, and as ion-modulated at LF due to ionic redistribution. The electronic resistance exclusively refers to the charge carriers (electrons and holes) that can follow the HF perturbation. In that sense, under OC conditions,³¹ the HF response is governed by recombination consistent with diode behavior. However, even at HF, the resistance can be affected by the effect of mobile ions via field screening and modification of the charge density profile (as seen in Fig. 7). Our results show that this “ionic–electronic contribution separation” is most valid at V_oc near flat-band conditions (Fig. 7(b) and (c), dashed line), while deviations arise at lower illumination or away from V_bi. This approximation remains valid over a broader range of V_app approaching to V_bi, particularly in devices with higher V_bi (Fig. 7(b and c)). Under OC conditions, LF features arise from ion-induced modulation of the internal electric field (linked to V_bi, see Fig. S4.12) and interfacial charge accumulation. Notably, devices with larger V_bi exhibit a reduced dependence of R_LF on the mobile ion concentration. By contrast, under SC conditions, both HF and LF resistive components are influenced by mobile ions through distinct mechanisms. Under low illumination conditions, the formation of a HF resistance plateau depends on the mobile ion concentration (if the electronic mobility is high enough), highlighting the impact of ionic screening on the nominally “electronic” response. At LF, R_LF is governed by interfacial charge accumulation and dependent on mobile ionic parameters. Therefore, mobile ions influence both HF and LF resistances, emphasizing the need for a unified ionic–electronic interpretation of IS spectra.

Experimental and simulated C_HF–V_OC profiles are shown in Fig. 7(d–f). In all cases, C_HF exhibits a bias-independent contribution up to 0.9 V, corresponding to the total geometrical capacitance (C^T_geo), followed by a pronounced increase (≈2–5 times within ∼200 mV), whose magnitude depends on V_bi and N_ion. Illustratively, a second sample also showed an apparent saturation at high values of V_OC > 1.0 V (Fig. 7(d)). The monotonic increase is consistent with the onset of chemical-like electronic capacitance associated with carrier accumulation, whereas the saturation behavior may indicate additional parasitic contributions, such as contact depletion capacitance.^36,37,47 However, additional effects from a temperature rise in the device during IS measurements at high Ψ cannot be fully excluded. As a first approximation, C_HF increases exponentially towards higher V_OC following the relation:

where C₀ corresponds to the chemical capacitance at dark equilibrium and m to the factor limiting the voltage-dependent activation related to electron and hole accumulation in the PK layer at a given forward bias.⁴⁸ The effective C_HF values presented in Fig. 7(d–f) were calculated following the fitting methodology presented in section S2 of the SI (eqn (S23)). A summary of the IS fitting results is provided in section S4 of the SI (Tables S4.1–S4.4). At HF, the CPE_HF fits generally present values of α_HF > 0.91, indicating a response close to an ideal capacitance behavior, with limited impact on the extracted C_HF and m_HF values.

From DD simulations in Fig. 7(e and f), we observe that the defined ΔV_B offset shifts the activation of C_HF (V) towards higher V_OC, likely by changing the activation factor m, as in eqn (5). For large ΔV_B (i.e., low V_bi) at low N_ion, the misalignment of the energy level at the PK/HTL interfaces increases the hole injection barrier under high V_OC, leading to electron accumulation in the PK bulk (see SI, Fig. S4.4).⁴⁹ Increasing N_ion effectively reduces this injection barrier due to ionic screening in the PK (see SI, Fig. S4.12). The saturation of C_HF at high V_OC is also reproduced in DD simulations, particularly for the case of large energy band offsets (Fig. 7(e)). Experimental extracted m values closer to 5 (Fig. 7(d)) suggest a high N_ion in the investigated PSCs. Although the parameter m can provide insight into the magnitude of N_ion, large extracted m values in an exponential fit may indicate that the capacitance–voltage dependence is not purely exponential, but instead associated with a transition between regimes and/or the overlap with polynomial or fractional space-charge capacitance contributions.

In this work, we do not include the analysis of additional inductive effects on performance loss, as reported in the IS literature for some PSCs. For all the IS fits presented, as shown in Fig. 2, CPE values at HF and LF for the selected ECM displayed a dominant capacitive nature. However, we do observe some incipient inductive signatures only towards limiting frequencies <1 Hz for some experimental measurements under OC conditions at high illumination close to 1 sun. From DD simulations, we note that dominant inductive features, from mid to low frequencies (see SI Section S4, Fig. S4.10), can emerge mainly under conditions where V_OC ≈ V_bi, as reported in literature.^32,50 The inductive behavior is generally associated with surface polarization and interfacial barriers that dynamically modulate charge injection and extraction under ion redistribution,^51,52 resulting in a phase delay between voltage and recombination currents.^51,53,54

Conclusion

By combining J–V, Suns-V_oc, and multi-bias IS with drift-diffusion simulations, we conclude that the interplay between mobile ions and interfacial energy band offsets at perovskite/CTL interfaces can limit the electronic transport and recombination in inverted (p–i–n) PSCs, ultimately affecting the device performance. Pronounced band offsets at the PK/CTL interfaces were identified as a key factor limiting FF and V_OC. Dark J–V and Suns-V_oc analyses indicate high mobile ion concentrations (N_ion = 10¹⁸–10¹⁹ cm⁻³), which enhance tolerance to interfacial band offsets and influence the extracted n_id. However, high N_ion values cannot fully compensate for reduced charge transport in the case of low carrier mobility in the perovskite (µ_PK ∼0.2 cm² V⁻¹ s⁻¹).

IS measurements under both SC and OC conditions combined with DD simulations were performed under equivalent bias and illumination, enabling a consistent interpretation of the impedance response. Experimental and simulated IS spectra were fitted with a common ECM as a function of J_sc and V_oc. IS under SC conditions enabled an independent estimation of the electronic mobility (0.2–2 cm² V⁻¹ s⁻¹), mobile ion concentration (10¹⁸ – 10¹⁹ cm⁻³), and the dark shunt resistance (10⁷–10⁸ Ω cm²). Complementary OC at IS revealed distinct signatures of coupled ionic–electronic processes, linking resistive and capacitive responses to ion density and effective built-in voltage.

The role of the mobile ion concentration was analyzed for both regimes, SC and OC. Under SC conditions, the high- and low-frequency resistances exhibit distinct dependencies on ion concentration, associated with ionic screening and interfacial charge accumulation, respectively, highlighting their different physical origins. Under OC conditions, the analysis reveals that the high-frequency response approaches a purely electronic recombination regime near flat-band conditions influenced by the static ionic distribution, while low-frequency features reflect ion-modulated recombination. Our simulations yield that the extracted ideality factor is also affected by the effective built-in voltage. Finally, we show that under dark conditions at 0 V, the R_LF resistance is dominated by the shunt resistance and is largely independent of recombination and N_ion. Consequently, the associated R_C time constant cannot be directly interpreted as a recombination lifetime.

Overall, this integrated methodology provides a physically grounded framework to disentangle transport, recombination, and ionic effects in perovskite photovoltaics, offering guidance for interface optimization and device performance analysis.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting the findings of this study, including experimental measurements and device characterization data, are available within the article and its supplementary information (SI). Additional raw data generated during the study are available from the corresponding authors upon reasonable request. Supplementary information is available. See DOI: https://doi.org/10.1039/d6el00034g.

Acknowledgements

This work was supported by the French National Research Agency (Agence Nationale de la Recherche, ANR; Grant Nos. ANR-21-CE05-0022 and ANR-IEED-002-01) and by the National Association for Research and Technology (Association Nationale de la Recherche et de la Technologie, ANRT; Grant No. 2021/1814). The authors gratefully acknowledge this financial support.

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