Quantifying recombination and charge carrier extraction in halide perovskites via hyperspectral time-resolved photoluminescence imaging

Hybrid perovskite solar cells have attracted tremendous attention in the scientific community over the past decade due to an unprecedented increase in power conversion efficiency, reaching 26% in the laboratory and 18.6% on modules.¹ The relatively simple and inexpensive fabrication of devices through solution processing,² together with the tunability of the bandgap by chemical substitution,^3–5 has made perovskites very attractive materials in many applications such as photovoltaics, light-emitting diodes,⁶ lasers,⁷ and photodetectors.⁸ They have remarkable characteristics such as long diffusion lengths,⁹ low exciton binding energies,¹⁰ and long carrier lifetimes exceeding 1 µs.^11,12

As perovskite solar cells become more and more efficient, surpassing the 25% efficiency benchmark, each layer and its properties need to be optimized to the highest level in order to further reduce the gap to the theoretical power conversion efficiency limit. The bulk, interfaces, and extraction layers need to be optimized to reduce nonradiative recombination, and the selective extraction of holes and electrons needs to be maximized, while the interface defect densities need to be kept to a minimum. In addition, all of the material properties need to be homogeneous on the length scale of full devices and, eventually, even full-size modules to achieve maximum performance. Consequently, high-resolution mapping techniques will become increasingly important.

The key techniques to assess recombination losses in solar cell devices are steady-state and time-resolved photoluminescence (PL and TRPL).¹³ They allow for contactless measurements of charge carrier recombination processes of films on glass, layer stacks, and complete devices, making them ideal tools for material characterization and optimization. Although TRPL is a commonly utilized method for determining the recombination coefficients and charge carrier lifetimes in halide perovskites and other semiconductors, the interpretation of the measured transients is not straightforward, and the characteristic decay time is often not equal to the minority carrier lifetime of the perovskite absorber. The injection level,^14,15 the surface recombination velocity, interface recombination,¹⁶ charge carrier separation and extraction, and interface charging^17–19 must be taken into account to correctly interpret the measurements. In recent years, powerful numerical simulations have been developed that give clear guidelines for analyzing and interpreting TRPL transients measured on perovskite absorbers, including extraction layers.¹⁸ Combining the knowledge gained from simulations with measurements performed under specific illumination conditions allows us to pinpoint the current bottleneck of the absorber layers with high accuracy.

Furthermore, quantifying lateral inhomogeneities in solar cells is increasingly important. To gain access to laterally resolved PL and TRPL results, hyperspectral photoluminescence imaging, or lifetime mapping, has been developed^20,21 that allows us to study all the quantities mentioned earlier as a function of position, ranging from sub-micrometer properties^22,23 to full devices,²⁴ wafers,²⁵ and even full-size modules.²⁶ Results on grain boundary activity,²² lateral heterogeneities,^27,28 variations in series resistance,²⁹ and reduction of nonradiative losses due to interface passivation^24,30 have been reported. On devices, voltage-dependent mapping techniques have also been used to identify differences in charge carrier extraction/selectivity.³¹ 

In this paper, we used time-resolved photoluminescence imaging to better understand the lateral inhomogeneities in state-of-the-art perovskite absorbers deposited on a TiO₂-based electron extraction layer. Samples with and without surface passivation layers were used to distinguish between surface recombination and charge carrier extraction. Previous studies have shown that perovskites deposited on TiO₂ exhibited lateral variations in PL.^31,32 To discriminate between surface recombination and carrier extraction, we collect the PL and TRPL signals by illuminating the sample from the front (perovskite) and backside (glass/TiO₂). We employ the established models to differentiate between surface recombination and carrier extraction. Our analysis shows that the TiO₂/perovskite interface is of high quality; however, the lateral variations lead to varying extraction efficiencies, which need to be circumvented to achieve even higher efficiencies.

Photoluminescence imaging and transient photoluminescence measurements were performed using a custom-built hyperspectral imaging setup. The system consists of an intensified charged coupled device (iCCD) camera, a tunable liquid crystal filter operating in a spectral range of 650–1100 nm, a tube lens, and an objective lens. We used a pulsed 532 nm laser (VISUV-532-HP; pulse width<1ns) to illuminate the sample with a beam size of 7 × 7 mm². The laser beam is further homogenized to have a uniform top-hat beam profile. The setup is calibrated for absolute photon counts, allowing the conversion of the raw intensity directly to a photoluminescence quantum yield $Qelum$⁠. A schematic of the photoluminescence setup is depicted in the supplementary material (Fig. S1).

The externally emitted photoluminescence yield is denoted as Y_PL(E) whereas the sun's photon spectrum is Φ_s(E) and a(E) is the absorptivity of the perovskite film. Measurements were carried out in two different modes. Imaging was carried out primarily by integrating the measured counts over a period of 1 s. The repetition frequency was set to 40 MHz to have a high photon flux and to be close to one sun equivalent condition, i.e., 1.7 · 10²¹ (photons/m²)/s for a bandgap of 1.57 eV. These measurements are used to deduce $Qelum$ values for the different types of absorbers. TRPL measurements were performed at a low repetition frequency of 750 kHz without a monochromator on the detection side. Here, the iCCD camera was used to trigger the laser, and photons were collected every 2.5 ns, with a gate width of 30 ns. This allowed us to collect laterally resolved transients with a time resolution of 2 ns, as deduced from the rising edge of the PL at the time the photon pulse hit the sample. The two methods allowed us to measure, on one hand, the laterally resolved $Qelum$ values, whereas the latter could be used to measure the transient behavior of the charge carriers. In order to compare the $Qelum$ values measured with the pulsed laser with those with a continuous-wave (CW) laser, the same sample was measured with a 637 nm CW laser operated at 0.5 and 1 sun equivalent conditions.

In this study, we used a (FAPbI₃)_0.97(MAPbBr₃)_0.03 perovskite deposited on a TiO₂ double layer consisting of a compact layer (c-TiO₂; 20–40 nm) and a mesoporous layer (mp-TiO₂; 100–150 nm). Details of the fabrication process and the device efficiencies (champion cell: 21.5%) can be found in Ref. 33. Surface passivation was accomplished by depositing a thin layer of biphenyl-4 4′-dithiol on top of the perovskite film, allowing higher efficiencies (champion cell: 23.8%), as reported in Ref. 34. All samples were stored in an N₂-filled glovebox and measured in N₂ or air, depending on the setup or geometry. We cross-checked that the samples did not degrade during the measurements in the air. Since mp-TiO₂ will be of special interest here, we briefly summarize the fabrication of this layer. The film was prepared with a commercial TiO₂ paste (Dyesol 30 NR-D) diluted in ethanol (1:6 weight ratio) and then spin-coated onto the c-TiO₂ layer. The films were then dried at 80 °C for 10 min, followed by sintering up to 450 °C. Finally, a 0.1M solution of Li-TFSI was spin-coated, followed by another sintering at 450 °C.

Before presenting the actual imaging results, we need to discuss how the $Qelum$ values, measured with a pulsed laser (operated at 40 MHz) compared to measurements carried out with a continuous wave (CW-laser). In the community, the choice of a laser source to perform photoluminescence (PL) experiments has been a topic of considerable interest and debate.¹⁹ 

In Fig. 1(a), the integrated PL yield is plotted as a function of the laser flux on a double logarithmic scale, whereas quasi-Fermi-level splitting (μ_QFL) as a function of sun-equivalents is presented in Fig. 1(b). PL measurements with a pulsed laser at 532 nm and a CW-laser at 637 nm were performed in two independent absolute-photon calibrated PL setups. From a linear fit to the data in Fig. 1(a), an optical diode factor k = 1.5 is deduced. The two data points at 1.7 · 10²¹ m⁻² s⁻¹ (1 sun equiv.) for both measurements are very close to each other and within the error bar of the calibration.

Having established the relationship between pulsed and CW-laser illumination, we proceed with the laterally resolved measurements on the perovskite films. Figure 2 depicts the $Qelum$ maps measured under 68% of one sun equivalent illumination conditions of two perovskite absorbers. Our laser could not go further to complete one sun in injection during the period of these measurements. Figure 2(a) depicts the sample without a passivation layer, whereas Fig. 2(b) shows the result after surface passivation with the organic molecule. The respective PL spectrum of these samples can be found in the supplementary material (Fig. S2). In both images, we see a stripe pattern consistent with previous reports in which perovskite absorbers were spin-coated on a TiO₂ double layer.^31,34 In addition to the stripes, we find local inhomogeneities with either reduced or enhanced quantum yields. Spectrally resolved PL maps show very similar PL peak positions for the two absorbers at a photon energy of 1.56 eV, in good agreement with previous results.³³ 

The most important difference between the two absorbers is the value of $Qelum$⁠, which is approximately an order of magnitude higher for the passivated absorber [Fig. 2(b)] compared to the non-passivated one [Fig. 2(a)]. In Figs. 2(c) and 2(d), the variations in $Qelum$ are represented as histograms. The average values $Qelum̄$ (4.2 · 10⁻⁴ vs 3.7 · 10⁻³) coincide with the average color in Figs. 2(a) and 2(b), and we find a FWHM value, which is in both cases ∼20% of the average value.

From Eq. (5), we see that variations in the perovskite thickness may very well impact τ_eff and consequently also $Qelum$⁠. To check whether the thickness of the perovskite layer or the thickness of TiO₂ is non-homogeneous, the following experiment was carried out. A sample with TiO₂ and perovskite was first mechanically scratched with a sharp knife, and a profilometer measurement perpendicular to the scratch was performed. The scratch was clearly visible in the optical image of the profilometer setup [Fig. 3(b)]. The measured profile is plotted in Fig. 3(a) in blue.

In a subsequent step, the perovskite layer was removed by dipping the sample in Dimethyl-formamide (DMF), allowing us to measure the corrugation of the mesoporous-TiO₂ in the same spot [Fig. 3(a), green line]. An image of the mesoporous-TiO₂ surface after the DMF treatment can be found in the supplementary material (Fig. S3). The comparison between the two curves showed that the height changes observed on the perovskite surface are due to the corrugation of the mp-TiO₂. From this set of measurements, we were also able to deduce the perovskite thickness (∼600 nm) with an average rms-roughness of 30 nm after subtracting the TiO₂ corrugation [Fig. 3(a) orange curve]. Importantly, the height variations cancel out almost completely, which further strengthens the assumption that the perovskite thickness is very homogeneous.

We concluded that the variations in $Qelum$⁠, as observed in Fig. 2, arose from the mesoporous-TiO₂, with an average period of $∼80μ$m and height of ∼100 nm for the hills and valleys. This was further reinforced by the PL measurement performed at the same spot as shown in Fig. 3(c), where a bright and dark contrast is observed, originating from the same hills and valleys, respectively. Therefore, we concluded that thickness variations of the perovskite, which could change τ_surf, are not responsible for the observed changes in $Qelum$⁠.

In the next step, the origin of the $Qelum$ variations arising from the inhomogeneous mesoporous TiO₂ will be further analyzed. We carried out TRPL measurements on the two sets of absorbers (passivated and unpassivated) in two different geometries, as shown in the insets of Figs. 4(a) and 4(b). In all measurements, the laser flux and repetition frequency were kept constant. In Fig. 4(a), the perovskite side was illuminated, which means that most of the photons were absorbed far away from the mesoporous-TiO₂ interface. This situation is similar to the one used in Fig. 2. In the next step, the sample was flipped 180°, and the measurements were repeated. The results are shown in Fig. 4(b), and in this case, most of the photons were absorbed close to the mesoporous-TiO₂ interface.

Krogmeier et al.¹⁸ showed that the transfer of carriers to the extraction layer will cause a reduction in the PL signal at an early time (extending some tens of nanoseconds after the pulse), which is not caused by recombination. Our measurements performed in the two different geometries can be used to quantify this extraction since the np product at the interface is strongly changed, which should also impact the TRPL transients. In the absence of a high surface/interface recombination velocity, the initial drop can, therefore, be assigned unambiguously to a charge-transfer process. However, a similar fast initial drop should occur in the case of a high surface recombination velocity; therefore, the comparison between passivated and non-passivated surfaces is crucial to distinguish between the two cases.

The first observation is that the TRPL transients measured from the perovskite side are different for passivated and unpassivated absorbers [see Fig. 4(a)]. For the passivated case, we observed an almost completely mono-exponential decay with an effective lifetime of ∼500 ns. The long decay time for the unpassivated absorbers is reduced by approximately a factor of two, i.e., only 250 ns. This difference is also visible in the differential lifetime plots shown in the supplementary material (Fig. S4).

Furthermore, the initial slopes right after the laser pulse were different. We observed a fast initial decay for the unpassivated absorber that was absent for the passivated case. Measurements made on the glass side, which is close to the TiO₂ interface, showed fast initial drops for both absorbers, independent of the passivation layer [see Fig. 4(b)]. In the following, we develop a model for the observed changes.

In the first step, we need to understand whether the measurements were performed under low- or high-injection conditions since this also impacts the shape of the TRPL transients. We note that from the extracted lifetime of the passivated absorber (500 ns) and the measured $Qelum$-value (3.5 · 10⁻³), we can estimate the bulk doping of the perovskite via Eq. (3). For an absorption coefficient of ∼1 · 10⁵ cm⁻¹, we deduce a value of 1 · 10¹⁵ cm⁻³, assuming a radiative recombination coefficient k_rad = 6 · 10⁻¹¹ cm³/s and p_e = 0.1.¹⁴ The measurements were conducted with a photon density per pulse of 2.4 · 10¹⁴ cm⁻³. Consequently, the measurements were performed under low injection conditions as Δn < N_A. This also explains why we do see a mono-exponential decay for the passivated absorber measured from the perovskite side, as shown in Fig. 4(a).

The TRPL measurements performed on the other geometry, that is, from the glass side, as presented in Fig. 4(b), are distinct from those in which the illumination was performed from the perovskite side. The differential lifetimes are very short right after the pulse and, after ∼50 ns, converge toward the same values as for the perovskite side illumination. Shortly after the pulse, we find τ_diff = 12 ns for the unpassivated case and τ_diff = 17 ns for the passivated case. If we use the same reasoning as before, we directly see that the τ_diff values right after the pulse for the passivated case are not compatible with the long τ_eff values of 500 ns if we relate them to interface recombination. Therefore, the fast drop measured immediately after the pulse can be assigned with high certainty to charge extraction at the TiO₂ interface, in agreement with the simulations performed by Krogmeier et al.¹⁸ This is also the reason why we do see the same effect on both passivated and non-passivated absorbers. The surface recombination velocity at the perovskite surface is not relevant. The surface recombination velocity at the TiO₂ interface is low, as otherwise, we would not be able to measure a lifetime of 500 ns for the passivated case. Consequently, the only possibility remaining is that TiO₂ induces a fast initial decay due to carrier extraction.

Having established a model that explains the observed average transients, we will now discuss the laterally resolved TRPL measurements in more detail. Due to the low injection conditions, the signal at a single-pixel level is very weak, making it difficult to extract transients with a good signal-to-noise ratio. Consequently, we divided the image into two components, one denoted as hills and the other as valleys. To separate the two components, we used a two-dimensional Fast Fourier transform (FFT) to identify the hills and valley regions using the program Gwyddion.³⁵ The Fourier transformation allowed us to identify the characteristic frequencies in the images, which were, in our case, the variations in the PL counts imposed by the changes in TiO₂ thickness. In the second step, only these frequencies were masked and extracted from the image. The generated image has the same modulated pattern, albeit with a much better signal-to-noise ratio. We then used this image to generate a binary image that we used as a mask to filter out the hills and valleys in the original images. The procedure is shown in supplementary material (Fig. S5).

For this analysis, we used glass side illumination, where the interface is common for both passivated and unpassivated samples. The results of the identification of the hills and valleys and the transients extracted are shown in Fig. 5. In the present case, the valleys were highlighted with a green overlay. Figure 5(b) shows the TRPL transients extracted from both regions, which were then used to compute the differential lifetimes depicted in the bottom plot of Fig. 5(b). The hills and valleys showed τ_diff = 30 ns and τ_diff = 17 ns, respectively, right after the pulse. After ∼100 ns, both curves converged to the same value of ∼200 ns, in agreement with the averaged data presented in Fig. 4.

Low initial differential lifetimes are indicative of a fast process taking place right after the pulse. The valleys exhibited smaller values, which meant that in such regions, the extraction is faster. The faster carrier extraction leads to an overall reduction in the TRPL signal, as shown in Fig. 5(b). This reduction could also explain the measurements shown in Fig. 2, where the integrated PL signal at high repetition frequency was used to generate $Qelum$-maps. However, under open-circuit conditions, which is the case for steady-state PL, there will be no net flow of carriers, and consequently, a constant drain of electrons from the perovskite to the TiO₂ will not take place. An additional recombination channel that reduces $Qelum$ must be active. It is known from the literature that the thickness of the TiO₂ extraction layer needs to be fine-tuned to achieve maximum performance. Furthermore, the TiO₂ layer needs to be doped to increase conductivity and improve band alignment with the perovskite film. The low thickness of mp-TiO₂ in the valleys is sufficient to allow efficient extraction of charge carriers, as illustrated by the small effective lifetimes; however, the recombination activity needs to be enhanced, which consequently leads to $Qelum$ losses and, therefore, V_OC losses in the final device.

Consequently, we attribute the differences between the hills and valleys to a slight modification of the conduction and valence bands coupled with a change in the recombination rate at this interface. It has been shown that the conduction band can be effectively changed via Li-doping. In the present case, we used Li-TFSI to enhance charge carrier extraction and reduce the trap density within the TiO₂ layer. However, the mp-TiO₂ thickness is not constant at all, with height variations up to 100 nm, as shown in Fig. 3. Therefore, the ratio between mp-TiO₂ and Li-TFSI has changed substantially, and this will certainly affect the electrical properties of mp-TiO₂. As a consequence, the TiO₂ properties vary on the length scale of ∼80 μm, with adverse effects on device performance. It will be imperative to improve the thickness homogeneity of the mp-TiO₂ layer to further improve the device’s performance.

Improving the power conversion efficiency of halide perovskites well beyond 20% requires fine-tuning all the properties of each layer. Here, we used photoluminescence imaging to deconvolute the various recombination and charge extraction processes occurring at the top surface and bottom interface of the state-of-the-art (FAPbI₃)_0.97(MAPbBr₃)_0.03 perovskite absorbers. We find that passivation with a thin layer of the organic molecule biphenyl-4 4′-dithiol reduces the surface recombination velocity at the perovskite/N₂ interface by approximately one order of magnitude (from 240 cm/s for the unpassivated one to 29 cm/s for the passivated one), causing an order of magnitude boost in $Qelum$⁠. The rear surface of the perovskite, which is in contact with a mesoporous TiO₂ layer, exhibits fast initial decay times, consistent with rapid electron charge extraction. However, periodic thickness variations of the mp-TiO₂ on the order of 100 nm lead to varying charge carrier extraction velocities, which also impact the photoluminescence quantum yields and consequently V_OC. To further improve device efficiency, a more homogeneous TiO₂ layer needs to be developed.

All the additional information and details in support of this paper are provided in the supplementary material.

This research was funded in whole, or in part, by the Luxembourg National Research Fund (FNR), Grant Reference [Nos. 11244141, 14757355, and 12246511]. The authors acknowledge technical support by B. Uder, U. Siegel, and R. Himelrick.

The authors have no conflicts to disclose.

H. Phirke: Conceptualization (equal); Formal analysis (lead); Investigation (lead); Methodology (lead); Visualization (equal); Writing – original draft (lead). S. Gharabeiki: Resources (equal). A. Singh: Investigation (equal); Methodology (supporting). A. Krishna: Resources (equal). S. Siebentritt: Resources (supporting); Supervision (lead). A. Redinger: Conceptualization (equal); Methodology (lead); Resources (supporting); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.