Current-matching and hysteresis behavior in perovskite-silicon tandem solar cells investigated with drift-diffusion simulations 

Introduction

The emergence of halide perovskites as photo-active semiconductors has opened new exciting avenues in photovoltaics (PV). [1] Besides demonstrations of their use in single junction solar cells, major efforts are currently dedicated to integrating perovskite absorbers within tandem devices. In silicon-perovskite tandem solar cells, halide perovskites are combined with the established silicon technology to yield higher efficiency solutions compared to single junction devices using only one of either the silicon or the perovskite active layer.  

Despite the promise of recent developments, the understanding of how mobile ions in halide perovskites influence device optimization strategies is largely work in progress. This is especially the case, when it comes to the investigation of current-matching and hysteresis in tandem solar cells. [2] Understanding the parameters affecting hysteresis in complete tandem devices is crucial to design appropriate measurement techniques and to interpret data correctly. In this blog post, we show how the use of drift-diffusion simulations using Fluxim’s software Setfos can guide the study of these questions.

Background

Halide perovskites are mixed ionic-electronic conductors, meaning that they allow for both electronic and ionic transport. [3] Mobile ions, such as halide vacancies, redistribute during halide perovskite solar cell operation, causing slow variations in solar cell performance, as evident from the hysteresis behavior observed in current-voltage measurements. Hysteresis is typically not visible at sufficiently fast (too fast for ions to follow the perturbation) or sufficiently slow (ions are able to follow the perturbation) scan-rates. In selected situations, hysteresis may not be visible at any scan rate, despite the redistribution of ions.

Understanding ionic transport is important for other reasons, for example it may unlock critical degradation pathways. One such pathway is reverse bias degradation, a widely investigated question in perovskite PV. Its origin has been assigned to possible reactivity of contact and active layers on large (reverse) polarization of interfaces. [4]

While ensuring that an individual perovskite solar cell is not operated under reverse bias is straightforward, this is not immediately obvious when considering perovskite solar cells embedded in a tandem architecture, where two (or more) sub-cells are connected in series. The current flowing through each of the sub-cells is the same, while the total voltage of the tandem device is the sum of each sub-cell’s voltage (up to losses due to the recombination junction). When operating the tandem device close to its maximum power point, the voltage dropping across the sub-cells does not necessarily correspond to their respective maximum power working points. For example, if sub-cell 1 delivers lower photocurrent than sub-cell 2, the operating voltage is pushed towards lower values for sub-cell 1 and towards larger values (up to VOC) for sub-cell 2. Even though the tandem device may be under forward bias, the photocurrent limiting cell may be even forced to operate in reverse bias. It becomes clear that the operating conditions of sub-cells within a tandem device can vary depending on the optical bias, even if a constant voltage is applied to the overall device. 

The investigation of photocurrent-matching between the sub-cells in a tandem device represents a priority in the field. As the potential at the third electrode in a tandem solar cell is generally not immediately accessible, interpreting and predicting device behavior can be challenging based on experiments only. Optical modelling combined with drift-diffusion simulations offer a powerful and convenient means to access such information. Here, we show the use of Fluxim’s software Setfos to evaluate the effect of current matching on tandem solar cell response. 

Methods

We run optical and drift-diffusion simulations of complete tandem solar cell devices using Setfos 5.5. The device stack under consideration is the one shown in Figure 1. [5] The input parameters for each layer’s optical and electrical properties are taken from the literature or set to representative values when appropriate information is unavailable.

Figure 1: Tandem solar cell stack used in this study. The textured surface profile is taken from Ref. [6]

To explore the effect of current matching, we consider modified versions of the solar spectrum with different weighing for the short and the long wavelength ranges. Based on the selected architecture, we define illumination spectra F(λ) that differ from the AM1.5G standard (FAM1.5G(λ)) according to the following relation (see Figure 2b): 

The values of the parameters kshort(λ) and klong(λ) are selected so that a variation in the maximum photogenerated current equal in magnitude but opposite in sign occurs in the two sub-cells. Such variation is quantified by the parameter z. Based on the analysis in Ref. [2], the photocurrent generated in the two sub-cells correspond to:

The parameter λm in (1) is an arbitrary wavelength that defines the “short” and the “long” wavelength range. Here, λm = 739 nm is selected as the wavelength at which the absorptance of the absorbers in the two sub-cells is the same (see simulated absorptance of the tandem stack in Figure 2a). The obtained spectral irradiances are shown in Figure 2b for values of -0.2 ≤ z ≤ 0.2.

Figure 2. (a) Absorptance of the perovskite and the silicon active layers of the two sub-cells. (b) Solar spectrum AM1.5G and modified spectra using different values of the parameter z (see equations 2 and 3). [2] The dashed lines in the two panels identify the value of .

Current-voltage (J-V) characteristics of the tandem solar cell are simulated at different illumination conditions. Simulations are performed to obtain the steady-state J-V curves for the sub-cells and the complete tandem device. Secondly, transient simulations are performed to evaluate the hysteresis response of the tandem solar cell. For such transients, a prebias voltage of 1.9 V is considered (starting point is a steady-state condition) unless stated otherwise. This voltage is close to the open circuit voltage of the tandem device, leading to a situation close to flat-band. The reverse and forward voltage scans are then performed sequentially, and the transient device current is evaluated as a function of the scan rate.

Results and Discussion

Figure 3a shows the electrical quantities in the stack relevant to the response of the tandem device and of the two sub-cells. The voltages of the complete tandem () and of the silicon and perovskite sub-cells are indicated in the schematics ( and , respectively). Figure 3b displays the steady-state J-V simulation performed for the tandem device, when AM1.5G illumination is considered. In the same figure, the current-voltage characteristics of the sub-cells under the same optical bias conditions are illustrated. Once again, the study of the sub-cell’s response under comparable operating conditions to the tandem device is not straightforward experimentally. Simulations give easy access to such information. Of note, the perovskite sub-cell J-V shows a small kink in the voltage range close to the maximum power point. This is due to an increase in recombination close to the interface with the C60 layer for increasing applied voltages in the 0.6—0.8 V range (Figure 3d), following the effect of ionic redistribution on the electron concentration profile. Such kink is not present in the tandem response in Figure 3c because of the negligible changes in the perovskite sub-cell voltage (see also below).

Figure 3. (a) Stack configurations used in the Setfos simulations to investigate the response of the tandem (left), and the silicon (middle) or perovskite (right) sub-cells. The relevant terminals, voltage and current of the probed device is indicated in each schematics. (b) Steady-state current-voltage curves for the complete tandem solar cell under 1 sun illumination (AM1.5G), and for the individual sub-cell based on the same optical stack as in Figure 1. (c) Close up of the current density in (b), where the working point of the sub-cells when the tandem is operating at 0 V is highlighted. (d) Voltage dependent recombination rate in the perovskite subcell. Data refer to the top cell simulation in (c). (e) Band profile of the tandem operating at 0 V.

Figure 3c emphasizes that, given an operating point of the complete device (short circuit under one sun AM1.5G), the operating condition of the sub-cells can be very different from each other, depending on the current-matching conditions. As in this case the silicon solar cell is the current limiting device, it operates in reverse bias (), while the perovskite solar cell operates at a voltage that is equal and opposite to the one dropping across the silicon cell ().

The band profile output by the Setfos simulation (Figure 3e) displays the same concept in a more visually accessible way. The values of the sub-cell voltages  and  multiplied by the elementary charge q is a proxy for the internal voltage of the devices associated with the quasi-Fermi level splitting, although large differences between the two values typically occur especially far from open-circuit conditions.

Figure 4. (a) Steady-state current-voltage curves for the complete tandem solar cell under different spectral illumination based on the value of the parameter z, as defined in equation 2 and 3. The inset highlights the presence of a small kink in the J-V curve for some of the simulated data. (b) Short circuit current density plotted vs z. The maximum photocurrent from each sub-cell based on the total optical generation is also illustrated.

Figure 4a illustrates the changes in the steady-state J-V characteristics when the parameter  is varied and either the bottom cell () or the top cell () limits the overall photocurrent. The short-circuit current density is the parameter that varies the most when varying , while the fill-factor and the open-circuit voltage of the device undergo less evident changes. Figure 4b emphasizes the dependence of the short-circuit current density simulated for the tandem device (crosses) on , displaying a maximum around the condition of current-matching. Such condition is achieved for slightly negative values of z (-0.05 < z < 0) for the device architecture considered here. The photocurrent is compared with the maximum photocurrent in the two sub-cells at different illumination conditions, displaying the current-limiting effect of the sub-cell experiencing the overall lowest optical generation. The mismatch between such maximum photocurrent data and the actual short-circuit current density simulated for the tandem is due to recombination losses in the limiting sub-cell.

As described in the introduction, during a J-V measurement the limiting cell can be pushed towards reverse bias, while the other remains at forward bias (assuming for simplicity a total voltage applied that is ≥0 V). Such an effect is illustrated in Figure 5 for the cases of z = -0.05 and z = 0, for which the perovskite or the silicon, respectively, experiences reverse bias voltage when the tandem is operated close to short circuit. The complete steady-state silicon and perovskite sub-cell voltage profiles during the J-V scans under the two illumination conditions is plotted in Figure 5b as a function of the voltage applied to the complete tandem. Shaded areas in the graph highlight the voltage regions where the limiting cell operates in reverse bias.

Figure 5. (a) Band profile illustrating the potential dropping in the perovskite and the silicon sub-cells at different operating conditions (short-circuit, maximum power point, open circuit) for optical bias with two different spectra. In the case of z = -0.05 the perovskite top cell limits the current, while for z = 0 the silicon bottom cell limits the current. (b) Steady-state sub-cell voltages as a function of the applied tandem voltage for the two values of z investigated in (a).

Such an analysis already points out the importance of the optical biasing on the operating conditions of sub-cells within a tandem device at steady-state. An important message is that the potential drop across each sub-cell changes significantly during a J-V measurement, only if that cell is the current-limiting one. If the limiting cell happens to be the perovskite sub-cell, such changes in voltage lead to redistribution of ions, which in turn can vary the collection efficiency of the device. Indeed, the kink in the J-V response of the perovskite sub-cell described for the steady-state data in Figure 3b-c is visible only in the steady-state J-V curves in Figure 4a (see inset) associated with illumination conditions leading to the perovskite sub-cell to be the limiting one (z = -0.05, -0.1, -0.2). Beyond its influence on the steady-state response, redistribution of ions due to changes in voltage during a transient simulation is likely to introduce hysteresis, an effect that is relevant to experimental characterization of these devices.

Figure 6. Transient current-voltage  simulations of tandem solar cells pre-biased at 1.9 V followed by a reverse scan to 0 V and a forward scan to 1.9 V. The results are shown for scans that are performed at different scan rates. (a) z = -0.05, (b) z = 0.

Here, we explore such transient behavior using Setfos’ transient solver option and run simulations of complete J-V scans for the tandem device under different illumination conditions. By scanning the voltage in the J-V simulations at different rates, it is possible to access different regimes as far as the ionic redistribution in the perovskite is concerned. Simulations in Figure 6a and b consider a preconditioning voltage of 1.9 V (close to VOC) followed by a reverse and a forward scan. Because only the limiting cell experiences a significant change in voltage during the measurement, when the silicon sub-cell is limiting (Figure 6b), negligible ion redistribution occurs in the perovskite sub-cell and almost no hysteresis is observed in the overall simulation of the tandem J-V. On the other hand, if the perovskite device is limiting (Figure 6a), the mobile ions profile is perturbed during the current-voltage scan. This occurs to different extents depending on the scan-rate: at fast scan rates almost no change is expected, yielding a forward and reverse scan that are essentially identical except for the contribution of the displacement current. At intermediate scan rates, the redistribution of the mobile ions leads to changes in charge recombination and in the charge collection efficiency in the top cell. This results in the tandem device’s J-V reflecting some of the features relative to the individual perovskite sub-cell. Indeed, the hysteresis features observed in the tandem resemble the ones observed when simulating the perovskite sub-cell alone (see Figure 7a, where the tandem J-V has been corrected by the silicon solar cell open circuit voltage).

Finally, we point out that the pre-bias condition and the voltage scanning sequence are critical to the response of the device. In Figure 7b, the simulated J-Vs obtained for a 0 V pre-biasing followed by a forward-reverse scanning sequence is compared to the simulation obtained using a 1.9 V pre-biasing followed by a reverse-forward scanning sequence. For these data, even a change in hysteresis is observed, with more negative current densities obtained for the reverse scan in the 1.9 V pre-bias case (commonly referred to as “normal hysteresis”) and a mixed behavior for the 0 V pre-bias data. This comparison emphasizes that different initial ionic profiles are reflected in different transient recombination properties of the solar cell.

Figure 7. Comparison of hysteresis behavior obtained in simulated J-Vs at 10 V/s. (a) J-V of the perovskite top cell and J-V of the complete top-limited tandem (z = -0.05). The data for the tandem device are plotted against a corrected voltage (actual voltage minus the open circuit voltage of the silicon solar cell) to allow for a qualitative comparison. (b) The tandem J-V in (a) obtained by using a reverse-forward voltage scanning routine is compared with results referring to a forward-reverse routine. The pre-bias voltage in either case corresponds to the first voltage value applied to the device at the beginning of the routine (see labels in the figure).

Conclusions

Drift-diffusion simulations coupled with optical modeling performed with Setfos allows access to the optoelectronic steady-state and transient response of silicon-perovskite tandem solar cells. This opens the possibility to evaluate questions such as current-matching, influence of mobile ions on electrical response, spectral conditions leading to reverse biasing of the sub-cells. We find that:

-          Manipulating the optical bias enables accessing different regimes in terms of current-limiting conditions

-          The limiting sub-cell experiences the most significant variation in voltage during a steady-state or transient current-voltage measurement

-          It follows that the current limiting sub-cell largely determines the steady-state and transient behavior of the complete tandem.

-          Specifically, for situations where the perovskite cell is limiting, this leads to significant ion redistribution which modulates recombination currents in the device. For transient simulations (and experiments), this results in hysteresis effects

-          The electrical response and apparent efficiency of the device may depend on factors such as: scan rate, pre-bias voltage, scan direction sequence

The results point to the importance of controlling optical bias when investigating the transient response and ionic properties of tandem devices. They also emphasize that lack of hysteresis does not imply absence of mobile ionic defects.

If we have sparked your interest to simulate and optimize silicon-perovskite multi-junction solar cells Setfos, get in contact with us or directly order a free of charge trial version of Setfos

References

[1]         L. Schmidt-Mende et al., Roadmap on organic–inorganic hybrid perovskite semiconductors and devices, APL Materials 9, 109202 (2021).

[2]         C. Messmer, D. Chojniak, A. J. Bett, S. K. Reichmuth, J. Hohl-Ebinger, M. Bivour, M. Hermle, J. Schön, M. C. Schubert, and S. W. Glunz, Toward more reliable measurement procedures of perovskite silicon tandem solar cells: The role of transient device effects and measurement conditions, Prog Photovolt Res Appl. 1 (2024).

[3]         T. Yang, G. Gregori, N. Pellet, M. Grätzel, and J. Maier, The Significance of Ion Conduction in a Hybrid Organic–Inorganic Lead‐Iodide‐Based Perovskite Photosensitizer, Angewandte Chemie 127, 8016 (2015).

[4]         R. A. Z. Razera et al., Instability of p–i–n perovskite solar cells under reverse bias, J. Mater. Chem. A 8, 242 (2020).

[5]         D. Turkay et al., Synergetic substrate and additive engineering for over 30%-efficient perovskite-Si tandem solar cells, Joule 8, 1735 (2024).

[6]         S. Altazin, L. Stepanova, J. Werner, B. Niesen, C. Ballif, and B. Ruhstaller, Design of perovskite/crystalline-silicon monolithic tandem solar cells, Opt. Express 26, A579 (2018).