Effect of Perovskite Thickness on Electroluminescence and Solar Cell Conversion Efficiency

A hybrid organic–inorganic perovskite in a diode structure can lead to multifunctional device phenomena exhibiting both a high power conversion efficiency (PCE) of a solar cell and strong electroluminescence (EL) efficiency. Nonradiative losses in such multifunctional devices lead to an open circuit voltage (Voc) deficit, which is a limiting factor for pushing the efficiency toward the Shockley–Queisser limit. In this work, we analyze and quantify the radiative limit of Voc in a perovskite solar cell as a function of its absorber thickness. We correlate PCE and EL efficiency at varying thicknesses to understand the limiting factors for a high Voc. With a certain increase in perovskite thickness, PCE improves but EL efficiency is compromised and vice versa. Thus, correlating these two figures of merit of a solar cell guides the light management strategy together with minimizing nonradiative losses. The results demonstrate that maximizing absorption and emission processes remains paramount for optimizing devices.

* sı Supporting Information ABSTRACT: A hybrid organic−inorganic perovskite in a diode structure can lead to multifunctional device phenomena exhibiting both a high power conversion efficiency (PCE) of a solar cell and strong electroluminescence (EL) efficiency. Nonradiative losses in such multifunctional devices lead to an open circuit voltage (V oc ) deficit, which is a limiting factor for pushing the efficiency toward the Shockley−Queisser limit. In this work, we analyze and quantify the radiative limit of V oc in a perovskite solar cell as a function of its absorber thickness. We correlate PCE and EL efficiency at varying thicknesses to understand the limiting factors for a high V oc . With a certain increase in perovskite thickness, PCE improves but EL efficiency is compromised and vice versa. Thus, correlating these two figures of merit of a solar cell guides the light management strategy together with minimizing nonradiative losses. The results demonstrate that maximizing absorption and emission processes remains paramount for optimizing devices.
O ver the past few years, the performance of lead halidebased perovskite solar cells (PSCs) has revolutionized the photovoltaic field. 1−5 Their strong absorption bands spanning the visible region and excellent charge transport properties together with low-cost solution processability make them ideal candidates for both photovoltaic (PV) devices and light-emitting diodes (LEDs). 6,7 Although the current power conversion efficiency (PCE) of ∼25% is remarkable, the open circuit voltage (V oc ) of these solar cells remains below their theoretical V oc limit of 1.32 V (corresponding to a 1.6 eV band gap, common for lead halide perovskites) at AM 1.5 G sunlight. 8,9 This loss arises from nonradiative recombination of photogenerated charge carriers, which demands a quantification and identification of the dominating recombination mechanisms. 10 Under a generalized Shockley−Queisser (SQ) approach, Uwe Rau proposed an optoelectronic reciprocity theorem between absorption and emission. Thus, a solar cell that has a theoretical maximum PCE will also give a maximum external quantum efficiency (EQE) of its electroluminescence (EQE EL %) emission. 11 There have been a few reports with high EL efficiency corresponding to high-efficiency devices, but there exists an enormous scope to maximize the emission. 10,12 Moreover, preparing a device that exhibits high PV performance and excellent EQE EL at the same time is a daunting task. 13 However, the key lies in maximizing absorption and emission processes for optimizing high-efficiency devices.
Because of the occurrence of nonradiative losses due to defects, traps, geometrical loss (like reflection, waveguiding, etc.), or other reasons in any real PV system, the EQE EL < 1. Therefore, the experimentally observed V oc values of solar cells are lower than the actual radiative limit and are given by 4,13,14 where V oc cell is the calculated V oc of the solar cell and V oc rad is the radiative limit. This reciprocity relation suggests that a higher EQE EL results in a higher V oc . Thus, although the physical mechanism of a solar cell (radiation energy into electricity) and EL (transformation of electrical energy into light) is different, the attainable V oc is related by virtue of eq 1. 13, 15 In this work, we use eq 1 to probe the V oc deficit in a Cs 0.2 FA 0.8 Pb(I 0.85 Br 0.15 ) 3 -based PSC by varying the perovskite thickness. The evaluation of V oc from eq 1 was first attempted in a MAPbI 3 PSC. 16,17 Whereas for a good PV device, a significant thickness is required to obtain enough light absorption and efficient charge carrier collection, its high EQE EL requires a minimum thickness to reduce waveguiding loss and quenching of EL emission. 18 Importantly, our objective is not to optimize the device structure for the best performance of PSC or EL emission. Instead, we aim to study the correlation between PCE and EL efficiency as a function of absorber thickness. To probe the nonradiative losses in the photoabsorber, we vary only the perovskite thickness, keeping other layers and the deposition technique the same. If a perovskite is sufficiently thick (in the range of its absorption coefficient), 19 then it leads to an excellent PV performance with enough current density produced. However, EL performance at this thickness is often compromised as photons that are emitted internally are likely to be trapped or reabsorbed (matching emission and absorption energy). This limits the luminescence yield and hence the V oc value. Herein, we fabricate a high-performance MA free perovskite [Cs 0.2 FA 0.8 Pb(I 0.85 Br 0.15 ) 3 ] with a stable and well-studied composition 20,21 for solar cells with a planar structure (n-i-p) using a single-step method and carefully elucidate the effect of its thickness, morphology, and transparency on the PCE and EL performance and illustrate how it defines the inherent losses. These two reciprocal device operations suggest a way to quantify the absorber quality and to minimize defects in the bulk absorber. Figure 1 illustrates the working mechanism of EL in a LED and PV together with the energy level scheme for a perovskite in an n-i-p structure. In EL, charges are injected through respective charge transport layers (i.e., in a forward bias) into the perovskite where they recombine to give bright nearinfrared (NIR) emission. In the PV device, the identical stack is put under 1 sun illumination where electron hole pairs are generated by absorbing light. The generated electrons are extracted by the SnO 2 layer electron transport layer (ETL) and hole transport layer (HTL) due to their suitable band matching. The PV device operates in both forward and reverse bias.
Ideally, for the best EL performance, EQE EL ∼ 1. In that case, from eq 1, we obtain V oc cell ∼ V oc rad , and hence, we approach the radiative limit of the V oc for a solar cell if the device stack is the same. However, making such a device that is equally good in both operations simultaneously is neither trivial nor straightforward. The perovskite is a defect tolerant material with a low trap density, and most of the radiative recombination happens through a band−band transition. 22 Figure S1, which shows the SEM (scanning electron microscopy) cross section of a series of devices.
The rest of the PV parameters are shown in Figure S3. There is a continuous increase in J sc with an increase in thickness approaching saturation at 22 mA/cm 2 for 1.4 M perovskite. Clearly, the thickness of the absorber is a key parameter for optimal carrier generation. However, crystal quality also plays a significant role in avoiding nonradiative losses of photogenerated carriers due to grain boundaries or other defects in the lattice. The role of a high-quality absorber becomes especially significant at low thicknesses where the level of carrier generation is already low. Figure S2 shows a smaller grain size for a thinner perovskite layer affecting the electrical properties of the material like the generation, transport, and collection of photogenerated carriers. For a thinner perovskite, lesser precursor solution is left for nucleated particles to grow, hence a smaller grain size. With an increasing concentration of perovskite, Ostwald ripening predominates, resulting in large grain growth.
For thicker devices, most of the light harvested by the perovskite contributes to the current. The PCE has a similar trend except that it drops at 1.4 M, as a result of a sudden decrease in V oc and FF due to an overly thick perovskite layer causing aggravated recombination loss. 24 Figure 2b shows the normalized external quantum efficiency (EQE PV ) of the PV devices showing that the loss in J sc occurs mainly at higher wavelengths (>600 nm). This is expected due to the wavelength-dependent absorption coefficient of perovskite (see Figure S4). The absorption decreases for a thin perovskite, which affects photogeneration especially at longer wavelengths. No significant change in band edge absorption is observed. Thus, we expect the same radiative limit of V oc for all of the devices.
The optical band gap is further calculated from the Tauc plot. Figure S4a shows the ultraviolet−visible absorption spectroscopy of perovskite films on SnO 2 substrates showing the signature peak of perovskite at 730−770 nm. The average visible transparency (AVT) decreases with an increase in concentration, which is summarized at the inset of Figure S4a. Whereas a low AVT is required for a high EQE PV as most of the absorbed light contributes to the photogenerated current, one needs a high AVT for EQE EL as it effectively suppresses waveguiding and improves light outcoupling. Due to the high refractive index of the perovskite (≈2.3 near the emission wavelength), waveguiding mode loss is a major loss channel for perovskite and strongly dependent on the thickness of the perovskite layer. 25 Thus, if one is interested in semitransparent PSC specifically for window applications (AVT ∼ 25−35%),  The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter these losses are, by default, controlled. 21 With an increase in thickness, therefore, it becomes essential to control it with interfacial texturing to enhance light trapping, which would generate a larger number of charge carriers and hence a higher J sc . Figure S4b shows the optical band gap of the perovskite being equal to ∼1.62 eV in agreement with Figure 2b. The Xray diffraction (XRD) pattern in Figure S5 confirms the cubic phase of the perovskite for different thicknesses. 26 Next, EL measurement was carried out on the same set of PV devices with different thicknesses by the charge carrier injection method. In the case of the EL mechanism, charge carriers are injected through the respective ETL and HTL layers in forward bias. 27 Panels a−e of Figure 3 show the current density and EL radiance behavior with respect to the applied voltage. There is no EL performance observed for a 1.4 M film, which can be attributed to the compromised absorber quality and complete quenching. We suspect that joule heating could also be the reason where a thicker perovskite layer forms a stronger barrier for efficient thermal dissipation leading to an elevated junction temperature. 25 For all of the concentrations, the onset of EL emission is at ∼1 V, which is close to the V oc . The plateau region of the EL radiance contracts continuously from 0.4 to 1.2 M with a decrease in its absolute value. This suggests that both EL efficiency and stability decrease as thickness increases. A possible explanation is the large portion of the input power that is converted to heat or self-quenching of EL emission. Also, EL degradation is faster for devices with a thicker perovskite layer, which supports the heat generation/ accumulation mechanism. A comparison of the relative intensity of EL spectra is shown in Figure 3f at a constant applied bias of 3 V (which is mostly the plateau region of radiance).
The EL intensity increases from 0.4 to 0.8 M and thereafter decreases. Although we have maximum EL emission for 0.8 M, we do not have a maximum radiance for the same. This is limited by a high level of carrier injection as shown in Figure  4a. EL emission intensity alone does not guarantee a good LED. Therefore, the EL performance is maximum when we have both a low injection current and a high radiative efficiency.
To analyze the effect of thickness on film quality, we performed photoluminescence (PL) measurements. The increase in film quality with thickness is corroborated by the improved PL performance (see Figure S6) in terms of a reduced FWHM (full width at half-maximum) and PL maxima shifting to lower wavelengths due to the reduction in grain boundaries (see Figure S2). 28 The time-resolved PL (TRPL) measurements presented in Figure S6d show faster carrier decay for a 1.2 M device than for a 0.4 M device. This can be attributed to various decay channels like bimolecular recombination, trapping, charge extraction, etc., which are subject to investigation (but beyond the scope of this study). For the sake of simplicity, as perovskite is coated on the ETL, which is equivalent to the short circuit condition in PL, 29 the fast decay can arise due to rapid charge carrier transport from the perovskite to the ETL layer. Whereas this sharp decay is beneficial for PV performance in terms of fast extraction of photogenerated carriers, it inhibits the recombination mechanism in EL measurement. Figure S7 further shows the EL and PL spectra plotted together where there is an absolute overlap in the case of 0.4 and 0.6 M but divergence is seen for higher concentrations. The EL maximum remains same, whereas the PL maximum blue shifts. The EL spectra for individual concentrations at a varying applied bias are shown in Figure  S8. Figure 4a shows the variation of carrier density [current density/(elementary charge × thickness)] with voltage for different concentrations. It suggests that the voltage requirement to obtain essentially the same carrier density increases with perovskite thickness (as shown by the vertical gray dotted lines corresponding to a carrier density of 2 × 10 25 cm −3 ). For a good EL emission, the carrier injection should happen at the minimum applied bias. The bias increases with absorber thickness as the spatial distribution of injected carriers offers resistance to recombination. 30,31 Figure 4b shows the EQE EL with respect to the injected current density for devices with different concentrations. By plotting ln(EQE EL ) as a function of ln J inj (injection current), we can determine the ideality factor (n) of the device. 32 If we compare where n is the ideality factor and EQE EL a function of injection current, we see that when n = 1, the EQE EL should be constant, whereas it should increase linearly with injection current when n = 2. 33 For a 0.4 M device, the slope is 1; i.e., EQE EL increases linearly with injection current, indicating that much of the recombination happens through defects/trap-assisted nonradiative recombination [Shockley−Read−Hall (SRH)]. Thus, the occurrence of SRH recombination suggests that n = 2, and for low-thickness absorbers, it can be attributed to shallow or surface defects originating from the low surface:volume ratio of the grains (see Figure S2). 34,35 With an increase in thickness, EQE EL becomes constant, i.e., n ≈ 1, implying band-to-band recombination. Thus, whereas the EL is strong and stable in thin absorbers, it has nonradiative decay channels due to grain boundary defects. As the thickness increases to optimum values, EL performance declines, but most of the recombination is radiative, suggesting a smaller number of defects. These counter behaviors largely affect the photovoltage values, and therefore, maximizing the EQE EL is the key. Table 1  Followed by calculating the dark saturation current (J o rad ) in the radiative limit: Finally, V oc rad and V oc non-rad are calculated using At last, using eq 1, the calculated V oc (V oc cell = V oc rad − V oc non-rad ) is derived.
We now see that V oc rad ∼ 1.2 V for our device and the calculated V oc matches the measured V oc . Although V oc rad is lower in our case than values reported in the literature, 17 being a device property, it relies on how well the device is made and how well measurements are performed. Clearly, V oc cell is closer to the radiative limit for thinner devices. Figure 5 shows the link between the PV and the EL performance as suggested by eq 1. Figure 5a shows that the V oc deficit (ΔV oc = V oc non-rad ) increases with concentration. In other words, it is a measure of nonradiative losses leading to the V oc deficit that shows an increment with thickness. In Figure 5b, the PV performance improves whereas EL performance decreases within a range of increasing concentrations. The major improvement in PCE comes from the current density, which is primarily a function of the absorber thickness, whereas EQE EL improves if we have a sufficiently thin absorber to overcome luminescence quenching. Absorber thickness is one common factor that collectively affects these two functionalities.
In conclusion, we used the same n-i-p device stack to study the PV and the EL behavior. To do that, we vary the perovskite thickness and follow the V oc deficit that determines the overall efficiency. Moreover, we analyzed the loss of the experimental V oc measured from the PV as compared to the V oc estimated from the EL. Clearly, thickness brings in major loss mechanisms, which decreases EQE EL . SRH recombination and insufficient photogeneration of carriers limit the PV performance of the thinner device. For the thicker device, the high carrier injection requirement to obtain EL limits device stability and accelerates degradation pathways. We conclude that to maximize PCE and EL efficiency, one must maximize absorptance and emittance. This can be done by quantifying the achievable V oc and improving the absorber accordingly. In the case of thin PSCs that show strong EL but poor current density, a photon management/concentration strategy can be adopted to overcome carrier limitation. Nonradiative recombination can be mitigated via the passivation of defects, particularly at grain boundaries and interfaces. For standard thicknesses with a high PV efficiency but a compromised EL, device texturing can be beneficial to limit the optical losses.
Experimental procedure for device fabrication and details of characterizations, SEM images, device performance, transmittance data, XRD measurements, and PL, TRPL, and EL measurements (PDF)