#### Contents

**Everyone is using - Voc-loss analysis helps you break through the ultra-high efficiency of perovskite solar cells!**

#### Contents

**Preface**

Research reports published in many top journals show that Voc-loss analysis is currently the most effective method used by many researchers to continuously break through the efficiency limit of perovskite solar cells (PSCs).

**Figure 1. Thesis Amount of adopting Voc-loss Analysis method for improving the PCE of Perovskite Solar Cells**

Figure 1 shows the statistics of published SCI papers related to Voc loss analysis in the field of perovskite solar cells. It can be seen from the trend that the open circuit voltage Voc loss has gradually attracted attention since 2015, and it has increased linearly. Although in 2019~2020, the number of papers has a stagnation period due to the Covid-19 epidemic, in 2021 there is a doubled increase in the number of papers. According to statistics, the number of SCI papers published by May 2022 has reached the level of the whole year of 2021. It is estimated that the number of papers in 2022 will also double the number of papers compared to 2021.

Next, we briefly review the important open-circuit voltage Voc loss applications over the past years to help readers quickly understand the role of Voc open-circuit voltage loss in practical perovskite solar cell research.

In 2018, Nam-Gyu Park and Hiroshi Segawa published “Research Direction toward Theoretical Efficiency in Perovskite Solar Cells” in ACS Photonics. This paper presents a pathway for the development of perovskite solar cells. Mentioned in this article, the short-circuit current density J_{SC} of perovskite solar cells has reached 97% of the theoretical limit of short-circuit current density J_{SQ} in 2018. In contrast, the open circuit voltage Voc at the same time only reaches about 77% of the theoretical limit of the open circuit voltage V_{SQ}. Compared with ultra-high conversion efficiency GaAs solar cells, Voc has reached 95% of the theoretical limit. Therefore, it is considered in this paper that to reach the theoretical limit of the conversion efficiency of perovskite solar cells, the research strategy of improving Voc (reducing loss) is far more important than improving J_{SC}. Thus, if there is a defect theoretical model to describe the loss of Voc, and there is a set of measurement tools for scientists to measure and analyze the loss mechanism of Voc, this will be very helpful for the research of perovskite solar cells.

Figure 2. Trend of improving the energy conversion efficiency of perovskite solar cells by increasing Jsc or reducing Voc loss (Quoted from: ACS Photonics; July 2, 2018; https://pubs.acs.org/doi/10.1021/acsphotonics.8b00124).

Since 2019, as the proportion of “open circuit voltage” in related papers on “perovskite solar cells” has increased year by year, “reducing Voc loss” has become an important strategy to improve the efficiency of perovskite solar cells. For example, In 2019, Nature Photonics published a 23.2% perovskite solar cell that broke the world efficiency record at that time. The strategy mentioned in the article is to reduce the loss of open circuit voltage Voc. This research uses Enlitech ELCT3011 and Enlitech REPS perovskite photovoltaic Voc loss analysis system to quantify non-radiative recombination loss of Voc. Through spectral data combined with thermodynamic theory confirmed the passivation effect of PEAI on the surface of perovskite thin films, increased open circuit voltage (Voc), and improved the overall conversion efficiency of perovskite solar cells.

Figure 3. A successful example of improving the energy conversion efficiency of perovskite solar cells by adopting strategies to reduce Voc loss in open circuit voltage (2019) (Quoted from: Nature Photonics; April 1, 2019; https://www.nature.com/articles/s41566-019-0398-2).

Figure 4. A successful example of improving the energy conversion efficiency of perovskite solar cells by adopting strategies to reduce Voc loss in open circuit voltage (2020) (Quoted from: Science; September 25, 2020; https://www.science.org/doi/10.1126/science.abb7167).

In 2020, South Korea’s Ulsan University of Science and Technology (UNIST) made another achievement, announcing that its research team experimentally fabricated a high-efficiency large-area perovskite cell of up to 24.8%, with a minimum voltage loss of 0.3 V, published in Science 2020 Journal (Stable perovskite solar cells with efficiency exceeding 24.8% and 0.3-V voltage loss). The efficiency breakthrough strategy focuses on the open circuit voltage Voc. Enlitech ELCT3010 (now Enlitech REPS perovskite photovoltaic Voc loss analysis system) is used to quantitatively test and analyze the Voc loss characteristics of perovskite solar cells.

The journal Science (IF 47.728) published the latest research results of Professor Zhu Zonglong of City University of Hong Kong in April 2022. The research team used ferrocenyl-bis-thiophene-2-carboxylate (FcTc_{2}) to provide a new idea for designing stable and efficient interface materials for perovskite solar cells. The ferrocene organometallic derivatives possess the excellent properties of both organic and inorganic materials. As a functionalized interface layer, they can effectively reduce the non-radiative recombination in the interface of inverted perovskite solar cells and accelerate the charge transfer at the same time.

The researchers conducted experiments by using Enlitech’s ELCT-3010 system (now Enlitech REPS perovskite photovoltaic Voc loss analysis system) and other instruments. The results showed that the open-circuit voltage (Voc) and fill factor (FF) of the device functionalized through the FcTc_{2} interface were improved. A record efficiency of 25% for inverted perovskite solar cells was reached (certified efficiency of 24.3%). In addition, it still maintained 98% of the initial efficiency after 1500 hours of long-term simulated AM1.5 illumination; the stability test in hot and humid environment (85°C/85% RH) passed the international standard of IEC 61215:2016.

**Figure 5. Prof. Zonglong Zhu’s research results of PSC photovoltaic performance.**

(A)J-V curves of the best performing devices with and without FcTc_{2}.

(B) EQE spectra and integrated current densities of the best-performing devices with and without FcTc_{2}.

(C)Stabilized power output at the MPP for the best-performing PSCs treated with FcTc_{2}.

(D)Histogram of the PCE values among 30 devices with and without FcTc_{2}.

(E) EQE_{EL} values of the PSCs with and without FcTc_{2} operating in light emitting diode (LED) mode under different voltages.

(F)EL spectra of the FcTc2-based PSC operating as an LED.

Enlitech’s REPS not only can detect the extremely low EL-EQE signal (as low as 10^{-5 }%, which is 7 orders of magnitude), but can also calculate thermodynamic Voc, radiative recombination Voc, and non-radiative recombination Voc (through its software SQ-VLA). In addition, it can also analyze ΔE1, ΔE2, and ΔE3 losses between different type of devices in one histogram chart. Most importantly, the analyzing software can help users match the calculated Voc-loss with the real Voc-loss of the device IV curve, thereby promoting the research progress and journal publication.

## What is Voc-loss analysis?

In the previous article, we roughly learned that in the field of solar cell efficiency research, the study of the loss of open circuit voltage is the most popular part. So, do we have to first understand what the open circuit voltage loss is looking at?

To understand the loss of open circuit voltage, let’s start with the basics of solar cells. Solar cells are composed of n-type and p-type semiconductors. When the energy of photons is greater than the energy gap of the semiconductors, the photons are absorbed by the semiconductors and generate electrons and holes. The entire operation mechanism goes through four stages: (1) Absorption, (2) Photocarrier Generation, (3) Transport, and (4) Collection, so that solar cells can provide us with electricity.

**Figure 6. Concept of solar cell and energy band diagram of solar cell** (Quoted from: National Taiwan University Department of Electrical Engineering, The principle and application of solar cells, https://ee.ntu.edu.tw/upload/hischool/doc/2014.04.pdf).

When light irradiates the solar cell, energy conversion occurs through the processes of photon absorption, photogenerated carriers, charge transport, and charge collection. The External Quantum Efficiency (EQE) of a solar cell is the ratio of the number of monochromatic light with a known number of photons irradiating the solar cell and the number of electrons transferred to the external circuit. The above four processes describe the solar cell being irradiated and absorbed by known incident photon, becoming photocarriers and transport to electrodes. The whole process is the external quantum efficiency EQE process and it shows the photon-electron transferring capability of solar cell. In other words, EQE spectrum represents the whole process of above mentioned 4 steps.

The ideal solar cell model should convert energy only through the radiative recombination pathway, i.e. obtain 100% external quantum efficiency EQE. However, in fact, there are often multiple non-radiative recombination pathways that affect the performance of the solar cell. It results in additional voltage loss, called Voc loss.

## The pain points of breaking through the ultra-high efficiency of perovskite solar cells?

Perovskite solar cells combine the advantages of high carrier mobility, long carrier lifetime and high radiation efficiency. Nonetheless, the complete device suffers from large nonradiative recombination losses, limiting its Voc to values well below the Shockley-Queisser limit.

Summarizing the research results of many outstanding scientists on Voc loss analysis of perovskite solar cells, in terms of structure, most of the focus is on the interface between the perovskite absorber and the charge transport layer. The origin of non-radiative recombination will bring great help to the continuous breakthrough of the efficiency limit of perovskite solar cells.

Based on the above requirements, two things have naturally become the most concerned factors in the field of perovskite research: (1) How to achieve accurate measurement? (2) How to quickly calculate and obtain thermodynamic loss (thermodynamic Voc Loss, ΔE1), radiative recombination Voc Loss (ΔE2) & non-radiative recombination Voc Loss (ΔE3) using measurement data Analysis results? This is also a common pain point in this research field.

Enlitech’s Perovskite and Organic Photovoltaic Voc Loss Analysis System (Enlitech REPS) is a complete system that can help scientists measure, calculate and analyze the Voc-loss of solar cells, and provide ideas for the next step of process improvement. Enlitech’s REPS not only can detect the extremely low EL-EQE signal (as low as 10^{-5 }%, which is 7 orders of magnitude), but can also calculate thermodynamic Voc, radiative recombination Voc, and non-radiative recombination Voc (through its software SQ-VLA). In addition, it can also analyze ΔE1, ΔE2, and ΔE3 losses between different type of devices in one histogram chart. Quickly providing researchers with effective test data and analysis results will not only saves researchers’ time, but also avoids errors caused by human calculations.

Figure 7. Enlitech’s perovskite and organic photovoltaic Voc loss analysis system (REPS) is used to analyze and improve the loss of perovskite solar cells, and the research results produced by the system can be seamlessly integrated and quickly published in journals.

## How to proceed Voc-loss analysis more systemically?

Physicist Shockley-Queisser’s SQ equilibrium limit theory provides the answer. In the SQ equilibrium limit, the three major losses of Voc include: ΔV₁ thermodynamic loss, ΔV₂ radiation loss, ΔV₃ non-radiative loss. Using the SQ equilibrium limit theory, the process of Voc loss can be explained in detail.

Figure 8. Schematic diagram of energy levels of thermodynamic loss, radiative recombination loss, and non-radiative recombination loss of SQ equilibrium limit theory.

Figure 9. For the explanation and understanding of the related mechanisms of radiative recombination loss and non-radiative recombination loss, readers can refer to Adv. Energy Mater. 2017, 1602358. In this paper, there are more detail information of Voc loss mechanisms caused by various defects.

## For the research of perovskite solar cells, can we obtain the open circuit voltage loss value by ourselves? How to do it?

The answer is yes. According to the Shockley-Quiser limit, the open circuit voltage Voc loss of a solar cell is determined by the three losses, which can be obtained by the following relationship:

where q is the basic charge, ΔV is the total open-circuit voltage loss, ΔV1 is the thermodynamic loss, ΔV2 is the loss caused by radiative recombination, and ΔV3 is the open-circuit voltage loss caused by non-radiative recombination.

From the relationship of the open circuit voltage loss, we can clearly see that as long as the energy is measuredE_{g}、V^{ SQ}_{OC}、V^{rad}_{OC}., these three loss values can be obtained.E_{g}、V^{ SQ}_{OC}、V^{rad}_{OC}. respectively represent the band gap E_{g} ,of the solar cell, the open circuit voltage under the Shockley-Quiser limitV^{ SQ}_{OC} , the open circuit voltage under the total radiation recombination V^{rad}_{OC}.

So what should we do to measure these three physical values including band gapE_{g} , Shockley-Quiser limit V^{ SQ}_{OC }and the open circuit voltage under the total radiation recombination V^{rad}_{OC }? Firstly, let’s write down the definitions of the three physical quantities:

In addition, with the diode model, theoretically Voc can be defined by the following formula:

Next, we use Enlitech ELCT-3010 (now Enlitech REPS perovskite photovoltaic Voc loss analysis system) to measure the external quantum efficiency of solar cell electroluminescence EQE_{EL} .

To use the perovskite open-circuit voltage loss analysis software (SQ-VLA), you need to set a name for this measurement and analysis.

Figure 10. Start-up snapshoot of perovskite open-circuit voltage loss analysis software (SQ-VLA).

After implementing the measuring data of QE-R, IVS-KA6000 and REPS, the results of the analysis and calculation are presented immediately, including the band gap , Shockley-Quiser limit , the open circuit voltage under the total radiation recombination , thermodynamic loss ΔV1, radiative recombination loss ΔV2 and non-radiative recombination loss ΔV3.

Figure 11. Snapshot of the data implement from QE-R, IVS-KA6000 and REPS.

Figure 12. SQ-VLA software shows the thermodynamic loss ΔV1, radiative recombination loss ΔV2 and non-radiative recombination loss ΔV3

Comparing the open-circuit voltage loss between the control group and the experimental group, we can clearly see whether the manipulation variable of the experimental group can effectively reduce the open-circuit voltage loss, thereby increasing the open-circuit voltage of perovskite solar cells.

Figure 13. SQ-VLA shows the comparison result of the thermodynamic loss ΔV1, radiative recombination loss ΔV2 and non-radiative recombination loss ΔV3 of control group and experimental group.

## More practical applications of the Voc-loss analysis systems

In the research on the efficiency of perovskite solar cells, we have selected several representative articles to understand how they do the loss analysis of open circuit voltage to improve the efficiency of perovskite solar cells.

Figure 14. Sep., 2021, Advance Functional Materials (IF 18.808) published a research result from Beihang University (BUAA), showing that reducing non-radiative composite loss ΔV3 can effectively improve PCE.

Although the power conversion efficiency (PCE) of 3D perovskite solar cell (PSC) has been improved to 25.5%, its poor stability is still not conducive to commercialization. Ruddlesden-Popper quasi-2D perovskites are expected to be candidates to replace traditional 3D perovskites due to their advantages of material stability and tunability. However, quasi-2D PSCs suffer its high voltage losses, resulting in PCEs still lagging behind 3D PSCs. Advance Functional Materials (IF 18.808) published a research result from Beihang University (BUAA) in September 2021. The research team uses the thermal-aged precursor solution (TAPS) to reduce the voltage loss of 2D PSC.

The research team used Enlitech’s solar simulator, QE-R quantum efficiency measurement system, FTPS Fourier transform photocurrent system and other instruments to assist in the measurement. The research results found that based on band gap≈1.60 eV (AA)2MA4Pb5I16 (n=5) quasi-2D perovskite absorber, a record open circuit voltage of 1.24 V was obtained and the PCE increased to 18.68%.

By elucidating the relationship between material properties and film quality, it is found that reducing non-radiative recombination loss, ΔVoc, and nonrad is crucial for enhancing Voc and improving PCE. Mechanistically, using heat-aging solution treatment, colloidal aggregation can be favorably induced to reduce the number of nucleation sites. Finally, high-quality quasi-2D perovskite films with compact morphology, preferential crystal orientation, and low trap density can be obtained. Also importantly, with the improvement of film quality, the thermal stability performance of PSCs is significantly improved, which is mainly attributed to the effective suppression of silver electrode corrosion caused by ion migration. This study opens up a new processing route for efficient and stable perovskite photovoltaic devices and practical energy conversion applications.

Other top journals such as Science, Nature, Energy & Environmental Science have pointed out that in order to improve the efficiency of perovskite solar cells, it is necessary to understand where the loss of open circuit voltage is mainly generated, and then measure the electroluminescence efficiency, analyze and improve non-radiative recombination losses.