# Influence of Interfacial Traps on the Operating Temperature of Perovskite Solar Cells

^{*}

## Abstract

**:**

## 1. Introduction

_{2}even at as low a temperature as 85 °C. Philippe et al. [11,12,13] have investigated the thermal stability of PSCs by maintaining them for 20 minutes at room temperature, 100 °C and 200 °C and observed that MAPbl3 starts to decompose into Pbl

_{2}at 100 °C. They carried out this experiment under high vacuum conditions of 10

^{−8}mbar. Also, it is found that the temperature becomes much too high at the points of creation of localized defects, which may lead to physical or chemical changes in any semiconductor device [14]. Another challenge with perovskites is that their crystal structure becomes unstable by increasing the temperature, leading to phase changes. For example, it is reported that the phase change from tetragonal to cubic can occur at around 327 K in PSCs [15,16,17]. However, methyl-ammonium (MA)-based perovskites show a higher phase stability in comparison to formamidinium (FA) [18,19]. Therefore, understanding and controlling the factors that may lead to an increase in the operating temperature of PSCs is crucial for increasing their efficiency and stability.

_{2}ETL modified with C60-SAM could effectively passivate the formation of trap states at the interfaces, which reduces the non-radiative recombination and suppresses the J-V hysteresis in PSCs thus fabricated. Thote et al. [11] have achieved efficient and stable ZnO-based PSCs using a high-working pressure sputtering technique. This technique produces higher quality ZnO films with fewer surface defects compared with conventional sputtering or sol-gel ZnO solution processes. However, the influence of passivation of the interfaces on the operating temperature which may lead to phase transition and degradation in the active layer of PSCs has not yet been clearly understood.

## 2. Methods

_{3}NH

_{3}PbI

_{3}as discussed later in the Results and Discussion section.

^{−3}s

^{−1}) is the rate of tail state recombination calculated by solving the Poisson and drift-diffusion equations [38,39,40], ${E}_{R}$ (eV) is the heat energy generated per recombination and $d$ (nm) is the active layer thickness. ${h}_{c,e-amb}$ is convection heat transfer from encapsulation surface to ambient, ${h}_{r,e-sky}$, ${h}_{r,e-ground}$ and ${h}_{r,e-sur}$ in Equation (4) are the radiation heat transfer coefficients from encapsulation surface to sky, ground and surrounding, respectively, ${T}_{amb}$ is ambient temperature, ${T}_{sky}$ is sky temperature which can be determined by ${T}_{sky}=0.0552\text{}{{T}_{amb}}^{1.5}$ [41]. ${T}_{ground}$ and ${T}_{sur}$ are ground and surrounding temperatures which are considered equal to ${T}_{amb}$.

## 3. Results and Discussions

_{3}NH

_{3}PbI

_{3}/PCBM/Al is presented here. However, first we would like to present the validation of our simulation by calculating the J-V characteristics of the above PSC considered in this paper and compare these with the experimental results measured by Kim et al. [45]. The input data required for the simulation of the J-V characteristics and operating temperature are listed in Table 1. The J-V characteristics obtained from the simulation are shown as a solid curve in Figure 5 along with the experimental results as the dotted curve. As it can be seen from Figure 5, our simulation results agree very well with the experimental ones.

_{ti}may reduce from 10

^{18}to 10

^{15}m

^{−3}(eV)

^{−1}passivating the interfaces. The operating temperature is calculated for N

_{ti}= 10

^{18}and 10

^{15}m

^{−3}(eV)

^{−1}at two different ambient temperatures of 300 K and 320 K and plotted as a function of the applied voltage ${V}_{a}$ as shown in Figure 6. According to Figure 6, for low applied voltages, ${V}_{a}\le {V}_{max}$, where ${V}_{max}$ is the voltage at the maximum power point, it is found that the (i) operating temperature remains constant and (ii) influence of the density of tail states in the interface on the temperature of the solar cell is not very significant. It may be noted that in Figure 6, the maximum voltage is ${V}_{max}\approx 0.77$ V at the ambient temperature ${T}_{amb}=300K$ and ${V}_{max}\approx 0.75$ V at ${T}_{amb}=320K$. However, at ${V}_{a}\ge {V}_{max}$, the operating temperature increases by nearly 21 K at the ${V}_{oc}$ at both the ambient temperatures of 300 K and 320 K in the PSC without the passivation of the interfaces with the higher density of tail states N

_{ti}= 10

^{18}m

^{−3}(eV)

^{−1}. This is in contrast with the passivated PSC with the lower density of tail states N

_{ti}= 10

^{15}m

^{−3}(eV)

^{−1}where the operating temperature remains nearly constant with the increase in the voltage. At the ambient temperature ${T}_{amb}$ = 300 K and applied voltage ${V}_{a}\approx $ 0.81 V, the temperature in the active layer of PSC without interface passivation increases to 327 K (red arrow), which is the temperature of phase transition in perovskite from tetragonal to cubic.

_{ti}of 10

^{18}and and 10

^{15}m

^{−3}(eV)

^{−1}in Figure 7a and b, respectively. As it can be seen in Figure 7a, for N

_{ti}= 10

^{18}m

^{−3}(eV)

^{−1}$P$ increases when x approaches the interfaces at all the applied voltages, and becomes red in colour at the interfaces, which means that it becomes high at the interfaces. This is expected because more non-radiative recombinations occur at the interfaces and hence more heat generation at the interfaces. However, according to Figure 7b for N

_{ti}= 10

^{15}m

^{−3}(eV)

^{−1}, the power generation at the interfaces is much less (blue in colour), showing much less heat generation at the interfaces due to the passivation. It may be noted that the power P plotted in Figure 7a and b is nearly independent of the ambient temperature ${T}_{amb}$.

_{ti}= 10

^{18}m

^{−3}(eV)

^{−1}and 10

^{15}m

^{−3}(eV)

^{−1}. According to Figure 8, $P$ is almost constant and close to 0 for N

_{ti}= 10

^{15}m

^{−3}(eV)

^{−1}at the interfaces, while it grows to roughly 5 W by increasing the voltage of the cell with N

_{ti}= 10

^{18}m

^{−3}(eV)

^{−1}. Therefore, it may be concluded that at an ambient temperature higher than 300 K, PSCs may degrade faster without the passivation of the interfaces if subjected to a higher applied voltage.

_{3}NH

_{3}PbX

_{3}single crystals with X = I, Br, and Cl is 0.34 ± 0.12, 0.44 ± 0.08, and 0.50 ± 0.05 $\mathrm{W}/(\mathrm{mK})$, respectively, at room temperature. By considering CH

_{3}NH

_{3}PbI

_{3}with a thickness of 200 nm and with wind velocity = 10 m/s, the Biot $\approx 2.6\times {10}^{-5}$, which is much less than 0.1. Therefore, the lumped capacitance method is effectively validated for a PSC. This implies that the temperature of the PSCs is spatially uniform at any instant, and the temperature gradient within the solar cell is negligible.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Schmager, R.; Gomard, G.; Richards, B.S.; Paetzold, U.W. Nanophotonic perovskite layers for enhanced current generation and mitigation of lead in perovskite solar cells. Sol. Energy Mater. Sol. Cells
**2019**, 192, 65–71. [Google Scholar] [CrossRef] - Prochowicz, D.; Runjhun, R.; Tavakoli, M.M.; Yadav, P.; Saski, M.; Alanazi, A.Q.; Kubicki, D.J.; Kaszkur, Z.; Zakeeruddin, S.M.; Lewiński, J.; et al. Engineering of Perovskite Materials Based on Formamidinium and Cesium Hybridization for High-Efficiency Solar Cells. Chem. Mater.
**2019**, 31, 1620–1627. [Google Scholar] [CrossRef] - Jeon, N.J.; Na, H.; Jung, E.H.; Yang, T.Y.; Lee, Y.G.; Kim, G.; Shin, H.W.; Il Seok, S.; Lee, J.; Seo, J. A fluorene-terminated hole-transporting material for highly efficient and stable perovskite solar cells. Nat. Energy
**2018**, 3, 682–689. [Google Scholar] [CrossRef] - Yang, D.; Yang, R.; Wang, K.; Wu, C.; Zhu, X.; Feng, J.; Ren, X.; Fang, G.; Priya, S.; Liu, S. High efficiency planar-type perovskite solar cells with negligible hysteresis using EDTA-complexed SnO
_{2}. Nat. Commun.**2018**, 9, 3239. [Google Scholar] [CrossRef] [PubMed] - Vidal, S.; Izquierdo, M.; Filippone, S.; Fernández, I.; Akin, S.; Seo, J.Y.; Zakeeruddin, S.M.; Grätzel, M.; Martín, N. Site-selective Synthesis of β-[70]PCBM-like Fullerenes: Efficient Application in Perovskite Solar Cells. Chem. A Eur. J.
**2019**, 25, 3224–3228. [Google Scholar] [CrossRef] [PubMed] - Oxford PV Perovskite Solar Cell Achieves 28% Efficiency. Available online: https://www.oxfordpv.com/news/oxford-pv-perovskite-solar-cell-achieves-28-efficiency (accessed on 20 December 2018).
- Milot, R.L.; Eperon, G.E.; Snaith, H.J.; Johnston, M.B.; Herz, L.M. Temperature-Dependent Charge-Carrier Dynamics in CH
_{3}NH_{3}PbI_{3}Perovskite Thin Films. Adv. Funct. Mater.**2015**, 25, 6218–6227. [Google Scholar] [CrossRef] - Zhang, H.; Qiao, X.; Shen, Y.; Wang, M. Effect of temperature on the efficiency of organometallic perovskite solar cells. J. Energy Chem.
**2015**, 24, 729–735. [Google Scholar] [CrossRef] - Mehdizadeh-Rad, H.; Singh, J. Influence of Urbach Energy, Temperature, and Longitudinal Position in the Active Layer on Carrier Diffusion Length in Perovskite Solar Cells. ChemPhysChem
**2019**, in press. [Google Scholar] [CrossRef] - Conings, B.; Drijkoningen, J.; Gauquelin, N.; Babayigit, A.; D’Haen, J.; D’Olieslaeger, L.; Ethirajan, A.; Verbeeck, J.; Manca, J.; Mosconi, E.; et al. Intrinsic Thermal Instability of Methylammonium Lead Trihalide Perovskite. Adv. Energy Mater.
**2015**, 5, 1500477. [Google Scholar] [CrossRef] - Thote, A.; Jeon, I.; Lin, H.S.; Manzhos, S.; Nakagawa, T.; Suh, D.; Hwang, J.; Kashiwagi, M.; Shiomi, J.; Maruyama, S.; et al. High-Working-Pressure Sputtering of ZnO for Stable and Efficient Perovskite Solar Cells. ACS Appl. Electron. Mater.
**2019**, 1, 389–396. [Google Scholar] [CrossRef] - Kim, H.S.; Seo, J.Y.; Park, N.G. Material and Device Stability in Perovskite Solar Cells. ChemSusChem
**2016**, 9, 2528–2540. [Google Scholar] [CrossRef] [PubMed] - Philippe, B.; Park, B.W.; Lindblad, R.; Oscarsson, J.; Ahmadi, S.; Johansson, E.M.J.; Rensmo, H. Chemical and Electronic Structure Characterization of Lead Halide Perovskites and Stability Behavior under Different Exposures—A Photoelectron Spectroscopy Investigation. Chem. Mater.
**2015**, 27, 1720–1731. [Google Scholar] [CrossRef] - Silverman, T.J.; Deceglie, M.G.; Sun, X.; Garris, R.L.; Alam, M.A.; Deline, C.; Kurtz, S. Thermal and Electrical Effects of Partial Shade in Monolithic Thin-Film Photovoltaic Modules. IEEE J. Photovolt.
**2015**, 5, 1742–1747. [Google Scholar] [CrossRef] - Quarti, C.; Mosconi, E.; Ball, J.M.; D’Innocenzo, V.; Tao, C.; Pathak, S.; Snaith, H.J.; Petrozza, A.; De Angelis, F. Structural and optical properties of methylammonium lead iodide across the tetragonal to cubic phase transition: implications for perovskite solar cells. Energy Environ. Sci.
**2016**, 9, 155–163. [Google Scholar] [CrossRef] - Baikie, T.; Fang, Y.; Kadro, J.M.; Schreyer, M.; Wei, F.; Mhaisalkar, S.G.; Graetzel, M.; White, T.J. Synthesis and crystal chemistry of the hybrid perovskite (CH
_{3}NH_{3})PbI_{3}for solid-state sensitised solar cell applications. J. Mater. Chem. A**2013**, 1, 5628–5641. [Google Scholar] [CrossRef] - Whitfield, P.S.; Herron, N.; Guise, W.E.; Page, K.; Cheng, Y.Q.; Milas, I.; Crawford, M.K. Corrigendum: Structures, Phase Transitions and Tricritical Behavior of the Hybrid Perovskite Methyl Ammonium Lead Iodide. Sci. Rep.
**2017**, 7, 42831. [Google Scholar] [CrossRef] [PubMed] - Stoumpos, C.C.; Malliakas, C.D.; Kanatzidis, M.G. Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. Inorg. Chem.
**2013**, 52, 9019–9038. [Google Scholar] [CrossRef] - Thote, A.; Jeon, I.; Lee, J.W.; Seo, S.; Lin, H.S.; Yang, Y.; Daiguji, H.; Maruyama, S.; Matsuo, Y. Stable and Reproducible 2D/3D Formamidinium-Lead-Iodide Perovskite Solar Cells. ACS Appl. Energy Mater.
**2019**, 2, 2486–2493. [Google Scholar] [CrossRef] - Ma, F.J.; Liu, H.; Liao, B.; Chen, J.; Du, Z.; Samudra, G.S.; Aberle, A.G.; Hoex, B.; Peters, I.M. Impact of Auger recombination parameterisations on predicting silicon wafer solar cell performance. J. Comput. Electron.
**2014**, 13, 647–656. [Google Scholar] [CrossRef] - Marinova, N.; Valero, S.; Delgado, J.L. Organic and perovskite solar cells: Working principles, materials and interfaces. J. Colloid Interface Sci.
**2017**, 488, 373–389. [Google Scholar] [CrossRef] - Bi, D.; Tress, W.; Dar, M.I.; Gao, P.; Luo, J.; Renevier, C.; Schenk, K.; Abate, A.; Giordano, F.; Correa Baena, J.P.; et al. Efficient luminescent solar cells based on tailored mixed-cation perovskites. Sci. Adv.
**2016**, 2. [Google Scholar] [CrossRef] [PubMed] - Marinova, N.; Tress, W.; Humphry-Baker, R.; Dar, M.I.; Bojinov, V.; Zakeeruddin, S.M.; Nazeeruddin, M.K.; Grätzel, M. Light Harvesting and Charge Recombination in CH
_{3}NH_{3}PbI_{3}Perovskite Solar Cells Studied by Hole Transport Layer Thickness Variation. ACS Nano**2015**, 9, 4200–4209. [Google Scholar] [CrossRef] [PubMed] - Wetzelaer, G.J.A.; Scheepers, M.; Sempere, A.M.; Momblona, C.; Ávila, J.; Bolink, H.J. Trap-Assisted Non-Radiative Recombination in Organic-Inorganic Perovskite Solar Cells. Adv. Mater.
**2015**, 27, 1837–1841. [Google Scholar] [CrossRef] [PubMed] - Wu, X.; Trinh, M.T.; Niesner, D.; Zhu, H.; Norman, Z.; Owen, J.S.; Yaffe, O.; Kudisch, B.J.; Zhu, X.Y. Trap States in Lead Iodide Perovskites. J. Am. Chem. Soc.
**2015**, 137, 2089–2096. [Google Scholar] [CrossRef] [PubMed] - Cui, P.; Fu, P.; Wei, D.; Li, M.; Song, D.; Yue, X.; Li, Y.; Zhang, Z.; Li, Y.; Mbengue, J.M. Reduced surface defects of organometallic perovskite by thermal annealing for highly efficient perovskite solar cells. RSC Adv.
**2015**, 5, 75622–75629. [Google Scholar] [CrossRef] - Sherkar, T.S.; Momblona, C.; Gil-Escrig, L.; Ávila, J.; Sessolo, M.; Bolink, H.J.; Koster, L.J.A. Recombination in Perovskite Solar Cells: Significance of Grain Boundaries, Interface Traps, and Defect Ions. ACS Energy Lett.
**2017**, 2, 1214–1222. [Google Scholar] [CrossRef] [PubMed] - Shao, Y.; Xiao, Z.; Bi, C.; Yuan, Y.; Huang, J. Origin and elimination of photocurrent hysteresis by fullerene passivation in CH
_{3}NH_{3}PbI_{3}planar heterojunction solar cells. Nat. Commun.**2014**, 5, 5784. [Google Scholar] [CrossRef] [PubMed] - Tress, W.; Marinova, N.; Moehl, T.; Zakeeruddin, S.M.; Nazeeruddin, M.K.; Grätzel, M. Understanding the rate-dependent J-V hysteresis, slow time component, and aging in CH
_{3}NH_{3}PbI_{3}perovskite solar cells: the role of a compensated electric field. Energy Environ. Sci.**2015**, 8, 995–1004. [Google Scholar] [CrossRef] - Wei, J.; Zhao, Y.; Li, H.; Li, G.; Pan, J.; Xu, D.; Zhao, Q.; Yu, D. Hysteresis Analysis Based on the Ferroelectric Effect in Hybrid Perovskite Solar Cells. J. Phys. Chem. Lett.
**2014**, 5, 3937–3945. [Google Scholar] [CrossRef] - Bergmann, V.W.; Weber, S.A.L.; Javier Ramos, F.; Nazeeruddin, M.K.; Grätzel, M.; Li, D.; Domanski, A.L.; Lieberwirth, I.; Ahmad, S.; Berger, R. Real-space observation of unbalanced charge distribution inside a perovskite-sensitized solar cell. Nat. Commun.
**2014**, 5, 5001. [Google Scholar] [CrossRef] - Ansari, M.I.H.; Qurashi, A.; Nazeeruddin, M.K. Frontiers, opportunities, and challenges in perovskite solar cells: A critical review. J. Photochem. Photobiol. C Photochem. Rev.
**2018**, 35, 1–24. [Google Scholar] [CrossRef] - Snaith, H.J.; Abate, A.; Ball, J.M.; Eperon, G.E.; Leijtens, T.; Noel, N.K.; Stranks, S.D.; Wang, J.T.W.; Wojciechowski, K.; Zhang, W. Anomalous Hysteresis in Perovskite Solar Cells. J. Phys. Chem. Lett.
**2014**, 5, 1511–1515. [Google Scholar] [CrossRef] [PubMed] - Wei, X.; Wang, X.; Jiang, H.; Huang, Y.; Han, A.; Gao, Q.; Bian, J.; Liu, Z. Numerical simulation and experimental validation of inverted planar perovskite solar cells based on NiOx hole transport layer. Superlattices Microstruct.
**2017**, 112, 383–393. [Google Scholar] [CrossRef] - Li, G.; Liu, L.; Wei, F.; Xia, S.; Qian, X. Recent Progress in Modeling, Simulation, and Optimization of Polymer Solar Cells. IEEE J. Photovolt.
**2012**, 2, 320–340. [Google Scholar] [CrossRef] - Incropera, F.P.; Dewitt, D.P. Fundamentals of Heat and Mass Transfer; Wiley: Hoboken, NJ, USA, 2007; p. A-5. [Google Scholar]
- Cheacharoen, R.; Rolston, N.; Harwood, D.; Bush, K.A.; Dauskardt, R.H.; McGehee, M.D. Design and understanding of encapsulated perovskite solar cells to withstand temperature cycling. Energy Environ. Sci.
**2018**, 11, 144–150. [Google Scholar] [CrossRef] - Rad, H.M.; Zhu, F.; Singh, J. Profiling exciton generation and recombination in conventional and inverted bulk heterojunction organic solar cells. J. Appl. Phys.
**2018**, 124, 083103. [Google Scholar] [CrossRef] - Kirchartz, T.; Pieters, B.E.; Kirkpatrick, J.; Rau, U.; Nelson, J. Recombination via tail states in polythiophene: fullerene solar cells. Phys. Rev. B
**2011**, 83, 115209. [Google Scholar] [CrossRef] - Mehdizadeh-Rad, H.; Singh, J. Combined influence of Urbach’s tail width energy and mobility of charge carriers on the photovoltaic performance of bulk heterojunction organic solar cells. J. Mater. Sci.: Mater. Electron.
**2019**, 30, 10064–10072. [Google Scholar] [CrossRef] - Adelard, L.; Pignolet-Tardan, F.; Mara, T.; Lauret, P.; Garde, F.; Boyer, H. Sky temperature modelisation and applications in building simulation. Renew. Energy
**1998**, 15, 418–430. [Google Scholar] [CrossRef] - Rad, H.M.; Ameri, M. Energy and exergy study of unglazed transpired collector-2stage. Sol. Energy
**2016**, 132, 570–586. [Google Scholar] [CrossRef] - McAdams, W.H. Heat transmission; Mcgraw-Hill Book Company, Inc.: London, UK, 1954; pp. 165–184. [Google Scholar]
- Ullbrich, S.; Fischer, A.; Tang, Z.; Ávila, J.; Bolink, H.J.; Reineke, S.; Vandewal, K. Electrothermal Feedback and Absorption-Induced Open-Circuit-Voltage Turnover in Solar Cells. Phys. Rev. Appl.
**2018**, 9, 051003. [Google Scholar] [CrossRef] [Green Version] - Kim, K.; Jung, B.; Kumar, N.; Eom, Y.; Kim, W. Modulation of light absorption by optical spacer in perovskite solar cells. Phys. Status Solidi (RRL) Rapid Res. Lett.
**2016**, 10, 592–595. [Google Scholar] [CrossRef] - Heiderhoff, R.; Haeger, T.; Pourdavoud, N.; Hu, T.; Al-Khafaji, M.; Mayer, A.; Chen, Y.; Scheer, H.C.; Riedl, T. Thermal Conductivity of Methylammonium Lead Halide Perovskite Single Crystals and Thin Films: A Comparative Study. J. Phys. Chem. C
**2017**, 121, 28306–28311. [Google Scholar] [CrossRef]

**Figure 1.**Schematic of heat transfer mechanisms in an illuminated solar cell: yellow arrows show incident solar power, orange arrow represents heat generation due to non-radiative recombination, blue arrows represent heat loss to the ambient air due to convection and black arrows represent heat loss due to radiation.

**Figure 2.**Division of the active layer of a PSC into meshes considered in the simulation. A distance of 5 nm from A: hole transport layer (HTL) and A: electron transport layer (ETL) interfaces into the active layer has been considered as the main areas of non-radiative recombination.

**Figure 5.**The $J-V$ characteristics of a PSC of structure Glass/PEDOT: PSS/CH

_{3}NH

_{3}PbI

_{3}/PC60BM/Al obtained from our simulation (solid curve) and from experiment [45] (dotted curve) to check the validity of our simulation.

**Figure 6.**The operating temperature in the active layer plotted as a function of the applied voltage at two ambient temperatures of 300 K and 320 K.

**Figure 7.**The contour plot of heat generation rate due to the non-radiative recombination as a function of position x in the active layer and applied voltage ${V}_{a}$ with (

**a**) N

_{ti}= 10

^{18}and (

**b**) N

_{ti}=10

^{15}m

^{−3}(eV)

^{−1}.

**Figure 8.**The total heat generation rate ($P$ in W) due to the non-radiative recombination through the active layer as a function of the applied voltage ${V}_{a}$.

**Table 1.**Input parameters used for simulation in this paper [9].

Parameter | Value |
---|---|

${\epsilon}_{c}$ | 0.9 |

$Ir$$\left({\mathrm{wm}}^{-2}\right)$ | 1000 |

$U$ (m/s) | 0.1 |

${T}_{amb}$ ($K$) | 300 |

$\alpha $ | 0.6 |

${E}_{g}$ (eV) | 1.5 |

$d\left(\mathrm{nm}\right)$ | $200$ |

${N}_{c}$, ${N}_{v}$ (${\mathrm{m}}^{-3})$ | ${10}^{26}$ |

${N}_{ti}$ (density of tail state at interface) ((${\mathrm{m}}^{-3}{\left(\mathrm{eV}\right)}^{-1}$) | ${10}^{15}$ |

${N}_{ta}$ (density of tail state in the active layer) $({\mathrm{m}}^{-3}{\left(\mathrm{eV}\right)}^{-1}$) | ${10}^{14}$ |

${\mu}_{n}\left({\mathrm{m}}^{2}{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}\right)$ | $0.5\times {10}^{-4}$ |

${\mu}_{p}\left({\mathrm{m}}^{2}{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}\right)$ | $0.5\times {10}^{-4}$ |

${\beta}_{n}^{0}$ (${\mathrm{cm}}^{3}{\mathrm{s}}^{-1})$ | 2.5 $\times {10}^{-10}$ |

${\beta}_{p}^{0}$ (${\mathrm{cm}}^{3}{\mathrm{s}}^{-1})$ | 5 $\times {10}^{-10}$ |

${E}_{Uc}={E}_{Uv}$$\left(\mathrm{meV}\right)$ | 45 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mehdizadeh-Rad, H.; Singh, J.
Influence of Interfacial Traps on the Operating Temperature of Perovskite Solar Cells. *Materials* **2019**, *12*, 2727.
https://doi.org/10.3390/ma12172727

**AMA Style**

Mehdizadeh-Rad H, Singh J.
Influence of Interfacial Traps on the Operating Temperature of Perovskite Solar Cells. *Materials*. 2019; 12(17):2727.
https://doi.org/10.3390/ma12172727

**Chicago/Turabian Style**

Mehdizadeh-Rad, Hooman, and Jai Singh.
2019. "Influence of Interfacial Traps on the Operating Temperature of Perovskite Solar Cells" *Materials* 12, no. 17: 2727.
https://doi.org/10.3390/ma12172727