Contents lists available at ScienceDirect Solar Energy journal homepage: www.elsevier.com/locate/solener Modeling the time-dependent characteristics of perovskite solar cells Iman Moeini a , Mohammad Ahmadpour a , Amir Mosavi b,c , Naif Alharbi e , Nima E. Gorji d, ⁎ a Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran b Institute of Structural Mechanics, Bauhaus University Weimar, Weimar, Germany c Institute of Automation, Kando Kalman Faculty of Electrical Engineering, Obuda University, Budapest, Hungary d Optoelectronics Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam e School of Industrial Engineering, Umm Al-Qura University, Saudi Arabia ARTICLE INFO Keywords: Modeling Solar cells Perovskite Defect generation Time-dependent ABSTRACT We proposed two different time-dependent modeling approaches for variation of device characteristics of per- ovskite solar cells under stress conditions. The first approach follows Sah-Noyce-Shockley (SNS) model based on Shockley–Read–Hall recombination/generation across the depletion width of pn junction and the second ap- proach is based on thermionic emission model for Schottky diodes. The connecting point of these approaches to time variation is the time-dependent defect generation in depletion width (W) of the junction. We have fitted the two models with experimental data reported in the literature to perovskite solar cell and found out that each model has a superior explanation for degradation of device metrics e.g. current density and efficiency by time under stress conditions. Nevertheless, the Sah-Noyce-Shockley model is more reliable than thermionic emission at least for solar cells. 1. Introduction Time dependent models have been rarely developed for curren- t–voltage (JV) characteristics of optoelectronic devices. Time-depen- dent models have much more realistic approaches to device function and provide the observation possibility to determine the degradation/ recovery behavior of a device operating under stress conditions such as long term reverse biasing (e.g. in solar cell, sensors, and photo- detectors) (Alsari et al., 2018; Turturici et al., 2014). The currently available models are presented mainly in static mode which ignores materials and structural changes in the device such as defect generation and intermix of the adjacent layers or in-diffusion of the metallic con- tacts towards the junction. These are the detrimental process that happen by time and cause degradation in device performance. A com- prehensive model must be able to trace the device characteristics by time. We have previously developed several time-dependent theories to model the characteristics of solar cells under stress conditions (Darvishzadeh et al., 2017a; Darvishzadeh et al., 2017b). There are few other publications in the literature which propose time-dependent models for current conduction mechanisms in various devices (Turturici et al., 2017). Turturici et al. have proposed a time dependent modeling for the forward current and reverse biased currents of a photodetector based on p-CdTe (Turturici et al., 2014; Turturici et al., 2017). We will partially use their modeling approach in this paper to develop from a static JV analysis to a time dependent JV curves or at least a current vs. time approach. In their modeling, Turturici et al. have assumed that the defect generation follows an exponential trend by time in the p-type layer and negatively impacts on carrier collection at reverse biases. Although this modeling approach is partly able to explain the current density variation by time, the direct role of electric field at the metal/p- type junction is not clear. A rather parametric model is required to understand how the electron, hole, acceptor, donor defects are involved in the carrier collection under the electric-field in the depletion width of a device. We have previously applied a strong modeling approach to CdS/CdTe solar cells which devices the carrier collection to drift and diffusion currents in within and outside of depletion width, respectively (Darvishzadeh et al., 2017a; Darvishzadeh et al., 2017b). Here, we propose the model in time-dependent form for pn junction and photo- detectors based on graphene. We use graphene based devices it has attracted the attention of many researchers not only for solar cell ap- plication but also for sensors, photodetectors, LEDs, etc. over 100 pa- pers have been published last year on graphene application in per- ovskite solar cells (Son et al., 2017; Singh et al., 2018). The recent review on these hybrid devices shows a power conversion efficiency between 10% and 15% for graphene and inorganic semiconductor- based hybrid heterojunction solar cells, and 15.6% for graphene-con- taining perovskite cells. Graphene or carbon nanolayers will act as a supressing layer for shunting process. Bi et al. have designed a https://doi.org/10.1016/j.solener.2018.05.082 Received 5 May 2018; Accepted 26 May 2018 ⁎ Corresponding author. E-mail address: nimaegorji@tdt.edu.vn (N.E. Gorji). Solar Energy 170 (2018) 969–973 0038-092X/ © 2018 Elsevier Ltd. All rights reserved. T