This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE JOURNAL OF PHOTOVOLTAICS 1 Two-Dimensional Model for Perovskite Nanorod Solar Cells: A Dark Case Study Nouran M. Ali , Tamer A. Ali, and Nadia H. Rafat, Senior Member, IEEE Abstract—Nanorod geometry has witnessed a massive focus in the past few years for enhancing the solar cells performance. It improves the cell efficiency because of the carrier transport perpendicular to light absorption directions. Perovskite materials, such as the methylammonium lead iodide also have attracted great attention because of the low cost, simple manufacture process, and good optical properties. These advantages of both nanorod structures and perovskite materials imply that PNSC is a very promising candidate in energy harvesting applications. This in- creases the demand for accurate and fast models for the analysis and for the optimization of these cells. In this article, we present an analytical model for nanorod solar cells. The model solves the semi- conductor equations (Poisson’s equation and continuity equations) in two-dimensional cylindrical coordinates. It is based on using the conformal mapping theory as an approximation for potential and electric field estimation. It also uses separation of variables process in solving the two-dimensional continuity equation for both radial and axial directions. The analytical model was applied on a TiO 2 / perovskite / spiro-MeOTAD cell to produce the dark current. The results of this model were compared with that of a numerical finite element model and achieved good matching. Index Terms—Conformal mapping, continuity equations, perovskite, photovoltaic, radial structure, Runge–Kutta method. I. INTRODUCTION I N THE past few years, perovskite nanorod solar cells (PNSC) was considered a high topic in the solar energy harvesting research [1]. Nanorod geometry, in which the light is absorbed in the axial direction and the carriers are collected in the radial direction, allows an effective optical absorption, and simultane- ous good collection of generated carriers [2]. Although silicon is considered the dominant material in photovoltaic solar cells with the record efficiency of 26.6% [3]–[5], perovskite solar cells (PSCs) had a rapid increase in efficiency that makes it a very promising choice [6]–[9]. As shown in Fig. 1, the efficiency of PSC started from 3.8% in 2009 [6] that reaches 24.2% in 2019 [1] with a predicted efficiency limit of 31% [7]. Manuscript received July 23, 2019; revised September 4, 2019; accepted September 6, 2019. (Corresponding author: Nouran M. Ali.) N. M. Ali and N. H. Rafat are with the Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt (e-mail: eng.nouranmohamed@gmail.com; nhrafat@ieee.org). T. A. Ali is with the Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University 12613, Giza, Egypt, and also with the Zewail City of Science and Technology, Giza 12578, Egypt (e-mail: tali@zewailcity.edu.eg). Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JPHOTOV.2019.2940852 Fig. 1. Power conversion efficiency versus years for PSC and Si solar cells. It is worthy to be mentioned that in 2019, silicon / perovskite tandem cell achieved an efficiency of 27.3% [10] The general chemical formula for perovskite compounds is ABX 3 , where “A” and “B” are two cations of very different sizes, and X is an anion that bonds to both [11]. Nanorods geometry enhances the performance of organic cells [12], and inorganic cells [13], [14]. For silicon nanowire cells, improvement in external quantum efficiency and absorp- tion efficiency were observed experimentally [15], analytically [16], and numerically when compared with conventional planar p-i-n thin-film Si solar cells [17]. Analytical modeling is a very efficient method to estimate solar cell performance. It concerns with the basic principles and equations that governs the nanorod solar cells (NRSC). Although perovskite cells are configured similar to the conventional solar cells, their operations are unique and require new models for cell characterization, and optimization [18]. Analytical models for nanorod structures started in 2005. Kayes and Atwater [16] showed analytically that extremely large efficiency enhancement (from 1.5% to 11%) for silicon cells can be achieved by applying the radial geometry. Then, in 2012, another analytical model was developed by Petrosyan et al. [19], where they calculated the potential distribution, and derived expressions to compute the depletion region width and capacitance. In 2014, other studies presented an analytical model based on Green’s function theory to calculate the current density, open circuit voltage, fill factor, and conversion efficiency [20], [21]. The use of Green’s function reduced the need for uniform 2156-3381 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.