ICECE 2013 , Benghazi _ Libya, 26-28 March 2013 1 | Page Computer simulation on solving Poisson’s equation for the silicon solar cell Ala Khalaf Jehad Physics department, Faculty of Science, Benghazi University P.O.Box 9480, Benghazi, Libya akjabed13@yahoo.com Ibrahim Hamammu Physics department, Faculty of Science, Benghazi University P.O.Box 9480, Benghazi, Libya Abstract The numerical solution of Poisson and continuity equations of the solar cell is among the most accurate methods and fastest ways to study its characteristics in order to determine its performance, efficiency and investigate how to improve them. One of these equations, which will determine the cell behavior is voltage, electric field, electric charge density and density of free carriers inside the solar cell. All of these can be done by solving Poisson equation. This equation is solved here for different donor and acceptor concentrations. Index terms : Silicon Solar cell, Simulation, poisson equation I. INTRODUCTION: With global energy demands reaching very high levels on one side, and a very limited rapidly decreasing non-renewable energy sources, the need for a sustainable renewable source of energy emerges. The solar energy is the most promising sustainable renewable source of energy, that can meet all future demands. The sun that illuminates our planet and supplying it by more than 800 times the global current energy consumption [1]. Photovoltaic cell is the most common way to convert the solar energy directly to electric energy. The main problem that obstacle advances in this technology is the low efficiency of the solar cell, in which the commercial solar cells efficiency about 17% at maximum. Some researchers announce the achievement of 25% efficiency for single crystalline solar cells[2]. Our study will focus on solving one of the two equations involved in govern the device. That is the numerical solution of the Poisson’s equation, which describe the potential at each point inside the device. II. THEORY Solar cell can be described by Semiconductor equations. These equations describe the behavior of charge carriers under the influence of an electric field or light in the case of solar cells. One of these equations is the Poisson equation, this equation relates the voltage gradient of space charge density. Which can be written in one dimension as: ) ( ) ( ) ( 2 2          D A N N p n q dx x dE dx x d   (1) Where  is electrostatic potential, E Electric field. q electric charge,  permittivity of the semiconductor, n,p are free carrier concentrations at equilibrium and A N , D N are acceptor and donor carrier concentration. This equation can be solved numerically by imposing that the conditions are stable and the number of charge carriers inside and outside semiconductor are fixed [2,3]. For stability and high precision arithmetic in the context of the one-dimensional case, two important elements must be identified, the mish size of grid  and time step  t. Which are subjected to the following conditions [4]. (1) The mesh size x is limited by the Debye length L D . Figure 1. np junction of solar cell