504 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 1, JANUARY 2014 Analytical Modeling of Industrial-Related Silicon Solar Cells Tobias Fellmeth, Florian Clement, and Daniel Biro Abstract—Fast and accurate simulation tools are key to increas- ing our understanding of silicon-based solar cells. A lucid graphical unit interface and experimentally obtained input parameters help make these tools accessible for a wide range of users. In this pa- per, we present a fast Excel tool based on the well-known two-diode model supporting conventional and metal-wrap-through cell archi- tectures. The selective emitter approach, spatial varying emitter re- combination, and optical simulations are taken into account. A set of consistent input parameters, including the emitter recombina- tion in the passivated case, as well as the metal contacted for both idealities, are given as a function of the emitter sheet resistance. This set on input parameters is associated with industrial-related technologies for conventional and metal-wrap-through silicon solar cells. Index Terms—Emitter, metal wrap through (MWT), modeling, solar cell. I. INTRODUCTION S IMULATION of silicon solar cells is of key importance for the whole photovoltaic industry. The different approaches can be classified into three different approaches, which differ in the degree of complexity. The first approach uses 2-D and 3-D device simulations with software tools like Sentaurus [1], ATLAS [2], or Comsol [3]. A symmetric element of the device is defined and meshed in finite elements. Boundary conditions for the differential equations for holes and electrons lead to a convergent solution on these elements. Since this approach is based on fundamental device physics using the transport and continuity equations, the highest degree of accuracy can be expected. However, inherently dealing with such complex software consumes computer and labor time. The second approach uses 3-D or pseudo-3-D network sim- ulations. In the software tool SPICE [4], a mesh needs to be defined in which local diodes are linked with resistors. The physics of the minority charge carriers are described in the two- diode model by the dark saturation current densities j 01 and j 02 1 for each node. Within this approach, the spatial characteristics of a solar cell are still represented accurately in the simula- tion, yet the overall simulation procedure is less complex. Since the two-diode model is used, ray tracing is not necessary, and Manuscript received May 3, 2013; revised June 17, 2013, July 30, 2013, and August 23, 2013; accepted August 28, 2013. Date of publication September 30, 2013; date of current version December 16, 2013. The authors are with the Fraunhofer Institute for Solar Energy Systems ISE, 79110 Freiburg, Germany (e-mail: tobias.fellmeth@ise.fhg.de; Florian. clement@ise.fhg.de; Daniel.biro@ise.fhg.de). Digital Object Identifier 10.1109/JPHOTOV.2013.2281105 1 Variables using a “j ” are always current densities and from now on will be denoted as currents only. no differential equations describing the minority charge carrier transport need to be solved, thus reducing the complexity of the simulation procedure. However, resistive effects caused by the majority charge carriers are still of the distributed kind and must be modeled in accordance with the Kirchhoff rules leading also to differential equations. The last approach is referred to 0-D or 1-D modeling by using one global two-diode model with a lumped series resistance for the whole device. This approach leads to the approximation of a spatial constant junction voltage V j that, in turn, leads to a spatial constant series resistance that only depends on device geometry and electrical properties such as metal resistivity or emitter sheet resistance. Computing time of such an approach lies in the range of seconds. In this paper, the authors present an Excel-based tool named Gridmaster, for silicon solar cells using the third approach de- scribed above. The tool optimizes the front metal grid pattern of conventional solar cells exhibiting the “H-grid” pattern, as well as back contact metal wrap through (MWT) [5] solar cells. The following features are included: 1) the two-diode model; 2) graphical unit interface; 3) selective emitter structures; 4) recombination at emitter/metal interfaces; 5) modeling of concentrator solar cells. II. EXCEL TOOL GRIDMASTER A. Basic Work Principle There is a fundamental tradeoff between light shading and electrical resistance in a solar cell with a metal grid on the light facing, or front side. Two quantities describe this tradeoff: 1) the photogenerated current j ph that reaches its maximum when the metal coverage fraction F M equals zero; 2) the series resistance r s of the whole solar cell device that describes heat dissipation at an ohmic resistor, which reaches its maximum when F M equals zero. Therefore, a parameter needs to be found that relates F M to r s and j ph . The front-side 2 electrode of a conventional solar cell is based on a so-called H-pattern, which exhibits a parallel grid finger structure perpendicular to the broad busbars. Thus, the quantity of the screen-printed grid fingers n f relates to j ph = j ph (n f ) and r s = r s (n f ) and, therefore, to the conversion efficiency η of the solar cell device. A typical graph exhibiting an optimum is shown in Fig. 1. 2 Corresponds always to the illuminated side of the solar cell. 2156-3381 © 2013 IEEE