Publication Date


Document Type


Committee Members

Amir Farajian (Committee Member), Hong Huang (Committee Member), James Menart (Advisor)

Degree Name

Master of Science in Renewable and Clean Energy Engineering (MSRCE)


While analytical models are limited in the situations that they can simulate, they are generally easier to implement than numerical models and provide a rapid view of the variables which affect a certain quantity. Analytical models are also very useful in educational situations; such as a graduate class on photovoltaics. The modeling of the interior workings of a solar cell can be complex and involved; and some of the equations can become quite lengthy. A focus of this thesis work is the derivation of the minority carrier density and minority current density equations for a p-n junction solar cell. The equations that are derived in this thesis are presented in the book The Physics of Solar Cells by Jenny Nelson. This book is currently used in the graduate Photovoltaics course being offered at Wright State University. During the offering of this class suspicions arose about the correctness of the minority carrier density equations and minority current density equations presented in this book. Thus these equations had to be checked and corrected if necessary. This is done in this thesis. These equations are derived from the proper form of the transport equations and validated against numerical results and limited case results from other analytical equations. Nelson does not present a derivation for these equations and another source that provides these equations in the same form as that shown in The Physics of Solar Cells could not be found. The Physics of Solar Cells has a rather unique formulation for these equations, in that it is more general and extensive than what other sources present. The derivation work done in this thesis confirms the suspicions of the instructor of this course and shows that errors were present in these equations. The correct form of these equations is presented in this thesis. After deriving the correct version of the minority carrier density equations and validating the corrected form against a number of published results, these equations are used to produce a large amount of survey results for GaAs solar cells. This is done by programing these equations in Microsoft Excel. Minority carrier densities are plotted for a GaAs solar cell in the dark under equilibrium conditions, in the dark with an applied voltage, under illumination where the cell is short circuited, and under illumination where the cell has an applied voltage. Surveys of the effects of the doping levels, the applied external voltage, the thickness of the p and n sides of the solar cell, the strength of the illumination on the solar cell, and the recombination speed of the minority carriers at the boundary are performed. For many of these results the minority and majority carrier densities are presented as a function of position in the cell. For the dark cases, minority and majority carriers are plotted for the p-side quasi-neutral region, the n-side quasi-neutral region, and the space charge region. For the illuminated cases carrier densities are only plotted in the quasi-neutral regions. Carrier density results are not presented for the space charge region under illuminated conditions as no analytical expressions are known to exist for this situation. Some space charge region thickness results and junction voltage results are presented for dark conditions.

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Department or Program

Department of Mechanical and Materials Engineering

Year Degree Awarded