NUMERICAL ANALYSIS OF SILICON SOLAR CELLS

MARK STEVEN LUNDSTROM, Purdue University

Abstract

To develop accurate models for silicon solar cells, a mathematical description of the physical mechanisms that control the performance of these devices is required. It is also essential to employ numerical techniques in order to simulate these devices in detail. The numerical techniques must be both accurate and computationally efficient. In this thesis, a set of equations which accurately describes the physics of modern, high-efficiency silicon solar cells is formulated and solved numerically. Transport equations for use in analyzing heavily doped semiconductor devices are first considered. These transport equations describe the effects of the nonuniform band structure and the influence of Fermi-Dirac statistics, which are important in heavily doped semiconductors. Previous workers {60-62} have derived transport equations in terms of the nonuniform band structure. These equations, however, are not convenient for use in semiconductor device analysis because the band structure of heavily doped semiconductors is not well known. In this thesis, the transport equations of Marshak and van Vliet {60-62} are recast into a simple, Boltzmann-like form in which the effects associated with the nonuniform band structure and degenerate carrier concentrations are described by two parameters, the effective gap shrinkage and the effective asymmetry factor. The experimental determination of both of these parameters is also discussed. Adler's contention {70}, that some important features of semiconductor device operation can be modeled accurately by using an electrically measured effective bandgap shrinkage with an arbitrarily chosen effective asymmetry factor, is also considered. The validity of this procedure, under certain simplifying assumptions, is established. A semiconductor device is described mathematically by Poisson's equation and two current continuity equations. Using the transport equations developed in this work, these equations were solved numerically in one dimension. The accuracy of the model was tested by comparing the results of computer calculations to exact, analytical results (for certain simple cases) and to experimental results. The model was shown to accurately describe high-efficiency silicon solar cells under a wide range of operating biases and for solar concentrations that varied from 1 to 250. This model found extensive use in analyzing and designing conventional silicon solar cells. By using the computer model, we were able to explain a physical mechanism which operates to degrade the performance of BSF solar cells operated under high solar concentration. The model was also used to design cells in which the effects of this degradation were minimized. A two-dimensional numerical solar cell model was also developed. This model represents a first step toward the goal of developing a computer tool for use in analyzing and designing two-dimensional silicon solar cells. An example of the use of this program in analyzing IBC solar cells is presented.

Degree

Ph.D.

Subject Area

Electrical engineering

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