A Simplified Approach to Solar Cell Modeling
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A SIMPLIFIED APPROACH TO SOLAR CELL MODELING RICHARD S. CRANDALL*, JEFFREY KALINA AND ALAN DELAHOY, Chronar Corporation, International Corporate Center, Princeton NJ ABSTRACT Procedures for analyzing hydrogenated amorphous silicon p-i-n solar cells are presented. Two closed form expressions, each containing a single unknown i layer transport parameter, are adequate to describe the light-intensity and temperature dependence of the current-voltage curve and photocapacitance for the majority of situations. Excellent agreement between theory and experiment is obtained. INTRODUCTION There are two approaches to amorphous silicon solar cell modeling. One is to simulate cell behavior by solving the complete transport equations on a computer[1]. The other is to make approximate solutions of these equations that have restricted domains of application. The latter approach (the Regional Approximation[2]) although sacrificing accuracy, retains the essential physics and is much easier to use. In fact the ease of use makes the approach useful for obtaining rapid feedback that can guide optimization of cell deposition parameters. The Regional Approximation has been found quite useful in modeling p-i-n cells in which the electric field can be approximated as nearly uniform across the i layer[3]. This is usually the case with thin, high-quality cells. In this situation a simple expression for the photocurrent (Jph) containing a single unknown parameter, gives excellent agreement with experiment[3,4]. This parameter, the collection length (Ic) varies linearly with the electric field across the i layer. It is defined as the sum of the mobility-lifetime products of holes and electrons times the electric field[3]. Under uniformly absorbed light[3] the current is Jph = Jo (Ic/L) [ 1-exp( -Lc)]
(1)
where Jo =eGL is the current when all the photocarriers are collected, L is the i layer thickness, and G is the generation rate of electron-hole pairs. Once Ic has been determined using Eq. (1), the current and fill factor can be obtained for white light illumination using a more complex expression[3]. In certain situations, most notably with thick i layers, at low temperature, or after light soaking, this simple,collection length expression agrees with experiment only when the voltage across the i layer is large. It is the purpose of this article to explain the failure of the uniform field model under certain conditions, and compare an alternative model[5] with measurements on p-i-n cells. The collection length expression (1) does not apply with a low voltage drop across the i layer because photo-generated space charge causes the electric field to become nonuniform. Under illumination, the free and shallow-trapped charge drifts in the applied field toward the doped layers: holes toward the p layer and electrons toward the n layer. This screens the field resulting in a high field near the p-i and n-i interfaces and a lower field in the interior of the cell. In the low-field region, the recombination rate is nearly equal to the generation rate
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