Extraction of diode parameters of silicon solar cells under high illumination conditions
Graphical abstract
We have developed an analytical method to determine the diode parameters of concentrator solar cells under high illumination conditions. The determined values of diode parameters have been used to compute the theoretical values of performance parameters. The computed values of the open circuit voltage, curve factor, and efficiency obtained using diode parameters determined with this method showed good agreement (<2% discrepancy) with their experimental values in the temperature range 298–323 K.
Introduction
The J–V characteristics of a p-n junction silicon solar cell based on a single diode model under a steady state in the IVth quadrant are described by the following equation [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20].where VT = kT/q, Jph = light generated current density, q = electronic charge, k = Boltzmann’s constant, and T = operating temperature of the solar cell.
There are several losses in the solar cells that affect the short circuit current density Jsc, open circuit voltage Voc, curve factor CF, and efficiency η of the cells. The parameters Jsc, Voc, CF, and η are referred as performance parameters of the solar cells [21]. The diode parameters (i.e. shunt resistance Rsh, series resistance Rs, diode ideality factor n, and reverse saturated current density J0) control the J–V characteristics of a solar cell at any given intensity of illumination and operating temperature of the solar cells.
The performance of as solar cell is monitored through the four performance parameters of the cell but the diode parameters dictate the values of the performance parameters at a given intensity of illumination and temperature. In fact, the diode parameters represent the different types of loss mechanisms that affect the performance of solar cells. There are four diode parameters based on the single diode model, whereas there are six diode parameters based on the double diode model. The two additional diode parameters in the double diode model are due to recombination in the space charge region. Most often, however, under normal illumination conditions, a single diode model, with the four diode parameters, adequately describes the functioning of the solar cells because of negligible recombination in the space charge region [8], [22], [23].
A low value of Rsh is due to a conductive path across the p-n junction and/or the edge of the solar cells. The Rsh value can affect the Voc, CF, and η of the solar cells. A lower value of Rsh indicates more shunting loss and gives lower values of Voc, CF, and η of the solar cells. Rs is the sum of the resistances of the front and back metallic contacts, the contact resistances of the metallic contact with the front and back surfaces, and the resistance of the semiconductor material. The value of n indicates the recombination in the bulk space charge regions and at the surfaces of the solar cells. A higher value of n gives a lower CF value.
However, the J0 value is also indicative of the recombination in bulk semiconductor materials and at the surfaces of solar cells. It decisively affects Voc of solar cells. A higher J0 value results in a lower Voc value, and thereby a lower value of η.
Determination of diode parameters has been studied by a number of groups [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [24]. Generally, most of the suggested methods [7], [17], [18] determine the value of Rsh by using the slope of the illuminated I–V curve at a short circuit condition. Some of the methods evaluate the value of Rs with measurements of illuminated I–V characteristics at one [7], [10], [11] two [12] or many [6], [13] intensities of illumination. Singh and Singh [10] used the values of illuminated current (IL), voltage (Vm) and current (Im) at the maximum power point to evaluate Rs. In their method [10] the value of n was assumed to fall between 2.5 and 3.0. It is thus necessary to assume the value of n or apply some other method to find the value. El-Adawi and Al-Nuaim [11] determined the values of Rsh and Rs using a single I–V curve. In this method it is also necessary to find the values of n and J0. Some methods use dark I–V characteristics [14], while others utilize both the dark and illumination I–V characteristics [15] to determine the value of Rs. Rajkanan and Shewchun [15] used the dark diode voltage and the Voc values corresponding to each short circuit current (Isc) at different illumination intensities for evaluation of Rs. Priyanka et al. [7] determined the value of Rs using the I, V values in the 3rd and 4th quadrants along withRsh, n, and I0 (reverse saturation current) of the cells. This method [7] gives different values of Rs at different points on the I–V curve. In this case [7] the value of Rs varies with the voltage applied across the p-n junction of the solar cells. Priyanka et al.’s method [7] hence fails to determine the accurate single value of Rs that justifies the whole illuminated I–V curve at a given intensity of illumination. Del Cueto [6] determined the value ofRs using the variation of slope at an open circuit condition with Jsc values. Some methods [7], [16] use Isc–Voc characteristics to determine the values of n and I0 of the solar cells. Khan et al. [17] used the values of Isc and Voc, slopes at short circuit and open circuit conditions at different illumination intensities in short spans of intensity to evaluate the values of Rsh, Rs, n, and I0 of a solar cell. Phang et al. [18] used single I–V characteristics to determine all four diode parameters of solar cells at a given intensity of illumination. Their method [18], however, sometimes yields a negative value of Rs [19]. Picciano [20] determined the values of Rs, n, and I0 using the values of Isc, Voc, Im, and Vm. He [20] assumed infinite Rsh to determine the values ofRs, n, and I0. Hence, for low values of Rsh, this method is not able to determine the accurate diode parameter values.
The cost of solar cells can be reduced by enhancing their performance (η). The η of solar cells can be enhanced by using concentrated sunlight (under high illumination conditions). Concentrated solar cells are designed to operate under illumination greater than 1 sun. For application of concentrator solar cells, the incident intensity of illumination is increased by focusing the light using optical elements such that a high intensity light beam shines the surface of the solar cells with small area. Concentrators have several potential advantages over 1 sun in terms of enhancing the efficiency and hence allowing lower cost. The Jsc value of a solar cell depends linearly on the intensity of illumination. However, this effect does not enhance the η value, since the incident power also increases linearly with the intensity of illumination. The Voc value of solar cells increases logarithmically with the intensity of illumination, resulting in enhancement of η. It is therefore important to determine the diode parameters to ascertain the actual performance of concentrator solar cells under high illumination conditions.
Most of the above methods are not suitable at high illumination levels because the diode parameters are not constant according to the intensity of illumination. Some numerical or curve fitting techniques have also been applied to extract all the diode parameters from a single I–V curve obtained under different illumination conditions [9], [25], [26]. Each of these curve fitting or numerical methods [9], [25], [26] uses a single I–V curve and requires special computational knowledge to determine the values of all the diode parameters of a solar cell [17]. Chan et al. [19] compared an analytical method with curve fitting and iterative methods. They [19] found that the analytical method yielded more accurate values of the diode parameters than the curve fitting and iterative methods. Khan et al. [27] investigated the variation of the values of diode parameters with intensity of illumination in an illumination range of 15–180 mW/cm2. They [27] found that the values of the diode parameters vary with the intensity of illumination. This method [27] uses many I–V curves and gives more accurate diode parameter values than the method using a single I–V curve under normal illumination conditions [28]. It was thus shown that methods that use a single I–V curve only provide accurate values of diode parameters under high illumination conditions [29]. Hamdy [29] used the slope values at an open circuit condition and Isc from a single I–V curve to determine the value of Rs at high illumination conditions. Most of the aforementioned methods are not applicable to determine the diode parameters under high illumination conditions.
In this work, we have developed a new analytical method to extract the diode parameters of concentrator silicon solar cells that is applicable at high illumination conditions. This method is based on single exponential models that uses the slope (dV/dJ) at short circuit (Rsc) and open circuit (Roc) conditions, Jsc, Voc, current density at maximum power point (Jm), and voltage at maximum power point (Vm). The value of Rsc is used to compute the value of Rsh. The values of Roc, Jsc, Voc, Jm, and Vm are used to extract the values of Rs, n, and J0. At high illumination conditions, the methods based on a single I–V curve are more convenient than the methods based on many I–V curves, because there is a very small change of Roc with increased intensity of illumination. In contrast, there is a fast change in the diode parameters at high illumination conditions. This method is thus applied to concentrator silicon solar cells under high illumination conditions. This method makes it possible to accurately determine all the diode parameters of silicon solar cells at higher intensity of illumination at different temperatures and under different illumination conditions. Most concentrator solar cells operate at temperature more than 298 K, and we determined the diode parameters at different temperatures in a temperature range of 298–323 K. We also investigated the variation of the diode and performance parameters with temperature under high illumination conditions.
Section snippets
Theoretical
At a short circuit condition (V = 0, J = −Jsc), Eq. (1) becomes
And at an open circuit condition (V = Voc, J = 0), it is
At maximum power point (V = Vm, J = −Jm) equation (1) becomes
From Eqs. (2), (3), also applying condition Rs ≪ Rsh [13], [14], we obtain
Similarly, from Eqs. (3), (4), we get
Differentiating equation (1) with respect to V, assuming the diode
Cell fabrication
For the present study, we have used mono-crystalline silicon (c-Si) solar cells for measurement of illuminated J–V characteristics. These cells were fabricated using p-type, FZ, 〈1 0 0〉 oriented c-Si wafers of ∼200 μm thickness and 1 Ω cm base resistivity. After cleaning the wafers in hot de-ionized water (DIW), damage removal was performed in a 20% NaOH solution at 353 K. After damage removal, texturization was carried out in a solution of 2% NaOH and 20% isopropyl alcohol (IPA) in DIW at 353 K. The
Result and discussion
We have developed a method to determine the values of Rsh, Rs, n, and J0 of a concentrator silicon solar cell under high illumination conditions using Eqs. (11), (16), (17), (18). The validity of the assumptions herein has been reported elsewhere [17]. In this study, we have used the values of Jsc, Voc, Rsc, Roc, Jm, and Vm of a single illuminated J–V curve of crystalline silicon (c-Si) solar cells under high illumination conditions. These parameters are defined in Fig. 1. This method has been
Conclusion
We have developed an analytical method to extract the values of diode parameters of concentrator c-Si solar cells using values of Jsc, Voc, Rsc, Roc, Jm, and Vm under high illumination conditions and at different operating temperatures. Eqs. (11), (16), (17), (18) have been combined to determine the values of Rsh, Rs, n, and J0 of concentrated solar cells using a single J–V characteristic. The values of performance parameters analytically predicted by our method showed good agreement with
Acknowledgements
This work was financially supported by the Pioneer Research Center Program through the National Research Foundation of Korea (2011-0001649) by the Ministry of Education, Science and Technology (MEST) and partially funded by the Energy International Collaboration Research & Development Program of the Ministry of Knowledge Economy (MKE) (2011-8520010050).
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