Spice Simulations of Solar Cells Electroluminescence Mapping

Transcription

1 Spice Simulations of Solar Cells Electroluminescence Mapping Matevž Bokalič 1, James R. Sites 2, Marko Topič 1 1 University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, SI-1000 Ljubljana, Slovenia 2 Colorado State University, Department of Physics 1875 Campus Delivery, Fort Collins, CO , USA Phone: Fax: ( Matevz.Bokalic@fe.uni-lj.si) Abstract Electroluminescence (EL) is a very convenient spatial characterization method for finished solar cells and modules. Simulation Program with Integrated Circuit Emphasis (SPICE ) provides a framework for electrical simulations which can be used for spatial analysis of solar cells. Cadmium telluride (CdTe) solar cells belong to a promising thin-film photovoltaic technology able to compete with silicon solar cells. Characterisation of CdTe solar cell including dark J-V and electroluminescence measurements provides the experimental data. Essential EL imaging processing is explained. Distributed solar cell SPICE model consisting of two resistive contacting layers and an active layer built of micro-cells is designed. A proposed model is verified and validated by a good agreement between measurements and simulations for both, dark J-V curve, and EL intensity obtained from spatial current distribution. 1 INTRODUCTION Electroluminescence (EL) is the method of choice for frequent characterisations of conversion efficiency distribution across solar cells and modules [1]. Electroluminescence images alone provide intuitive judgement of the device quality [2, 3], however in-depth analysis of EL mapping must be performed for comprehensive understanding of the background physics [4]. The best tools for understanding circumstances inside the solar cell [5, 6] and optimizing their performance [7, 8] are optical and electrical simulations. In this paper we report on design of an appropriate spatially distributed electrical solar cell model for Simulation Program with Integrated Circuit Emphasis (SPICE) and provide a link between current distribution throughout the cell and electroluminescence radiation from the cell. The particular model will be based on the Cadmium Telluride (CdTe) solar cells; however all the procedures, the model, and the results can be applied to other types of solar cells with minor modifications. CdTe solar cells have a 1.45 ev band gap, which is almost optimal for single-junction solar cells. They have one of the best price performance ratios among all solar cells, and they are the most widely spread thin film technology [9]. Despite the good properties, there is still room for improvement, especially with increasing their operating voltage [10], and that can only be achieved with research work, where the proposed approach helps to understand the spatial variations of electrical circumstances inside the cell. 2 EXPERIMENTAL Two techniques are used in this paper for adequate characterization of CdTe cell. First, a dark J-V curve of the cell must be obtained in order to get the complete one-diode model of the cell. Second, electroluminescence images of the cell must be taken with different forward biasing conditions. 2.1 Fabrication of the CdTe cell The CdTe solar cell was manufactured in Materials Engineering Laboratory at Colorado State University, Fort Collins, Colorado, USA. A 10 by 10 cm 2 master plate is built on plasma cleaned Pilkington Tec10 transparent conductive oxide (TCO) coated glass in a superstrate configuration. A thin cadmium sulphide (CdS) and a thicker CdTe layer are deposited by close-spaced sublimation (CSS). Afterwards, the master plate is heat-treated with cadmium chloride (CdCl 2 ) and a thin copper chloride layer is deposited and annealed in order to form a buffer layer before applying a nickel graphite back contact. Nine circular shields with 1 cm diameter are placed on a master plate in a 3 by 3 square grid and unprotected material is sandblasted off. Due to hardness the TCO should not be damaged by sandblasting. Master plate is then cut to nine separate cells. Indium ring is soldered on the TCO around each cell providing a good front contact. The cell used in this paper has an area of 0.75 cm 2 and exhibits 11.5 % STC efficiency with fill factor of 67 %. For all the measurements the cell is mounted 109

2 on a custom holder prepared for 4-wire measurement configuration. Two negative probes are placed close together on the indium ring, and two positive probes are placed close together in the middle of the back contact of the cell. 2.2 Dark J-V characterization Measurement Dark J-V characterization is performed in a dark box. The cell is biased with a Keithley 230 Programmable Voltage Source from -0.2 V to 0.9 V, while exact voltage and current are measured by two HP 34401A multimeters in 4-wire configuration One-diode solar cell model Parameters of one-diode solar cell model shown on Figure 1 are extracted from dark J-V curve using graphical best fit method. 2.3 Electroluminescence Image acquisition The heart of the EL setup is an Apogee Alta U8300 CCD camera, utilizing an 8-megapixel Kodak KAF-8300 silicon sensor with improved NIR response, low-noise electronics and active cooling. The CCD is cooled down to -25 C during the measurement. Karl Zeiss Makro-Planar T* 2/50mm ZF.2 lens is used with a 30 mm extension tube and 13 mm mounting rings. The cell is forward biased with 2.5, 5, 10, 20, 30 and 40 ma/cm 2 current density by Agilent E3634A power supply. During the measurement voltage and current are monitored by two HP 34401A multimeters in a 4-wire configuration. The temperature is monitored by a thermocouple attached to the back of the cell. Figure 1: One diode model of the solar cell. Parameters of the fitted dark J-V curve are shown in Table 1. I ph [A] I s [A] n R sh [Ω] R s [Ω] Table 1: Parameters of one-diode solar cell model in the dark Good agreement between the dark J-V measurement and one-diode model is shown on Figure 2. Figure 3: Normalized vignetting correction image. In addition to CdTe cell s electroluminescence radiation, an image of spatially homogeneous light source is acquired. According to Topič et al. [11] an LCD monitor displaying homogeneous red colour can be used. In our case we have added TCO glass on the top of the monitor to mimic optical circumstances in CdTe solar cell. After processing as described in chapter 2.3.2, except vignetting correction, Gaussian blur filter and normalization, the image is used to correct the cell s EL image for lens vignetting Image processing Figure 2: Dark J-V curve of the CdTe solar cell fitted with one-diode model (cell area 0.75 cm 2 ). Raw images of cell s EL radiation must be processed in order to extract the actual EL signal radiated towards the CCD of the camera. We are using image processing package FIJI [12], based on ImageJ [13], for image processing. 110

3 CCD sensors have a large number of pixels, some of them being noticeably more susceptible to thermal noise charge accumulation. These pixels show up on the raw image as pixels with extremely large electron count, i.e. much brighter than the others. These are removed using a bright outliers removal process embedded in FIJI. CCD camera noise management is specific for each camera. Apogee Alta considers image acquisition parameters such as exposure time, CCD sensor temperature and electronics temperature for subtraction of predicted read-out noise from raw electron counts, setting zero noise pixel value to an arbitrary value of 1270 counts. We subtract this value from all pixel values before further processing. The final step in image processing is vignetting correction. In this step we divide the processed image by the normalized vignetting correction image shown on Figure 3. Image processed using the above procedure represents only cell s EL emission towards the camera, excluding influences of CCD sensor, CCD camera and optics. An example of such an image is shown on Figure 4. 3 SPICE SIMULATIONS Figure 4 reveals some general trends in EL intensity distribution, such as increased intensity in the centre of the cell, increasing intensity towards the edge of the cell and decreased intensity around the centre of the cell. Taking into account the nature of EL, one might assume that current distribution throughout the cell is not homogeneous due to finite resistances of the front and back connecting layers. This assumption can be verified with SPICE (Simulation Program with Integrated Circuit Emphasis) simulations. Generally, SPICE is not intended for spatial simulations, but with careful model design and correct interpretation of results such simulations can also be conducted. In this paper LT SPICE IV [14] is used for simulations 3.1 SPICE Model A special electrical circuit that adequately describes the cell topology is designed in order to conduct spatial simulation in SPICE. A distributed solar cell model is built on a discrete square mesh of 31 by 31 nodes. The model consists of three layers as shown on Figure 5. The top layer is a resistive grid (R TCO ) representing the TCO layer and the indium ring (R met ) around the active area of the cell. Probe is connected to a node on the metal ring. The bottom layer is also a resistive grid (R BC ) representing the nickel graphite back contact with a small 3 by 3 nodes area with lower resistance (R met ) representing the area covered and connected together by the connecting probe. The top and bottom layer are connected together with an active layer consisting of N = 553 microcells (μcell). Each μcell is represented with a one-diode model of the solar cell shown on Figure 1. Figure 4: Processed EL image of the CdTe cell (~1 cm diameter) forward biased with 40 ma/cm 2. In order to exclude the majority of bulk cell inhomogeneities influencing EL response we use a circular averaging technique to obtain a general line scan through the cell. We select a 100 pixels wide line through the cell and extract averaged pixel values. Then, we rotate a line for 22.5 and extract averaged pixel values again. We repeat the process for the whole circle. Finally all the line scans are averaged in a circular averaged line scan shown as Measurement on Figure 8. Figure 5: Distributed electrical model of CdTe solar cell for SPICE simulations. There are eight parameters in the proposed model. Five parameters are needed to describe the μcell with one-diode model: I ph photocurrent, I s diode saturation current, n diode ideality factor, R sh shunt resistance and R s series resistance. The μcell (x -μc ) parameters are calculated from one-diode model 111

4 parameters fitted to the dark J-V curve in chapter using the following relations: I ph-μc = I ph / N, I s-μc = I s / N, n μc = n, R sh-μc = R sh N, R s-μc = R s N. Due to additional resistive elements connected in quasi series to μcells, R s-μc is just an initial value for iterative procedure described in chapter 3.2. These parameters are also expressed in their equivalent values (x -eq ) that represent the values of the whole active layer for easier evaluation and comparison to other parameters. I ph [A] I s [A] n R sh [Ω] R s [Ω] x -eq x -μc Table 2: Parameters of the μcell model. x -eq denotes the equivalent parameter values for all μcells connected in parallel. x -μc denotes the parameter values for each μcell. Three more parameters are needed for resistive network description: R TCO TCO resistance, R BC back contact resistance and R met indium ring resistance. Initial value of R TCO is obtained from the datasheet of the TCO glass. Initial value of R BC is based on comparison to R TCO. Value of R met was measured. μcell series resistance, R TCO TCO resistance and R BC back contact resistance. All three parameters influence the simulated CdTe cell s J-V curve as well as the current distribution throughout the cell. Simulations were repeated while parameters were tweaked to get a sufficiently good fit to dark J-V curve and EL measurement simultaneously. 4 RESULTS 4.1 Relation between EL intensity and bias current In order to compare EL measurements with SPICE simulations, we must first determine the relation between the EL intensity and forward bias current. This relation can be obtained from mean EL intensity values of the active area of the cell measured at different bias currents. Processed images must be used. R TCO [Ω/ ] R BC [Ω/ ] R met [mω] Table 3: Parameters of the resistive network J-V simulation A voltage source V1 is connected to the provided nodes on the distributed electrical model and a direct current (.DC) source sweep analysis of V1 is performed, ranging from -0.2 V to 1.2 V with 10 mv step. The result of the simulation is a dark J-V characteristic of the model Electroluminescence simulation A 30 ma (40 ma/cm 2 ) forward bias current source I1 is connected to the provided nodes on the distributed electrical model and an operating point (.OP) analysis is performed. The results of the simulation are voltages of all nodes and currents of all elements. The most informative way of presenting the results is a line scan of currents flowing through the diodes in μcells. When an appropriate relation between current and EL intensity is applied to such a line scan it can be directly compared with a circular averaged line scan obtained by EL measurements. 3.2 Iterative simulation procedure There are three unknown parameters in the circuit, initial values of which have been predicted: R s-μc Figure 6: mean EL intensity values versus forward bias current density. Linear interpolation will be used for calculating the EL intensity from simulated current density in the following steps. 4.2 Final CdTe solar cell model parameter value label name initial final I ph-eq [A] photocurrent 0 0 I s-eq [A] diode saturation current n -eq [] diode ideality factor R sh-eq [Ω] shunt resistance R s-eq [Ω] serial resistance R TCO [Ω/ ] TCO resistance R BC [Ω/ ] back contact resistance R met [mω] indium ring resistance Table 4: Parameters of the final CdTe cell model. 112

5 The Iterative simulation procedure described in chapter 3.2 and relation between current density and EL intensity described in chapter 4.1 yield the model parameters shown in Table 4. Verification of the final parameters is presented on Figure 7 and Figure 8 for dark J-V curve and EL intensity respectively. Exceptionally good agreement is achieved for both verification procedures. Linear interpolation is used to calculate EL intensity from simulated current density. Distributed solar cell SPICE model consisting of two resistive contacting layers and the active layer built of micro-cells is proposed. Initial parameters of the model are obtained from the measured dark J-V curve. Only two resistive model parameters are tweaked in the iterative simulation procedure until the proposed model corresponds to both, the dark J-V measurement and the measured EL intensity distribution. A good fit to both measurements is presented and thus validates the proposed model and simulating approach. Acknowledgments Figure 7: Simulated dark J-V curve vs. measured dark J-V curve. The authors acknowledge the financial support from the Slovenian Research Agency (Research Programme P2-0197). M. B. personally acknowledges the Slovenian Research Agency for providing PhD funding and Javni sklad Republike Slovenije za razvoj kadrov in štipendije for funding a 4-month research visit to Colorado State University. Materials Engineering Laboratory and Photovoltaic Laboratory at Colorado State University, Fort Collins, Colorado are acknowledged for cell fabrication and cell measurement equipment respectively. References Figure 8: Simulated EL intensity vs. vignetting averaged measured line scan (~1 cm cell diameter). Comparison between the initial parameter values and the final parameter values reveals that only two parameters were changed during the iterative simulation procedure. Back contact resistance R BC value was only estimated before the measurement and its change was expected. μcell series resistance R s-μc cannot be measured directly and can be obtained by simulations only. No other parameters were changed or guessed during the iterative simulation procedures, certifying the trustworthiness of described simulation approach. 5 CONCLUSIONS This paper presents the complete approach to spatial characterisation of CdTe solar cells based on electroluminescence and SPICE simulations. EL image acquisition procedure is described in detail, including essential image processing steps. [1] M. Bokalič, G. Černivec, A. Demolliens, J. Revel, M. Topič, M. Poličnik, and U. Merc, Electroluminescence findings and IR LED I-V curve measurement in (wafer-based) solar cell module production, presented at the 25th European Photovoltaic Solar Energy Conference and 5th World Conference on Photovoltaic Energy Conversion, Valencia, Spain, 2010, pp [2] M. Bokalič and M. Topič, Luminescence Imaging Techniques for Solar Cell Local Efficiency Mapping, in 47th International Conference on Microelectronics, Devices and Materials and the Workshop on Organic Semiconductors, Technologies and Devices, MIDEM 2011 proceedings, Ajdovščina, Slovenija, pp [3] M. Bokalič, U. Opara Krašovec, and M. Topič, Electroluminescence as a spatial characterisation technique for dye-sensitized solar cells, Progress in Photovoltaics: Research and Applications, [4] C. Shen, H. Kampwerth, and M. A. Green, Spatially-Resolved Luminescence Imaging of All Essential Silicon Solar Cell Parameters, in 38th 113

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