Abstract Title

First Author’s name <First Name><LAST NAME>1, Co-Author’s name <First Name><LAST NAME>2

1First Author’s Organisation, Country2Co-Author’s Organisation, Country

ABSTRACT

Please provide your abstract here in 90 – 100 words.

INTRODUCTION

Please provide an overview of your study in 300 – 350 words.

RESULTS

Please provide the results of your study here. You may include any figures, tables and graphs with relevant captions. The content should be around 250 words. The number of words can be redistributed with the word count under “ANALYSIS”.

ANALYSIS

Please provide the details of your analysis here. You may include any figures, tables and graphs with relevant captions. The content should be around 250 words. The number of words can be redistributed with the word count under “RESULTS”.

CONCLUSIONS

Please provide a succinct conclusion here in 90 – 100 words, detailing the main conclusions derived from your study.

REFERENCES

Please cite your references in APA style.

Instructions:1. Please refer to the next page for an example of a long abstract submission.

2. Please submit your abstracts in .doc or .docx formats.

3. Please remember to upload high-resolution files of your images used here in the online portal as well under “Supporting Documents” in any of the following formats: .jpeg, .png, .jpg, .tif.

Finite Element Model Analysis of Solar Cell Luminescence Images

1

Johnson Wong, Vinodh Shanmugam

Solar Energy Research Institute of Singapore (SERIS), Singapore, Singapore

ABSTRACT

A comprehensive finite-element model is constructed to represent a solar cell as interconnected diodes. By simulating the voltage distribution and luminescence intensity across the cell plane, and fitting them to measured voltages and luminescence images, resistance and recombination parameters related to different parts of the cell can be extracted unambiguously. Four measurement and fitting routines are described, each designed to resolve different sets of cell parameters, ranging from the edge recombination diode saturation current density, metal contact recombination, to the metal-semiconductor contact resistance and metal finger conductance statistical distribution.

INTRODUCTION

The advent of photoluminescence (PL) and electroluminescence (EL) imaging as a routine method to characterize solar cells in the last decade have opened up a myriad of possibilities to determine solar cell diode parameters and their spatial distributions in a non-invasive manner. Glatthaar and co-workers have neatly categorized two models in the model-based evaluation of luminescence images: 1) the terminal connected diodes model, which simply describes a large area solar cell by many diodes, each of which is directly connected via a resistor to the terminal; 2) the interconnected diodes model, which is a more realistic depiction of the solar cell as many diodes interconnected in a network [1]. The first model is used almost exclusively in the analysis of series resistance distributions in the solar cell, because it is by far the mathematically simpler treatment. Numerous methods and algorithms have been proposed to map the effective series resistance, which is the value of the resistor connecting the local diode to the terminal that effectively has a meaning only within the model. However there is no known way to convert the effective series resistance map into one which describes the physical resistance of the various cell parts, such as contact resistance and line resistance. It is also uncertain whether the terminal connected diodes model can extract local diode parameters that are highly inhomogeneous, such as when wafer edge recombination is present, by accurately accounting for lateral balancing currents. In this paper, we introduce a new approach which uses the finite-element method (FEM) to implement the interconnected diodes model of the large area solar cell [2]. The FEM model consists of various regions of interest such as the metal grid, metal-semiconductor contact regions, emitter layer, and wafer edges, each of which are characterized by resistance and diode recombination parameters. The FEM model thus represents a detailed construction of the solar cell whose parameters can be extracted accurately by simulating and fitting the PL and EL images. Below we will show a few examples.

ANALYSIS OF EDGE RECOMBINATION

Figure 1 illustrates the FEM model approach of fitting luminescence images. The top row shows a monocrystalline silicon solar cell and its 1-Sun PL image. The bottom row shows a faithful FEM construction, with the geometrically correct front metal grid H-pattern, assuming emitter sheet resistance of 80 Ω/sq, fingers width and sheet resistance of 62 µm and 3 mΩ/sq, respectively, and a metal-semiconductor contact resistance of 3 mΩ-cm2. The bottom row also shows the simulated 1-Sun PL image under the realistic laser illumination intensity distribution. By tuning only three sensitive recombination parameters in the solar cell model, namely the wafer saturation current densities J01, J02, and the edge recombination parameter J01,edge, a remarkably good match can be made between the measured PL image and the simulation. Fitting to PL images taken at different light intensities (3.6, 2, 1, 0.3, 0.1, 0.03 Suns) ensures unambiguous determination of densities J01, J02, and J01,edge. Figure 2 shows the extracted parameters for five groups of solar cell samples, each group having been laser scribed near the wafer edge with different laser power and repetition. Here it is clearly seen that the FEM simulation and fitting yields similar J01 and J02 for all groups, but different J01,edge in a trend that is as expected from the degree of laser scribe severity for the groups. This demonstrates the ability of the interconnected diodes model in extracting highly localized recombination parameters such as the edge recombination.

Solar Cell

FEM Model

Luminescence Image (False Colour)

Simulated Luminescence Image

Figure 1 (Top row) A monocrystalline silicon solar cell and its 1-Sun photoluminescence image; (Bottom row) The corresponding FEM model and the simulated luminescence image with appropriate inputs of illumination intensity distribution and edge recombination parameters.

2

0

100

200

300

400

500

600

1 2 3 4 5

J01

(fA/c

m2)

Edge Laser Scribe Severity

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5

J02

(nA

/cm

2)

Edge Laser Scribe Severity

0

500

1000

1500

2000

2500

1 2 3 4 5

J01,

edge

(fA

/cm

2)

Edge Laser Scribe Severity

Edge Laser Scribe Severity

J01 (fA/cm2) J02 (nA/cm2) J01,edge (fA/cm2)

Figure 2 Extracted parameters for five groups of solar cell samples, each group having been laser scribed near the wafer edge with different laser power and repetition.

ANALYSIS OF METAL RECOMBINATION

The solar cell recombination parameters can be further resolved into a total of five parameters: J01,semi, J02,semi, J01,metal, J02,metal, J01,edge, wherein the saturation current densities J01, J02 take on different values in the passivated regions of the emitter and in the metal contacted regions. In order to reliably extract the metal recombination parameters to aid optimization of silicon wafer solar cell designs, a test metallization pattern with regions of varying metal contact fractions is screen printed to create special test cells, alongside solar cells with a standard H-pattern print. Both the test pattern and H-pattern cells are analysed using intensity-dependent PL imaging (Suns-PL), and the H-pattern cells are additionally probed at each busbar to monitor their open-circuit voltage (via Suns-Voc measurements). The resultant voltage data and images are fitted in FEM constructions of the H-pattern and test pattern cells, using a common set of recombination parameters.

Figure 3 (Top row) 1-Sun photoluminescence image of the H-pattern solar cell and the corresponding FEM simulation; (bottom row) 0.1-Sun photoluminescence pattern of the same cell and the corresponding simulation.

Figure 3 compares the FEM simulations to the experimental PL images of the H pattern cell at 1 Sun and 0.1 Suns, and Figure 4 shows a similar comparison for the test pattern cell. The simulated images are

generated using the best fit values of J01,semi, J02,semi, J01,metal, J02,metal, J01,edge. A good qualitative agreement can be seen, in particular for the relative PL intensities in the eight regions of interest in the test pattern cell, and also in the gradient of the PL intensity towards the wafer edges. Simultaneous FEM fitting to both the test pattern and H pattern is very advantageous for the unambiguous determination of the five recombination parameters.

CONCLUSIONS

This paper demonstrates that luminescence imaging and finite-element model simulations can be arranged into powerful analysis routines to extract a variety of solar cell resistance and recombination parameters. The advantage of using a detailed model is that the physical parameters being sought can be easily traced to different parts of the cell, and ultimately to manufacturing processes. Thus this level of detailed modelling might be a promising approach towards building the ultimate imaging system of solar cells, which will enable the future production line to implement real-time feedback and automated process control.

REFERENCES

[1] M. Glatthaar, J. Haunschild, R. Zeidler, M. Demant, J. Greulich, B. Michl, W. Warta, S. Rein, and R. Preu, “Evaluating luminescence based voltage images of silicon solar cells”, Journal of Applied Physics 108, 014501 (2010); doi: 10.1063/1.3443438[2] J. Wong, "Griddler: Intelligent computer aided design of complex solar cell metallization patterns," in Photovoltaic Specialists Conference (PVSC), 2013 IEEE 39th, 2013, pp. 0933-0938.[3] V. Shanmugam, J. WONG, I. M. Peters, J. Cunnusamy, M. Zahn, A. Zhou, R. Yang, X. Chen, A. G. Aberle, T. Mueller, “Analysis of fine-line screen and stencil printed metal contacts for silicon wafer solar cells”, IEEE Journal of Photovoltaics, in print (2015).

3