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1
Finite Element Model Analysis of Solar Cell Luminescence Images
Johnson Wong, Vinodh Shanmugam
Solar Energy Research Institute of Singapore (SERIS), Singapore, Singapore
ABSTRACT
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 J 01,
J02, and the edge recombination parameter J 01,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.
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.
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.
ANALYSIS OF EDGE RECOMBINATION
2
J01 (fA/cm2)
600
10
J02 (nA/cm2)
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.
J01,edge (fA/cm2)
2500
9
2000
7
400
300
200
6
5
4
3
2
100
J01,edge (fA/cm2)
8
J02 (nA/cm2)
J01 (fA/cm2)
500
1500
1000
CONCLUSIONS
500
1
0
1
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.
0
0
2
3
4
5
1
2
3
4
5
Edge Laser Scribe Edge
Edge
Laser
Scribe
Laser
Scribe
Severity
Severity
Severity
1
2
3
4
5
Edge Laser Scribe
Severity
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: J 01,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 opencircuit 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.
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).
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
experimental PL images of
and 0.1 Suns, and Figure 4
for the test pattern cell.
FEM simulations to the
the H pattern cell at 1 Sun
shows a similar comparison
The simulated images are
3