Extracción de datos de celdas solares individuales a partir de imágenes de electroluminiscencia de módulos fotovoltaicos y curvas corriente-tensión

Alexia Suca de Azevedo; Matías Córdoba; Kurt Taretto

Extracting individual solar cell data from

photovoltaic module electroluminescence images

and current-voltage curves

Extracción de datos de celdas solares individuales a partir de imágenes de

electroluminiscencia de módulos fotovoltaicos y curvas corriente-tensión

Alexia Suca de Azevedo, Matías Córdoba

, Kurt Taretto

Departamento de Electrotecnia (Facultad de Ingeniería) – Instituto PROBIEN, Universidad Nacional del Comahue-

CONICET

Neuquén, Argentina

matias.cordoba@fain.uncoma.edu.ar

kurt.taretto@fain.uncoma.edu.ar

Abstract— Electroluminescence (EL) imaging is explored as

a non-destructive method for quality assessment and

characterization of solar modules. Here, we demonstrate the

acquisition of dark I(V) characteristics for each individual cell

within a solar photovoltaic module from complete module EL

images. This enables a detailed diagnosis of module failure by

individualizing cell parameters, such as series resistance and

dark saturation current density. Such analyses become

increasingly important with module aging, enhancing the

possibilities for module or cell recycling. The method is checked

for consistency with module parameters extracted from the

measured module dark I(V) characteristics.

Keywords: electroluminescence imaging; series resistance;

photovoltaic module characterization.

Resumen— El ensayo de electroluminiscencia (EL) se explora

como un método no destructivo para la evaluación de la calidad

y la caracterización de módulos solares. Aquí, demostramos la

adquisición de la característica I(V) a oscuras para cada celda

individual dentro de un módulo solar fotovoltaico a partir de

imágenes de EL del módulo completo. Esto permite un

diagnóstico detallado de las posibles fallas que pueda presentar

el módulo al individualizar los parámetros de cada celda, como

la resistencia serie y la densidad de corriente de saturación.

Estos análisis son cada vez más importantes con el

envejecimiento del módulo, permitiendo predecir, por ejemplo,

las posibilidades de reciclaje de módulos o celdas. La

consistencia del método se contrasta con los parámetros del

módulo extraídos de la medición de la característica I(V) a

oscuras del módulo.

Palabras clave: ensayo de electroluminiscencia; resistencia

serie; caracterización de módulos fotovoltaicos.

I. INTRODUCTION

Electroluminescence (EL) imaging, combined with dark

I(V) characterization, provides valuable insights into the

structural and electrical properties of photovoltaic modules.

Particularly, EL imaging enables defect detection and local

characterization by means of device parameter mapping [1]-

[3], supplementing global device parameters extracted from

the I(V) characteristics obtained under dark conditions.

In current research on EL imaging, a predominant focus

lies on methods meant for individual solar cells rather than

entire modules, requiring the evaluation of isolated cell data.

An approach that extends this analysis to modules is

presented by Potthoff et al. [4], in which the operating voltage

of individual cells are determined from entire module images.

This analysis allows for a detailed diagnosis of modules not

only at manufacturing but after aging during years of

operation, or to diagnose early module failure.

In this contribution, EL imaging and dark I(V)

characterization are conducted on a polycrystalline silicon

module for in-depth study by extracting individual solar cell

data from the module images. To study cells individually, this

procedure is applied at different injected module currents,

generating a dark I(V) curve for each cell.

Global series resistance values are then calculated from the

resulting cell dark I(V) curves and compared to total module

series resistance to assess the results, showing excellent

agreement. Therefore, this method is validated to obtain the

individual series resistance of a given solar cell in a module,

allowing for a detailed diagnosis of module aging or failure.

Complementarily, we apply a second method that yields

series resistance and dark saturation current density maps of

individual cells in a module, further expanding the

diagnostics capabilities of the technique.

II. THEORY

EL is the emission of photons when a solar cell is subjected

to a forward bias in the absence of solar illumination, i.e. the

opposite of its normal operating condition of converting light

to electricity. The EL emission occurs by the mechanism of

radiative recombination taking place in the semiconductor

material of the cell.

In silicon solar cells, although Auger and defect-assisted

recombination are the predominant mechanisms for

recombination, the level of radiative recombination is still

sufficient to be detectable by an external sensor such as a

CCD camera, delivering images that contain valuable

Revista elektron, Vol. 8, No. 1, pp. 19-24 (2024)

ISSN 2525-0159

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eative Commons License - Attribution-NonCommercial-

NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

https://doi.org/10.37537/rev.elektron.8.1.191.2024

Student Article

information about the spatial uniformity of the cells. A

typical setup for EL characterization is shown in Fig. 1,

where a power source provides the forward bias polarization

to the cell (or module), and the emitted photons are detected

by a camera.

Fig.1: Schematic drawing of the measurement setup for spatially resolved

EL.

EL theory states that the EL photon flux



emitted

locally at the coordinate r on the surface of a solar cell or

module depends on local voltage V(r) according to [5]

(1)

where V

is the thermal voltage, and C(r) is a calibration

factor that takes different values depending on the position r

and is related to optical and material properties of the module

and the camera system. In particular, local variations of C(r)

are dictated by the external quantum efficiency (EQE)

dependence on r, which comprise optical and recombination

losses, while V(r) accounts for resistive losses.

Therefore, Eq. (1) sets the foundation for identifying

regions of increased losses over the surface of the cells within

a module, which will appear as darker contrasts in the EL

images. An ideal cell would have a uniform, bright image

without any visible dark spots, cracks, or defects. Eq. 1 also

allows for calculating voltage drops within the module, by

capturing EL images at different operating conditions.

For this purpose, let us consider the model of independent

diodes for solar cells, in which a cell is taken as an array of

parallel equivalent circuits, as illustrated in Fig. Fig.2.

Fig. 2. Equivalent circuit of a solar cell under dark conditions, assumed as a

discretization of the solar cell’s continuum. This is defined as the

independent diode model for EL imaging, where V

is the voltage at the

solar cell contacts. See text for further details.

Each EL image pixel r is described by one such equivalent

circuit, and the parameters for each circuit are taken as local

parameters for the cell. In this context, overall lumped

parameters are referred to as global parameters.

This model allows for a better understanding of how the

cell characterizing parameters behave at the local level.

Every circuit at position r = (x, y) consists of a diode with a

local dark saturation current density j

(r) and a local series

resistance R

(r), which describes the resistance along the

current path from pixel r to the cell contacts.

To distinguish whether a dark contrast in an EL image is

caused by recombination effects or by resistive effects, we

apply the non-linear method presented in Section B [6].

A. Extracting Cell Operating Voltages

We assume a typical module, where cells are connected in

series, operated under forward bias during EL imaging. The

measured module voltage V

mod

equals the sum of all operating

cell voltages plus the sum of the voltage drop across the

module resistances, which can be expressed according to

(2)

and

(3)

Here, I is the module current, which equals the cell’s

current for the series connected module. From this equation,

we see that this model splits R

(r) into two components;

int

(r) accounts for the resistance of the contact grid and the

contact resistance between the metal grid and the

semiconductor, while R

ext

accounts for the resistance of the

interconnectors, the contact resistance between the

interconnector and the solar cell and the bulk resistance of the

semiconductor. The total series resistance of the module R

mod

is calculated as a contribution of both R

int

and R

ext

of each cell.

This is illustrated in Fig. 3, in which the independent diode

model for each cell is now accompanied by the

interconnector resistance R

ext

Fig. 3. Module representation for EL imaging, highlighting series resistance

parameters.

In order to proceed calculating individual cell operating

voltages V

from Eq. (1), we assume that the voltage drop

over R

int

(r) can be neglected at the point of highest EL

emission r

max

. This means that R

mod

can be written as

(4)

cells

being the number of solar cells in series. The same

ext

value can be assumed for all cells considering the same

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resistance for all interconnectors and a homogeneously

distributed contact resistance, as assumed in Eq. (4).

Additionally, the optical and material properties at the point

with the highest EL emission are considered to be

comparable on different cells i. Then, the same optical

calibration factor C

max

) can be assumed for all cells in the

module, evaluated at the position of highest EL emission r

max

for each cell. With these assumptions, the module voltage can

be expressed as [4]

(5)

Now, notice that if the voltage drop R

mod

I in Eq.(5) can be

neglected for currents below 10% of the module current at

forward bias equalling the magnitude of the short circuit

current I

, the calibration factor C can be calculated. Having

obtained this factor C(r

max

) for all cells, R

mod

(and therefore

ext

) can then be calculated from Eq. (5) for currents above

10% of I

Ultimately, the cell bias voltage is given by

(6)

This equation again holds for a negligible voltage drop

over R

int

max

). Therefore, this methodology allows for the

calculation of the operating voltages for each solar cell in the

module subjected to the conditions of EL testing, that is, dark

conditions.

B. Calculating Cell Series Resistance Maps

Two EL images at different current-voltage points (one at

a higher voltage point V

and one at a lower voltage point V

)

are used to generate maps according to the iterative method

by Dost et al. [6], applied to an individual cell. Here, the local

series resistance R

(r) is given by [7]

(7)

whereas the local dark saturation current density j

(r) is

approximated by

(8)

In this method, C(r) is the calibration factor calculated for

each pixel of the EL image at the lower bias condition. C

max

is then taken as the highest value found for C(r). Here, the

saturation value C

max

calibrates the contrasts in R

(r) and j

(r)

maps, i.e., separating series resistance effects from

recombination effects. Note here that j

(r) is tied to variations

in C(r) and hence EQE, and it follows that j

maps reflect

local recombination effects.

The proportionality in Eq.(8) yields dimensionless maps

for R

(r) and j

(r). In order to obtain quantified values, a

scaling factor must be applied, f according to [6]

(9)

implying the transformations R

(r) → f R

(r) and j

→

(r)/f where R

Smean

is the dimensionless mean value of the

unscaled R

(r) map.

In this method, an iterative approach is proposed to

improve the quality and speed of the measurements. The aim

is to avoid taking high exposure time images required at very

low bias levels, as in traditional EL imaging methods. Since

high exposure times are no longer necessary, the signal-to-

noise ratio is not compromised. This is achieved by taking

the image at a higher bias level V

, and correcting the lower

bias local voltage values V

(

𝑟

) according to [6]

(10)

for iteration k. When the image is taken at a voltage level

slightly lower than the highest adopted bias level, an error is

introduced at the first iteration of the resulting series

resistance. Eq. (10) reduces this error with each iteration.

This enables a more precise calculation of the calibration

factor C(r), and therefore improved local voltage values to

determine R

(r) [6].

The diagram in Fig. 4 depicts the step-by-step process of

this method. As the convergence criteria, we first calculate

for every pixel the relative error between iterations, |R

k+1

(r)

- R

(r)| / |R

k+1

(r)|. The maximum error for a given pixel

should not be higher than 0.01%.

Fig. 4. Diagram representation of the iterative method by Dost et al.

C. Definitions of Series Resistances

Table I summarizes the different definitions of resistances

considered in this work. Establishing cell bias voltages at

different current levels according to Eq.(6) serves a dual

purpose: first, it facilitates the creation of dark I(V) curves

for each cell, and second, it enables the generation of series

Revista elektron, Vol. 8, No. 1, pp. 19-24 (2024)

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resistance and dark saturation current density maps. Each cell

series resistances R

is calculated from the corresponding

I(V) curve, using curve fitting methods assuming a one-diode

model.

The sum of all R

is then contrasted to the module series

resistance R

Smod

determined from the module dark I(V) curve.

Note that the calculation of this module resistance value

differs from R

mod

obtained from Potthoff et al.'s method [4].

TABLE I

DEFINITIONS OF SERIES RESISTANCES

(r)

Local series resistance value for a given cell, at

coordinate r over the cell’s plane.

Global series resistance value for a given cell.

int

(r)

Subcomponent of R

(r), local value dependent on

position r.

ext

External series resistance to each cell, subcomponent

of R

(r).

mod

Global value for a module, calculated from Potthoff

et al.'s method [4].

Smod

Global value for a module, determined from its dark

I(V) curve.

Smean

Dimensionless mean value of the unscaled R

(r)

map.

III. METHODOLOGY

Imaging is achieved with a silicon charged coupled device

(CCD) sensor. The camera model is the ST-7 Dual SBIG,

including the Kodak KAF 0400 sensor with a resolution of

765x510 pixels. Noise occurs randomly in the images and

could be originated either from incoming photons from the

environment, or from the CCD system and the reading

process. Dark currents due to the rise of temperature in the

sensor increase linearly with time. This effect is reduced by

the camera cooling system, which keeps the material at 262

K during testing.

In this work, measurements are conducted on a

polycrystalline silicon module, comprised of 18 cells, each

with an area of 42.94 cm

. Fig. 5 shows the module and its

EL image at 3 A injected current. The nameplate short-circuit

current of the module is I

= 1.14 A. The image covers an

area of 0.311 mm

per pixel.

The module is biased with a forward direct current while

placed in a dark environment. The current is set and fed to

the module with the OWON ODP6062 programmable DC

power supply. The module is kept at a room temperature of

293 K during testing. Current and voltage are measured with

the four terminals method with a multimeter to minimize

errors due to contact resistance.

In order to obtain individual cell dark I(V) curves, it is

necessary to capture EL images at various different bias

levels. Also, at least one image must be acquired at a current

below 10% of I

as mentioned previously. In order to obtain

sufficient resolution of the dark I(V) curves, 20 images were

taken at different bias levels, ranging from 0.15 A to 3 A.

Fig. 5. Module electroluminescence image at 3 A.

A. Calculating Cell Global Series Resistance Values

Images will be obtained at different bias levels for this

method. The first step to calculate individual cell voltage-

current points is to obtain the calibration factor C for all cells

using Eq. (5), and one image taken at a current below 10% of

and neglecting R

mod

The additional images will each determine a new point of

the I(V) curve of each cell, until enough data points are

collected to cover a significant portion of the curve. The

calibration factor C is employed to calculate R

mod

values from

Eq. (5) for all other bias levels, and thus R

ext

values according

to Eq. (4). The final step is to determine the operating

voltages for each solar cell in the module using Eq. (6) for

every image.

Lastly, global series resistance values are extracted from

the resulting dark I(V) curves of each cell. This is achieved

by plotting dV/dI vs. I

-1

, which gives R

according to

(11)

B. Calculating Cell Local Series Resistance Values

Only two images of the complete module are required to

map the spatial variations of series resistance in individual

cells. A first image selected from a lower bias level is used to

calculate the calibration image C(r), according to Eq. (1).

The second image, taken at a higher bias level, is

calibrated to voltage, once again according to Eq. (1), and

employing the calibration image.

The value of C

max

is first approximated as the highest value

found in C(r). The dark saturation current density can then be

approximated using Eq. (8). With this data, a first iteration of

the cell local series resistance is calculated.

To improve the precision of the voltage values from the

image taken at a lower bias, new values are calculated

according to Eq. (10). The procedure is then repeated for the

Revista elektron, Vol. 8, No. 1, pp. 19-24 (2024)

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new values, recalculating the local series resistance values,

iterating until results of Eq. (7) converge.

The calibration factor can be optimized by varying C

max

and continuing iterations to optimize contrasts in the R

(r)

and j

(r) images. The final step is to scale these images

according to a known global value of cell series resistance.

The method, which is represented in Fig. 4, is

implemented with MATLAB to compute the final local series

resistance values. All images are taken as arrays, or matrices,

of square pixels arranged in columns and rows, where each

pixel is presented by one matrix element (an integer value).

The resulting matrices are then depicted as final images, as

will be shown in the following Section.

IV. RESULTS AND DISCUSSION

For the module shown in Fig. 5, cell number 16 is taken as

cell sample for individual study. Qualitative observations

such as defects and contrasts due to local variations of device

parameters can be clearly observed. Some contrasts may be

quickly identified as finger defects, as the one seen in the

upper right corner of the cell. Investigating such contrasts

requires further analysis, which is beyond the scope of this

text.

The dark I(V) curve from Fig. 6 yields the module series

resistance R

SGmod

= 129 ± 50 mΩ, directly obtained from the

high voltage part of the curve by fitting the resulting

conductance [see, e.g. 7]. This parameter is compared to the

results calculated from EL measurements.

The I(V) curve calculated for cell number 16 is shown in

Fig. 7, with the cell series resistance value R

SG16

= 7.68 mΩ.

Fig. 6. Module measured dark current-voltage characteristics.

Fig. 7. Dark current-voltage characteristics extracted from EL images for

cell 16.

Likewise, the series resistance values for all cells are

calculated and shown in the table in Fig. 8.

As demonstrated in the previous section, this is achieved

by applying a straightforward direct method to extract

individual cell operating voltages, although it requires n

images to plot n points of a cell's dark I(V) curve.

Fig. 8. Calculated global series resistance values for all individual cells.

Errors associated with the resulting images cannot be

directly extracted. To assess the calculated series resistance

values, we consider the sum of R

from all cells compared

to R

SGmod

obtained from the dark I(V) characteristics. The

sum of all values shown in Fig. 8 for all cells equates to

128.37 ± 33.24 mΩ, which falls within the range specified by

the error boundaries of 129 ± 50 mΩ.

These results, together with the obtained images, are now

used for parameter mapping. Fig. 9 shows the generated R

(r)

and j

(r) maps for cell number 16, computed as described in

Section II - B. They provide quantitative data on local

variations of these parameters. Displayed side-by-side, the

maps distinguish contrasts due to variations in the dark

saturation current density as well as series resistance.

Identifying these contrasts helps detect the impact of

manufacturing defects like faulty contact manufacture,

screen printing issues, or finger defects on the cell series

resistance distribution. Quantifying these contrasts also

enables comparison between different cell regions, giving

insights into manufacturing process and material

effectiveness.

Similarly, variations in dark saturation current density

seen in Fig. 9 provide information on non-radiative

recombination effects, which will show as brighter contrasts

in the j

maps.

Fig. 9. El image (left), and the obtained maps of dark saturation current

density (center) and local series resistance R

(r) (right) for cell 16.

This is particularly notable in the map in Fig. 9 because of

the intrinsic defects in polycrystalline silicon, such as

dislocations and grain boundaries, where losses due to non-

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radiative recombination are higher than in monocrystalline

silicon solar cells.

By studying these maps, manufacturers could also

implement targeted optimization strategies to improve

overall cell performance and efficiency.

In addition to the advantages of EL characterization

mentioned above, it is also important to recognize the

flexibility in optical system configurations, and adaptable

testing setups for both lab and field environments. Different

methods may be considered for a module or cell, as long as a

compromise can be reached between the time and resources

available, and the depth and quality of the study required. R

[mΩ] of all 18 cells in the module:

V. CONCLUSIONS

Electroluminescence (EL) imaging was applied to study

solar cells and modules quantitively, obtaining local

information of series resistance and saturation current density.

The total module series resistance obtained from EL imaging

is compared to the series resistance obtained by traditional

current-voltage characterization, obtaining excellent

agreement. This exemplifies the validity of the EL analysis

in silicon solar cells not only as a qualitative, but also as a

quantitative characterization method, enabling for fast and

reliable quantitative characterization.

Moreover, we show that the combination of module EL

images and current-voltage characteristics delivers not only

global module parameters but also individual cell properties,

in this case current-voltage curves for each cell, and series

resistance values.

The information gathered also provides the necessary data

for local characterization of individual cells in terms of

saturation current density and series resistance. This allows

for a detailed module diagnosis during manufacturing as well

as after in-field use, or at the end of module lifetime, allowing

to assess the recyclability of individual cells of a module.

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