NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

A Novel Approach for 

Correlating Capacitance Data 

with Performance During 

Thin-Film Device Stress Studies

Preprint

R.L. Graham and D.S. Albin 

National Renewable Energy Laboratory

L.A. Clark 

Primestar Solar

Presented at the SPIE Optics + Photonics 2011

San Diego, California

August 21-25, 2011

Conference Paper

NREL/CP-5200-52392

August 2011
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1 

A Novel Approach for Correlating Capacitance Data with 

Performance during Thin-Film Device Stress Studies 

Rebekah L. Graham*a, Laura A. Clark b, and David S. Albina

a

National Renewable Energy Laboratory, 1617 Cole Blvd., Golden, CO 80401 

b

Primestar Solar, 14401 West 66th Way, Unit B, Arvada, CO 80004 

*Rebekah.graham@nrel.gov; phone 1 303 275-4531; fax 1 303 630-2045; www.nrel.gov

ABSTRACT

A new data mining algorithm was developed to identify the strongest correlations between capacitance data (measured 

between -1.5 V and +0.49 V) and first- and second-level performance metrics (efficiency [η%], open-circuit voltage 

[VOC], short-circuit current density [JSC], and fill-factor [FF]) during the stress testing of voltage-stabilized CdS/CdTe 

devices. When considering only correlations between first- and second-level metrics, 96.5% of the observed variation in 

η% was attributed to FF. The overall decrease in VOC after 1,000 hours of open-circuit, light-soak stress at 60 oC was 

about -1.5%. The most consistent correlation identified by the algorithm in this particular experiment between FF and 

third-level metric capacitance data during stress testing was between FF and hysteresis in the apparent CdTe acceptor 

density (Na) between reverse and forward voltages scans, as determined in forward voltage bias. Since the contribution 

of back-contact capacitance to total capacitance increases with increasing positive voltage, this result suggests that 

degradation in FF was associated with decreases in Na hysteresis near the CdTe/back contact interface.

Keywords: chemometrics, CdTe solar cell, durability, reliability, efficiency, capacitance-voltage measurement, data 

mining, algorithm

1. INTRODUCTION

Understanding solar cell efficiency and reliability is crucial for advancing the field of photovoltaic research. Changes in 

efficiency can be investigated as a function of processing, measurement, and stress conditions. As efficiency changes 

during accelerated lifetime testing (ALT), various measurement techniques can be used to observe which other 

performance characteristics also change as a function of a particular stress condition. With the increasing scope of 

measurement capability and information storage, it is increasingly important to be able to quickly analyze large amounts 

of data and determine the significance of and interconnectedness between different types of measurements. The ultimate 

goal is to accurately associate changes in efficiency with the degradation mechanisms responsible for those changes.

The “bottom line” for the photovoltaic industry is to increase module power output (efficiency) and to limit power loss 

(improved reliability) at a competitive price. A previous investigation [1] used first- and second-level correlations 

between changes in η% and changes in VOC, JSC, and FF in order to ascertain the durability of a set of high-efficiency 

cells over a range of stress temperatures from 60-120 °C. Since solar cell η% is determined by

η% = 

inc

OC JV SC FF

φ (1)

(where φinc, the incident power density, is typically normalized to a solar value of 100 mW/cm2

), a comparison of the 

linear correlation coefficients (R2

) of Δη% versus ΔVOC, ΔJSC, and ΔFF during stress testing was performed as a function 

of stress temperature. This analysis is shown in Figure 1. As a reference, a linear fit of a perfectly correlated set of y

and x has R2 = 1, and a linear fit of a completely non-correlated set of y and x has R2 = 0. The moderate correlation of 

∆η% with ∆JSC, seen at lower stress temperatures, was associated with reduced optical attenuation due to S out-diffusion 

from the CdS. The most important variable affecting ∆η% over the entire temperature range, approaching perfect 
2 

correlation at 120 °C, was ∆FF. This figure clearly shows that understanding the loss in FF would be helpful in 

understanding the loss in η%. 

1.0

0.8

0.6

0.4

0.2

0.0

R

2

 (0 to 1)

60 80 100 120

Stress Temperature (C)

 deltaEff vs deltaX

 X = Voc

 X = Jsc

 X = FF

Figure 1. Linear correlation coefficient (R2) of Δη% versus ΔVOC, ΔJSC, and ΔFF, as a function of stress 

temperature (ref. [1]).

Arrhenius plots of overall efficiency change as a function of inverse temperature identified two dominant temperaturedependent degradation mechanisms. An activation energy for S diffusion into CdTe of 2.94 eV was determined for low 

stress temperatures (60-80 oC). At higher temperatures (100-120 oC), an activation energy for Cu diffusion into CdTe of 

0.63 eV was determined to be responsible for the decreases in VOC and FF observed at these temperatures.

The data mining technique described in this paper was developed to facilitate rapid identification of correlations between 

third-level metrics obtained with capacitance-voltage (C-V) measurements and first- (η%) and second- (VOC, JSC, FF, 

light series resistance [RS], and light and dark shunt resistance [RSH,L and RSH,D]) level performance metrics. The 

technique is not limited to only C-V data and can be applied to other measurement techniques (e.g., photoluminescence, 

x-ray diffraction, deep-level transient spectroscopy, secondary ion mass spectrometry, etc.). This technique is optimally 

used for determining degradation mechanisms in a specific set of devices, preferably a set fabricated and stressed 

identically.

2. THE ALGORITHM

Chemometrics is a formal methodology applied to optimizing complex systems where many input variables contribute to 

one or more output parameters. The case for solar cells is obvious. Optimizing the performance, reliability, and cost of 

solar cells involves investigating many different materials (types of semiconductors, transparent conductors, metallic 

conductors, encapsulants, etc.), processes (evaporation, sputtering, close-spaced sublimation, etc.), and conditions of 

processing (temperatures, times, film thicknesses, deposition rates, etc.). The “design of experiment” approach using 

multivariate analysis is one chemometric approach for doing this efficiently. The latter was demonstrated, for example, 

in the fabrication of CdS/CdTe devices [2], where efficiency was optimized within the scope of input parameter 

variations associated with film thickness, CdCl2 treatments, and back contact preparation. An important result of that 

study was that optimal performance did not result in optimal durability, the latter determined by stressing cells under 

one-sun illumination, open-circuit bias, and elevated temperature.
3 

In the same way that correlations between first- and second-level metrics during stress testing are useful for broadly 

determining why cells degrade, similar correlations between second- and third-level metrics should be useful for more 

specifically identifying degradation mechanisms. C-V measurements have recently been used in cell stress studies [3-6] 

to qualitatively determine electronic changes in the device while performance changes with stress. To date, these studies 

have focused mostly on changes in the depletion width (W) and the apparent net acceptor density (Na) as a function of 

stress. Advanced C-V analysis can also yield more intricate details associated with band offsets and interface states [7] 

as well as deconvolution of junction capacitance and back contact capacitance from total device capacitance [8].

Three important aspects we advocate when incorporating C-V measurements into stress studies include measuring 

capacitance as a function of voltage-sweep direction (reverse-to-positive bias [forward] versus positive-to-negative bias 

[reverse]), not exposing the cell to conditions too far removed from those the cell might encounter in actual module use 

(i.e., limit voltage), and the ability to collect data quickly in order to handle large sample sets for statistical purposes. 

The hysteretic behavior of C-V data (see for example [3]) is commonplace in CdTe (and in CuInGaSe2 films, for that 

matter), can result in a bimodal distribution of C-V-derived parameters like W and Na (something that device models 

should consider), and directly contributes to transient behavior in modules [9]. It is for this reason that our approach 

incorporates both forward- and reverse-direction voltage scans.

There are three levels of analysis in the data mining technique presented in this paper. These levels will be demonstrated 

within the context of a stress study, where measurements are made as a function of time during ongoing stress testing. 

In this example, the first- and second-level metrics and C-V are measured at several times during the stressing of a set of 

solar cell devices. The first level of analysis, shown in Figure 2(a), is to correlate η% with VOC, JSC, and FF, as a 

function of stress time. If η% is highly correlated with FF, as in this example, then looking for causes of FF degradation 

will illuminate possible causes of η% degradation and will suggest a road map for improved cell durability. The second 

level of analysis, shown in Figure 2(b), is to correlate FF with measurements of third-level metrics, such as capacitance, 

conductance (G), net acceptor density, and depletion width. Those C-V-derived data can be determined for each value of 

voltage in each voltage scan direction. This is performed for several identically processed devices, such that values of R2

between that data and FF can be determined. In doing so, the voltage at which the highest correlation occurs (V1) will 

be identified. The third level of this analysis technique, shown in Figure 2(c), is to choose the measurement condition of 

highest correlation and to look at the raw data, for example, FF versus W at V = V1 as measured during the forward scan 

from negative to positive voltage bias.

Figure 2. Outline of the (a) first, (b) second, and (c) third levels of the data mining technique presented in this 

paper. In order to understand power loss, this technique quickly reveals correlations between changes in the 

metrics that contribute to degradation of the output power.
4 

The overall algorithm for this data mining technique is shown in Figure 3. For each device, light and dark currentvoltage (J-V) scans yield values of η%, VOC, JSC, FF, RS, RSH,L, and RSH,D. This data is stored in a database. The data 

mining code, currently written in but not limited to LabVIEW, then computes a y-versus-x linear fit at every fixed 

measurement condition, where y = η%, VOC, JSC, FF, RS, RSH,L, and RSH,D, and x = the specified measurement at the fixed 

condition (e.g., x = W at a specific voltage and in a specific direction of scanned voltage). Every linear fit produces a 

slope, intercept, and value of R2

. 

Figure 3. The data mining algorithm. The third-level metrics include any measurement data beyond the usual J-V

measurement, with C-V-derived data shown as an example.

The linear fit, as opposed to any other type of fit, was chosen purely due to its predictive capabilities, i.e., we do not 

presume that a linear relationship exists. If two parameters are highly correlated, then it is possible to use the 

information from one of those parameters to predict the other parameter, without requiring both measurements. This 

correlation is especially valuable in stress studies, where it is useful to predict at what time a parameter will degrade 

beyond some specified value, which could indicate the predicted lifetime of the device.

3. RESULTS AND DISCUSSION

3.1 Algorithm Validation

This data mining approach will be demonstrated for a group of laboratory cells that show improved VOC durability 

compared to what we have reported in the past. Figure 4 shows the variation in VOC, measured as a function of stress 

time during elevated temperature, one-sun, open-circuit bias ALT for four representative groups. Cells in group A were 

stressed at 100 °C and are standard devices where the CdTe layer is relatively thick (9 to 10 μm). These devices show 

an overall decrease in VOC of about 1.5% after 2,000 hours. Cells in group B were also stressed at 100 °C and were 

made by the same processing conditions, except that the CdTe thickness was considerably reduced (2 to 3.5 μm). With 

only nominal changes in cell fabrication procedure, the degradation of the thinner cells is significantly greater (>10% 

VOC degradation after 270 hours of stress). The conclusion from Figure 4(a) is that thinner CdTe devices are clearly less 

stable than thicker devices. Figure 4(b) again compares thicker (9 to 10 μm) CdTe cells in group C with thinner 

(approximately 4 μm) cells in group D, where both groups were stressed at 60-65 °C. In this case, the thinner cells of 

group D do not show the typically large decrease in VOC during ALT. VOC degradation after 1,000 hours for groups C 

and D is similar, with a decrease of around 1.2 to 1.3%. Obtaining stable CdTe devices while reducing film thickness is 

important because the latter is a major driver for reducing CdTe module cost [10]. Further discussions in this paper will 

concentrate primarily on devices from group D.
5 

Figure 4. Degradation of VOC for different processing variations during ALT at (a) 100 °C and (b) 60-65 °C. 

A set of five CdS/CdTe devices in group D were stressed with 1,000 hours of ALT at 65 °C. In order to track 

performance changes during stress, these cells were characterized using J-V measurements at ALT times of 

0 (unstressed), 60, 120, 300, 450, 675, and 1,000 hours. The J-V-derived parameters are shown as a function of stress 

age in Figure 5. RS in Figure 5(e) was calculated from the inverse-slope of J-V at J = 0 mA/cm2 under one-sun 

illumination. RSH,L, and RSH,D in Figures 5(f) and 5(g) were calculated from the inverse-slope of J-V at V = 0 V with and 

without one-sun illumination, respectively. C-V measurements (at 100 kHz, with AC amplitude of 50 mV) were also 

performed in parallel with J-V measurements in order to validate the data mining algorithm.

Figure 5. Graphs of (a) η%, (b) VOC, (c) JSC, (d) FF, (e) RS, (f) RSH,L, and (g) RSH,D versus age. Lines connect data 

collected from each of the five devices.

The first-level metric was plotted as a function of the second-level metrics, as shown in Figure 6. In Figure 6(c), η% has 

a 96.5% correlation with FF over the entire range of stress times, which indicates that 96.5% of the variation in η% can 

be explained by variations in FF. Furthermore, this means that if FF can be measured, then η% can be predicted with 

96.5% accuracy. The relative stability of VOC suggests that recombination is not a strong contributor to FF loss, thus FF

loss was believed to be due primarily to degradation in either RS or RSH. 
6 

Figure 6. Graphs of η% versus (a) VOC, (b) JSC, (c) FF, (d) RS, (e) RSH,L, and (f) RSH,D for the aggregate of all five 

devices at all seven stress ages, shown with linear fits and corresponding values of R2

. 

The power of the data mining algorithm will now be demonstrated as applied to C-V measurements. As mentioned 

previously, the algorithm determines all possible correlations between performance metrics (η%, VOC, JSC, FF, RS, RSH,L, 

and RSH,D) and a family of C-V-derived dependent variables for each set of different stress times, each voltage scan 

direction, and each incremental change of voltage. For illustration, Figure 7 shows a small subset of these correlations 

before stress (t = 0), between FF and C, G, W, and Na, over the entire voltage range of the measurement, in both forward 

and reverse voltage scans. Also shown is the difference in C, G, W, and Na determined between the two voltage scan 

directions (hysteresis, defined as the value measured in the forward scan minus the value measured in the reverse scan).

Figure 7. Correlation graphs showing R2 at every voltage step for FF versus (columns, from left to right) C, G, W, 

and Na as calculated from the (first row) reverse voltage scan, (second row) forward voltage scan, and (last row) 

difference between the measurements during the two scan directions, all for unstressed devices (t = 0).
7 

Correlation graphs for y = η%, VOC, JSC, RS, RSH,L, and RSH,D are not shown. In Figure 7, it is easy to see that the correlation 

between first- and second-level metrics and third-level C-V metrics varies considerably with voltage but, in general, 

changes continuously. The data shown in Figure 7 is only for the set of C-V and performance data at t = 0, i.e., 

unstressed. The algorithm performs similar calculations at all stress times and, using a set of selection criteria and error 

checking routines to account for non-continuous behavior (like those shown for reverse bias in the FF versus Na column 

in Figure 7), is able to identify the most consistent correlation during ALT studies useful for identifying degradation 

mechanisms.

Out of a possible set of 588 correlations, the algorithm identified two correlations as being the most consistent for this 

particular set of devices. These involved FF = f(Na hysteresis) (shown for three arbitrary stress times in Figure 8) and 

η% = f(Na hysteresis), where Na hysteresis was determined between the forward and reverse voltage sweeps at a voltage 

of +0.49 V. This result is in complete agreement with the first- and second-level correlation analysis shown in Figure 6. 

Since η% is so strongly correlated with FF, it is not surprising that the result of the algorithm included both FF and η%. 

The correlation with Na hysteresis, however, is not a possible conclusion after only considering correlations between 

first- and second-level metrics.

Figure 8. Graphs of FF versus Na hysteresis at 0.49 V, as calculated between the forward and reverse voltage 

scans, after stress times of (a) 60 hours, (b) 120 hours, and (c) 675 hours.

The correlation between FF and Na (in the forward and reverse scan directions and in the hysteresis between the two) at 

0.49 V observed for all stress times is shown in Table 1. Since the correlation of FF = f(Na hysteresis) shown in Figure 7 

appears likely to increase with voltages higher than 0.49 V, we plan to use higher positive voltages in the future. The 

use of higher voltages during ALT, however, will require careful consideration of how higher forward currents during 

these measurements might compromise degradation. A likely explanation for why higher voltages yield better 

correlations in this particular experiment may be found in the literature. As shown in Figure 3 of the paper by

Burgelman, et al. [8], in increasing the voltage beyond 0.49 V, the total cell capacitance is no longer determined by Na

hysteresis near the junction, but also by Na hysteresis near the back contact. Based on this result, our data mining 

algorithm not only corroborates the information extracted from considering only first- and second-level metrics alone, 

but goes further in suggesting that cell degradation in this experiment is due to a decrease in Na hysteresis near the 

interface between the CdTe and the back contact.

Stress Age R2

 (FF vs. Na, forward scan) R2 (FF vs. Na, reverse scan) R2 (FF vs. Na, hysteresis)

0 0.686 0.568 0.733

60 0.810 0.513 0.845

120 0.600 0.125 0.884

300 0.678 0.254 0.862

450 0.690 0.124 0.528

675 0.861 0.474 0.750

1000 0.408 0.001 0.698

Table 1. R2 values for linear fits of FF versus Na at 0.49 V, as calculated during the forward voltage scan, at each 

stress time. 
8 

4. CONCLUSIONS

A data mining approach was developed to efficiently analyze large amounts of data and to quickly identify correlations 

between first- and second-level performance metrics with third-level characterization data. It was applied specifically to 

C-V data collected during stress testing of laboratory cells, but should be applicable with other characterization 

techniques.

From a simple consideration of the correlation between cell efficiency and second-level metrics (VOC, JSC, FF), we 

determined that 96.5% of the variation in efficiency during stress for this set of devices could be explained by variations 

in FF. The data mining approach corroborated this result. With the algorithm, a large amount of data was reduced to 

only two correlations, both involving hysteresis in the apparent net acceptor density (Na) measured at the maximum 

voltage used in our data collection (0.49 V) calculated from the difference in Na between the forward and reverse voltage 

scans. With forward voltage bias, the measured capacitance sees contributions due to the reverse-biased back contact 

capacitance in addition to the forward-biased junction capacitance. The latter is also affected by injected charge 

(electrons) under forward bias, which is not considered in this paper. With this additional caveat, our results to date 

suggest that degradation in these cells is related to a decrease in Na hysteresis at the CdTe/back contact interface.

5. ACKNOWLEDGEMENTS

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 with the 

National Renewable Energy Laboratory (NREL) and Primestar Solar through Cooperative Research and Development 

Agreement (CRADA) No. CRD-06-196 with Primestar Solar. The authors would also like to acknowledge discussions 

and assistance from Wyatt Metzger, Samuel Demtsu, Mark Pavol, Bogdan Lita, and Wes Dobson at Primestar Solar and 

James Johnson, Bastiaan Korevaar, and Oleg Sulima at the GE-Global Research Center during the duration of this work.

6. REFERENCES

[1] Albin, D., “Accelerated stress testing and diagnostic analysis of degradation in CdTe solar cells,” Proc. SPIE 7048, 

704825 (2008).

[2] Albin, D., Demtsu, S., McMahon, T., “Film thickness and chemical processing effects on the stability of cadmium 

telluride solar cells,” Thin Solid Films 515, 2659-2668 (2006).

[3] Albin, D., Dhere, R., Glynn, S., del Cueto, J., Metzger, W., “Degradation and capacitance hysteresis in CdTe 

devices,” Proc. SPIE 7412, 74120I (2009).

[4] Mendoza-Perez, R., Sastre-Hernandez, J., Contreras-Puente, G., Vigil-Galan, O., “CdTe solar cell degradation 

studies with the use of CdS as the window material,” Solar Energy Materials & Solar Cells 93, 79-84 (2009).

[5] Demtsu, S., Albin, D., Pankow, J., Davies, A., “Stability study of CdS/CdTe solar cells made with Ag and Ni backcontacts,” Solar Energy Materials & Solar Cells 90, 2934-2943 (2006).

[6] Corwine, C., Pudov, A., Gloeckler, M., Demtsu, S., Sites, J., “Copper inclusion and migration from the back contact 

in CdTe solar cells,” Solar Energy Materials and Solar Cells 82, 481-489 (2004).

[7] Castillo-Alvarado, F.L., Inoue-Chavez, J.A., Vigil-Galan, O., Sanchez-Meza, E., Lopez-Chavez, E., ContrerasPuente, G., “C-V calculations in CdS/CdTe thin films solar cells,” Thin Solid Films 581, 1796-1798 (2010).

[8] Burgelman, M., Nollet, P., Degrave, S., “Electronic behaviour of thin-film CdTe solar cells,” Appl. Phys. A 69, 

149-153 (1999).

[9] Del Cueto, J., Deline, C., Albin, D., Rummel, S., Anderberg, A., “Striving for a standard protocol for 

preconditioning or stabilization of polycrystalline thin film photovoltaic modules,” Proc. SPIE 7412, 741204 (2009).

[10]Woodhouse, M., and Goodrich, A., private communication.