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Contract No. DE-AC36-99-GO10337 

J.A. del Cueto and S.R. Rummel 

Prepared for the 31st IEEE Photovoltaics Specialists 

Conference and Exhibition 

Lake Buena Vista, Florida 

January 3–7, 2005 

February 2005 • NREL/CP-520-37444 

Comparison of Diode Quality 

Plus Other Factors in 

Polycrystalline Cells and 

Modules from Outdoor and 

Indoor Measurements 
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COMPARISON OF DIODE QUALITY PLUS OTHER FACTORS IN POLYCRYSTALLINE 

CELLS AND MODULES FROM OUTDOOR AND INDOOR MEASUREMENTS 

J.A. del Cueto, S. R. Rummel, National Renewable Energy Laboratory (NREL), 1617 Cole Blvd., Golden, CO 80401, USA 

ABSTRACT 

The Outdoor Test Facility (OTF) at NREL is equipped 

with data acquisition systems that monitor the performance of modules deployed outdoors in real time, including

the measurement of current-voltage traces every 15 minutes during all daylight hours. This affords us the ability to

analyze performance across many levels of illumination

which allows the determination of factors that affect module performance and that serve as indicators of module 

quality, including average diode quality factors, series resistances values, and reverse-saturation currents of the 

cells. This study focuses on several polycrystalline thinfilm modules, including cadmium telluride. CIS, and polycrystalline silicon. We present these parameters, acquired

from outdoor measurements, and compare the results with

measurements obtained from more canonical methods. 

INTRODUCTION 

Current-voltage (I-V) measurements are routinely 

used to derive materials’ properties in photovoltaic (PV)

cells [1]. Routine measurements performed on cells like

dark and light I-V measurements and analyses yield information on semiconductor and contact material quality,

including diode quality factors and series resistance, allowing correlation with any shortcomings in performance. 

Albeit, the size and distribution of series resistance and 

currents present in modules can skew the analysis and

accurate determination of this information garnered from

these measurements [2]. 

Oftentimes, we tend to avoid executing the same

analyses on modules that are performed on cells, perhaps 

because of the perceived difficulty in interpreting the results for modules. Typically, one can only obtain average

cell parameter values over the whole module without doing destructive testing or other special techniques that can

isolate individual cells [3]. However, this limitation should

not preclude our attempting to analyze valuable data, especially when it is already amply present and can provide 

useful information. Even the accurate determination of

series resistance is oftentimes lacking, instead while using

the slope of the I-V trace at the open-circuit condition

measured at 1-sun intensity. In this paper, the data taken

from many I-V traces recorded outdoors are analyzed to

obtain series resistance values, diode quality factors and 

reverse saturation currents. Those results are compared

with measurements for the same modules taken indoors

using a solar simulator to the trace dark and light I-V characteristics. 

ANALYTIC CONSIDERATIONS 

A canonical method used to calculate the series resistance Rs, the diode quality factor A, and the reverse saturation current density (J0) in PV devices is derived from

the I-V curves. This method relies on the ideal singlediode model with lumped series and shunt resistance

terms, as detailed in the literature [1]. This model is formulated by Eqn. 1, reproduced below, where J is the total

current density, J0 is the saturation current density, V is

the voltage measured at the external contacts, Rs and G 

are the lumped parasitic series resistance and shunt conductance terms, respectively, q is the electronic charge, A

is the diode quality factor, k is Boltzman’s constant, T is 

the absolute temperature in °K, and JL is the photogenerated current, which may be replaced with the shortcircuit current density JSC, if shunting is negligible. 

[ 1] (1) ( )

0 L

q V R J AkT J J e GV J S = ⋅ − + − ⋅ −

The validity of this model is dependent on the applicability of the principle of superposition, whereby the effect

of illumination is simply to displace the current by an

amount equal to JL everywhere along the I-V curve and

whereby all other terms in Eqn. 1 retain their unilluminated and/or unbiased values. Reference [1] and

many others generally execute the analysis using either

the dark I-V data—special case where JL is zero—and/or

light I-V data at one-sun illumination. However, there really

is nothing sacrosanct about performing the analysis at just

these two illuminations, especially since some of the parameters entering into Eqn. 1 can be either bias or light 

dependent. An equally viable or perhaps even better, albeit more protracted, strategy would be to apply similar

analysis but under varying illumination levels. Towards this

end, the Rs, A and J0 are derived using equations 2 and 3,

as previously reported [4]. The symbols for terms used in

equations 2 and 3 are the same as those in Eqn. 1, plus

Roc is the slope of the I-V curve at the open-circuit condition. The analysis requires performing a sufficient number 

of I-V traces to obtain Voc and Roc at a range of illuminations, resulting in various JL all referenced to the same

temperature. In practice, this measurement strategy and 

analysis are time consuming and seldom executed. However, with the benefits of automatic data acquisition, plus 

modules and time, this is no longer an impediment. 

( ) (2) 1

L 0 OC

OC S q J J GV

AkT R R

+ − = + ⋅

1
(1 ) (3) 0 Ln J J

q

AkT VOC + L = ⋅

Equations 2 and 3 are otherwise very similar to the

formulae used in single-trace analysis. However, in Eqn. 2 

on the left-hand side, Roc is the slope of the curve (dV/dJ) 

at open circuit, and on the right-hand side the denominator

term is J0+JL-GVoc instead of J+JL. In Eqn. 3, Voc and JL

have now replaced V and J. However, for a module, the

term for the diode factor A present in equations 2 and 3 is

now replaced by the sum of all of the diode quality factors

for the cells connected in series in the module, and the

and Rs and G are now the sum of lumped distributed series and shunt conductance terms. From Eqn. 2, at high

enough illumination, one can usually neglect the terms J0

and GVoc in the denominator. Equations 2 and 3 are hereafter referred to as the alternate method of derivation. 

EXPERIMENTAL METHOD 

Outdoor performance data for three distinct PV technologies are scrutinized: 3 cadmium telluride (CdTe) modules (A, B, C); 2 copper indium diselenide (CIS) modules

(A, B) and 2 polycrystalline silicon (pc-Si) modules (A, B). 

Their I-V characteristics are analyzed: the behavior of the

open-circuit voltage (Voc), short-circuit current (Isc), fill factor (FF), plus the slope of the I-V curves at the open-circuit

condition (Roc) and their respective temperature coefficients are derived from outdoor measurements, for irradiance levels ranging from low (50 W/m2

) to high (1200 

W/m2

), with module temperatures ranging from 20° to

65°C. Irradiance data were measured with a broadband

pyranometer mounted in the same plan-of-array as the

modules; the temperatures represent back-of-module

measurements; both are sampled simultaneously with the

I-V traces. The featured modules are deployed facing

south at fixed latitude tilt on the Performance and Energy

Ratings Testbed (PERT) on the roof of the OTF at NREL. 

The noted I-V parameters were evaluated at 25°C in

discreet intervals of irradiance going from low (50 W/m2

) to 

high (1200 W/m2

) values. This was accomplished by leastsquares fitting the individual parameters (Voc, Isc, Roc, etc.)

to a linear function of module of temperature in each bin 

followed by evaluation at 25°C. The data were then normalized to unit-area cell values: for Voc by dividing by the 

number of cells in series; for Jsc by dividing by the area of

the unit cell in each module, taken as the aperture area

divided by the number of series-connected cells. The parameter evaluations at 25°C were subsequently fit according to equations 2 and 3, in order to obtain values for Rs, A 

and J0. The modules were removed from the PERT recently, to measure dark and light I-V performed on the

Large-Area Continuous Solar Simulator (LACSS) at standard test conditions (STC) followed by the standard analysis applied to obtain the same parameters. For CdTe

modules, there are two tests performed for each dark and

light I-V on the LACSS: one in the so-called ‘storage state’

and a second labeled the ‘light-stabilized state.’ This additional testing for CdTe is performed to mitigate transient 

effects, whereby the module is exposed to 10-min or more

continuous illumination at open circuit. 

RESULTS 

Figure 1 is a graph depicting the unit-area cell, normalized slope at open-circuit conditions (Roc), plotted

against the reciprocal of Jsc for various illuminations, 

evaluated at 25°C for the seven modules featured. This 

data represents a severe condensation of outdoor data,

with each point representing at least several hundred individual statistics, for irradiance between 150 W/m2

 and

1150 W/m2

, where high-illumination data occur towards

the origin. The data for the two pc-Si modules appear near 

the bottom of the figure almost coincident on top of one

another. The CIS A and B modules occupy the next niche

of resistance values higher up, and then the CdTe modules appear at the largest resistance values. Both the CIS 

and pc-Si data appear to behave fairly linearly within this

range of illumination, as well as that for the CdTe A module. Within a slightly more restricted linear range, the

terms J0 and GVoc in the denominator of Eqn. 2 may be

neglected. Hence, from the intercept of the data with the

abscissa one obtains the series resistance as per Eqn. 2. 

From the slope, the values of A are derived, as well. 

1/Jsc (cm2/A)

Roc( Ω-cm2 )

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

0 40 80 120 160 200 240 280 320 360

CIS B

CdTe B

pc-Si A

pc-Si B

CIS A

CdTe A

CdTe C

Fig. 1. Unit-area cell Roc plotted against the reciprocal of

Jsc, from variable illumination outdoor data reduced to 

25°C temperature for seven polycrystalline modules.

Figure 2 portrays Jsc on a semilog abscissa against 

Voc along the ordinate axis for the same seven modules, 

from the sampled outdoor data taken between 50 W/m2

and 1150 W/m2

 irradiance, reduced to 25°C temperature. 

The range of Jsc values covered in this graph is not as

great as one usually obtains for J in single traces, but note

the rather straight linear behavior with the log of Jsc, except for the lowest illuminations. The data for the pc-Si

modules appear largely near middle within the 0.48–0.6

voltage range. The CdTe A and B modules’ data appear at 

the extreme right, and the CIS A module is at extreme left. 

The CIS B data is between the pc-Si and CdTe modules’

data, and CdTe C data run across the entire voltage

range. Any non-linear behavior between the log of Jsc and

Voc are likely to result from sizable shunt conductance.

From the characteristic slope of Voc as a function of log of

Jsc, one obtains the diode factor A and J0. 

2
Voc(V)

Jsc ( mA/cm2) 10-4

10-3

10-2

10-1

1

0.34 0.38 0.42 0.46 0.50 0.54 0.58 0.62 0.66 0.70 0.74 0.78

CIS A CIS B CdTe A CdTe B

CdTe C pc-Si A pc-Si B

Fig. 2. Unit-area cell Jsc plotted along the semilog abscissa, against cell Voc along the ordinate from variable

illumination outdoor data reduced to 25°C temperature. 

Figure 3 depicts the slopes dV/dJ of the light I-V data

normalized to unit cell area measured on the LACSS at

STC plotted against 1/(J+JL) for six polycrystalline modules, shown in forward bias typically greater than the optimum operating point voltage. The data for the pc-Si B

module has been omitted for clarity because it is so similar 

to that of pc-Si A module. On Fig. 4, the slopes dV/dJ of

the dark I-V data, normalized to unit-area values and

measured on the LACSS at 25°C, are plotted against the

1/J for the same six modules. These data are measured

out to voltages corresponding to 120%–125% of the respective Voc for each module, albeit the currents at these

voltages aren’t always as large as the 1-sun Isc values. 

The abscissa in Fig. 4 has been extended in order to depict the data for all six modules, including CdTe data that 

are substantially larger than those in Fig. 1. 

 dV/dJ (Ohms-cm2)

0

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

1/(J+JL) (cm2/A)

0 50 100 150 200 250 300 350 400 450 500

CIS A

CIS B

CdTe A STAB

CdTe B STAB

CdTe C STAB

pc-Si A

Fig. 3. Normalized slopes dV/dJ of light I-V traces plotted

against 1/(J+JL), as measured on LACSS at STC for six 

polycrystalline modules. 

dV/dJ (Ohms-cm2)

1/J (cm2/A)

0 50 100 150 200 250 300 350 400 450 500

0

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84

88

CIS A

CIS B

CdTe A STOR

CdTe A STAB

CdTe B STOR

CdTe B STAB

CdTe C STOR

CdTe C STAB

pc-Si A

Fig. 4. Normalized slopes dV/dJ of dark I-V traces plotted

against 1/J, measured on LACSS at 25°C for six polycrystalline modules, also showing storage (STOR) and lightstabilized (STAB) data for the CdTe modules.

Two different data sets, storage (STOR) and stabilized (STAB), are depicted in Fig. 4 for each CdTe module,

respectively, representing measurements taken immediately after storage in low-light level conditions and after

light stabilization under the LACSS. For one of the CdTe

modules (B) there are significant differences between the

‘storage’ and ‘stabilized’ data. However, for CdTe modules 

A and C, these differences are small. For the CdTe modules, only the light-stabilized data are portrayed in Fig. 3. 

Note that for CdTe modules, there are substantial differences between the slopes obtained from the dark and light

I-V data sets. Generally, the slopes are shifted to lower

values for the light I-V data, and for the CdTe B module, 

there is a large shift in the data toward lower values present. For the pc-Si A and both CIS modules, however, the 

differences between dark and light data are slight. 

ANALYSIS 

From the data in Figures 1–4, and from the light and

dark I-V traces taken on the LACSS, values for series resistance Rs, A and J0 were derived. The standard analysis

using single dark and light I-V traces follows that of reference [1] to obtain the parameters, with dual values of A

realized. The outdoor data are analyzed by the alternate

method formulated by Equations 2 and 3, and also results

in dual values for A. These data are organized in Tables 1

and 2, respectively, for the standard and alternate analyses. In both tables, the first left columns list the modules, 

and the second rows list the method used for derivation. 

3
Table 1. Parameters obtained from single dark and light 

I-V Traces using the standard analysis. 

Dark I-V Light I-V 

dV/dJ-1/J Log(J)-V dV/dJ-1/(J+JL) Log(J+JL)-V

Rs

Ω-cm2

A J0

A/cm2

A Rs

Ω-cm2

A J0

A/cm2

A 

CIS A 5.6 1.9 5.3E-07 1.9 3.2 2.1 2.1E-06 2.1 

CIS B 1.5 2.2 8.1E-08 2.2 1.2 2.2 2.0E-07 2.3 

CdTe A 9.9 2.2 2.9E-09 2.2 6.2 3.4 2.2E-06 3.4 

CdTe B 44.7 4.4 1.1E-05 4.3 8.2 4.2 2.0E-05 4.3

CdTe C 2.9 4.6 2.6E-05 4.9 -2.2 7.7 5.0E-04 8.1 

pc-Si A 1.0 1.5 6.0E-09 1.6 1.2 1.5 1.2E-08 1.6 

Table 1 is split into two sections, shown at left and 

right, respectively, representing values derived from dark

I-V data, and from the light I-V data. The second and sixth

data columns list the Rs obtained from the dark and light 

I-V traces, respectively. Columns three and five list the A 

factors derived, respectively, from the intercepts of the

dV/dJ vs. 1/J and from the slope of V versus the log(J), for 

the dark I-V traces; columns seven and nine list the A values obtained similarly respectively for light I-V data. Table

1 shows that for the thin-film modules at least, the Rs obtained from light I-V data are lower than those obtained

from dark I-V traces. Note for the CdTe C module, the 

series resistance derived from light I-V is negative and 

meaningless. Yet, that is consistent with expectation from

crudely drawing a straight-line fit to the data for this module shown in Fig. 3, suggesting extreme sensitivity to fitting range. Also note the drastic change in Rs for CdTe B 

that appears between dark and light measurements. 

Table 2. Parameters derived from outdoor data I-V data

across varying illumination, using the alternate method. 

Rs

Ω-cm2 A J0

A/cm2 A Module

Roc - 1/ Jsc Voc - Log( Jsc ) 

CIS A 1.8 2.5 5.2E-09 1.3 

CIS B 1.3 2.3 4.7E-10 1.5 

CdTe A 6.8 3.9 1.2E-20 0.7 

CdTe B 7.1 6.1 3.4E-11 1.5 

CdTe C 2.7 4.1 4.2E-11 1.4 

pc-Si A 1.1 1.5 3.9E-11 1.1 

pc-Si B 1.0 1.5 1.8E-11 1.1 

Table 2 summarizes the values for the same parameters obtained via alternate analysis. The second column

lists the Rs values obtained from the intercept of the characteristics of the slopes of Roc against 1/Jsc. Columns

three and five list the A factors derived, respectively, from

the intercepts of the Roc versus 1/ Jsc and from the slope of

Voc versus the log of Jsc. Values for J0 are similarly drawn

from the application of Eqn. 3. Comparing A values derived by the Roc - 1/ Jsc and Voc - log( Jsc ) methods listed 

in Table 2, the parameters derived by the latter method

generally result in lower values than those achieved by the

former. With the exception of the CdTe A module, all of 

the A values attained with the latter method appear quite

reasonable and less than or equal to 1.5. The values for J0

calculated appear reasonable but possibly a little low. For

the CdTe A module, both the derived A and J0 calculated, 

respectively, as 0.7 and ~ 1*10-20 A/cm2

 are almost certainly artificially low. It is noted that these data were calculated from those depicted in Fig. 2, for Jsc equal to or larger than ~ 0.0065 A/cm2

. Using the Roc - 1/ Jsc method,

the parameters were derived for values where the data

portrayed in Fig. 1 exhibit linear behavior, generally, for

values of 1/ Jsc equal to or less than ~180 cm2

/A. 

DISCUSSION AND CONCLUSIONS 

As pointed out [2], the A factors derived for cells or 

modules with non-negligible series resistance will appear

larger than those of the actual cells, due to the generation

of a non-uniform voltage distribution across the cells. This 

probably cannot be factored using the standard analysis.

Comparing the A values obtained from the standard versus the alternate methods, it is noted that using the alternate method results in lower values of A, by either way:

Roc–1/Jsc or Voc–log(Jsc). Also, the Roc–1/Jsc method

makes use of the slope Roc at a multiple number of traces,

all at the open-circuit conditions, where the current vanishes and therefore any non-uniform voltages across the

cells in the module are likely to be minimized. With the

standard method, the resulting values of the series resistance are subsequently used to correct for the voltage

across the junction (V-RsJ) to derive both A and J0, from

single traces. As noted in Figs. 3 and 4, and to a lesser 

degree in Fig. 1, oftentimes it is a judgement call as to

what the proper linear range to fit the data might be. If 

there is sizable error in the derived series resistance, this 

is likely to propagate into and confound the calculation.

For parameters derived from Voc–log(Jsc), one does not

need to correct the data for series resistance, and nonuniform voltage distribution is likely to be less of a problem, but, one does need to ensure that the fitting range

isn’t befuddled with the effects of shunt conductance. 

ACKNOWLEDGEMENTS 

The authors would like to thank Alan Anderberg of the

Cell and Module Measurements Team at NREL for assisting with the LACSS measurements at STC. This work was 

supported by the U.S. Department of Energy under Contract No. DE-AC36-99GO10337. 

REFERENCES

[1] S.S. Hegedus, W. N. Shafarman, “Thin-Film Solar

Cells: Device Measurements and Analysis,” Prog. in

PV: Res & Appl. 12, 2004, pp. 155-176. 

[2] I.L. Eisgruber, Ph.D. Dissertation “Role of Nonuniformity in Thin-Film Polycrystalline Module Characterization,” Colorado State Univ., Fort Collins, CO, 

1996, pp. 44–57. 

[3] T.J. McMahon, T. Basso, S.R. Rummel, “Cell Shunt

Resistance and Photovoltaic Module Performance,”

Proc. 25th IEEE PVSC, 1996, p.1291.

[4] J.A. del Cueto, “Method for Analyzing Series Resistance and Diode Quality Factors from Field Data Part 

II: Applications to Crystalline Silicon,” Sol. Ener. Mats.

& Sol. Cells, 59, 1999, pp. 393-405.

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Comparison of Diode Quality Plus other Factors in Polycrystalline 

Cells and Modules from Outdoor and Indoor Measurements 

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J.A. del Cueto and S.R. Rummel 

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14. ABSTRACT (Maximum 200 Words)

The Outdoor Test Facility (OTF) at NREL is equipped with data acquisition systems that monitor the performance of 

modules deployed outdoors in real time, including the measurement of current-voltage traces every 15 minutes 

during all daylight hours. This affords us the ability to analyze performance across many levels of illumination which 

allows the determination of factors that affect module performance and that serve as indicators of module quality, 

including average diode quality factors, series resistances values, and reverse-saturation currents of the cells. This 

study focuses on several polycrystalline thin-film modules, including cadmium telluride. CIS, and polycrystalline 

silicon. We present these parameters, acquired from outdoor measurements, and compare the results with 

measurements obtained from more canonical methods. 

15. SUBJECT TERMS

PV; diode quality; module; polycrystalline cells; current-voltage traces; series resistances values; reverse-saturation 

currents; thin-films; cadmium telluride; 

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