Saturation current (I 0) and ideality factor (n) of a p-n junction solar cell are an indication of the quality of the cell. These two parameters are usually estimated from dark current-voltage measurements. In this study, a quick and easy method to determine these two parameters by measuring open-circuit, V oc , and short-circuit current, I sc , is presented. Solar cell designers can use this method as a grading or diagnostic tool to evaluate degradation in photovoltaic (PV) modules. In order to verify the V oc-I sc method, a series of experiments have been conducted on a single cell and a 36-cell module. Good agreement between our V oc-I sc method and dark I-V measurements was obtained. An application of the method on the performance degradation of a single-junction a-Si:H module revealed that the module's I 0 increased by more than three orders of magnitude and n increased by 65% after an outdoor exposure of 130 kWh/m 2. This increase in n indicates that after exposure, the recombination current in the cells' space charge region increased due to the light-induced formation of metastable defects. The method is also used to assess the quality of five PV module technologies and proved to be reliable despite defective cells in a module.

Photovoltaic (PV) cell or module saturation current (I 0 ) and ideality factor (n) are usually determined by fitting the Shockley equation to dark current-voltage (I-V) measurements. This is done by nonlinear parameter estimation software employing iterative methods. These methods require a minimum number of dark I-V points (100 in our case) measured very accurately in the microamp range. Photovoltaic research laboratories are more likely to have a solar simulator only and lack a high-cost semiconductor characterization system. Therefore, the capability of varying the irradiance in a simulator allows the extraction of ideality factor and recombination current. In this study, the relation between open-circuit voltage (V oc ) and short-circuit current (I sc ) of PV cells and modules has been investigated. By measuring V oc and I sc at different irradiance levels, a good linear correlation was found between these two parameters as expected from theoretical predictions. The interpretation of this linear relation is based on the assumption that the PV cells have no significant shunt paths across their junction. In fact, it is shown that if the relation between V oc and I sc is not linear for a cell, the cell is expected to have significant shunt paths or low shunt resistances. Comparing results obtained from V oc -I sc measurements to dark I-V measurements indicate that the V oc -I sc method is a reliable and accurate way to quickly and easily determine the otherwise obscure parameters, I 0 and n. PV simulations were also used to verify the method, and I 0 and n obtained from the V oc -I sc method are in excellent agreement with the values of I 0 and n used in the simulations. Due to the simplicity of the method, it is a useful tool for grading cells and modules during manufacturing and also for analyzing any infield degradation. This paper presents, verifies, and applies the V oc -I sc method used to determine a cell or module's saturation current and ideality factor.

Solar cells are diodes formed by joining n-type and p-type semiconductor materials. When forming this p-n junction, electrons diffuse across the junction to the p-side where they recombine with holes. Similarly, holes diffuse across the junction to the n-side where they recombine with electrons giving rise to the diffusion component of the recombination current. On leaving the n-side, electrons leave behind positively ionized donor atoms and the holes leave behind negatively ionized acceptor atoms. These ionized atoms form a space charge region (SCR) giving rise to an electrical field directed from the n-type region towards the p-type region

2.1. Dark Current. When the p-n junction diode in Figure 1 is forward biased, the built-in potential barrier is lowered.

The total diffusion current in the n-and p-regions (I D1 + I D2 ), which also constitutes ideal recombination, is given by the Shockley equation

where I 01 = reverse saturation current corresponding to the diffusion and recombination of electron and holes in the pand n-regions, respectively; n = ideality factor = 1; k = Boltzmann's constant; T = absolute temperature. The last component of the dark current is a result of recombination of electrons and holes in the SCR, I D3 . This current constitutes nonideal recombination and is given by

where I 02 = reverse saturation current corresponding to the generation and recombination of electron and holes in the SCR region; n = ideality factor > 1; The total dark current comprises the components given in (1) and (2):

Equation (3) can be written as a single exponential formula:

where I 0 = reverse saturation current governed by diffusion and recombination of electron and holes; n = 1 if the dark current, I D , is solely determined by diffusion; and n > 1 if recombination in the SCR also contributes to I D . Apart from the recombination current given in (4), parasitic series and shunt resistances are also present in a practical solar cell.

n-region p-region SCR qV bi Figure 1: Energy band diagram of a p-n junction at thermal equilibrium.

International Journal of Photoenergy

From the figure, it is evident that the current through the cell is given by

where I D is given by (4) and I sh is obtained from Kirchhoff's voltage rule. Substitution yields the equation governing the dark I-V characteristics of a cell or module:

2.2. Photogenerated Current. When the p-n junction solar cell is illuminated, the junction is forward biased and the cell produces a photogenerated current, I ph .

The equation governing the I-V characteristics of a PV cell or module is then given by

The short-circuit current, I sc , of the solar cell is obtained by setting V in (8) equal to zero and assuming that R s is negligibly small; thus,

Similarly, the cell's open-circuit voltage, V oc , is obtained when no external current flows, that is, I = 0 in (8). Assuming that I 0 ≪ I sc and R sh ≫ V oc /I sc , V oc is then given by

From (10), it is evident that a plot of V oc versus lnI sc should be linear. The gradient of this linear plot allows the determination of ideality factor, n, and the y-intercept yields the reverse saturation current, I 0 :

To verify the validity of (11), a series of experiments were conducted on a monocrystalline Si cell and a 36-cell multicrystalline Si module. A PV simulation program (PVSIM)

Equations (10) and (11) assume that the ideality factor is not influenced by irradiance levels and subsequently by voltage. This is however not the case. The ideality factor has a distinct dependence on voltage. This dependence is governed by unusual or nonideal recombination and parasitic series and shunt resistance.

At low voltages (corresponding to very low irradiance levels), the ideality factor is governed by shunt paths across the p-n junction. At intermediate voltages, the ideality factor

n-region n-region SCR International Journal of Photoenergy is very "stable", and at high voltages (irradiance levels), it is governed by series resistances [9]. in results in a voltage range corresponding to the "stable" ideality factor region in

The advantage of the V oc -I sc method is that it will show that the assumptions in (10) are not met when the V oc -I sc curve is sublinear. Therefore, when the curve is sublinear, it is expected or suspected that the cell/module have shunting behavior, low series resistance, and/or nonideal recombination taking place.

3.1. Monocrystalline Si Cell. The diode ideality factor and saturation current can be accurately extracted by fitting (6) to a set of measured dark current-voltage (I-V) data using nonlinear parameter estimation software

3.2. 36-Cell Multicrystalline Si Module. The method of extracting I 0 and n from V oc -I sc measurements was also used on a 36-cell multicrystalline Si module. The shunt resistance of the module was measured using an individual cell shunt measurement system

resistance was more than 10 MΩ. This value was confirmed by dark I-V measurements.

Values for I 0 and n obtained from both measured and simulated data are listed in

3.3. Simulation of a 36-Cell Si Module. In the previous section, a PV simulation program (PVSIM) has been used to simulate the multicrystalline module. In this section, an arbitrary 36-cell module is simulated. The simulations are conducted for different irradiance levels from which V oc -I sc data points are obtained. Our method of extracting I 0 and n was then applied to these data points. The result is then compared to the values for I 0 and n used by PVSIM. Figure 10 shows the relation between the simulated V oc and I sc . Listed in the accompanying table are the values of R s , R sh , I 0 , and n used in the simulations. It is evident from this table that the values for I 0 and n obtained from the V oc -I sc method are in excellent agreement with I 0 and n used by PVSIM.

4.1. Degradation Analysis. Although the primary application of the V oc -I sc method is to obtain the obscure parameters of I 0 and n from I-V measurements in a solar simulator, the method can also be employed to establish and or confirm performance degradation when the tests are done periodically on modules deployed outdoors. In a study where a 14 Wp a-Si:H module was deployed outdoors

Parameter Figure 10: Relation between V oc and I sc of a 36-cell module simulated with PVSIM. The accompanying table lists the values of R s , R sh , I 0 , and n used in the simulations and compares I 0 and n with that obtained from the V oc -I sc method. International Journal of Photoenergy obtained from V oc -I sc measurements before, during, and after a 180 kWh/m 2 outdoor exposure. The increase in ideality factor implies that after each exposure, the recombination current in the SCR contributed more towards the dark current. This is also evident from the increase in the saturation current with exposure. When the a-Si:H cells are exposed to sunlight, the incoming photons generate electron-hole (e-h) pairs. When these e-h pairs recombine, a photon or phonon may be released. The emitted photons break the weak Si-Si bonds in the SCR. These broken bonds form metastable defects in the SCR, which enhances recombination there. The photons emitted from the enhanced recombination cause even more metastable defects to form and, thus, enhance recombination even more

4.2. Quality Assessment. The V oc -I sc method presented in this paper can be used to assess the quality of various modules. Because of its simplicity, module manufacturers, PV system designers, and researchers can use this method to quickly and easily assess module or cell quality. In this study, five modules comprising different module technologies were subjected to the V oc -I sc method. The modules are presented in

The V oc -I sc method was used to assess module quality in terms of I 0 and n.

The relatively higher n for the thin-film modules reveals that their cell quality is lower than the crystalline cells. It also implies that nonideal recombination takes place especially 7 International Journal of Photoenergy for the a-Si:H module with n close to 2. The high I 0 of the CuInSe 2 (CIS) module is due to the fact that the CIS module showed shunting behavior

In this paper, it has been successfully shown that the saturation current, I 0 , and the ideality factor, n, of cells and modules can be extracted from measuring V oc and I sc at different irradiance levels. In comparison to dark I-V measurements and simulations, the underlying physics and implementation of our method are much simpler and in good correlation with results obtained from both dark I-V measurements and simulations. The assumption R sh >>V oc /I sc is generally true for cells and modules. If the relation between V oc and lnI sc is sublinear for a cell or module, it can be concluded that the cell or module exhibits shunting behavior.

Due to its simplicity, our method can be used in any PV laboratory with a simulator as well as outdoors. These outdoor measurements would involve the physical measurements of V oc and I sc with an appropriate multimeter and place clear mesh layers over the modules to vary the incident irradiance on the modules. If the module temperature also varies, corrections need to be made for that. It can also be used on measurements taken outdoors with common laboratory equipment

The authors declare that there is no conflict of interest regarding the publication of this paper.

Figure 2: (a) Components of the recombination current in a forward biased p-n junction solar cell [2]. (b) Energy band diagram of a forward biased p-n junction corresponding to Figure 2(a).

b) shows the dependence of voltage for our cell on irradiance level as obtained from PVSIM. From this fig- ure, it is clear that the irradiance range that we are working

Figure 4: (a) Equivalent circuit model for an illuminated p-n junction solar cell connected to a load. (b) Energy band diagram of an illuminated solar cell corresponding to Figure 4(a).

Figure 6: V oc -I sc data for the 36-cell module. The symbols indicate measured data and the solid line indicates simulations. Also shown is the effect of low cell shunt resistances on the relation between V oc and I sc (dashed line).

Figure 8: V oc and I sc measured (symbols) at different irradiance levels. The solid line is a linear fit.

Figure 9: I-V characteristic of the 36-cell module measured (symbols) at STC and simulated (solid line) using PVSIM [8]. The performance parameters shown are those obtained from measurement.

Figure 11: Normalized I-V characteristics of the five module technologies used.

FitAll |

I 0 and n obtained from a nonlinear fit to measure dark I-V data of a single mono-Si cell. Parameter Estimated value Absolute deviation (%) I 0 (A) 5 39 × 10 −5 3 05 × 10 −3 n 2.83 0.03 |

I 0 and n for the 36-cell module obtained from V oc -I sc measurements compared to that simulated using PVSIM. Parameter V oc -I sc PVSIM I 0 (A) 2 44 × 10 −8 3 08 × 10 −8 n 1.24 1.26 |

Saturation current and ideality factor for a 14 Wp a-Si:H module obtained from V oc -I sc measurements. Parameter Exposure 0 kWh/m 2 80 kWh/m 2 130 kWh/m 2 I 0 (A) 5 47 × 10 −9 3 51 × 10 −6 2 59 × 10 −5 n 1.71 2.47 2.96 |

Module technology P max rated (W) P max @ STC (W) η (%) CIS 10.0 10.76 9.19 a-Si:H 14.0 12.98 4.41 EFG-Si 32.0 31.64 11.3 Multi-Si 30.0 30.62 11.0 Mono-Si 65.0 64.45 10.7 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 V/V oc I/I sc CIS a-Si:H EFG-Si Multi-Si Mono-Si |

Parameters (n and I 0 ) obtained for various module technologies from V oc -I sc measurements. Module CIS a-Si:H EFG-Si Multi-Si Mono-Si n 1.38 1.71 1.07 1.15 1.19 I 0 (nA) 486 5.47 1.28 5.82 40.7 |