# Shockley’s Equation Fit Analyses for Solar Cell Parameters from I-V Curves

Authors: Markus Diantoro; Thathit Suprayogi; Arif Hidayat; Ahmad Taufiq; Abdulloh Fuad; Risa Suryana
Journal: International Journal of Photoenergy
 (2018)

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## Abstract

Some of the technical problems that appear are obtaining solar cell parameters from I-V curve measurement data. One simple method is using linear graphical fit at zero current or voltage conditions. Although the accuracy of the obtained values is acceptable, other problems may arise regarding the number of parameters which could be obtained. We report a comparison between manual or graphical fit and fit using Shockley’s equation. The single I-V curve under the lighting was inferred to obtain the intrinsic parameters of the solar cells’ performance. The fittings were performed using the nonlinear equation of Shockley by determining some initial values of fittings such asRs, Rsh, n, I0, Iph, and T. In the case of the Shockley equation fit, the iteration was performed several times to obtain the least possible inferred parameters. We have successfully obtained a better result of nonlinear Shockley fitting compared to the manual linear fit.


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## Body

## 1. Introduction

Rapid growth in science, technology, and industry has increased electric energy needs. About 87% of the world’s energy consumption comes from fossils (oil, natural gas, and coal) which are a natural resource that cannot be renewed and lead to negative impact on the environment [1]. Therefore, developing electric energy from other natural resources which is eco-friendly is urgently required, such as the development of electric energy from solar energy [2]. Technically, solar energy can be converted into electric energy with a solar cell [3]. The solar cell is a device for green and clean electric power generation from solar energy. Solar cells have continued to evolve from single crystal silicon, thin film, organic solar cell, dye-sensitized solar cell (DSSC), and perovskite solar cell (PSC). Solar cell performance is continuously studied to raise conversion efficiency and capacity.So far, the developing solar cell efficiency has been performed by improving the materials [4], construction [5, 6], contact systems [7], and characterizations [8, 9]. The solar cell optimization could also be optimized for analysis and modeling. One model for solar cell analysis is proposed based on the Shockley diode model. The analysis model of the solar cell from I-V characterization is with or without illumination.One model for analyzing solar cell work is the single-diode model shown in Figure1. At a given illumination, the current/voltage relationship is given by (1) from the Shockley equation.
(1)I=Iph−I0expqV+RsInkBT−1−V+RsIRsh,where Iph, I0, Rs, Rsh, q, n, kB, and T are the photocurrent, the saturation current of the diode, the series resistance, the shunt resistance, the electron charge, the ideality factor, the Boltzmann constant, and the temperature, respectively.Figure 1
Single-diode model for a solar cell.The parameters in (1) correspond to the intrinsic characteristic of solar cell construction. The series resistance Rs represents the total resistance of the cell and is a composite of (1) the interfacial and active layer resistances, (2) the electrode resistances, and (3) the various contact and interconnect resistances [10]. The shunt resistance Rsh represents the p-n junction solar cell [11]. Parameters Rs and Rsh correspond to the fill factor (FF) of energy conversion in the solar cell.
(2)FF=ImaxVmaxIscVocDecreasingRs makes Isc and Vmax increase, and increasing Rsh makes Voc and Imax increase [11, 12]. Many researchers develop solar cell trough variation Rs [10] and Rsh [13, 14]. The ideality factor n is related to the diode and its recombination [15]. In the case of n=1, it represents a perfect crystalline structure with no structural defects [16]. The value of n>2 is associated with the tunneling effect or the reduction of mobility due to the defects or less crystalline material [15].The intrinsic solar cell parameters have been extracted from any method, such as a manual method with ideality factor approximation [17]. So, Rs and Rsh values correspond to the slope near Voc and Isc, respectively. By using this technique, many other parameters have not been found, such as Iph, I0, and n. Many researchers have done extraction of the solar cell parameter from the I-V curve. The parameters from (1) were extracted using the nonlinear fitting technique on a single I-V curve [18, 19]. However, the stability of the extraction results is difficult to achieve. Therefore, to extract the solar cell parameters like Iph, I0, Rs, Rsh, and n, the orthogonal distance regression with implicit equation model of the Shockley equation using origin lab was implemented.


## 2. Materials and Method

Data analysis technique on the I-V curve solar cell was needed to prove solar cell performance. Analysis of the I-V characteristic curve was done using the single-diode model equivalent circuit as shown in Figure1 and (1). The intrinsic parameters of the solar cell were extracted using manual linear and nonlinear fitting methods using orthogonal distance regression.The essential parameters of the solar cell based on the single-diode model was analyzed using the manual method with ideality factor value approximation [17]. Figure 2 shows how to determine the series resistance (Rs) and shunt resistance (Rsh) from an inverse slope near the Voc and Isc, respectively [17, 20].Figure 2
Series and shunt resistance extraction from a single I-V curve under illumination.The nonlinear fit was done using orthogonal distance regression using implicit model function (1) with origin lab. The initial value of the parameters was determined from the manual method for Rs and Rsh. The regression was done using about 500 iterations on the I-V curve until the best fit between the model and experimental data is obtained. By using this procedure, we found the intrinsic solar cell parameters of Iph, I0, Rs, Rsh, and n.


## 3. Results and Discussion

The comparison manual and nonlinear fittings of the I-V curve solar cell were applied to any solar cell generation. The comparison of two different equations was performed to know the effectivity for obtaining solar cell parameters based on the single-diode model. The intrinsic solar cell parameters were used to optimize the solar cell conversion efficiency.


### 3.1. Application to Silicon Solar Cell

The first result of the solar cell parameters of a silicon solar cell (R.T.C France) [21] using two different equation is presented. Figure 3 shows a comparison between the manual and nonlinear methods. It is observed that the linear method only fits in a particular area. Both the linear (solid blue line) and the nonlinear (solid red line) agree with experimental data of the I-V curve. Table 1 shows the result of the comparison of any extraction method.Figure 3
Curve fit on a silicon solar cell (R.T.C France) using the manual method (a) and the nonlinear curve fit using the Shockley equation (b).
(a)
(b)Table 1
Comparison of manual and Shockley nonlinear fit on any solar cell. The Δ is from reference whileχ2 is from this work.
Number
Solar cell
Voc (V)
Isc (A)
Iph (A)
I0 (μA)
Rs (Ω)
Rsh (kΩ)
n
T (°C)
Δ/χ2
1
Cell Si (R.T.C France) [21]
0.5728
0.7608
0.7608
0.3223
0.0364
0.0538
1.484
33
8.9 × 10−7
Manual
0.567
0.758
—
—
0.11
0.0324
—
—
Previous work [18]
0.57
0.76
0.77
0.2
0.037
0.032
1.4
5.6 × 10−7
Nonlinear fit
0.568
0.758
0.7595
0.186
0.047
0.0355
1.418
2.9 × 10−6
2
Module Si (Photowatt-PWP-201) [21]
16.778
1.03
1.0318
3.2876
1.2057
0.549
48.45
45
8.3 × 10−6
Manual
14.57
0.979
—
—
2.196
0.312
—
—
Previous work [18]
17
1
1
2.3
1.3
0.83
47
6.3 × 10−6
Nonlinear fit
14.69
0.979
0.98
10
0.518
0.404
46.83
7 × 10−5
3
Organic solar cell: ITO/CuPc/PTCBI/Ag [22]
—
—
—
—
—
—
—
20
—
Manual
1.203
0.00449
—
—
78.59
1.222
—
—
Previous work [18]
1.2
0.0046
0.0047
0.92
48
1.4
5.8
1.1 × 10−3
Nonlinear fit
1.204
0.00449
0.00468
0.918
48.34
1.232
5.74
3.13 × 10−10
4
Organic solar cell-based p-type NiO: glass/ITO/NiO/P3HT:PCBM/LiF/Al [23]
—
—
—
—
—
—
—
27
Manual
0.638
0.0113
—
—
6.468
1.757
—
—
Previous work [10]
0.0117
0.365
1.4
3.96
2.38
—
Nonlinear fit
0.6406
0.0113
0.0113
0.0747
2.196
2.438
2.08
3.2 × 10−9
5
Perovskite solar cell: mp-TiO2/CH3NH3PbI [9]
—
—
—
—
—
—
—
—
Manual
0.944
0.018
—
—
8.687
0.503
—
27
—
Nonlinear fit
0.938
0.018
0.0182
0.0558
1.115
0.513
2.87
6.36 × 10−8
6
DSSC [8]
0.704
0.00206
—
0.035
43.8
3.736
2.5
20
—
Manual
0.708
0.002
—
—
93.27
3.532
—
—
Nonlinear fit
0.702
0.00206
0.0021
0.0345
38.55
3.402
2.55
1.4 × 10−10Figure4 shows the result of the I-V curve fit on a silicon solar cell module (Photowatt-PWP-201) [21]. It shows that the nonlinear fit method agrees with experimental data of the I-V curve and previous work.Figure 4
I-V curve fit on a silicon solar cell module (Photowatt-PWP-201) using the manual method (a) and nonlinear curve fit using the Shockley equation (b).
(a)
(b)


### 3.2. Application to Organic Solar Cell

Comparison manual and nonlinear fit method on the I-V curve of an organic solar cell, ITO/CuPc/PTCBI/Ag [22], is shown in Figure 5. Not only silicon solar cell but also organic solar cell parameters can be extracted using nonlinear fit using orthogonal distance regression. Table 1 shows the result of comparison of any extracted method and the previous work.Figure 5
I-V curve fit on an organic solar cell based on ITO/CuPc/PTCBI/Ag: (a) manual method and (b) nonlinear curve fit.
(a)
(b)The comparison manual and nonlinear curve fit applied to other organic solar cell-based p-type NiO, glass/ITO/NiO/P3HT: PCBM/LiF/Al [23], is shown in Figure 6. It shows suitability between the experimental data and nonlinear fit.Figure 6
Organic solar cell based on p-type NiO: (a) manual method and (b) nonlinear curve fit.
(a)
(b)


### 3.3. Application to Perovskite Solar Cell

Not only silicon and organic solar cells but also a perovskite solar cell I-V curve can be used to compare the manual and nonlinear curve fit based on the Shockley equation. Figure7 shows the comparison between experimental data and fitting method on a perovskite solar cell. Table 1 shows the result of the fitting method for perovskite solar cell parameters. The parameter of PSC can be used to upgrade solar cell conversion efficiency based on mesoporous TiO2 and CH3NH3PbI [9].Figure 7
Fitting I-V curve perovskite solar cell based on mp-TiO2 with CH3NH3PbI: (a) manual fit and (b) nonlinear curve fit.
(a)
(b)


### 3.4. Application to DSSC

The manual and nonlinear fit methods are applied to extract solar cell parameters on DSSC with TiO2 as the photoanode and ruthenium as the sensitizer [8], and the results are shown in Figure 8. The I-V curve fit result of the DSSC parameter is shown in Table 1. The analyses of carboxyl effects on the TiO2 photoanode has been studied using a single-diode model. The analyses were performed by determining DSSC intrinsic parameters in terms of carboxyl effects. It was found that the use of carboxyl acid gives rise to reducing the Rs value, which indicates the increase of electrical contact among TiO2 particles [8].Figure 8
I-V curve fit of DSSC: (a) manual method and (b) nonlinear curve fit.
(a)
(b)


## 3.1. Application to Silicon Solar Cell

The first result of the solar cell parameters of a silicon solar cell (R.T.C France) [21] using two different equation is presented. Figure 3 shows a comparison between the manual and nonlinear methods. It is observed that the linear method only fits in a particular area. Both the linear (solid blue line) and the nonlinear (solid red line) agree with experimental data of the I-V curve. Table 1 shows the result of the comparison of any extraction method.Figure 3
Curve fit on a silicon solar cell (R.T.C France) using the manual method (a) and the nonlinear curve fit using the Shockley equation (b).
(a)
(b)Table 1
Comparison of manual and Shockley nonlinear fit on any solar cell. The Δ is from reference whileχ2 is from this work.
Number
Solar cell
Voc (V)
Isc (A)
Iph (A)
I0 (μA)
Rs (Ω)
Rsh (kΩ)
n
T (°C)
Δ/χ2
1
Cell Si (R.T.C France) [21]
0.5728
0.7608
0.7608
0.3223
0.0364
0.0538
1.484
33
8.9 × 10−7
Manual
0.567
0.758
—
—
0.11
0.0324
—
—
Previous work [18]
0.57
0.76
0.77
0.2
0.037
0.032
1.4
5.6 × 10−7
Nonlinear fit
0.568
0.758
0.7595
0.186
0.047
0.0355
1.418
2.9 × 10−6
2
Module Si (Photowatt-PWP-201) [21]
16.778
1.03
1.0318
3.2876
1.2057
0.549
48.45
45
8.3 × 10−6
Manual
14.57
0.979
—
—
2.196
0.312
—
—
Previous work [18]
17
1
1
2.3
1.3
0.83
47
6.3 × 10−6
Nonlinear fit
14.69
0.979
0.98
10
0.518
0.404
46.83
7 × 10−5
3
Organic solar cell: ITO/CuPc/PTCBI/Ag [22]
—
—
—
—
—
—
—
20
—
Manual
1.203
0.00449
—
—
78.59
1.222
—
—
Previous work [18]
1.2
0.0046
0.0047
0.92
48
1.4
5.8
1.1 × 10−3
Nonlinear fit
1.204
0.00449
0.00468
0.918
48.34
1.232
5.74
3.13 × 10−10
4
Organic solar cell-based p-type NiO: glass/ITO/NiO/P3HT:PCBM/LiF/Al [23]
—
—
—
—
—
—
—
27
Manual
0.638
0.0113
—
—
6.468
1.757
—
—
Previous work [10]
0.0117
0.365
1.4
3.96
2.38
—
Nonlinear fit
0.6406
0.0113
0.0113
0.0747
2.196
2.438
2.08
3.2 × 10−9
5
Perovskite solar cell: mp-TiO2/CH3NH3PbI [9]
—
—
—
—
—
—
—
—
Manual
0.944
0.018
—
—
8.687
0.503
—
27
—
Nonlinear fit
0.938
0.018
0.0182
0.0558
1.115
0.513
2.87
6.36 × 10−8
6
DSSC [8]
0.704
0.00206
—
0.035
43.8
3.736
2.5
20
—
Manual
0.708
0.002
—
—
93.27
3.532
—
—
Nonlinear fit
0.702
0.00206
0.0021
0.0345
38.55
3.402
2.55
1.4 × 10−10Figure4 shows the result of the I-V curve fit on a silicon solar cell module (Photowatt-PWP-201) [21]. It shows that the nonlinear fit method agrees with experimental data of the I-V curve and previous work.Figure 4
I-V curve fit on a silicon solar cell module (Photowatt-PWP-201) using the manual method (a) and nonlinear curve fit using the Shockley equation (b).
(a)
(b)


## 3.2. Application to Organic Solar Cell

Comparison manual and nonlinear fit method on the I-V curve of an organic solar cell, ITO/CuPc/PTCBI/Ag [22], is shown in Figure 5. Not only silicon solar cell but also organic solar cell parameters can be extracted using nonlinear fit using orthogonal distance regression. Table 1 shows the result of comparison of any extracted method and the previous work.Figure 5
I-V curve fit on an organic solar cell based on ITO/CuPc/PTCBI/Ag: (a) manual method and (b) nonlinear curve fit.
(a)
(b)The comparison manual and nonlinear curve fit applied to other organic solar cell-based p-type NiO, glass/ITO/NiO/P3HT: PCBM/LiF/Al [23], is shown in Figure 6. It shows suitability between the experimental data and nonlinear fit.Figure 6
Organic solar cell based on p-type NiO: (a) manual method and (b) nonlinear curve fit.
(a)
(b)


## 3.3. Application to Perovskite Solar Cell

Not only silicon and organic solar cells but also a perovskite solar cell I-V curve can be used to compare the manual and nonlinear curve fit based on the Shockley equation. Figure7 shows the comparison between experimental data and fitting method on a perovskite solar cell. Table 1 shows the result of the fitting method for perovskite solar cell parameters. The parameter of PSC can be used to upgrade solar cell conversion efficiency based on mesoporous TiO2 and CH3NH3PbI [9].Figure 7
Fitting I-V curve perovskite solar cell based on mp-TiO2 with CH3NH3PbI: (a) manual fit and (b) nonlinear curve fit.
(a)
(b)


## 3.4. Application to DSSC

The manual and nonlinear fit methods are applied to extract solar cell parameters on DSSC with TiO2 as the photoanode and ruthenium as the sensitizer [8], and the results are shown in Figure 8. The I-V curve fit result of the DSSC parameter is shown in Table 1. The analyses of carboxyl effects on the TiO2 photoanode has been studied using a single-diode model. The analyses were performed by determining DSSC intrinsic parameters in terms of carboxyl effects. It was found that the use of carboxyl acid gives rise to reducing the Rs value, which indicates the increase of electrical contact among TiO2 particles [8].Figure 8
I-V curve fit of DSSC: (a) manual method and (b) nonlinear curve fit.
(a)
(b)


## 4. Conclusion

The application of manual and nonlinear fit methods on any solar cell single I-V curve has been performed. The nonlinear fit using Shockley’s equation by employing orthogonal distance regression produces more solar cell parameters. It is also demonstrated that operating the nonlinear Shockley equation to several solar cell systems is highly agreeable with experimental data compared to the manual linear method.



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*Source: 9214820-2018-04-01.xml*