# Simulation section

Now, to justify the experiment section, we use the computer simulation, which is an important tool for investigating the behaviour of semiconductor devices and for optimising their performance. Extraction and optimisation of semiconductor device parameters is an important area in device modelling and simulation (Chergaar. M et al, 2008; Bashahu M et al, 2007; Priyanka et al, 2007). The current-voltage characteristics of photocells, determined under illumination as well as in the dark, represent a very valuable tool for characterizing the electronic properties of solar cells. The evaluation of the physical parameters of solar cell: series resistance (Rs), ideality factor (n), saturation current (Is), shunt resistance (Rsh) and photocurrent (Iph) is of a vital importance for quality control and evaluation of the performance of solar cells when elaborated and during their normal use on site under different conditions. I-V characteristics of the solar cell can be presented by either a two diode or by a single diode model. Under illumination and normal operating conditions, the single diode model is however the most popular model for solar cells. In this case, the current voltage (I-V) relation of an illuminated solar cell is given by:

Iph, Is, n, Rs and Gsh (=1/Rsh) being the photocurrent, the diode saturation current, the diode quality factor, the series resistance and the shunt conductance, respectively. Ip is the shunt current and p=q/kT is the usual inverse thermal voltage. The circuit model of solar cell corresponding to equation (1) is presented in figure (4).

 Fig. 4. Equivalent circuit model of the illuminated solar cell.

Determination of Rsh

The shunt resistance is considered Rsh = (1 / Gsh) >> Rs. the shunt conductance Gsh is evaluated from the reverse or direct bias characteristics by a simple linear fit (Nehaoua. N et al, 2010). The calculated value of Gsh gives the shunt current Ip = GshV.

Determination of n and Rs

Before extracting the ideality factor and the series resistance, our measured I-V characteristics are corrected considering the value of the shunt conductance as obtained from the linear fit and for V+RsI>>kT, the current voltage relation becomes:

(2)

The method concerns directly the usual measured I-V data by writing Eq. (2) in its logarithmic form:

ln(Iph – I) = lnIs +-П(V + IRs) (3)

For a point defined by (V0, I0) we have:

ln Vph -10 ) = ln Is + "“(V + І0 Rs) (4)

By subtracting Eq. (3) and Eq. (4) and after a simplification we get a linear equation given by:

Y =“(Rs + X) For I>>IS n

where:

(Vo, I0) is a point of the I-V curve.

We consider a set of Ii-Vi data giving rise to a set of X-Y values, with i varying from 1 to N. Then, we calculate X and Y values for I0 = Ii0 and I=Ii0+1 up to I=IN. This gives (N-1) pairs of X-Y data. We start again with I0 = Ii0+1 and I = Ii0+2 up to IN and get (N-2) additional X-Y data, and so on, up to I0 = IN-1. Finally, we obtain N(N-1)/2 pairs of X-Y data that means more values for the linear regression. The linear regression of equation (5) gives n and Rs.

Determination of Iph

For most practical illuminated solar cells we usually consider that Is<<Iph, the photocurrent can be given by the approximation Isc » Iph, where Isc is the short-circuit current. This approximation is highly acceptable and it introduces no significant errors in subsequent calculations (Nehaoua. N et al, 2010).

Determination of Is

The saturation current Is was evaluated using a standard method based on the I-V data by plotting ln(Iph-Icr) versus Vcr equation (8). Note that I-V data were corrected taking into account the effect of the series resistance.

ln (Iph — Icr )= ln (Is )+ £ Vc (8)

When we plot ln (Ic) where (Ic=Iph-Icr) versus Vcr, it gives a straight line that yields Is from the intercept with the y-axis.

4.1 Application

The method is applied on the too type of Dey-sensitized solar cell, the first one is based on TiO2 nanostructures and ZnO nanotube under different condition of fabrication, illumination and temperature. The current-voltage (I-V) characteristics of TiO2 nanostructures DSSC is taken from the work of (Fang Sho et al, 2010) and The current – voltage (I-V) characteristics of ZnO nanotube is taken from the work of (Jingbin Han et al, 2010). The two characteristics correspond to the higher photovoltaice performance, where П=6.00%, FF=58.33%, Isc=15.25mAcm-2 and Voc=0.67V for TiO2 nanostructures, and for ZnO nanotube n=1.18%, FF=0.58%, Isc=3.24mAcm-2 and Voc=0.68V.

4.2 Results and discussion

The shunt conductance Gsh = 1 / Rsh was calculated using a simple linear fit of the reverse or direct bias characteristics. The series resistance and the ideality factor were obtained from the linear regression (5) using a least square method.

In order to test the quality of the fit to the experimental data, the percentage error is calculated as follows:

Є =(Ii – h, cal )(100/Ii) (9)

Where Ii, cai is the current calculated for each Vi, by solving the implicit Eq.(1) with the determined set of parameters ( Iph, n, Rs, Gsh, Is). (I, Vi) are respectively the measured current and voltage at the ith point among N considered measured data points avoiding the measurements close to the open-circuit condition where the current is not well-defined (Chegaar M et al, 2006).

Statistical analysis of the results has also been performed. The root mean square error (RMSE), the mean bias error (MBE) and the mean absolute error (MAE) are the fundamental measures of accuracy. Thus, RMSE, MBE and MAE are given by:

RMSE = (X|e|2 / N)1/2

MBE = £ ei / N (10)

MAE = £|e. / N

N is the number of measurements data taken into account.

The extracted parameters obtained using the method proposed here for the Dey-Sensitized solar cell based on TiO2 nanostructures and ZnO nanotube are given in Table 3. Satisfactory agreement is obtained for most of the extracted parameters. good agreement is reported. Statistical indicators of accuracy for the method of this work are shown in Table 3.

 DSSC-TiO2 nanostructures DSSC-ZnO nanotube G, h(£2-‘) 0.001269 0.000588 R_ (Q) 0.025923 0.383441 n 1.(-.29251 3.560949 U(h A) 0.3355b 0.16553 lrh(m А/cm2) 15.99 3.25 RMSE 0.850353 1.875871 MBE 0.232276 0.727544 MAE 0.757886 1.053901
 Table 3. Extracted parameters for Dey-Sensitized solar cell based on TiO2 nanostructures and ZnO nanotube.

Figures 5 and 6 show the plot of I-V experimental characteristics and the fitted curves derived from equation (1) with the parameters shown in Table 3 for Dey-Sensitized solar cell based on TiO2 nanostructures and ZnO nanotube. The interesting point with the procedure described herein is the fact that we do not have any limitation condition on the voltage and it is reliable, straightforward, easy to use and successful for different types of solar cells. Extracting solar cells parameters is a vital importance for the quality control and evaluation of the performance of the solar cells, this parameters are: series resistance, shunt conductance, saturation current, the diode quality factor and the photocurrent. In this work, a simple method for extracting the solar cell parameters, based on the measured current – voltage data. The method has been successfully applied to dey-Sensitized solar cell based on TiO2 nanostructures and ZnO nanotube under different temperatures.

 DSSC TiO2 nanostructures Solar Cell Fig. 5. Experimental (•) data and fitted curve of TiO2 nanostructures DSSC.

 x 10-3 ZnO nanotube DSSc solar cell Fig. 6. Experimental (•) data and fitted curve of ZnO nanotube DSSC.

Figures 5 and 6 shows the plot of I-V experimental characteristics and the fitted curves derived from equation (1) with the parameters shown in Table 3 for the dey-Sensitized solar cell based on TiO2 nanostructures and ZnO nanotube solar cell. Good agreement is observed for the different structure, especially for the TiO2 nanostructures solar cells with statistical error less than 1%, and 2% for ZnO nanotube DSSC solar cells respectively, which attribute mainly to lower parasitic losses, where we can observe a low series resistance 0.025923Q compared to 0.383441 Q for TiO2 nanostructures and ZnO nanotube solar cell respectively. The interesting point with the procedure described herein is the fact that we do not have any limitation condition on the voltage and it is reliable, straightforward, easy to use and successful for different types of solar cells.

5. Conclusion

In this contribution, a simple comparative study between experimental and simulation works to improve the dey-sensitized solar cell performance of two DSSCs based on TiO2 nanostrucures and ZnO nanotube, under differents condition of temperature. We compare the different parameters which are: the conversion efficient, the fill factor, the short-circuit photocurrent and the open-circuit voltage, where we observe a high photovoltaic performance for TiO2 nanostrucures with maximun conversion efficient 6% compared to

1. 18% for ZnO nanotube. In second time, an evaluation of the physical parameters of solar cell: series resistance (Rs), ideality factor (n), saturation current (Is), shunt resistance (Rsh) and photocurrent (Iph) from measured current-voltage characteristics by using a numerical method proposed by th authors. Extracting solar cells parameters is a vital importance for the quality control and evaluation of the performance of solar cells when elaborated and during their normal use on site under different conditions. Good resuts are given by the differents DSSCs, and specialy for on dey-sensitized TiO2 nanostrucures, which justify the experimental work.