Normalized Area Solar Cell and Potential Applications

Nowadays in laboratories and in industries, distribution of solar cells sizes could be very large, hence; for the first time it is rather difficult to compare photovoltaic parameters which are size dependent (current, serial resistance, shunt resistance...) and performances of these cells. Also, it will be useful for scale effect to extrapolate performances calculated on a unit size solar cell to commercial products, especially in the case of heterogeneous wafers used for the device.

Single diode model for illuminated solar cell could be used here [4,5,6], this model take in account the shunt across the junction (rsh), the lumped resistance (rs).
In this model, the output (I-V) characteristic is given by the equation 1 .
. 1 ) ) .( exp( Rsh Equation 1: (I-V) analytical expression for one exponential model solar cell The difficulty in equation 1is that two kinds of parameters coexists, intensive parameter such as voltage (V), temperature (T),… and extensive ones such as current (I), resistances (Rs and Rsh).If we want a quantitative comparison between solar cells with different surface areas (S), it is necessary to give the current density, J, versus voltage, V, equation.This expression is simply derived from (1) with the assumption: We can now introduce a normalized area solar cell (S = 1cm 2 for instance) with resistance specifications given in .cm 2 units.

S Rs rs
.  (4) And It is now obvious that for a given solar cell (material and process) the serial and shunt resistance decrease if the area increases.To highlight this, for two solar cells with S and S' area respectively and if S' > S, equations Applications and results

-Surface area effect on photovoltaic properties in one sun application
Thanks to this model, it is relatively easy to extrapolate photovoltaic parameters computed for a unit size solar cell to another size, just by calculating Rs and Rsh for the size S.The formula used in this case is: For size S: S rs Rs  and S rsh Rsh  In order to verify this assumption, PC1D and SPICE codes are used, we have modelized a unit solar cell with parameters generally used in conventional p-type silicon solar cells.Table 2 shows values obtained for three surface areas, it is clear that these results are in good agreement with the previous assumption.

-Serial resistance loss in concentrated photovoltaic CPV solar cells
Concentrated photovoltaic is very attractive due to the fact that for the same solar cell size, the photovoltaic properties are increased with X, when the device is illuminated under X sun.
A current question is whether conventional solar cells can be used for low concentration applications, typically X<10.
With our model, it is evident that it is not possible, because of the high serial resistance value.In fact, figures 2a and 2b show the drastic effect of the serial resistance.If solar flux is concentrated on conventional solar cells (rs = 1.5 .cm 2 ), Jsc increases linearly if X < 10 and saturates after this value, but and most importantly, there is a decrease in conversion efficiency.
If you want to optimise this possible utilisation for conventional solar cells, the rs value must be divided by a factor of ten (rs = 0.15 .cm 2 ), which is not easy with today's technology.

-Solar cell modelized by N unit solar cells
In a solar cell, global performances are largely relative to local ones, specifically in heterogeneous material such as multi-crystalline silicon.
To evaluate local properties it is useful to divide a large size into N unit solar cells, in figure 3 in order to illustrate this method, we have chosen N = 4, the USCs are connected in parallel.Evidently, the performances for the final solar cell are conserved, but this ideal case could be attributed to an homogeneous solar cell, in terms of materiel, for instance monocrystalline wafer and uniform processes.Generally, especially for multicrystalline ingots, heterogeneous properties govern final solar cell performances.In a rapid approach we can evaluate the effects of local defects at the scale of individual USC on global performance, such as local shunt (rsh), local bad electrical contact (rs) and local bad photon collection or conversion (Jph) Now, to evaluate the impact of unit solar cells on the final device, we have chosen to see the influence of rs, rsh and Jph after a 50% variation of their initial value.

Application 2: Serial resistance discrepancy
In the electrical model figure 1, serial resistance rs is a lumped value that takes into account contact resistance on the emitter and the base, grid line contact and semiconductor resistivity.This final value depends greatly on the process and also on possible degradation during the solar cell's lifetime.In this case, illustrated by figure 5a, b and c, we have just increased the rs value for one cell, this modified value is equal to 2,25 ohms, which represents also 50% variation.We can see in figure 5c, that only conversion efficiency of the solar cell is affected and decreases to 14,81 %.

Application 3: Shunt resistance discrepancy
For this case, we have taken into account a 50% decrease of the shunt resistance in the unit solar cell (figure 6a, b, and c).Especially in multicristalline wafers, shunt leakage must be attributed to crystallographic defects decorated with metallic impurities crossing the junction.During the solar cell fabrication, shunt resistance degradation must appear at the aperture of the junction process.We can see that for this local variation, the total properties of the cell are not greatly affected, but evidently if the shunt leakage increases the impact will be more important.This case must be attributed to an accidental partial shadowing of the cell, or more problematically to a local area with poor electronic quality due to the presence of electrical recombining impurities for instance.We have also kept with the same total variation (50%) of the unit Jsc value, 17.5 mA/cm 2 instead of 35 mA/cm 2 , and the results are described in figure 7a, b and c.It is obvious that this situation is the worst case, because of the degradation of all photovoltaic parameters (V oc , J sc and )

Conclusion:
We have proposed a method seeking to explain properties of solar cell by local analysis thanks to a normalized area solar cell concept.Most of actual solar cells technologies are based on multicristaline materials (Si, CIGS, CdTe,) and for each category as we have done for silicon, parameters for each unit solar cell must be defined.
As we have described in this article, several applications could be concerned with this analysis and for further studies, it will be such interesting to implement and compare this model with local photoelectrical characterizations as Light Beam Induced Current (LBIC), Photoluminescence and Electroluminescence Imaging.

Figure 1 :
Figure 1: One diode electrical model of illuminated solar cell

Figure 3 :Application 1 :Figure 4 :
Figure 3: Homogeneous solar cell composed by four parallel Unit Solar Cells

Application 4 :
Local photocurrent generation discrepancy

Best values for parameters used in equation
(6)To estimate Jo, Jph, a, rs and rsh values, we have made some statistical measurements on elaborated solar cells characterized under standard one sun test condition (AM1,5G) (Table1 )

Table 1 :
Electrical and photovoltaic parameters average values for p-type multi-crystalline silicon solar cells (surface area size = 1 cm 2 )

Table 2 :
Evolution of photovoltaic parameters with the surface areas of the cells