Solar cells

The solar cells used in CPV are made with many different technologies, depending on the kind of used concentrator. In general, for low and medium concentration level, up to about

300 Suns, cells made of Silicon are still used; for higher concentrations, cells based on III-V semiconductors are usually employed; these latter cells allow for efficiency in the order of 40% and find their natural application under high concentration. Due to the high cost of the base materials and processes, these ultra-high efficiency cells found application for space satellites and for terrestrial concentrators. Thin film solar cells, in particularly made of CIS – CIGS, have given interesting results under concentration too (Ward et al, 2009), but, till now, no significant applications have been developed out of the laboratory scale.

The light concentration, through the increasing of the concentration of the minority carriers, improves the efficiency of the solar cells logarithmically. The produced current is linearly proportional to the irradiation level; because of the generated power is given by the product between the current and the voltage and the voltage increases logarithmically with the concentration level as in (9), the power increases in the mentioned super-linear way. In (9) C is the concentration level, while Jph_isun is the photo-generated current under one standard sun level of irradiation.

Подпись: (9)ln Г CJVh1Sun

q I J0

Where Jo is the dark current of the diode and A is the ideality factor of the device.

An additional advantage for CPV cells is the performances reduction with the temperature, which is lower under concentrated light respect to the same effect under one Sun of irradiation, for the same kind of cell. This is true in general, for all semiconductor; in addition, III-V cells, often used in CPV, have a lower temperature coefficient than standard crystalline silicon solar cells. For example, the interdigited back contact silicon solar cells have a voltage temperature coefficient of about -1.78 mV/°C under one sun and of about – 1.37 mV/°C at 250 suns (Yoon, 1994), while for GaAs from -2.4 mV/°C under one sun, to – 1.12 mV/°C at 250 suns (Siefer, 2005). The dependence of the temperature coefficient with the concentration appears, in first approximation, with a logarithmic behaviour, as in (10); considering the Voc as the voltage associated to the energy gap between the quasi-Fermi energy levels of the illuminated cell, as from fig. (8), this value is given by (11), where C is the concentration level, while B is a parameter dependent on various physical characteristics of the material.

image051p

n


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Fig. 8. Schematic band diagram of an illuminated p-n junction of a cell in open circuit conditions

Подпись: V =E v oc — ln( CB)

q

So, the temperature coefficient becomes:

dV k ln(-^)

l2j_oc^__ VC^ (11)

dT q

One of the main differences in the technology fabrication between concentrator solar cells and standard solar cell is the requirement for the CPV cells, producing high current density, to have low series resistance.

Подпись: J = Jph - J0exP Подпись: q(v + JRs) AkT Подпись: V + JRS Подпись: (12)

A simplified formula describing the I-V characteristics of a solar cell taking into account the resistance effect is eq.(12); two electrical resistances can be considered: a series resistance, Rs, and a parallel resistance, Rshunt. In a simple one dimensional model they are represented using the solar cell equivalent electrical circuit of fig.(9). It’s a rough electrical schematization of the SC, because of the resistances are lumped; a more precise equivalent circuit should require distributed parameters in 3-D (Galiana et al., 2005).

Подпись: Fig. 9. Simplified 1D equivalent electric circuit of a solar cell

Where Jo is the dark current of the diode and Jph represents the photo-generated current.

The simplified electrical equivalent circuit of fig.(9) is enough to explain the importance of attaining Rs as low as possible, especially in the case of concentrator solar cells. Indeed, the higher the current, the higher the voltage drop across the series resistance; in this way, the diode senses a voltage higher than that one on the external load, so its exponential behaviour reduces the current in the external circuit when the voltage on the diode is closed to its threshold voltage. The discrepancy between the voltage on the diode and the voltage on the external load gives a shortage in the current delivered from the cell in the region of the I-V characteristic with higher V.

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