Two types of tapering with the aim to improve the LSC performance have been considered in the past. Goetzberger and Schirmer (1979) proposed a taper along the LSC edge consisting of a higher refractive index material than the bulk of the LSC. This concept, depicted in Figure 20, received further attention from other groups (Barnham, et al., 2000; Hermann, 1982) due to its potential to boost the concentration ratio by reducing the required area of solar cell material.
Kennedy (2007) carried out raytrace simulations on a variant that had a PV cell only on one LSC edge and was tapered towards that PV cell edge (see Figure 21), with the motivation to reduce
Figure 19. The effect of back reflectors under diffuse irradiation, simulated with the raytrace model. The diffuse light was assumed to be incident over a hemisphere.
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Fraction of total photons
the PV cell area and improve the cost per unit power. However, it was found that in this case light originally trapped by TIR can escape while travelling towards the cell as the angled bottom surface gradually changes the internal angle upon reflection. The overall outcome was that tapering towards the edge with the PV cell always leads to a loss in optical concentration and hence in the cost per unit power.
A different type of tapered geometry is examined in this section, one that also has only one PV cell edge, but is tapered towards the edge opposing the PV cell, as shown schematically in Figure 22. In contrast to the previous two concepts, where the tapering had the purpose of reducing the cell area and thereby increasing the geometric gain and hence the optical concentration, in this concept, the tapering is intended to improve the light guiding properties. The idea behind this is similar to the principle ofthe wedge-shaped concentrator proposed by Maruyama (1999): the angle of the bottom surface can impart a preferential direction upon reflection that facilitates the light transport towards the PV cell edge. This design could be modified to allow for PV cell coverage on all four LSC edges, for example by tapering the LSC radially towards the centre. However, the simplified case with only once PV cell edge should suffice for the purpose of determining the benefit of the tapered design.
Raytrace simulations were carried out on an LSC with 50×50 cm2 top surface area where the thickness of the PV cell edge was held constant and the thickness ofthe opposing edge was varied, as illustrated in Figure 22. A refractive index of 1.49 and constant background absorption of 2m-1 were input, and the QD400 (see Figure 17) with a QY of 90% was modelled as the luminescent species. The photon flux into the PV cell relative to the case without tapering was recorded. This relative photon flux is proportional to the optical concentration since the dimensions ofthe PV cell and the LSC top surface area were kept constant. Clearly, the average thickness of the LSC decreases as the tapering becomes more pronounced, so a decrease in the overall absorption of incident light is expected with increasing tapering.
Initial simulations based on an LSC with a 10 cm thick PV cell edge showed improvements in the photon flux into the PV cell of 30-40% with tapering (see Figure 23). Figure 23 also shows a decrease in the relative photon flux when the thickness of the tapered edge is less than:10% the thickness of the PV cell edge. This loss is attributed to a weakened overall absorption due to the smaller average LSC thickness.
Since an LSC thickness of 10 cm is considered impractical, the simulations were repeated using a more realistic thickness of 3mm. As can be seen from the results in Figure 24, the improvements with tapering are small (approximately 10%) in this case.
In conclusion, the tapered geometry presented in this section can improve the light guiding within the LSC. However, to allow for PV cell coverage on all LSC edges, a more complicated design would be required with a constant edge thickness and a tapered centre. Moreover, structural integrity arguments would limit the extent of the tapering in a real application. Given the complications and the marginal advantages, the tapered design is unlikely to be pursued further.