Page 169 - A Comprehensive Guide to Solar Energy Systems

170 A CoMPrehensIVe GuIde To soLAr enerGy sysTeMs

FIGURE 8.19 Maximum conversion efficiency in dependence on bandgap (spectrum AM 1.5).

bandgaps. Consider that the light enters the first cell of material with W g1 , where a part of
the spectrum (shorter wavelengths) is absorbed. The unabsorbed light then penetrates
into the second cell of material with W g2 (W g2 < W g1 ), where it is absorbed. If the irradiation
/
hc W g1
∫λminhc/Wg1Wg1Φ 0 (λ)dλ power ∫ W g1 Φ () λ
λ d is transferred in electron–hole pair generation in the first cell and
0
/
λ min hc W g 2
∫hc/Wg1hc/Wg2Wg2Φ 0 (λ)dλ the irradiation power ∫ W g 2 Φ () λ
λ d is transferred in electron–hole pair generation in
0
/
hc W g1
the second cell, the ultimate efficiency of the tandem structure η ut is given by
/ /
hC W e1 hC W e1
∫ W g1 Φ () λ + ∫ W g 2 Φ () λ
λ d
λ d
0
0
/
λ min hC W e1 = n . (8.28)
∞ hC ut
∫ λ Φ () λ
λ d
0
∫λminhc/Wg1Wg1Φ 0 (λ)dλ+∫hc/Wg1hc/ λ min
Wg2Wg2Φ 0 (λ)dλ∫λmin∞hcλΦ 0 (λ)dλ=nut.
Comparing eqs. (8.27) and (8.28) it is clear that the ultimate efficiency of the tandem
structure consisting of two cells from materials of different bandgap can overcome the
Quasier–shockley limit and η ut > η u . This is demonstrated in Fig. 8.20 for a tandem of
GaInP and of Ge.
Adding more layers can bring a further increase in the ultimate efficiency of multima-
terial structures with suitably selected bandgaps [3, 7], as demonstrated in Table 8.1. For
infinite number of layer, the maximum efficiency is 68% for terrestrial applications.
note that in multimaterial structures the individual cells are connected in series. There-
fore, the current in-series connected cells are limited by the cell that delivers the lowest
current generated—that makes a special demand on material selection.
Joining of different materials may have a limit in a lattice structure mismatch and
there are also some more technological difficulties. however, multilayer cells with ef-
ficiency over 45% have already been realized. More details about construction and tech-
nology of these structures can be found in literature(e.g. [3, 7]). There are also some other