The optimum bandgap combination depends slightly on the materials properties; for the air mass zero spectrum, using idealized materials, maximum efficiency of a two element series-connected cascade occurs at bandgaps of 1.75 for the top cell and 1.05 for the bottom cell [44]. For the efficiencies of Fig. 1, this results in a maximum efficiency of 33%, about 50% higher than the efficiency of 24.4% calculated for a single bandgap cell. Cascades can be configured as monolithic, in which the top cell is integrally deposited on the bottom cell (or vice-versa), or mechanically stacked, in which the two sets of cells are formed separately. Electrical interconnections can be set up as two terminal, three terminal, or four terminal configurations. In general, monolithic modules must be two terminal or possibly three terminal devices; while mechanically stacked modules can be configured as four-terminal devices as well. For a two- terminal current-matched cascade, the current through the top cell must equal that through the bottom. This means that once the bandgap of one component has been chosen, the bandgap of the other is determined. Four terminal cascades allow separate connection to the top and bottom cells. If the power is taken separately from each set of sub-cells, this connection requires no matching of voltage or current. The maximum efficiency is almost the same for all configurations. However, the current-matched configuration is very sensitive to the bandgaps, and loses efficiency very rapidly when the matching condition is not exactly met. The four-terminal system is relatively insensitive to the exact bandgap, while voltage-matched configurations are intermediate in sensitivity. Figure 5 shows efficiencies calculated by Fan [44] for cascade solar cells at AMO in both the series connected and in the independent operation mode. The maximum efficiency is about the same for both, but the independent operation allows a much wider range of bandgaps. An important element in a monolithic cascade is a shorting junction to connect the base of the top cell to the emitter (or window layer) of the bottom cell to allow current to flow from the first to the second. The main question about monolithic cascades is whether the technology can be made to work. In particular, the deposition of the second cell must not cause the first cell to degrade, either by thermal effects due to the heat of deposition causing decomposition or interdiffusion of the first cell, or by material incompatibility, such as might happen if diffusion of some component of the second cell into the first reduces minority carrier lifetime. For cascades where the top cell bandgap is lower than the optimum bandgap for current matching, it is possible to create a current-matched cascade if the top cell is made to pass through some of the light that would normally be absorbed. This is discussed in [41], There is a wide range of possible thin-film semiconductors for a two-cell cascade. Only a few, however, have to date shown potential for producing good thin-film solar cells. Experimental Results The best currently demonstrated thin-film cascade, reported by ARCO Solar [45], uses an amorphous silicon top cell on a CuInSe2 bottom cell. The achieved efficiency is 12.5% AMO. In this cell the two elements were deposited separately, the a-Si on a glass superstrate and the CuInSe2 on a metal-coated glass substrate, and the two
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