Application Limits for the Ideal Conditions
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The solar cells covered in the previous chapters are idealized solar cells, which allowed us to evaluate the efficiency limits under various conditions. Of course, besides the conditions employed so far (like the transmission of photons with Ephoton < Eg), there exist plenty of other factors that lead to losses in the amount of generated electricity and thus are important for the actual development of solar cells. Due to these losses, the conversion efficiency of an actually fabricated solar cell is smaller than the theoretical efficiency limit. For example, if we use silicon (Si) for the solar cell absorber material, the detailed balance limit of the conversion efficiency is about 30%. This value can be obtained from Fig. 5.10 in Chap. 5 by looking up the efficiency for the curve (b) at 1.1 eV, which is the band gap of Si. On the other hand, when we look up the present values for actual Si p–n junction solar cells, we find that the single crystal type has reached a maximum of 26.3% and the multi-crystalline type has reached a maximum of 22.3%, both being well below the theoretical efficiency limit. In Chap. 3, we discussed the trade-off relation between the transmission and thermalization losses in the single-junction solar cell and derived the conversion efficiency limit that is imposed by these two types of losses. In considerations on the solar cell performance, such trade-off relations exist for various parameters. As another example for a trade-off relation, in the following sections, we introduce the semiconductor light absorption characteristics, which differ for each material. With this new concept, we discuss the solar cell conversion efficiency from a viewpoint that is different from the detailed balance model elaborated in the previous chapters. The trade-off presented in the following sections is a trade-off between the thickness of the semiconductor that is required for sufficient light absorption and the distance that can be travelled by the generated electrons and holes. The latter property is essential for the efficient extraction of carriers at the electrodes. It is straightforward that a thicker semiconductor can absorb more light. On the other hand, if the semiconductor is too thick, the distance that has to be travelled by the photoexcited electrons and holes also becomes longer. If the path to be travelled is long, there is a high probability for the electron to collide with an obstacle before its electrical energy can be used. Then the energy is unfortunately lost in spite of the efforts to generate it. A thicker semiconductor is not necessarily better; we have to consider the optimum thickness for efficient extraction of the electrical energy. After discussing the light absorption characteristics of semiconductors in Sect. 7.1, we explain the transport of the generated electrons and holes inside the semiconductor in Sect. 7.2. In the last section, we consider two specific semiconductor materials, Si and GaAs, as examples and discuss the optimum semiconductor thickness in a solar cell.