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14     CHAPTER 1 Solar Cells and Arrays: Principles, Analysis, and Design


















                         FIGURE 1.11
                         The process of photogeneration of electron hole pairs.

                         pairs except with a very small probability as this process requires the collision of
                         photons with two electrons simultaneously if it is a direct process.
                            The absorption coefficient alpha is a function of the incident wavelength of the
                         photons and it is a material property. Fig. 1.12 shows the absorption coefficient of
                         different semiconductors as a function of the wavelength [12]. The energy gap of
                         the material is also given. It is clear from this figure that materials absorb light appre-
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                         ciably (a > 10 m ) only if E ph   E g . A second important observation is that a of
                         Si rises slowly with decreased wavelength compared with the other materials shown
                         in the diagram. This is because of the indirect nature of band gap of this material.
                            The longer wavelength photons with smaller alpha need a thicker layer of the
                         semiconductor to be absorbed; otherwise, they can be transmitted across the layer.


























                         FIGURE 1.12
                         Absorption coefficient as a function of wavelength for different materials.
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