The thickness of a solar cell must be chosen carefully to ensure photons are properly

Chapter 8, Problem 13

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The thickness of a solar cell must be chosen carefully to ensure photons are properly absorbed; even metals can be partly transparent when rolled out into very thin foils. If the incident light flux (number of photons per unit area per unit time) at the solar cell surface (x = 0) is given by \(\Phi_{0}\), and the intensity of light a distance x inside the solar cell is given by \(\Phi(x)\), the behavior of \(\Phi (x)\) is described by the equation \(d \Phi/dx + \alpha \Phi = 0\). Here, \(\alpha\), known as the absorption coefficient, is a constant specific to a given semiconductor material. (a) What is the SI unit for \(\alpha\)? (b) Obtain an expression for \(\Phi(x)\) in terms of \(\Phi_{0}\), \(\alpha\), and x. (c) How thick should the solar cell be made in order to absorb at least 38% of the incident light? Express your answer in terms of \(\alpha\). (d) What happens to the light which enters the solar cell at x = 0 but is not absorbed?