"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 dPhi/dx + alphaPhi = 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?"