The skin depth is defined for a conductor as the distance reached by the wave when its amplitude is decreased by 1/e of its previous value. How one defines this for a semiconductor and does it relate to the refractive index in an explicit manner?
You can relate it thorough the complex part of the refractive index (k). It gives you the absorption coefficient (alpha) for a given wavelength of your semiconductor thorough alpha=((4Pi/lambda) x k). The absorption coefficient is related to the skin depth as alpha=2/skindepth.