Rigorous coupled-wave analysis was used to compute the absorptance of a metallic surface-relief grating coated with a semiconductor layer. The grating is formed by periodic bumps on an otherwise planar layer of a suitable metal. When the period of the surface-relief grating is appropriate, at a certain incidence angle the incident light excites a p-polarized surface-plasmon- polariton (SPP) wave if the semiconductor layer is homogeneous. However, if the semiconductor layer is periodically non-homogeneous normal to the mean metal/semiconductor interface, more than one SPP waves with different polarization states, phase speeds, and attenuation rates can be excited. The use of a periodically nonhomogeneous semiconductor layer for excitation of multiple SPP waves with different polarization states, phase speeds, and attenuation rates can help enhance light absorption in thin-film solar cells.