Material with refraction index similar to Si
Over the range of the visible spectrum, ~1.8 - 3.1 eV, or 700-400 nm, the refractive index (nD) of Si varies from about 3.5 - 5, though it is also absorbent and somewhat reflective over that range. Gallium(III) phosphide, $\ce{GaP}$ is one material that comes close to that. It should be fairly stable in air at STP.

Of course, it all depends on your intended use. At what wavelength should nD match that of Si? At what temperature and in what atmosphere will the material be? Does the crystal structure of the material need to match that of Si, so that a regular layer can be deposited? More information is needed for the answer to be of any use.