Silicon-silicon dioxide core-shell nanowires grown on gold-coated silicon wafers by thermal evaporation of silicon monoxide sometimes show an oscillation in diameter. The two possible causes for this behaviour are a self-oscillation process during the growth or the so-called Rayleigh instability. By analyzing the thickness distribution of the nanowires, we will show that a self-oscillation process is responsible for the periodic instability during growth. In contrast, during post-growth etching and oxidation the nanowires can develop Rayleigh instabilities, leading to silicon nanocrystals embedded in silicon dioxide nanowire.