A method of filling one or more trenches formed in a silicon substrate includes the steps of forming a thin polycrystalline silicon film in a trench such that the thin polycrystalline silicon film is sufficiently thin so as to not close the trench; forming an amorphous silicon film on thin polycrystalline film and the surface of the substrate and in the trenches; and annealing the amorphous silicon film such that the amorphous silicon layer migrates to fill the trenches to a first level. The deposition and annealing steps are performed in ambient atmospheres having low partial pressures of H.sub.2 O and O.sub.2, the annealing temperature is higher than the deposition temperature, and the annealing pressure is greater than the deposition pressure.