Amorphous Si films containing crystal seeds can be converted to a polycrystal by an ion beam with heating at 350 °C on silica glass substrates, and the density of the crystal grain is almost the same as that of the initial seed. However, the size and density of the crystal seed decrease when the ion irradiation is performed without external heating. The average grain size in the completely crystallized film can be controlled by decreasing the crystal seed density before crystallization. The growth process of crystal grains (average grain diameterRand standard deviation &sgr;R) is reported and the gradient &Dgr;&sgr;R/&Dgr;Ris estimated to be about 0.15. A model calculation is performed to estimate the gradient on the assumption that the growth rate is governed by the plane (111) crystallization and the calculated value is 0.05.