A fast in situ spectroscopic ellipsometry technique has been adopted to investigate the nucleation and growth of carbon on a Si substrate in a DC glow discharge of 100% methane in a temperature range from 1170 to 1270 K, Firstly, a model consisting of a carbonizing layer of Si1-xCx on a Si substrate was constructed for analyzing the initial carbonization process, and both a growth rate of 0.1 nm/s and a time-dependent average composition x of the layer was obtained within the spectral change of the optical constants at a wavelength range of 280-760 nm at 1200 K, The maximum value of x was estimated to be 0.15 +/- 0.01 under this condition. Secondly, the average rate of surface coverage of the carbon nuclei at this second stage was found to be 5%/min, where nucleation was assumed to take place on the carbonized layer. This model gave a good fit to the time-dependent spectral data. Thirdly, a growth rate of 0.1 nm/s and optical constants of the carbon film were determined. It was found to consist of graphite microcrystals in the present experimental condition by Raman scattering spectroscopy.