Raman image measurements have been made to determine the free carrier distribution in modulation-doped 6H-SiC crystals, which have a stripe like-distribution of nitrogen donor concentration. The distribution of the donor impurity is controlled by alternate on-off of the doping N-2-gas Supply during the crystal growth. The carrier concentration, in other words the impurity concentration is determined from the line shape analysis of the LO phonon plasmon coupled mode. The thickness of the transition region between the doped and undoped regions after the shut-off of the doping gas is determined from Raman profiles. The residual time of the N-2 gas on the growth surface inferred from the thickness and the growth rate is longer than the residence time of the N-2 gas in the furnace. This result indicates that N-2 atoms attach to the wall and source side in the furnace during the gas supply. The relation between the carrier mobility and carrier concentration is also determined from the analysis of the LO phonon plasmon coupled modes at different positions.