Abstract
Micro-Raman imaging measurements of $n$-type $4H\text{\ensuremath{-}}\mathrm{Si}\mathrm{C}$ crystals with graded donor concentration were carried out, and spatial distributions of the free carrier concentration, carrier mobility, and longitudinal optical (LO) phonon damping were obtained from a line shape analysis of the LO phonon-plasmon coupled (LOPC) mode. The damping of free carriers and optic phonons was determined as a function of free carrier density. We obtained an empirical relationship between carrier concentration and relative Raman shift of the LOPC mode, which is in close agreement with the relationship calculated for the damping-free coupled mode. It is found that the LO phonon damping deduced from the analysis increases linearly with carrier concentration. This LO mode behavior is mainly attributed to the interaction of the LO phonon and ionized impurities (free electrons).
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