Study of the dielectric function of PbSnTe epitaxial film by far-infrared reflectivity

Far-infrared reflectivity measurements have been carried out from ∼40 to 320 ${\mathrm{cm}}^{-1\mathrm{}}$ on a ${\mathrm{Pb}}_{0.88}$ ${\mathrm{Sn}}_{0.12}$ $\mathrm{Te}$ epitaxial film of low carrier concentration ($p\sim {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$) on a high-carrier-density ($p\sim {10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$) ${\mathrm{Pb}}_{0.78}$ ${\mathrm{Sn}}_{0.22}$Te substrate. The reflectivity data were analyzed using a two-oscillator dielectric function including free-carrier and phonon linewidths. An upper bound for the LO-phonon frequency was determined to be 115.7 ${\mathrm{cm}}^{-1\mathrm{}}$ at room temperature and 113.5 ${\mathrm{cm}}^{-1\mathrm{}}$ at liquid-${\mathrm{N}}_2$ temperature. Other parameters obtained were the phonon linewidth $\gamma =19\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ at room temperature and 12 ${\mathrm{cm}}^{-1\mathrm{}}$ at liquid-${\mathrm{N}}_2$ temperature, and the substrate free-carrier linewidth $\nu =81\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ at room temperature and ∼70 ${\mathrm{cm}}^{-1\mathrm{}}$ at liquid-${\mathrm{N}}_2$ temperature. An analysis of the oscillatory behavior of the reflectivity at frequencies above the highest plasmon-phonon mode permitted the determination of the spatial variation of carrier concentration in the region of the film-substrate interface.