Dispersion Analysis of Magnesium Stannide Reflectivity

The optical reflectivity of ${\mathrm{Mg}}_2$Sn measured between 10 and 45 $\mu$ at temperatures of 80, 296, and 473°K shows the effects of both lattice-vibration and free-carrier absorption. For the range of carrier concentrations investigated, ${10}^{17}$ to ${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$, the plasma edge, broadened by the short relaxation time of the carriers, occurs on both sides of the transverse-optical lattice frequency, and the effects of both absorption mechanisms are superimposed. Values for the lattice dispersion parameters and carrier effective masses and relaxation times are obtained from the best fit to the experimental reflectivity curves. The relative contribution of the two mechanisms to the total reflectivity is illustrated for a heavily doped ${\mathrm{Mg}}_2$Sn sample at low temperature; in addition, the masking of the lattice vibration reflectivity as a function of free-carrier concentration and relaxation time is discussed.