Infrared Absorption of Magnesium Stannide

Abstract

Infrared transmission and reflection measurements have been made on $n$- and $p$-type semiconducting ${\mathrm{Mg}}_{2}$Sn single crystals of different impurity concentrations between 2 and 30 \ensuremath{\mu}, at temperatures ranging from 15 to 296\ifmmode^\circ\else\textdegree\fi{}K. At incident energies less than 0.22 eV, strong free-carrier absorption is present; with $\ensuremath{\alpha}$ as the absorption coefficient and $\ensuremath{\lambda}$, the wavelength, this may be expressed as $\ensuremath{\alpha}=c{\ensuremath{\lambda}}^{\frac{3}{2}}$ at all temperatures where acoustical mode lattice scattering predominates. The absorption spectra due to other mechanisms has been analyzed after subtraction of the ${\ensuremath{\lambda}}^{\frac{3}{2}}$ free-carrier dependence. At energies of 0.22 eV and above, the rapid increase in absorption is attributed to the intrinsic edge. From the energy dependence of the absorption coefficient in the edge region, the mechanism of indirect transitions between the valence and conduction band can be established, with a phonon energy of 0.008 eV. A band in the 0.08 to 0.22 eV energy range present at all temperatures in $n$-type and above 196\ifmmode^\circ\else\textdegree\fi{}K in $p$-type samples is interpreted in terms of transitions between two conduction band minima separated by 0.165 eV at 15\ifmmode^\circ\else\textdegree\fi{}K. Below 0.06 eV an additional sharp rise in absorption occurs. A peak in this absorption at 26 \ensuremath{\mu} may correspond to a second harmonic of the fundamental lattice vibration which is centered around 53 \ensuremath{\mu}. An energy band picture for ${\mathrm{Mg}}_{2}$Sn is suggested, and conductivity (${{m}_{n}}^{*}=0.15m,{{m}_{h}}^{*}=0.10m$), and density of states (${{m}_{n}}^{*}=0.12m,{{m}_{p}}^{*}=1.3m$) effective masses are calculated.