Electronic structure ofPbTePb1−xSnxTeTe superlattices

${\mathrm{P}\mathrm{b}\mathrm{T}\mathrm{e}/\mathrm{P}\mathrm{b}}_{0.88}$ ${\mathrm{Sn}}_{0.12}$Te Te superlattices were prepared with individual thicknesses of about 50 nm and periodicities of 100-250 nm on ${\mathrm{BaF}}_2$ substrates. The lattice constant mismatch of $\frac{\Delta a}{a}=2.5\mathrm{}\times {10}^{-3\mathrm{}}$ introduces a misfit strain in the constituent layers and there is an additional tensile strain caused by the substrate. These strains were determined by x-ray diffractometry. The electrical properties of this many-valley type-I superlattice were investigated by conductivity, Hall effect, and weak-field magnetoresistance (WFMR) experiments. For electrons or holes confined in the Pb-Sn-Te layers, the angular dependence of the WFMR data is consistent with quasi-two-dimensional transport. The band structure of these many-valley PbTe/Pb-Sn-Te superlattices is calculated by matching propagating or evanescent envelope functions at the boundaries of consecutive layers and considering the $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ Hamiltonian for cubic IV-VI compounds at the $L$ point of the Brillouin zone. The evolution of the PbTb/Pb-Sn-Te band structure with increasing superlattice periodicity is calculated and energy-momentum dispersions are given for the samples of interest. The observed quasi-two-dimensional transport is explained by these $E\left(\overrightarrow{\mathrm{k}}\right)$ relations, yielding, for appropriate superlattice periodicities, cylinders as surfaces of constant energy.