Carrier concentration and temperature dependence of the electronic transport properties of epitaxial PbTe and PbTe/PbSe nanodot superlattices

Abstract

The electrical conductivity, Seebeck coefficient, and power factor of $n$- and $p$-type PbTe were calculated over the temperature range of 300--700 K and carrier concentration range of $1\ifmmode\times\else\texttimes\fi{}{10}^{17}\ensuremath{-}4\ifmmode\times\else\texttimes\fi{}{10}^{19}\text{ }{\text{cm}}^{\ensuremath{-}3}$ by using the Boltzmann transport equation and relaxation time approximation and were compared to measurement results. A three-band model for PbTe was used and included scattering from screened polar optical phonons as well as the deformation potential of acoustic and optical phonons. Nonparabolicity and anisotropy of the principal conduction and valence bands at the $L$ point in the Brillouin zone were taken into account, and the calculated transport properties were in excellent agreement with measurement results over the full range of carrier concentrations and temperatures. The Lorenz number was also calculated and seen to vary from 0.54 to 0.89 of ${L}_{0}$ $(2.44\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }\text{W}\text{ }\ensuremath{\Omega}\text{ }{\text{K}}^{\ensuremath{-}2})$ depending on the carrier concentration and temperature. The measured in-plane transport properties of epitaxially grown $n$- and $p$-type PbTe/PbSe nanodot superlattice (NDSL) samples with $\ensuremath{\sim}13%$ PbSe by volume fraction are also presented and discussed in comparison to the baseline homogeneous PbTe. The presence of the PbSe nanodots in a PbTe matrix was observed to reduce the carrier mobility by $\ensuremath{\sim}25%--35%$ while having no effect on the Seebeck coefficient, thus resulting in a reduced power factor for PbTe/PbSe NDSLs compared to PbTe. The properties of the NDSL samples were also observed to have the same temperature dependence as PbTe.