Temperature Dependence of the Effective Masses in PbTe

Abstract

The study presented here includes experimental data obtained from three $n$-type and two $p$-type single-crystalline samples of PbTe. Measurements of the Hall coefficient, thermoelectric power, and electrical conductivity have been made between 77 and 300°K, and infrared reflectivity data have been obtained at 4, 77, 190, and 300°K. The free-carrier concentration of all samples is in the range 2-4×${10}^{18}$ carriers/${\mathrm{cm}}^3$. From the thermoelectric power, we have deduced the temperature dependence of the reduced Fermi potential for each sample and have calculated the density-of-states effective mass $m_d$. A pronounced temperature dependence has been observed for $m_d$. At 77°K we have observed that $m_{\mathrm{dn}}=0.20\mathrm{} m_o$ and $m_{\mathrm{dp}}=0.14\mathrm{} m_o$, whereas at 300°K they have increased monotonically to the values $m_{\mathrm{dn}}=0.30\mathrm{} m_o$ and $m_{\mathrm{dp}}=0.25\mathrm{} m_o$. The minimum of the infrared reflectivity has been utilized in obtaining values for the conductivity effective mass $m_c$. The temperature dependence noted for $m_c$ has been very similar to that obtained for $m_d$. At 4°K we obtained the values $m_{\mathrm{cn}}=0.050\mathrm{} m_o$ and $m_{\mathrm{cp}}=0.039\mathrm{} m_o$, and they increase monotonically to their values at 300°K which have been determined to be $m_{\mathrm{cn}}=0.103\mathrm{} m_o$ and $m_{\mathrm{cp}}=0.11\mathrm{} m_o$. These values of the effective masses have been used to deduce the number of equivalent ellipsoids of constant energy $N_v$. For the conduction band, we find $N_v=4\mathrm{}$ indicating that the (111) minima are at the edge of the zone. For the valence band we are unable to be as quantitative because of the presence of a maximum at the center of the zone as well as the maxima positioned along the $〈111〉$ axes. However, assuming that all ellipsoids are equivalent, we calculate $N_v\approx 2.5$ from which it is inferred that the zone-centered maximum plays a prominent role in the energy-band picture.