Valence-band structure of highly efficient<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-type thermoelectric PbTe-PbS alloys

Abstract

Experimental evidence is given relevant to the temperature dependence of the valence band structure of PbTe and PbTe${}_{1\ensuremath{-}x}$S${}_{x}$ alloys ($0.04\ensuremath{\le}x\ensuremath{\le}0.12$), and its effect on the thermoelectric figure of merit $ZT$. The $x=0.08$ sample has $ZT\ensuremath{\sim}1.55$ at 773 K. The magnetic field dependence of the high-temperature Hall resistivity of heavily $p$-type ($&gt;{10}^{19}$ cm${}^{\ensuremath{-}3}$) Na-doped PbTe${}_{1\ensuremath{-}x}$S${}_{x}$ reveals the presence of high-mobility electrons. This casts doubts on prior analyses of the Hall coefficient suggesting that temperature induces a rapid rise in energy of the ``heavy'' hole relative to the ``light'' hole bands. The electron-like behavior is likely induced by the topology of the Fermi surface when the L- and \ensuremath{\Sigma}-bands merge. Negative values for the low-temperature thermopower are also observed. The data show that PbTe continues to be a direct-gap semiconductor at temperatures where the $ZT$ and ${S}^{2}\ensuremath{\sigma}$ of $p$-type PbTe are optimal, e.g., 700--800 K.