4.4 Lead Telluride and its Alloys

Lead telluride (PbTe) as well as lead tin telluride (Pb$_{1-x}$ Sn$_{x}$ Te) have their operational temperature ranges between those of bismuth telluride and silicon-germanium. Although the maximum figure of merit is slightly lower than that of bismuth telluride, lead telluride extents the temperature range covered for thermoelectric applications with comparable good efficiencies. Electrical properties can be controlled by variations of the material composition through changing the stoichiometric ratio. While excess usage of lead results in an n-type semiconductor, a shift to more tellurium gives a p-type semiconductor. However, the maximum carrier concentration achievable by this mechanism is in the order of $10^{18} \,\ensuremath{\mathrm{cm^3}}$ , which is lower than the ideal doping for thermoelectric applications [11]. Higher carrier concentrations can be achieved by doping. While PbI$_2$ , PbBr$_2$ , or Ge$_2$ Te$_3$ are used as extra donors, Na$_2$ Te or K$_2$ Te are applied for elevating acceptor concentrations.

Both PbTe and Pb$_{1-x}$ Sn$_{x}$ Te can be manufactured as single crystals as well as sintered materials. Sintered samples are usually fabricated at temperatures around 1000$\,$ K [151] and are distinguished from single crystals by their lower thermal and electrical conductivities due to additional scattering at grain boundaries.

A comprehensive elaboration of the physical properties of lead telluride and lead tin telluride as well as according models for application within device simulation is given in Chapter 5.

M. Wagner: Simulation of Thermoelectric Devices