Specific Heat of $n$- and $p$-Type ${\mathrm{Bi}}_2$${\mathrm{Te}}_3$ from 1.4 to 90°K

The specific heats of $n$-type bismuth telluride with carrier concentrations ranging between 2.2×${10}^{18}$ and 8.3×${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$, $p$-type ${\mathrm{Bi}}_2$ ${\mathrm{Te}}_3$ with a carrier concentration of 1.3×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$, and bismuth selenide have been measured from 1.3 to 90°K. At low temperatures, there are measurable differences in the electronic specific heat of $n$-type ${\mathrm{Bi}}_2$ ${\mathrm{Te}}_3$ as a function of carrier concentration. These differences can be explained on the basis of a conduction band consisting of six ellipsoidal minima and an additional heavy-mass band lying approximately 30 meV above them. The electronic specific heat of $p$-type ${\mathrm{Bi}}_2$ ${\mathrm{Te}}_3$ is consistent with a six-ellipsoid model. For both $n$- and $p$-type ${\mathrm{Bi}}_2$ ${\mathrm{Te}}_3$, as well as ${\mathrm{Bi}}_2$ ${\mathrm{Se}}_3$, departure of the lattice specific heat from the Debye ${\mathrm{T}}^3$ approximation begins well below the lowest temperatures measured. The extrapolated Debye temperature at absolute zero is (162±3)°K for ${\mathrm{Bi}}_2$ ${\mathrm{Te}}_3$, which agrees well with the value of (165±2)°K obtained from the low-temperature elastic constants. ${\mathrm{Bi}}_2$ ${\mathrm{Se}}_3$ has been found to have a limiting Debye temperature of (182±3)°K.