Broadband phonon scattering in PbTe-based materials driven near ferroelectric phase transition by strain or alloying

The major obstacle in the design of materials with low lattice thermal conductivity is the difficulty in efficiently scattering phonons across the entire frequency spectrum. Using first-principles calculations, we show that driving PbTe materials to the brink of the ferroelectric phase transition could be a powerful strategy to solve this problem. We illustrate this concept by applying biaxial tensile (001) strain to PbTe and its alloys with another rocksalt IV-VI material, PbSe; and by alloying PbTe with a rhombohedral IV-VI material, GeTe. This induces extremely soft optical modes at the zone center, which increase anharmonic acoustic-optical coupling and decrease phonon lifetimes at all frequencies. We predict that PbTe, Pb(Se,Te), and (Pb,Ge)Te alloys driven close to the phase transition in the described manner will have considerably lower lattice thermal conductivity than that of PbTe (by a factor of $2–3$). The proposed concept may open new opportunities for the development of more efficient thermoelectric materials.

Figure 1

(a) Phonon dispersions at 0 K for PbTe (solid black lines) and PbTe driven to the verge of the phase transition by tensile (001) strain of $\eta =1.15$% (dotted red lines). Frequencies of the soft transverse optical modes at the zone center, $\mathrm{TO}\left(\mathrm{\Gamma }\right)$, are represented with circles for PbTe, and rectangles for PbTe driven to the transition. (b) Phonon dispersions at 0 K for ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ (solid black lines) and ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ driven to the verge of the phase transition by tensile (001) strain of $\eta =1.32$% (dotted red lines). $\mathrm{TO}\left(\mathrm{\Gamma }\right)$ frequencies are shown in circles for ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$, and rectangles for ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ driven to the transition. (c) Phonon dispersions at 0 K for PbTe (solid black lines), ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ (dash-dotted blue lines), and ${\mathrm{Pb}}_{0.51}{\mathrm{Ge}}_{0.49}\mathrm{Te}$ alloy at the verge of the phase transition (dotted red lines). $\mathrm{TO}\left(\mathrm{\Gamma }\right)$ frequencies are represented with circles for PbTe, diamonds for ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$, and rectangles for ${\mathrm{Pb}}_{0.51}{\mathrm{Ge}}_{0.49}\mathrm{Te}$. Phonon dispersions for alloys were calculated using the virtual crystal approximation.

Figure 2

(a) Anharmonic (three-phonon) lifetimes at 300 K as a function of frequency for PbTe (black pluses) and PbTe driven to the verge of the phase transition by tensile (001) strain of $\eta =1.15$% (red crosses). Inset: Frequency dependence of lifetimes averaged over frequency at 300 K for PbTe (solid black line) and PbTe driven to the transition (dotted red line). (b) Anharmonic lifetimes at 300 K and their frequency averages (inset) as a function of frequency for ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ (black pluses and solid line) and ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ driven to the verge of the phase transition by tensile (001) strain of $\eta =1.32$% (red crosses and dotted line). (c) Anharmonic lifetimes at 300 K and their frequency averages (inset) as a function of frequency for PbTe (black pluses and solid line), ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ (blue circles and dash-dotted line), and ${\mathrm{Pb}}_{0.51}{\mathrm{Ge}}_{0.49}\mathrm{Te}$ alloy at the verge of the phase transition (red crosses and dotted line).

Figure 3

(a) Lattice thermal conductivity versus temperature for PbTe (solid black line), PbTe driven near the phase transition by tensile (001) strain of $\eta =1.15$% (dotted red line), ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ (dashed green line), ${\mathrm{PbSe}}_{0.5}{\mathrm{Te}}_{0.5}$ driven near the transition by tensile (001) strain of $\eta =1.32$% (dash-dotted blue line), and ${\mathrm{Pb}}_{0.51}{\mathrm{Ge}}_{0.49}\mathrm{Te}$ alloy near the transition (dash-double-dotted purple line). Conductivity for strained materials is shown for the out-of-plane direction. (b) Out-of-plane lattice thermal conductivity of PbTe at 300 K as a function of (001) strain. Inset: Lowest transverse optical mode frequency at the zone center, $\mathrm{TO}\left(\mathrm{\Gamma }\right)$, for PbTe at 0 K versus (001) strain. (c) Lattice thermal conductivity of ${\mathrm{Pb}}_{1-x}{\mathrm{Ge}}_x\mathrm{Te}$ alloys at 450 K as a function of Ge content $x$: full calculation (black crosses), calculation without mass disorder (red circles), and linearly interpolated values between those calculated for PbTe and GeTe (dashed green line). Inset: $\mathrm{TO}\left(\mathrm{\Gamma }\right)$ frequency of ${\mathrm{Pb}}_{1-x}{\mathrm{Ge}}_x\mathrm{Te}$ at 0 K versus Ge content $x$.