Phonon anharmonicity, lifetimes, and thermal transport in ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ from many-body perturbation theory

Lattice vibrations in ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ are strongly interacting, with double-well instabilities present at the Brillouin zone boundary. Analysis within a first-principles lattice-dynamics framework reveals anharmonic potentials with short phonon quasiparticle lifetimes and mean free paths. The phonon behavior is distinct from the inorganic semiconductors GaAs and CdTe where three-phonon interaction strengths are three orders of magnitude smaller. The implications for the applications of hybrid halide perovskites arising from thermal conductivity, band-gap deformation, and charge-carrier scattering through electron-phonon coupling, are presented.

Figure 1

Harmonic phonon dispersion up to 5 THz in the (a) low-temperature (orthorhombic) and (b) high-temperature (cubic) perovskite phases of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$. They are calculated from lattice dynamics using forces from density-functional theory (PBEsol electron exchange and correlation).

Figure 2

Potential-energy surface from frozen-phonon calculations of the imaginary eigenmode present at the $R$ point in the high-temperature perovskite phase of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$. $Q$ represents the normal mode coordinate (phonon amplitude). The solution of a 1D Schrödinger equation (states shown as horizontal lines with wave functions in the upper panel) are used to generate a thermalized probability density of states (DOS; lower panel).

Figure 3

Results from anharmonic lattice-dynamics calculations on ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$, GaAs, and CdTe. Average phonon modal interaction strength ($P$) and group velocity ($\mathbf{v}$), as well as the $T=300$ K values of modal lifetime ($\tau$) and thermal conductivity ($\kappa$) are shown. Only the 0–5 THz range is shown for ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$. The data points are colored according to the band index.

Figure 4

Lattice thermal conductivity of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$, GaAs, and CdTe calculated from three-phonon interactions within the relaxation time approximation (excluding isotope effects). The calculated values of 38 ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ (GaAs) and 9 ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ (CdTe) at $T=300$ K compare well to the measured values of 45 and 7 ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, respectively [31]. The corresponding value calculated for ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ is 0.05 ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ .