Longitudinal Optical Phonons Modified by Organic Molecular Cation Motions in Organic-Inorganic Hybrid Perovskites

We performed terahertz time-domain spectroscopy for methylammonium (MA) lead halide perovskite single crystals and characterized the longitudinal optical (LO) phonons directly. We found that the effective LO phonon wave number does not change in the wide temperature range between 10 and 300 K. However, the coupling between MA cation modes and the LO phonon mode derived from lead halide cages induces a mode splitting at low temperatures and a damping of the LO phonon mode at high temperatures. These results influence the interpretation of electron-LO phonon interactions in perovskite semiconductors, as well as the interpretations of mobility, carrier diffusion, and polaron formation.

Figure 1

The reflection coefficients of the $\mathrm{MAPb}{X}_3$ [$X=\mathrm{I}$ (a), Br (b), and Cl (c)] single crystals at low temperature (blue curve) and room temperature (red curve). The THz pulses were $p$ polarized and had an incidence angle of $\theta =30°$.

Figure 2

The imaginary parts of the dielectric constants for the three $\mathrm{MAPb}{X}_3$ single crystals. The black dots indicate the mode positions related to the lead halide cage at low temperature. The black arrows show the positions of the theoretically predicted MA cation modes, reported in Ref. [53].

Figure 3

The 2D image plots of ${ϵ}_2$ for $\mathrm{MAPb}{X}_3$ [$X=\mathrm{I}$ (a), Br (b), and Cl (c)] single crystals as a function of the temperature (horizontal axis) and wave number (vertical axis). The labels O, T, and C represent orthorhombic, tetragonal, and cubic phases, respectively. The black arrows on the top axis show the positions of the theoretically predicted MA cation modes reported in Ref. [53].

Figure 4

The left-hand panel shows the energy loss function $\mathrm{Im}(-1/\epsilon )$ of the $\mathrm{MAPb}{X}_3$ [$X=\mathrm{I}$ (a), Br (b), and Cl (c)] single crystals at different temperatures. The closed circles in the right-hand panels show the peak wave numbers in (d) ${\mathrm{MAPbI}}_3$ and (e) ${\mathrm{MAPbBr}}_3$ single crystals as a function of the temperature. The open squares show the wave numbers of effective LO phonon. The labels O, T, and C represent orthorhombic, tetragonal, and cubic phases, respectively.

Figure 5

(a) The PL spectra from the ${\mathrm{MAPbI}}_3$ and (b) ${\mathrm{MAPbBr}}_3$ single crystals at different temperatures. (c),(d) The corresponding spectral widths of the luminescence from the free exciton as a function of the temperature. The red curves show the predicted bandwidth including acoustic and LO phonon interaction. The parameters ${\mathrm{\Gamma }}_0/hc$, ${\gamma }_{\mathrm{LO}}/hc$, $E_{\mathrm{LO}}/hc$, and ${\gamma }_{\mathrm{ac}}/hc$ are $32{\mathrm{cm}}^{-1}$, $\text{310\hspace{0.17em}\hspace{0.17em}}{\mathrm{cm}}^{-1}$, $131{\mathrm{cm}}^{-1}$, and $0.7{\mathrm{cm}}^{-1}/\mathrm{K}$ for $X=\mathrm{I}$, and $16{\mathrm{cm}}^{-1}$, $505{\mathrm{cm}}^{-1}$, $162{\mathrm{cm}}^{-1}$, and $1.0{\mathrm{cm}}^{-1}/\mathrm{K}$ for $X=\mathrm{Br}$. The labels O, T, and C represent the orthorhombic, tetragonal, and cubic phases, respectively.