Phonon modes in perovskite semiconductors play a fundamental role in determining their electronic, optical, and thermal properties. The lattice dynamics of perovskites are characterized by complex interactions involving soft modes, anharmonicity, and electron-phonon coupling, which influence phenomena such as thermal conductivity, hot-carrier cooling, and spectroscopic signatures. Understanding these aspects is critical for optimizing perovskites for optoelectronic and quantum applications.

Soft modes are low-frequency vibrational modes that often precede structural phase transitions in perovskites. These modes exhibit a temperature-dependent frequency softening as the material approaches the transition point, leading to lattice instabilities. In hybrid organic-inorganic perovskites like MAPbI3, the soft modes arise from the dynamic disorder of the organic cations and the tilting of PbI6 octahedra. The presence of soft modes contributes to the unusually low thermal conductivity observed in these materials, as they enhance phonon-phonon scattering processes. In fully inorganic perovskites such as CsPbBr3, soft modes are linked to displacive phase transitions driven by octahedral rotations.

Anharmonicity in perovskites is a key factor governing their lattice dynamics. Unlike harmonic approximations, which assume small atomic displacements, anharmonic effects account for large-amplitude vibrations and nonlinear interactions between phonons. Lead halide perovskites exhibit strong anharmonicity due to the heavy Pb atoms and the polarizability of halide ions. This results in phenomena such as phonon lifetime shortening, frequency renormalization, and the formation of intrinsic localized modes. Anharmonicity also contributes to the suppression of thermal conductivity by increasing Umklapp and normal scattering processes. Experimental studies using inelastic neutron scattering and Raman spectroscopy have confirmed the dominance of quartic anharmonicity in CsPbI3, where phonon energies shift nonlinearly with temperature.

Electron-phonon coupling in perovskites mediates energy transfer between charge carriers and the lattice, influencing carrier mobility, recombination dynamics, and hot-carrier cooling rates. Strong Fröhlich coupling between longitudinal optical (LO) phonons and electrons is observed in lead halide perovskites due to their high dielectric constants and ionic character. This coupling leads to the formation of large polarons, which screen charge carriers and reduce scattering rates. In contrast, deformation potential coupling with acoustic phonons dominates in nonpolar perovskites. The interplay between these mechanisms determines the hot-carrier relaxation pathways, with LO phonon emission being the primary cooling channel in materials like FAPbI3.

Thermal conductivity in perovskites is heavily influenced by their phonon dispersion and scattering mechanisms. The low thermal conductivity of hybrid perovskites, often below 1 W/mK, arises from a combination of soft modes, anharmonicity, and organic cation disorder. Inorganic perovskites exhibit slightly higher thermal conductivity due to reduced anharmonicity but still remain low compared to conventional semiconductors. Phonon transport is further affected by grain boundaries and defects, which introduce additional scattering centers. First-principles calculations reveal that three-phonon processes dominate heat conduction in CsPbBr3, with optical phonons contributing significantly due to their low group velocities.

Hot-carrier cooling dynamics in perovskites are governed by the efficiency of electron-phonon energy dissipation. Slow cooling rates, observed in materials like MAPbI3, are attributed to a phonon bottleneck effect where hot carriers accumulate in high-energy states due to inefficient LO phonon emission. This phenomenon is enhanced by the large polaron formation and the screening of carrier-phonon interactions. Time-resolved spectroscopy studies indicate cooling timescales ranging from picoseconds to nanoseconds, depending on the perovskite composition and excitation density. Slower cooling is advantageous for hot-carrier solar cells, where excess energy can be harvested before thermalization.

Raman spectroscopy provides critical insights into the phonon modes and lattice dynamics of perovskites. The spectra of lead halide perovskites exhibit distinct peaks corresponding to Pb-X stretching (50-150 cm-1) and bending modes (100-200 cm-1), along with organic cation vibrations in hybrid variants. Temperature-dependent Raman studies reveal mode softening near phase transitions and the emergence of new peaks due to symmetry breaking. Anharmonicity is evidenced by the asymmetric line shapes and frequency shifts of Raman-active modes. In layered perovskites, interlayer shear and breathing modes appear below 50 cm-1, reflecting weak van der Waals interactions.

The unique phonon properties of perovskites underscore their potential for advanced optoelectronic applications. The interplay between soft modes, anharmonicity, and electron-phonon coupling defines their thermal and electronic behavior, offering avenues for engineering materials with tailored lattice dynamics. Future research may explore the role of phonon coherence in carrier transport and the design of perovskites with ultralow thermal conductivity for energy conversion.