Phonon-exciton interactions play a critical role in determining the optical and thermal properties of semiconductors, influencing phenomena such as exciton linewidth broadening, polaronic effects, and energy relaxation dynamics. These interactions are particularly significant in materials like Cu2O and GaAs, where strong coupling between lattice vibrations (phonons) and excitons leads to measurable effects on excitonic behavior. This article explores the mechanisms of phonon-exciton coupling, polaronic modifications to exciton states, and temperature-dependent exciton linewidths in these systems.

In semiconductors, excitons are bound electron-hole pairs that interact with the surrounding lattice through phonons. The strength of this interaction depends on the material’s electronic structure, lattice dynamics, and temperature. In Cu2O, a prototypical material for studying exciton physics, the exciton-phonon coupling is dominated by longitudinal optical (LO) phonons due to the material’s polar nature. The Fröhlich interaction, which describes the coupling between charge carriers and LO phonons, is particularly strong in polar semiconductors like GaAs and Cu2O. This interaction leads to the formation of polarons, quasiparticles consisting of an exciton dressed by a cloud of virtual phonons. The polaron effect renormalizes the exciton energy and increases its effective mass, altering its optical response.

Polaronic effects manifest in several ways. First, the exciton binding energy is modified due to the self-energy correction from phonon interactions. In GaAs, for instance, the exciton-LO phonon coupling reduces the exciton energy by several meV, a shift observable in photoluminescence spectra. Second, the exciton mobility is affected because the phonon cloud increases scattering rates, particularly at higher temperatures. In Cu2O, the large exciton radius and weak dielectric screening enhance the polaronic contribution, making it a key factor in exciton transport. Experimental studies have shown that the exciton diffusion length in Cu2O decreases with temperature due to increased phonon scattering, highlighting the role of phonon-exciton interactions in exciton dynamics.

Temperature-dependent exciton linewidths provide direct insight into phonon-exciton coupling. The linewidth of an excitonic transition broadens with temperature due to interactions with acoustic and optical phonons. In GaAs, the exciton linewidth follows a well-established trend, where the broadening is proportional to the Bose-Einstein occupation factor of phonons. At low temperatures (below 50 K), the linewidth is dominated by acoustic phonon scattering, while at higher temperatures, LO phonon scattering becomes dominant. The temperature dependence can be described by the expression Γ(T) = Γ₀ + γₐT + γₛ/(exp(ħωₛ/kT) - 1), where Γ₀ is the inhomogeneous broadening, γₐ represents the acoustic phonon contribution, and γₛ and ħωₛ account for the LO phonon contribution. Measurements in GaAs align with this model, showing a clear transition from acoustic to optical phonon dominance as temperature increases.

In Cu2O, the situation is more complex due to the presence of multiple exciton states (ortho- and para-excitons) and their distinct coupling to phonons. The ortho-exciton, with a triplet spin configuration, exhibits stronger phonon coupling than the para-exciton, leading to a more pronounced temperature-dependent linewidth broadening. Additionally, the high exciton binding energy in Cu2O (around 150 meV) means that phonon interactions do not dissociate the exciton but instead modify its kinetic properties. Studies have shown that the linewidth of the ortho-exciton in Cu2O increases linearly with temperature up to 100 K, beyond which higher-order phonon processes contribute to additional broadening.

The role of phonon-exciton interactions extends beyond linewidth effects to influence exciton relaxation pathways. In GaAs, excitons generated above the bandgap rapidly thermalize via emission of LO phonons, a process known as hot exciton cooling. The efficiency of this process depends on the exciton-phonon coupling strength and the phonon density of states. Time-resolved spectroscopy reveals that LO phonon emission occurs on a picosecond timescale, with the cooling rate increasing at higher temperatures due to enhanced phonon populations. In Cu2O, the relaxation dynamics are slower because of the weaker coupling to acoustic phonons, but LO phonons still play a significant role in redistributing exciton energy.

The interplay between phonons and excitons also affects the formation of exciton-polaritons in microcavities. In GaAs-based cavities, strong coupling between excitons and photons leads to polariton formation, but phonons introduce decoherence and energy shifts. The polariton linewidth exhibits temperature-dependent broadening analogous to that of bare excitons, with additional contributions from cavity photon leakage. In Cu2O, the large exciton binding energy makes polariton formation less common, but recent advances in high-quality cavities have enabled observations of phonon-mediated polariton relaxation.

Material-specific differences in phonon-exciton interactions are evident when comparing GaAs and Cu2O. GaAs, with its zinc-blende structure, has a simpler phonon dispersion compared to the cubic structure of Cu2O, leading to different coupling mechanisms. The deformation potential coupling, which describes interactions with acoustic phonons, is stronger in GaAs, while the Fröhlich coupling dominates in Cu2O. These differences are reflected in the temperature dependence of exciton properties, with GaAs showing a more pronounced LO phonon contribution and Cu2O exhibiting a stronger influence from acoustic phonons at lower temperatures.

Understanding phonon-exciton interactions is crucial for optimizing semiconductor devices. In light-emitting devices, phonon-induced broadening can reduce emission efficiency, while in excitonic solar cells, phonon scattering affects exciton diffusion and dissociation. Advances in material engineering, such as strain tuning and heterostructure design, offer ways to modulate phonon-exciton coupling. For example, strained GaAs layers exhibit modified phonon dispersion, altering the exciton-phonon interaction strength. Similarly, embedding Cu2O in a dielectric matrix can suppress acoustic phonon scattering, enhancing exciton mobility.

In summary, phonon-exciton interactions are a fundamental aspect of semiconductor physics, governing exciton linewidths, polaronic effects, and energy relaxation. Materials like Cu2O and GaAs serve as excellent platforms for studying these phenomena due to their distinct coupling mechanisms. Temperature-dependent studies reveal the interplay between acoustic and optical phonons, while polaronic effects highlight the renormalization of exciton properties. These insights not only deepen our understanding of exciton dynamics but also inform the design of advanced optoelectronic devices. Future research may explore engineered materials with tailored phonon-exciton interactions to achieve desired optical and thermal responses.