In polar semiconductors such as gallium arsenide (GaAs) and zinc oxide (ZnO), lattice vibrations play a crucial role in determining their thermal, optical, and electronic properties. Among these vibrations, longitudinal optical (LO) and transverse optical (TO) phonon modes are particularly significant due to their strong coupling with electromagnetic fields and their influence on charge carrier dynamics. These modes arise from the relative displacement of positively and negatively charged ions in the crystal lattice, leading to macroscopic polarization fields that distinguish them from acoustic phonons. The interaction between these phonon modes and electrons, known as the Fröhlich interaction, is a key mechanism governing carrier scattering and polaron formation in polar semiconductors.

The distinction between LO and TO phonon modes stems from their different oscillation directions relative to the wave propagation vector. In TO modes, atomic displacements are perpendicular to the wavevector, resulting in no net charge density fluctuation and thus no long-range electric field. In contrast, LO modes involve displacements parallel to the wavevector, generating alternating regions of positive and negative charge density that produce a macroscopic electric field. This field contributes to the LO-TO splitting, a phenomenon where the LO phonon frequency is higher than that of the TO phonon due to the additional restoring force from the Coulomb interaction.

The dielectric response of polar semiconductors is closely tied to these phonon modes. The frequency-dependent dielectric function can be described by the Lyddane-Sachs-Teller relation, which connects the LO and TO phonon frequencies to the static and high-frequency dielectric constants. For GaAs, the LO and TO phonon frequencies at room temperature are approximately 292 cm⁻¹ and 269 cm⁻¹, respectively, while ZnO exhibits more pronounced splitting with LO and TO frequencies near 574 cm⁻¹ and 407 cm⁻¹ due to its stronger ionic character. The large LO-TO splitting in ZnO is indicative of its high polarity, which enhances the Fröhlich interaction and impacts carrier mobility.

Infrared spectroscopy is a powerful tool for probing these phonon modes, particularly the TO mode, which directly interacts with incident infrared radiation. When the frequency of incident light matches the TO phonon frequency, strong absorption occurs due to resonant excitation of the lattice vibrations. In contrast, the LO phonon does not couple directly to transverse electromagnetic waves in bulk materials but can be observed in oblique incidence or through attenuated total reflectance techniques. The Reststrahlen band, a region of high reflectivity between the TO and LO frequencies, is a hallmark feature of polar semiconductors in infrared spectra.

Raman scattering provides complementary information, enabling the detection of both LO and TO phonons through inelastic light scattering. In this process, incident photons exchange energy with phonons, resulting in shifted peaks in the scattered light spectrum. The selection rules for Raman activity depend on the crystal symmetry and scattering geometry. For example, in zinc blende GaAs, the LO phonon is Raman-active in backscattering configurations, while the TO mode is forbidden. In wurtzite ZnO, both A₁(LO) and E₁(TO) modes are observable, with their intensities varying based on the polarization of the incident and scattered light.

The Fröhlich interaction, which describes the coupling between LO phonons and electrons, is a critical factor in the electrical properties of polar semiconductors. This interaction is responsible for the formation of polarons—quasiparticles consisting of an electron and its induced lattice distortion. The strength of the Fröhlich interaction is quantified by the dimensionless coupling constant α, which depends on the LO phonon frequency and the dielectric properties of the material. For GaAs, α is relatively small (~0.06), indicating weak coupling, whereas ZnO exhibits stronger coupling (α ~ 1.2), leading to more significant polaron effects.

Temperature also influences the behavior of LO and TO phonons. As temperature increases, phonon frequencies typically soften due to anharmonic effects, while damping broadens the spectral lines. In GaAs, the LO phonon frequency decreases by about 0.02 cm⁻¹ per Kelvin, while ZnO shows a more pronounced temperature dependence due to its higher bond ionicity. These shifts can be accurately measured using temperature-dependent Raman or infrared spectroscopy, providing insights into lattice anharmonicity and thermal expansion.

The study of phonon modes extends beyond bulk materials to low-dimensional systems, where quantum confinement and surface effects modify the vibrational spectra. In nanostructures such as quantum wells or nanowires, the reduced dimensionality alters the phonon dispersion relations, leading to shifts in LO and TO frequencies and the appearance of interface modes. For instance, GaAs/AlAs superlattices exhibit confined phonon modes whose frequencies depend on the layer thickness, while ZnO nanowires show surface optical phonons that differ from bulk modes.

Experimental techniques must be carefully chosen to accurately resolve LO and TO phonons. Fourier-transform infrared spectroscopy (FTIR) excels in measuring TO modes but requires specialized configurations for LO mode detection. Raman spectroscopy, on the other hand, offers greater flexibility in probing both modes but may suffer from signal-to-noise challenges in weakly scattering materials. Combining these methods with first-principles calculations based on density functional theory (DFT) allows for a comprehensive understanding of phonon dynamics and their coupling to other excitations.

In summary, longitudinal and transverse optical phonon modes in polar semiconductors are fundamental to their optical and electronic behavior. The interplay between these modes, governed by dielectric responses and Fröhlich interactions, shapes phenomena ranging from infrared absorption to carrier scattering. Infrared and Raman spectroscopies serve as indispensable tools for characterizing these vibrations, providing detailed insights into material properties across bulk and nanostructured systems. Understanding these phonon modes is essential for advancing the design and optimization of polar semiconductors for future scientific and technological applications.