Surface plasmon polaritons (SPPs) are electromagnetic waves coupled to electron oscillations that propagate along the interface between a semiconductor and a dielectric. These waves arise from the interaction of light with free carriers in conductive materials, leading to strong field confinement at the nanoscale. SPPs at semiconductor interfaces exhibit unique dispersion properties, excitation mechanisms, and applications distinct from those in metals, owing to the tunable carrier densities and optical responses of semiconductors.

**Excitation Mechanisms**
SPPs are excited when the momentum of incident light matches that of the surface plasmon mode. In semiconductors, this is achieved through prism coupling, grating coupling, or near-field excitation. Prism coupling, such as the Kretschmann configuration, uses a high-index prism to enhance the wavevector of incident light, enabling phase matching. Grating coupling relies on periodic nanostructures to provide the necessary momentum via diffraction orders. Near-field techniques, including scattering-type scanning near-field optical microscopy (s-SNOM), directly probe SPPs with subwavelength resolution. The excitation efficiency depends on the semiconductor's complex dielectric function, which is influenced by doping levels, temperature, and wavelength.

**Dispersion Relations**
The dispersion relation of SPPs at a semiconductor-dielectric interface is derived from Maxwell's equations and the boundary conditions for electromagnetic fields. For a semiconductor with a dielectric function ε₁(ω) and a dielectric medium with ε₂, the SPP wavevector kₛₚₚ is given by:
kₛₚₚ = (ω/c) √(ε₁ε₂ / (ε₁ + ε₂)),
where ω is the angular frequency and c is the speed of light. In doped semiconductors, ε₁(ω) is described by the Drude model:
ε₁(ω) = ε∞ - (ωₚ² / (ω² + iγω)),
where ε∞ is the high-frequency permittivity, ωₚ is the plasma frequency, and γ is the damping rate. The plasma frequency ωₚ = √(ne² / ε₀m*) depends on the carrier concentration n and effective mass m*. This tunability allows SPPs in semiconductors to span mid-infrared to terahertz ranges, unlike noble metals confined to visible frequencies.

**Materials for SPPs**
Doped silicon is a widely studied platform for SPPs due to its compatibility with CMOS technology. By adjusting the doping concentration (typically 10¹⁸–10²⁰ cm⁻³), the plasma frequency can be shifted across the infrared spectrum. III-V semiconductors like InAs and GaN offer high electron mobility and direct bandgaps, enabling low-loss SPP propagation and integration with optoelectronic devices. Transparent conducting oxides (TCOs), such as indium tin oxide (ITO) and aluminum-doped zinc oxide (AZO), exhibit near-zero permittivity in the near-infrared, making them ideal for epsilon-near-zero (ENZ) plasmonics. These materials enable dynamic SPP modulation via electrical gating or optical excitation.

**Nano-Patterning for SPP Control**
Nanostructuring techniques are critical for manipulating SPP propagation and localization. Electron-beam lithography and focused ion beam milling create precise gratings and resonators to couple and guide SPPs. Self-assembled nanoparticle arrays offer a scalable alternative for broadband SPP excitation. For example, periodic arrays of silicon nanopillars or III-V nanodisks enhance light-matter interaction through localized surface plasmon resonances (LSPRs). Metasurfaces composed of TCO nanostructures achieve phase and amplitude control of SPPs, enabling flat optics applications.

**Applications in Sensing**
SPP-based sensors exploit the high sensitivity of plasmon modes to refractive index changes. Semiconductor SPP sensors operate in the infrared, where molecular vibrations provide chemical specificity. For instance, doped silicon waveguides functionalized with antibodies detect biomolecules through shifts in the SPP resonance wavelength. TCO-based sensors offer real-time monitoring of gas adsorption due to their electrically tunable optical properties. The figure of merit (FOM) for these sensors depends on the semiconductor's carrier mobility and the interface quality.

**Waveguiding and Optoelectronic Enhancement**
SPP waveguides confine light below the diffraction limit, enabling dense photonic integration. Semiconductor-insulator-semiconductor (SIS) waveguides support long-range SPPs with propagation lengths exceeding millimeters in the mid-infrared. Hybrid plasmonic waveguides, combining semiconductors with low-index dielectrics, balance confinement and loss. In optoelectronics, SPPs enhance light absorption in thin-film solar cells by trapping light in active layers. III-V nanowire lasers utilize SPPs to reduce the lasing threshold by Purcell enhancement of spontaneous emission.

**Challenges and Future Directions**
Despite progress, semiconductor SPPs face challenges such as ohmic losses and fabrication tolerances. Advances in hyperbolic phonon-polaritons in anisotropic materials may overcome these limitations. Future work will focus on integrating SPPs with quantum emitters and 2D materials for hybrid quantum plasmonic systems. The development of ultrafast switching mechanisms using all-optical or electro-optical control will expand applications in signal processing and computing.

In summary, SPPs at semiconductor interfaces offer a versatile platform for nanophotonics, combining tunable optical properties with existing fabrication technologies. Their applications in sensing, waveguiding, and optoelectronics highlight the potential for next-generation integrated photonic systems.