In semiconductor physics, bound electron-hole states play a critical role in determining optical and electronic properties. Among these, excitons and trions are quasiparticles formed through Coulomb interactions between electrons and holes, influencing absorption, emission, and energy transport processes. Understanding their formation, classification, and behavior is essential for applications in optoelectronics, photovoltaics, and quantum technologies.

An exciton is a bound state of an electron and a hole attracted to each other by electrostatic forces. It is electrically neutral and can move through the crystal lattice as a single entity. Excitons are typically formed when a photon with energy equal to or greater than the bandgap of the semiconductor excites an electron from the valence band to the conduction band, leaving behind a hole. The electron and hole then interact via Coulomb attraction, forming a transient pair. The binding energy of an exciton depends on the dielectric constant of the material and the effective masses of the charge carriers. In materials with high dielectric constants and low effective masses, such as gallium arsenide (GaAs), excitons have relatively low binding energies (a few meV), making them stable only at low temperatures. In contrast, materials with low dielectric constants, such as organic semiconductors, exhibit Frenkel excitons with binding energies on the order of hundreds of meV, allowing stability at room temperature.

Excitons are broadly classified into two types: Mott-Wannier and Frenkel excitons. Mott-Wannier excitons are found in inorganic semiconductors with extended electronic wavefunctions. The electron and hole are separated by a distance much larger than the lattice constant, and their behavior is analogous to that of a hydrogen atom, with a Bohr radius extending over several unit cells. The binding energy of Mott-Wannier excitons is typically low, ranging from 1 to 100 meV, depending on the material. These excitons dominate the optical response of conventional semiconductors like silicon and GaAs.

Frenkel excitons, on the other hand, are localized and occur in materials with tightly bound electrons and holes, such as molecular crystals and organic semiconductors. Here, the electron-hole pair is confined to a single molecule or a small cluster of atoms, resulting in a much smaller Bohr radius. Frenkel excitons exhibit higher binding energies, often exceeding 100 meV, making them stable even at elevated temperatures. Due to their localized nature, Frenkel excitons play a crucial role in the optical properties of organic light-emitting diodes (OLEDs) and photosynthetic systems.

Beyond excitons, more complex bound states can form under specific conditions. A trion is one such state, consisting of an exciton bound to an additional charge carrier—either an electron or a hole. A negatively charged trion (X⁻) comprises two electrons and one hole, while a positively charged trion (X⁺) consists of two holes and one electron. Trions typically form in doped semiconductors or under high excitation densities where excess charge carriers are present. Their binding energy is generally weaker than that of excitons, often by a factor of two or more, due to increased Coulomb screening. Trions are particularly relevant in monolayer transition metal dichalcogenides (TMDCs) like MoS₂, where strong Coulomb interactions and reduced dielectric screening enhance their stability.

Another bound state is the biexciton, a molecule-like complex formed by two excitons. Biexcitons are stabilized by exchange interactions and typically require high excitation densities for formation. Their binding energy is usually a fraction of the exciton binding energy, and they play a role in nonlinear optical phenomena such as four-wave mixing and stimulated emission. In quantum dots, biexcitons exhibit enhanced binding due to quantum confinement effects, making them important for applications in single-photon sources and quantum information processing.

The formation and dynamics of these quasiparticles are influenced by several factors, including temperature, doping, and external fields. At low temperatures, excitons and trions dominate the photoluminescence spectra of semiconductors, appearing as distinct peaks below the bandgap energy. As temperature increases, thermal dissociation reduces their populations, leading to broader emission features. Doping introduces additional charge carriers, promoting trion formation at the expense of neutral excitons. External electric and magnetic fields can further modify their energy levels and recombination pathways, enabling tunable optoelectronic devices.

In optoelectronic applications, excitons and trions are central to light emission and absorption processes. In light-emitting diodes (LEDs) and lasers, exciton recombination produces photons with energies slightly below the bandgap due to their binding energy. Efficient exciton harvesting is crucial for high-performance devices, particularly in organic and perovskite-based systems where exciton diffusion lengths limit charge collection. In photovoltaic devices, exciton dissociation at heterojunctions or interfaces generates free carriers, contributing to photocurrent. Materials with long exciton diffusion lengths, such as certain organic semiconductors and perovskites, are highly sought after for solar cell applications.

Quantum confinement in low-dimensional systems further modifies the properties of bound electron-hole states. In quantum wells, wires, and dots, reduced dimensionality enhances Coulomb interactions, increasing exciton binding energies and stability. For instance, in monolayer TMDCs, exciton binding energies can exceed 500 meV due to strong confinement and reduced dielectric screening. This makes such materials promising for room-temperature excitonic devices, including sensors, modulators, and valleytronic systems.

In summary, excitons, trions, and other bound electron-hole states are fundamental to the optical and electronic behavior of semiconductors. Their classification into Mott-Wannier and Frenkel excitons reflects differences in spatial extent and binding mechanisms, influencing their stability and applicability. Trions and biexcitons represent higher-order complexes that emerge under specific conditions, offering additional avenues for controlling light-matter interactions. Understanding these quasiparticles is essential for advancing optoelectronic technologies, from energy-efficient displays to next-generation quantum devices. The continued exploration of their properties in emerging materials will drive innovations in photonics, electronics, and beyond.