8.4 Excitons
7 min read•august 21, 2024
Excitons are bound that play a crucial role in the optical and electronic properties of semiconductors and insulators. They influence light absorption, emission, and energy transfer processes, making them essential for understanding and designing optoelectronic devices.
Excitons come in different types, including Wannier-Mott and Frenkel excitons, each with unique characteristics. Their , spatial extent, and lifetime depend on material properties and environmental factors, affecting how they interact with light and move through crystal lattices.
Fundamental concepts of excitons
- Excitons play a crucial role in the optical and electronic properties of semiconductors and insulators in condensed matter physics
- Understanding excitons provides insights into light-matter interactions and energy transfer processes in solid-state materials
- Excitons influence the design and performance of optoelectronic devices, making them a key area of study in condensed matter physics
Definition and formation
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- Bound state of an electron and a hole held together by electrostatic Coulomb force
- Created when a photon excites an electron from the valence band to the conduction band, leaving behind a positively charged hole
- Formation process involves absorption of energy greater than or equal to the material's band gap
- Excitons can move through the crystal lattice as a single entity, transferring energy without net charge flow
Types of excitons
- Wannier-Mott excitons characterized by large spatial extent and small binding energy, typically found in semiconductors with high dielectric constants
- Frenkel excitons localized to a single atom or molecule, common in organic materials and insulators
- Charge-transfer excitons occur when the electron and hole are located on adjacent molecules or atoms
- Surface excitons form at the interface between two different materials or at a material's surface
Binding energy
- Energy required to separate the electron-hole pair into free carriers
- Inversely proportional to the dielectric constant of the material
- Typically ranges from a few meV in semiconductors to several eV in insulators
- Calculated using the hydrogen-like model:
- μ represents the reduced mass of the electron-hole pair
- ε is the dielectric constant of the material
Exciton properties
Optical characteristics
- Excitons absorb and emit light at energies slightly below the material's band gap
- Excitonic absorption peaks appear as sharp features in optical spectra
- Radiative recombination of excitons produces with characteristic wavelengths
- Exciton-polaritons form when excitons strongly couple with photons, leading to unique optical properties
Spatial extent
- Bohr radius of excitons determines their spatial extent in the material
- Wannier-Mott excitons have large Bohr radii, typically 10-100 times the lattice constant
- Frenkel excitons are localized within a single unit cell, with Bohr radii comparable to atomic dimensions
- Spatial extent affects the exciton's interaction with defects, impurities, and other excitons in the material
Lifetime and decay
- Exciton lifetime ranges from picoseconds to microseconds depending on material properties and environmental factors
- Radiative decay occurs when the electron and hole recombine, emitting a photon
- Non-radiative decay processes include Auger recombination and phonon-assisted recombination
- length determined by the product of lifetime and diffusion coefficient
- Temperature dependence of exciton lifetime due to thermal dissociation and phonon scattering
Excitons in semiconductors
Band structure effects
- Exciton formation and properties strongly influenced by the electronic band structure of semiconductors
- Direct band gap semiconductors (GaAs) facilitate efficient exciton formation and radiative recombination
- Indirect band gap materials (silicon) require phonon assistance for exciton formation and recombination
- Valence band degeneracy leads to light-hole and heavy-hole excitons with different effective masses and binding energies
Wannier-Mott vs Frenkel excitons
- Wannier-Mott excitons predominate in inorganic semiconductors with high dielectric constants
- Large spatial extent allows for delocalization across multiple unit cells
- Binding energies typically in the range of 1-100 meV
- Frenkel excitons common in organic semiconductors and insulators with low dielectric constants
- Localized nature results in stronger electron-hole interactions
- Binding energies can exceed 1 eV
Exciton-polaritons
- Hybrid quasiparticles formed by strong coupling between excitons and photons in semiconductor microcavities
- Exhibit unique dispersion relations with upper and lower polariton branches
- Enable novel phenomena such as polariton lasing and Bose-Einstein condensation at elevated temperatures
- Tunable properties through cavity design and external fields make them attractive for optoelectronic applications
Experimental techniques
Photoluminescence spectroscopy
- Measures light emission from exciton recombination after optical excitation
- Provides information on exciton energy levels, binding energies, and recombination dynamics
- Temperature-dependent measurements reveal exciton dissociation and thermal activation processes
- Time-resolved photoluminescence tracks exciton lifetimes and relaxation pathways
Absorption spectroscopy
- Probes exciton formation by measuring light absorption as a function of wavelength
- Excitonic absorption peaks appear below the band edge in semiconductors
- Allows determination of exciton binding energies and oscillator strengths
- Magneto-absorption studies reveal exciton behavior in strong magnetic fields
Time-resolved measurements
- Ultrafast spectroscopy techniques (pump-probe, transient absorption) investigate exciton dynamics on femtosecond to nanosecond timescales
- Reveal exciton formation, relaxation, and dissociation processes
- Two-dimensional spectroscopy maps energy transfer pathways between different excitonic states
- Terahertz spectroscopy probes intra-excitonic transitions and exciton transport
Applications of excitons
Light-emitting diodes
- Exciton recombination drives light emission in organic and quantum dot LEDs
- Control of exciton formation and decay crucial for improving LED efficiency and color purity
- Phosphorescent materials harness triplet excitons to achieve nearly 100% internal quantum efficiency
- Thermally activated delayed fluorescence (TADF) utilizes reverse intersystem crossing to convert triplet excitons to singlets
Solar cells
- Exciton dissociation at donor-acceptor interfaces key to charge generation in organic photovoltaics
- Singlet fission process in certain materials generates multiple excitons from a single photon, potentially exceeding the Shockley-Queisser limit
- Hot carrier extraction from excitons before thermalization can improve solar cell efficiency
- Quantum dot leverage size-tunable exciton properties for spectrum-matched absorption
Quantum information
- Excitons in quantum dots serve as qubits for quantum computing applications
- Controlled creation and manipulation of entangled exciton pairs enable quantum cryptography protocols
- Exciton-polaritons in microcavities proposed for quantum simulation of many-body systems
- Coupling of excitons to defect spins (nitrogen-vacancy centers) for long-lived quantum memories
Excitons in low-dimensional systems
Quantum wells
- Two-dimensional confinement of excitons in thin semiconductor layers
- Increased due to reduced dielectric screening and enhanced Coulomb interaction
- Quantum-confined Stark effect allows electric field tuning of exciton properties
- Formation of indirect excitons in coupled quantum wells with long lifetimes and high mobility
Quantum wires
- One-dimensional confinement leads to enhanced exciton binding energies and oscillator strengths
- Exciton transport along the wire axis with reduced scattering compared to bulk materials
- Unique optical selection rules due to broken symmetry in the confined directions
- Carbon nanotubes as prototypical one-dimensional systems for studying exciton physics
Quantum dots
- Zero-dimensional confinement results in discrete excitonic energy levels
- Size-dependent optical properties enable tuning of emission wavelength
- Strong quantum confinement increases exciton binding energies to hundreds of meV
- Multi-exciton complexes (biexcitons, trions) play important roles in quantum dot optoelectronics
Many-body effects
Exciton-exciton interactions
- Dipole-dipole interactions between excitons lead to energy shifts and broadening of spectral features
- Exciton-exciton annihilation processes limit the maximum exciton density in materials
- Formation of excitonic molecules (biexcitons) through attractive interactions between excitons
- Repulsive interactions at high densities can lead to exciton Mott transition and electron-hole plasma formation
Biexcitons and trions
- Biexcitons consist of two bound excitons, analogous to hydrogen molecules
- Trions are charged excitons formed by binding an additional electron or hole to a neutral exciton
- Biexciton binding energies typically 10-20% of the exciton binding energy
- Trion formation in doped semiconductors influences optical and transport properties
Bose-Einstein condensation
- Excitons, as composite bosons, can undergo Bose-Einstein condensation at sufficiently low temperatures and high densities
- Exciton-polaritons in semiconductor microcavities exhibit condensation at elevated temperatures due to their light
- Condensed exciton phases display macroscopic quantum coherence and superfluid behavior
- Potential applications in low-threshold lasers and quantum simulation devices
Theoretical models
Effective mass approximation
- Treats electrons and holes as free particles with modified masses reflecting the band structure
- Simplifies the description of excitons in semiconductors with parabolic bands
- Effective masses determined from band curvature:
- Breaks down for materials with complex band structures or strong electron-hole correlations
Hydrogen-like model
- Describes excitons as analogous to hydrogen atoms with reduced mass and screened Coulomb interaction
- Exciton energy levels given by:
- Eg represents the band gap energy
- n is the principal quantum number
- Predicts hydrogenlike absorption series converging to the band edge
- Accurately describes Wannier-Mott excitons but fails for Frenkel excitons
Computational approaches
- Density functional theory (DFT) with appropriate functionals for excited states (time-dependent DFT)
- GW approximation combined with Bethe-Salpeter equation for accurate description of exciton energies and wavefunctions
- Quantum Monte Carlo methods for treating strong electron-hole correlations
- Tight-binding and k·p models for efficient calculation of exciton properties in nanostructures
Excitons in novel materials
Transition metal dichalcogenides
- Atomically thin semiconductors (MoS2, WS2) with strong excitonic effects due to reduced dielectric screening
- Large exciton binding energies (hundreds of meV) enable room temperature applications
- Valley-specific optical selection rules allow for valley-tronic devices
- Formation of interlayer excitons in van der Waals heterostructures with long lifetimes and high mobility
Perovskites
- Hybrid organic-inorganic materials (CH3NH3PbI3) with excellent optoelectronic properties
- Exciton binding energies tunable through composition and dimensionality
- Defect tolerance and long carrier diffusion lengths contribute to high solar cell efficiencies
- Dynamic disorder and polaronic effects influence exciton behavior and charge transport
Carbon nanotubes
- One-dimensional systems with diameter-dependent electronic and optical properties
- Excitons dominate optical response due to strong Coulomb interactions and reduced screening
- Dark excitons and triplet states play important roles in relaxation dynamics
- Chirality-dependent exciton properties enable applications in near-infrared optoelectronics and biosensing
Key Terms to Review (16)
Binding energy: Binding energy is the energy required to separate a system into its constituent parts. In the context of excitons, it refers to the energy that holds an exciton together, a bound state of an electron and a hole created in a semiconductor when light is absorbed. This energy is crucial in understanding how excitons form, their stability, and how they interact with other particles and fields.
Bose-einstein condensation of excitons: Bose-Einstein condensation of excitons is a quantum phenomenon where a group of excitons, which are bound states of electrons and holes, occupy the same quantum state at low temperatures, leading to collective behavior. This phenomenon showcases the unique properties of bosonic particles, enabling them to condense into a macroscopic quantum state, resulting in new optical and electronic properties in materials.
Effective Mass: Effective mass is a concept used in solid-state physics to describe how the motion of charge carriers, such as electrons or holes, responds to external forces within a material. This term captures the effect of the periodic potential of the crystal lattice on the dynamics of these particles, allowing us to treat them as if they possess a different mass than their actual mass. The effective mass plays a crucial role in determining how particles behave under various conditions, linking it to phenomena like energy bands, wave functions, and excitonic effects.
Electron-hole pairs: Electron-hole pairs are entities formed when an electron in a semiconductor material absorbs energy, typically from light, and moves to a higher energy state, leaving behind a vacancy known as a hole. This process is critical in the behavior of semiconductors and plays a vital role in the formation of excitons, which are bound states of an electron and a hole that can move through the material together.
Exciton binding energy: Exciton binding energy is the energy required to dissociate an exciton into its constituent electron and hole. This concept is crucial in understanding the stability of excitons, which are bound states formed when an electron is attracted to a hole created in a semiconductor or insulator due to the absorption of light. A higher exciton binding energy indicates that the exciton is more stable and less likely to separate into free charge carriers, which is vital for various optical and electronic properties in materials.
Exciton diffusion: Exciton diffusion refers to the process by which excitons, bound pairs of electrons and holes, move through a material after their formation. This movement is crucial for understanding the efficiency of energy transfer in various systems, such as solar cells and light-emitting devices. The diffusion process can significantly affect the overall performance of devices that rely on excitons, as it determines how effectively they can reach interfaces or other components for energy conversion.
Exciton-Polariton: Exciton-polaritons are quasiparticles formed by the coupling of excitons, which are bound states of an electron and a hole, with photons in a solid material. They exhibit hybrid characteristics, combining properties of both light and matter, leading to unique phenomena such as superfluidity and Bose-Einstein condensation. These properties arise due to their ability to exist in a coherent state, making exciton-polaritons significant for studying light-matter interactions.
Excitonic annihilation: Exciton annihilation refers to the process in which two excitons (bound states of an electron and a hole) interact and combine, resulting in the transfer of energy or the conversion into other forms, such as phonons or photons. This phenomenon plays a significant role in the dynamics of excitons in semiconductor materials and can impact their optical properties and overall efficiency.
Excitons transport: Exciton transport refers to the movement of excitons, which are bound states of an electron and a hole that arise when a photon is absorbed by a semiconductor or insulator. This process is essential for understanding how energy is transferred in materials, particularly in organic semiconductors and photovoltaic devices, where the efficiency of light absorption and energy transfer plays a crucial role in device performance.
Frenkel Exciton: A Frenkel exciton is a type of bound state formed when an electron is excited from its ground state to a higher energy level, creating a hole in the original state. This exciton is characterized by its localization, meaning it tends to remain within the same unit cell of a solid rather than spreading out over several cells, which is typical for other types of excitons. Understanding Frenkel excitons is essential as they play a significant role in the optical properties and energy transfer processes in materials like organic semiconductors and molecular crystals.
Optical devices: Optical devices are instruments designed to manipulate and control light in order to produce images, transmit information, or enhance visual perception. These devices often rely on principles of optics, such as refraction, reflection, and diffraction, to achieve their functions. In the context of phenomena like quantum confinement and excitons, optical devices can exhibit unique properties and behaviors due to their interaction with light at microscopic scales.
Photoluminescence: Photoluminescence is the process by which a material absorbs photons (light) and then re-emits them, often at a longer wavelength. This phenomenon is critical in understanding the optical properties of materials, especially in semiconductor physics, as it reveals insights about energy levels, defects, and carrier dynamics within materials such as quantum wells and excitonic systems.
Photon-exciton interaction: Photon-exciton interaction refers to the coupling between photons and excitons, which are bound states of electrons and holes in a semiconductor or insulator. This interaction is crucial for understanding light-matter interactions, as it enables processes like absorption, emission, and scattering of light in materials, thereby influencing their optical properties and behavior.
Solar cells: Solar cells are semiconductor devices that convert light energy directly into electrical energy through the photovoltaic effect. They are essential components in solar panels and are primarily made from silicon, which can be manipulated to create both intrinsic and extrinsic semiconductors to enhance their efficiency in converting sunlight into electricity.
Time-resolved spectroscopy: Time-resolved spectroscopy is a powerful technique used to study the dynamic processes of materials by measuring how their optical properties change over time after being excited by a light source. This method allows researchers to investigate the temporal evolution of excited states, such as excitons, enabling insights into their formation, lifetime, and interactions in various materials. By capturing data at extremely short timescales, it plays a critical role in understanding fundamental processes in condensed matter physics.
Wannier-Mott exciton: A Wannier-Mott exciton is a bound state of an electron and a hole in a semiconductor or insulator, where the electron and hole are spatially separated but interact through their Coulomb attraction. This type of exciton occurs when the electron and hole are well-defined quantum states that can be treated within a more extended spatial range, resulting in a larger Bohr radius compared to Frenkel excitons. Wannier-Mott excitons are critical for understanding optical properties and excitonic phenomena in various materials.