3.2 Excitons, biexcitons, and multi-exciton states

Quantum dots showcase fascinating interactions between electrons and holes. These tiny semiconductor particles host excitons, biexcitons, and multi-exciton states, which greatly impact their optical properties. Understanding these states is crucial for harnessing quantum dots' potential in various applications.

The formation, recombination, and dynamics of excitons in quantum dots are influenced by factors like size, shape, and composition. These characteristics affect energy levels, binding energies, and optical transitions, making quantum dots versatile tools for light emission and absorption in advanced technologies.

Excitons in Quantum Dots

Exciton Definition and Formation

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• An exciton is a bound state of an electron and a hole in a semiconductor (quantum dot) formed by the absorption of a photon with energy greater than the bandgap
• The confinement of electrons and holes in a quantum dot leads to discrete energy levels and enhanced Coulomb interactions, which play a crucial role in the formation and properties of excitons
• Exciton formation occurs when an electron is excited from the valence band to the conduction band by absorbing a photon, leaving behind a hole in the valence band
• The excited electron and hole are bound together by Coulomb attraction, forming a neutral quasi-particle (exciton)

Biexcitons and Multi-exciton States

• Biexcitons are two excitons that are bound together in a quantum dot, forming a quasi-particle with a lower energy than the sum of two individual excitons
• Multi-exciton states refer to the presence of multiple excitons (more than two) in a single quantum dot, which can occur under high excitation conditions
• The formation of biexcitons leads to a redshift in the emission spectrum compared to single excitons, due to the lower energy of the biexciton state
• Multi-exciton states can result in complex emission spectra, with multiple peaks corresponding to different exciton and multi-exciton transitions (single exciton, biexciton, triexciton)

Exciton Formation and Recombination

Exciton Recombination Processes

• Exciton recombination involves the electron relaxing back to the valence band and recombining with the hole, releasing energy in the form of a photon (radiative recombination) or heat (non-radiative recombination)
• The confinement of electrons and holes in quantum dots leads to enhanced overlap of their wave functions, increasing the probability of radiative recombination compared to bulk semiconductors
• The recombination dynamics of excitons are influenced by factors such as the size, shape, and composition of the quantum dot, as well as the presence of surface states and defects
• Non-radiative recombination can occur through various mechanisms, such as Auger recombination or phonon-assisted processes, which reduce the overall emission efficiency

Factors Influencing Exciton Dynamics

• Temperature plays a crucial role in exciton dynamics, with higher temperatures leading to increased phonon interactions and a higher probability of non-radiative recombination, reducing the exciton lifetime and emission efficiency
• Surface properties, such as the presence of surface states, defects, or ligands, can influence the non-radiative recombination rates and the overall exciton lifetime
• The composition of the quantum dot, including the choice of semiconductor materials (CdSe, InP) and any intentional doping, can impact the bandgap, exciton binding energy, and charge carrier dynamics

Biexcitons and Multi-excitons in Optical Properties

Influence on Absorption and Emission

• Biexcitons and multi-exciton states in quantum dots can significantly influence the optical properties, such as absorption, emission, and nonlinear optical responses
• The presence of biexcitons and multi-exciton states can lead to phenomena such as exciton-exciton annihilation, where the recombination of one exciton provides energy for the dissociation of another, affecting the overall emission efficiency
• Multi-exciton states can contribute to broadening and spectral shifts in the absorption and emission spectra of quantum dots

Nonlinear Optical Properties

• Biexcitons and multi-exciton states can contribute to nonlinear optical properties, such as two-photon absorption and multi-photon emission, which have potential applications in quantum information processing and imaging
• The strong confinement and enhanced Coulomb interactions in quantum dots can lead to efficient multi-photon absorption processes, enabling the generation of entangled photon pairs or single photons
• The presence of biexcitons and multi-exciton states can also result in phenomena such as exciton-exciton interaction-induced shifts in the emission energy (biexciton binding energy)

Exciton Stability and Dynamics

Quantum Dot Size and Shape Effects

• The stability and dynamics of excitons are influenced by the size, shape, and composition of the quantum dots
• Smaller quantum dots exhibit stronger quantum confinement effects, leading to increased exciton binding energy and stability compared to larger quantum dots
• The shape of the quantum dot, such as spherical or elongated (nanorods), can affect the symmetry and degeneracy of the exciton states, influencing their energy levels and optical transitions

External Field Effects

• External factors, such as electric and magnetic fields, can modulate the exciton properties and dynamics in quantum dots
• The quantum-confined Stark effect occurs when an external electric field is applied, leading to a shift in the exciton energy levels and a change in the absorption and emission spectra
• Magnetic fields can induce Zeeman splitting of the exciton states, resulting in a splitting of the emission peaks and a modification of the exciton spin dynamics
• The manipulation of excitons using external fields has potential applications in quantum information processing, such as qubit control and spin-photon interfaces