Quantum dots (QDs) are nanoscale semiconductor crystals with unique optoelectronic properties governed by quantum confinement effects. Their electronic and optical behaviors differ significantly from bulk materials due to their discrete energy levels, tunable bandgaps, and strong excitonic interactions. These characteristics make them highly versatile for applications ranging from light-emitting diodes to biomedical imaging. The fundamental principles underlying their optoelectronic properties include quantum confinement, bandgap engineering, and exciton dynamics, all of which are influenced by their size, shape, and chemical composition.

Quantum confinement is the most defining feature of quantum dots. When the physical dimensions of a semiconductor crystal become smaller than the exciton Bohr radius, the motion of electrons and holes is spatially restricted, leading to discrete energy levels. This confinement increases the bandgap energy, causing a blue shift in both absorption and emission spectra as the QD size decreases. For example, CdSe quantum dots exhibit tunable emission across the visible spectrum, ranging from 450 nm (blue) for smaller dots (~2 nm) to 650 nm (red) for larger dots (~6 nm). The relationship between size and bandgap can be approximated using the particle-in-a-box model, where the energy gap scales inversely with the square of the QD radius.

Bandgap tuning is achieved not only through size variation but also by altering the composition of the quantum dot. Different semiconductor materials possess distinct bulk bandgap energies, which influence the confinement effects in their nanostructured forms. CdSe, PbS, and InP are three widely studied QD materials, each with unique optoelectronic characteristics. CdSe QDs have a bulk bandgap of ~1.74 eV and exhibit strong quantum confinement, making them ideal for visible-light applications. PbS QDs, with a smaller bulk bandgap of ~0.41 eV, are suited for near-infrared (NIR) applications, with emission tunable between 800 nm and 2000 nm. InP QDs, with a bulk bandgap of ~1.35 eV, serve as a cadmium-free alternative for visible to NIR emission, though their optical properties are highly sensitive to surface passivation due to higher surface defect densities.

The absorption and emission spectra of quantum dots are marked by sharp excitonic peaks, reflecting their discrete electronic states. The absorption spectrum typically shows a series of peaks corresponding to transitions between quantized conduction and valence band states. The first excitonic peak, representing the lowest energy transition, is particularly prominent and shifts to higher energies with decreasing QD size. Emission spectra, on the other hand, are influenced by exciton recombination processes. In high-quality QDs, photoluminescence (PL) spectra exhibit narrow linewidths, often below 30 nm full-width-at-half-maximum (FWHM), indicating minimal inhomogeneous broadening and uniform size distribution.

Excitonic effects play a crucial role in the optical properties of quantum dots. An exciton, a bound electron-hole pair, forms upon photoexcitation and can recombine radiatively to emit light or undergo non-radiative decay pathways. The exciton binding energy in QDs is significantly enhanced compared to bulk materials due to spatial confinement and reduced dielectric screening. For instance, CdSe QDs exhibit exciton binding energies on the order of tens of meV, much higher than the ~15 meV observed in bulk CdSe. This strong binding leads to efficient radiative recombination at room temperature.

Carrier dynamics in quantum dots involve multiple processes, including exciton formation, relaxation, and recombination. Upon excitation, hot carriers rapidly thermalize to the band edges through electron-phonon interactions, typically occurring on picosecond timescales. Radiative recombination lifetimes range from nanoseconds to microseconds, depending on the material and surface quality. However, non-radiative processes such as trapping at surface defects or Auger recombination can dominate in poorly passivated QDs. Auger recombination, a three-particle interaction where an electron and hole recombine non-radiatively by transferring energy to a third carrier, is particularly detrimental in QDs due to their small volume and strong Coulomb interactions. This process becomes significant at high excitation densities and limits the performance of QDs in applications like lasers or high-brightness LEDs.

The composition of quantum dots profoundly influences their optoelectronic properties. CdSe QDs are known for their high photoluminescence quantum yields (PLQY) and narrow emission spectra, making them a model system for fundamental studies. However, their toxicity and environmental concerns have driven research into alternative materials like InP. InP QDs, while less toxic, require careful surface passivation to achieve comparable PLQY due to their higher susceptibility to oxidation and defect formation. PbS QDs, with their narrow bulk bandgap, are advantageous for infrared optoelectronics but face challenges related to air stability and Auger recombination suppression. Alloyed quantum dots, such as CdSe/ZnS core-shell structures, combine the benefits of different materials by passivating surface traps and enhancing emission efficiency. The ZnS shell, with its wider bandgap, confines charge carriers to the CdSe core while reducing non-radiative recombination at the surface.

Surface chemistry also plays a critical role in determining the optoelectronic properties of quantum dots. Ligands bound to the QD surface influence charge carrier localization, defect passivation, and environmental stability. For example, thiol-based ligands on PbS QDs can stabilize the surface but may introduce mid-gap states that quench emission. Conversely, halide passivation of perovskite QDs significantly improves their PLQY by eliminating undercoordinated lead atoms. The dynamic interaction between QDs and their surrounding ligands can lead to reversible changes in optical properties under external stimuli such as light or heat.

Quantum dots also exhibit unique phenomena such as blinking, where their photoluminescence intermittently turns on and off under continuous excitation. This behavior arises from charge carrier trapping at surface or interface states, leading to temporary quenching of emission. While blinking is undesirable for applications requiring stable emission, strategies such as shell encapsulation or electrochemical control have been developed to mitigate it.

In summary, the optoelectronic properties of quantum dots are governed by quantum confinement, composition-dependent bandgap tuning, and excitonic interactions. Their absorption and emission spectra are highly tunable, with carrier dynamics influenced by radiative and non-radiative processes. Auger recombination remains a critical challenge, particularly for small QDs or those with high excitation densities. Material composition dictates the spectral range, stability, and efficiency of QDs, with CdSe, PbS, and InP serving as key examples. Understanding these fundamental properties is essential for harnessing the full potential of quantum dots in next-generation optoelectronic technologies.