Ellipsometry is a powerful optical technique used to study thin films and nanostructures by measuring changes in the polarization state of reflected light. In quantum-confined semiconductor structures such as quantum wells and quantum dots, ellipsometry provides critical insights into dielectric functions, layer thicknesses, and electronic transitions influenced by quantum confinement. The method is non-destructive and highly sensitive, making it ideal for probing nanoscale phenomena in semiconductors.

Quantum confinement modifies the dielectric function of semiconductor nanostructures due to discrete energy levels and altered optical transitions. In bulk semiconductors, the dielectric function is governed by continuous bands, but in quantum wells and dots, the reduced dimensionality leads to quantization of energy states. This results in sharp features in the dielectric function, corresponding to transitions between confined electron and hole states. Ellipsometry detects these modifications by analyzing the amplitude ratio (Ψ) and phase difference (Δ) of polarized light reflected from the sample.

For quantum wells, ellipsometry can determine well thickness with sub-nanometer precision. The technique measures optical transitions between quantized subbands, which shift to higher energies as the well width decreases. In III-V materials like GaAs/AlGaAs quantum wells, ellipsometry reveals distinct excitonic peaks in the dielectric function, corresponding to transitions between electron and heavy-hole or light-hole states. The energy separation between these peaks provides information about the well width and barrier composition. For example, in a 5 nm GaAs quantum well, the first electron-heavy-hole transition typically appears around 1.6 eV, while a 10 nm well shifts it closer to 1.5 eV.

Quantum dots exhibit even stronger confinement effects due to their three-dimensional confinement. The dielectric function of quantum dots shows discrete transitions instead of the broad features seen in bulk materials. Ellipsometry can resolve these transitions and extract parameters such as dot size, composition, and carrier confinement energies. In II-VI quantum dots like CdSe, the bandgap increases with decreasing dot diameter due to the quantum size effect. For instance, CdSe dots with a 3 nm diameter exhibit a bandgap near 2.3 eV, while 5 nm dots have a bandgap around 2.1 eV. Ellipsometry tracks these shifts by modeling the dielectric function with appropriate effective medium approximations.

The analysis of ellipsometric data for quantum-confined structures requires advanced modeling approaches. For quantum wells, a multilayer model incorporating the well and barrier dielectric functions is used. The well's dielectric function is often described using an anisotropic model due to the in-plane versus out-of-plane confinement. For quantum dots, effective medium theories such as the Maxwell-Garnett or Bruggeman models are employed to account for the dot-matrix system. These models help separate the contributions of the dots and the surrounding material to the overall optical response.

In III-V nanostructures, ellipsometry has been applied to study InAs/GaAs quantum dots, where the strain and composition affect the dielectric function. The technique identifies transitions between confined states and quantifies the indium content in the dots. For example, InAs dots embedded in GaAs show transitions around 1.0-1.3 eV, depending on their size and strain. Ellipsometry also detects wetting layer effects, which are critical for understanding dot formation and optical properties.

II-VI quantum dots like ZnSe/CdSe core-shell structures exhibit complex dielectric functions due to interfacial strain and carrier localization. Ellipsometry resolves the contributions from the core, shell, and interface regions, enabling precise control over growth parameters. In such systems, the dielectric function shows signatures of type-II band alignment, where electrons and holes are spatially separated. This manifests as a redshift in the optical transitions compared to the individual components.

Ellipsometry also plays a role in studying doping effects in quantum-confined structures. In doped quantum wells, the dielectric function reflects changes in the free carrier concentration and plasma frequency. For instance, n-doped GaAs wells show a Drude-like response at low energies, which ellipsometry can quantify. In quantum dots, doping introduces additional states within the bandgap, altering the dielectric function's line shape. Ellipsometry helps distinguish these states from intrinsic transitions.

Temperature-dependent ellipsometry provides further insights into confinement effects. As temperature changes, the dielectric function shifts due to thermal expansion and electron-phonon interactions. In quantum wells, the temperature coefficient of the transition energy differs from bulk due to confinement. Ellipsometry measurements at varying temperatures reveal these differences and help quantify the contributions of thermal effects versus quantum confinement.

The technique's sensitivity to interfacial layers makes it valuable for studying heterostructures. In quantum well systems, interfacial roughness and interdiffusion affect the dielectric function. Ellipsometry can detect these effects by analyzing deviations from ideal layer models. For quantum dots, the interface between the dot and the matrix influences carrier confinement and optical properties. Ellipsometry helps optimize growth conditions to minimize interfacial defects.

Recent advances in spectroscopic ellipsometry extend its capabilities to ultrafast processes in quantum-confined structures. Pump-probe ellipsometry measures transient changes in the dielectric function following photoexcitation. This reveals carrier dynamics such as relaxation and recombination in quantum wells and dots. For example, in InGaN quantum dots, ultrafast ellipsometry tracks the relaxation of hot carriers into confined states, providing insights into their potential for optoelectronic applications.

Ellipsometry is also used to study coupling effects in coupled quantum dot systems. When dots are closely spaced, their electronic states interact, leading to hybridization. The dielectric function of such systems shows additional transitions compared to isolated dots. Ellipsometry identifies these features and quantifies the coupling strength, which is crucial for designing quantum dot arrays for applications like quantum computing.

In summary, ellipsometry is a versatile tool for investigating quantum-confined semiconductor structures. It extracts critical parameters such as layer thicknesses, transition energies, and dielectric functions, all modified by quantum confinement. Applications in III-V and II-VI nanostructures demonstrate its ability to resolve size effects, interfacial properties, and carrier dynamics. With ongoing advancements in modeling and instrumentation, ellipsometry continues to be indispensable for understanding and engineering quantum-confined systems.