ELECTRONIC & OPTICAL PROCESSES IN QUANTUM DOT’S IN THE PRESENCE OF ELECTROMAGNETIC FIELDS

Abstract

Nanotechnology term signifies a novel realm of scientific exploration focused on fabricating devices that harness the extraordinary properties of materials at the nanoscale, typically ranging from 1 to 100 nanometres. Due to quantum confinement effect, semiconductor nanostructures offer a great promise by exhibiting superior optical & electronic properties as compared to that of bulk semiconductors & have diverse applications in the field of optical sensors, photo catalysts for environmental protection, flat panel displays, storage devices, laser diodes, and LED’s (light emitting diodes). Semiconductor sensor and photo catalyst nanostructures are found to be of more particular importance out of all the applications due to their intricately connection with the appraisal of environmental clean-up technologies. Nonlinear processes, including multiphoton transitions, have been explored extensively both theoretically and experimentally in atomic and molecular systems, as well as in bulk matter. However, the emergence of quantum nanostructures which includes quantum wells, quantum wires, and quantum dots, has given birth to a new class of nonlinear materials for studying multiphoton phenomena and nonlinear optical properties. These nanostructures have found applications in optoelectronic devices such as optical switching, THz multi-photon quantum well infrared photodetectors, multi photon bioimaging, and frequency up-conversion. Moreover, the field of semiconductor physics has witnessed a shift towards investigation of external perturbations including hydrostatic pressure, temperature, electric field & magnetic field as well as spin-dependent phenomena due to its wide xii range of potential applications, including spin transistors, spin filters, and quantum computing. The study of spin-related effects in semiconductor nanostructures often involves considering the spin-orbit interaction. Understanding the spin-orbit interaction is crucial for studying its impact on nonlinear optical processes in quantum nanostructures. Theoretical investigations of various physical phenomena arising from the interaction between quantum nanostructures and strong fields, in the presence of spin-orbit interaction, have become paramount. Such studies allow us to gain insights into fundamental physics and optimize spin-based devices in nanostructures. Consequently, external parameters such as static magnetic fields, static electric fields, photon energy, hydrostatic pressure, temperature and laser intensity have also become vital aspects in exploring the linear and nonlinear properties associated with inter subband transitions in nanostructures like quantum dots and quantum wells. In this thesis, the linear and nonlinear optical properties of quantum nanostructures mainly quantum dots & quantum well have been explored within the presence of hydrostatic pressure, temperature, electric field and magnetic field, as well as Rashba spin-orbit interaction. To observe nonlinear processes, high laser intensities are required, necessitating the use of non-perturbative methods for their study. Chapter 1 provides a brief introduction about the nanostructures, external perturbations, linear & nonlinear properties, and multiphoton processes. A brief discussion about the desired characteristics of nanostructures i.e., Quantum well and quantum dots, as well as about the chosen material by highlighting their unique properties is given in this chapter. xiii The effects of external perturbations that includes hydrostatic pressure, temperature, electric field & magnetic field on the behavior of low-dimensional semiconductors are enlightened in the chapter, as these perturbations can significantly influence the optical and electronic properties of these systems. Understanding these effects is crucial for studying their behavior and potential applications. Next, the chapter discusses about the specific types of low-dimensional semiconductor structures, including quantum dots, quantum well. Each structure is defined and explained, highlighting their unique properties and characteristics. Furthermore, the introduction section of Chapter I provides definitions and explanations of various optical properties and nonlinear optical properties. The behavior of materials while interacting with light, such as absorption, reflection, and transmission denotes the optical properties. Nonlinear optical properties, on the other hand, describe the response of materials to intense light, where the relationship between the input and output light is nonlinear. Overall, Chapter I serves as an overview, setting the foundation for the subsequent chapters by introducing the key concepts, structures, and properties associated with low-dimensional semiconductors and their optical behavior. In Chapter 2, we investigate the optical rectification coefficient of a GaAs quantum dots under the influence of radius, hydrostatic pressure & temperature for an excitonic system. A detailed discussion about the mathematics to find out the eigenvalues and eigen-energies using density matrix approach under effective mass approximation is presented in chapter 2. Our findings indicate that an increase in the radius, hydrostatic pressure & Temperature as well as excitons strongly play a role in affecting the peak xiv position as well as blue/red shift is observed in optical rectification coefficient. The results are presented as functions of incident photon energy for different parameter values. Our findings reveal that the hydrostatic pressure causes a red shift in the ORC (optical rectification coefficient) peaks, while the temperature shift these peaks towards the blue end of the spectrum. Furthermore, an increase in the quantum dot radius is found to induce a red shift in the peaks. Chapter 3 of the study focuses on investigating the (THG) third harmonic generation coefficients of InxGa1−xAs quantum dots in the presence of confining potential, magnetic field, hydrostatic pressure & temperature with Rashba spin-orbit interaction. Density matrix procedure within the effective mass approximation have been employed to determine the energy levels and wave functions. The study reveals that the THG coefficients depend on several factors, including the confining potential, -orbit interaction strength, magnetic field strength, Rashba spin, and photon energy. The consequences reveal that increasing the Rashba spin-orbit interaction coefficient has a strong impact on the THG peak positions. Additionally, it can be observed that the coefficient of THG is significantly enhanced by increasing/decreasing the magnetic field or confinement potential. This feature makes them valuable for optical control in spintronics, indicating potential applications in spin photodetectors and ultra-sensitive spintronic devices. Overall, Chapter 3 provides a detailed investigation of the THG coefficients in InxGa1−xAs quantum dots under the influence of THz laser fields with Rashba spin-orbit interaction and a magnetic field. The results highlight the importance of various xv parameters in controlling the spin dynamics and optical properties of quantum dots, paving the way for potential advancements in spintronics and bioimaging devices. Chapter 4 of the study focuses on the investigation of the linear and nonlinear absorption coefficients, as well as the change in refractive index in a semi-harmonic potential spherical GaAs excitonic quantum dot (QD). The chapter begins by discussing the Hamiltonian, applied potential & density matrix formalism employed to obtain the linear and nonlinear optical properties of the quantum dots. This formalism allows for a detailed analysis of the effects of various parameters on the optical behavior of the QD. The study analyzes the linear and nonlinear absorption coefficients, as well as the refractive index change, under the influence of external hydrostatic pressure and temperature. Additionally, the influence of the excitons is also investigated, and a comparison is made between the cases of with and without excitonic effects as well as a detailed comparison is carried out between theoretical observed results and experimental data. The results are expressed as functions of the incident photon energy for dissimilar parameter values. The findings reveal that the application of hydrostatic pressure leads to a red shift in the absorption peaks, both for linear and third-order processes. On the other hand, temperature causes a shift of these peaks towards the blue end of the spectrum. Similar effects are observed in the dispersion regions of the refractive index change. Also, it can be noticed from the results that the results obtained using taking excitons in consideration are found to be more prominent than the case of where excitons are not taken into account. xvi In summary, Chapter 4 provides a detailed analysis of the linear and nonlinear absorption coefficients, as well as the refractive index change, in a GaAs excitonic quantum dot under the influence of hydrostatic pressure and temperature. The results highlight the effects of these external parameters on the optical properties of the quantum dot and provide valuable insights into the behavior of inter subband transitions. Chapter 5 delves into the investigation of the effect of transverse electric field, hydrostatic pressure & temperature on a quantum dot with finite square well potential. We focus on determining the nonlinear optical rectification as well as nonlinear refractive index changes for a finite well. Our findings reveal that the transverse electric field as well as temperature blue shifts the peaks of the optical rectification coefficient as well as nonlinear refractive index changes, while hydrostatic pressure shift these peaks towards the red end of the spectrum. These findings suggest the potential to control the electronic and optical properties. In conclusion, this study is expected to stimulate both experimental and theoretical investigations, contributing significantly to the understanding of nonlinear optical properties in nanostructures particularly for quantum dots and quantum well with external perturbations such as electric field, magnetic field, hydrostatic pressure & temperature and Rashba spin-orbit interaction. By investigating the influence of external perturbations such as electric field, magnetic field, hydrostatic pressure & temperature and Rashba Spin Orbit interactions, the thesis explores the possibility of tuning the effective band gap and other material properties in the studied system. This xvii tunability is particularly relevant for optical applications in devices utilizing narrow bandgap semiconductors. The attained results are anticipated to be highly advantageous for gaining an advancement in optical applications in narrow-bandgap semiconductor devices. Furthermore, the outcomes of this research are anticipated to inspire further experimental studies in this field in the near future. Finally, we provide a summary and concise conclusion of the work presented in the preceding chapters of the thesis, along with an outline of future aspects to be explored in this research. The references are provided in numbers within square brackets, appearing in the order in which they appear in the text, and a bibliography is presented at the end of each chapter. The equation numbers are indicated within small brackets.