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Nonlinear Interband Optical Response in Excitonic δ ‐Doped GaAs/AlGaAs Multiple Quantum Wells Under External Fields, Pressure, Temperature and Barrier Width Effects

Deepanshu Lal, Taruna Gulati, Monica Gambhir

Published Jun 1, 2026• 0 citations
Publisher

Abstract

This work presents a detailed theoretical study of the linear and third‐order nonlinear optical properties of excitonic δ ‐doped GaAs/AlGaAs multiple quantum wells under an external magnetic field. The electronic structure is modelled within the effective mass approximation, and the correlated excitonic states are obtained by diagonalising the full electron–hole Hamiltonian in a realistic multi‐well potential using a centred finite‐difference method. The Coulomb interaction is treated using a softened potential appropriate for quasi‐one‐dimensional confinement. The model incorporates band offsets, pressure‐ and temperature‐dependent material parameters and magnetic field–induced confinement effects. The linear and third‐order nonlinear optical absorption coefficients, along with the associated refractive index changes, are calculated using the density‐matrix formalism. Magnetic fields (1–5 T) induce blue shifts of 6–12 meV with reduced peak intensity. Increasing barrier width (2–6 nm) produces larger blue shifts (30–40 meV), while pressure and temperature cause characteristic blue and red shifts, respectively. These results demonstrate tuneable excitonic energies and nonlinear optical responses in engineered multiple quantum wells for tuneable photonic device applications. A rigorous theoretical analysis of excitonic linear and third‐order nonlinear optical responses in δ ‐doped GaAs/AlGaAs multiple quantum wells is presented. The electron–hole interaction is treated using a regularised Coulomb potential. The combined influence of magnetic field, hydrostatic pressure, temperature and barrier widths reveals rich and controllable optical behaviour, offering insights for advanced optoelectronic device design.

DOI
10.1002/pssb.70225

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This work presents a detailed theoretical study of the linear and third‐order nonlinear optical properties of excitonic δ ‐doped GaAs/AlGaAs multiple quantum wells under an external magnetic field. The electronic structure is modelled within the effective mass approximation, and the correlated excitonic states are obtained by diagonalising the full electron–hole Hamiltonian in a realistic multi‐well potential using a centred finite‐difference method. The Coulomb interaction is treated using a softened potential appropriate for quasi‐one‐dimensional confinement. The model incorporates band offsets, pressure‐ and temperature‐dependent material parameters and magnetic field–induced confinement effects. The linear and third‐order nonlinear optical absorption coefficients, along with the associated refractive index changes, are calculated using the density‐matrix formalism. Magnetic fields (1–5 T) induce blue shifts of 6–12 meV with reduced peak intensity. Increasing barrier width (2–6 nm) produces larger blue shifts (30–40 meV), while pressure and temperature cause characteristic blue and red shifts, respectively. These results demonstrate tuneable excitonic energies and nonlinear optical responses in engineered multiple quantum wells for tuneable photonic device applications. A rigorous theoretical analysis of excitonic linear and third‐order nonlinear optical responses in δ ‐doped GaAs/AlGaAs multiple quantum wells is presented. The electron–hole interaction is treated using a regularised Coulomb potential. The combined influence of magnetic field, hydrostatic pressure, temperature and barrier widths reveals rich and controllable optical behaviour, offering insights for advanced optoelectronic device design.
In this paper, we explore the optical properties of AlGaAs/GaAs semi-parabolic quantum well (QW) under different temperature, hydrostatic pressure and applied magnetic field. We calculate the nonlinear optical absorption coefficients and the refractive index changes (RICs) with the compact density-matrix approach and iterative method. Then, within the framework of the effective mass and parabolic-band approximations, the energy eigenvalues and the corresponding wave functions for semi-parabolic QW have been obtained by the finite difference method. The theoretical findings show that (1) the energy spectrum depends strongly on temperature, hydrostatic pressure and applied magnetic field; (2) the linear and third-order nonlinear optical absorption coefficients and the RICs are quite sensitive to temperature, hydrostatic pressure and applied magnetic field. Our study provides a theoretical basis for the fabrication of QW structure.
Abstract In this study, we thoroughly investigate the impacts of hydrostatic pressure, temperature, and position-dependent mass (PDM) on the nonlinear optical properties of asymmetric triple δ-doped GaAs quantum wells. Our analysis covers total optical absorption coefficients, relative refractive index changes, nonlinear optical rectification, second harmonic generation, and third harmonic generation. Initially, we employ PDM to solve the time-independent Schrödinger equation using the diagonalization method under effective mass and parabolic band approaches, considering pressure and temperature dependencies. Utilizing the first four energy eigenvalues and eigenfunctions, we apply the compact density matrix method to compute the system’s nonlinear optical properties numerically. The results indicate a shift in optical property peak positions toward lower (higher) energy spectra with increasing hydrostatic pressure (temperature). Furthermore, the influence of PDM shifts the system’s optical properties toward the higher energy spectrum, resembling the effect of temperature. From an experimental and theoretical perspective, one of the topics that researchers work on most is GaAs-based δ-doped systems (δ-doped heterojunction bipolar transistors, δ-doped field effect transistors, δ-multiple independent gate field effect transistors, etc.). We believe these findings will provide valuable insights for the researchers involved in GaAs-based δ-doped optoelectronic device design.
In the present paper, the linear and non-linear optical properties of GaAs/AlGaAs multiple quantum well with on-center and on-edge delta doping are studied within the effective mass approximation. The delta potential is analytically modeled within each quantum well potential to obtain the energy levels and the corresponding wave functions using the robust finite difference method. The linear and non-linear optical absorption coefficients and changes in the refractive index are studied in the presence of a static magnetic and a periodic laser field using the density matrix approach. The obtained results show that the position of resonances and the amplitude of the optical absorption coefficients and the refractive index changes can be modified by varying the magnetic field and strength and position of doping potential. Lastly, an increase of the optical intensity appreciably changes the total absorption coefficient, as well as the total refractive index changes. Obtained results are important for the design of various electronic components such as high-power FETs and infrared photonic devices based on the intersubband transition of electrons in δ-doped multiple quantum wells.
External fields modify the confinement potential and electronic structure in a multiple quantum well system, affecting the light–matter interaction. Here, we present a theoretical study of the modulation of the nonlinear optical response simultaneously employing an intense non-resonant laser field and an electric field. Considering four occupied subbands, we focus on a GaAs/AlGaAs symmetric multiple quantum well system with five wells and six barriers. By solving the Schrödinger equation through the finite element method under the effective mass approximation, we determine the electronic structure and the nonlinear optical response using the density matrix formalism. The laser field dresses the confinement potential while the electric field breaks the inversion symmetry. The combined effect of both fields modifies the intersubband transition energies and the overlap of the wave functions. The results obtained demonstrate an active tunability of the nonlinear optical response, opening up the possibility of designing optoelectronic devices with tunable optical properties.
In the present paper, the linear and non-linear optical properties of GaAs/AlGaAs with on-center and on-edge delta doping are studied within the effective mass approximation. The delta potential is analytically modeled within each quantum well potential to obtain the energy levels and the corresponding wave functions using the robust finite difference method. The linear and non-linear optical absorption coefficients and changes in the refractive index are studied in the presence of a static magnetic and a periodic laser field using the density matrix approach. The obtained results show that the position of resonances and the amplitude of the optical absorption coefficients and the refractive index changes can be modified by varying the magnetic field and strength and position of doping potential. Lastly, an increase of the optical intensity appreciably changes the total absorption coefficient, as well as the total refractive index changes. Obtained results are important for the design of various electronic components such as high-power FETs and infrared photonic devices based on the intersubband transition of electrons in δ-doped MQWs.
Abstract In our investigation, we analyzed the variations in both linear and nonlinear optical properties of the GaAs/GaAlAs single quantum well heterostructure with modified Lennard-Jones potential under the conditions where external fields and the adjustable physical parameters of the structure are changed. We get the solution of the Schrödinger equation for identifying the subband energy levels with their wave functions taking advantage of the diagonalization method, effective mass approach, and parabolic band model. As a result, we find that the changes in the applied external fields and structure parameters have effects on the total optical absorption coefficients and total relative refractive index changes. While the optical response becomes red-shifted with the increment of applied electric, magnetic and intense laser fields and the well width, it becomes blue-shifted with the increment of the well depth.