Electron Transition Energy for Vertically Coupled InAs/GaAs Semiconductor Quantum Dots and Rings

Abstract

We investigate the transition energy of vertically coupled quantum dots and rings (VCQDs and VCQRs) with a three-dimensional (3D) model under an applied magnetic field. The model formulation includes (1) the position-dependent effective mass Hamiltonian in the nonparabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in the parabolic approximation for holes, (3) the finite hard-wall confinement potential, and (4) the Ben Daniel-Duke boundary conditions. We explore small VCQDs and VCQRs with disk (DI) and conical (CO) shapes. For small VCQDs and VCQRs, the electron-hole transition energy is dominated by the interdistance d which plays a crucial role in the tunable states of structures. Under zero magnetic field, there is about 25% variation in the electron ground state energy for both InAs/GaAs DI-shaped VCQDs and VCQRs with d varying from 0.4 nm to 4.8 nm. The energy spectra of the CO-shaped VCQDs are the most stable against the structure interdistance deviations (among dots and rings of the same volume). For a fixed d, VCQDs show diamagnetic shift; contrarily, VCQRs imply a nonperiodical transition among the lowest electron energy states. The energy band gap of VCQRs oscillates nonperiodically between the lowest electron and holes states as a function of external magnetic fields. Our investigation is constructive for studying the magneto-optical phenomena of the nanoscale semiconductor artificial molecules.

Magnetization and Magnetic Susceptibility in Nanoscale Vertically Coupled Semiconductor Quantum Rings

“…1, under the applied magnetic fields, we consider the disk-shaped VCQRs with the hard-wall confinement potential. The effective Hamiltonian for electrons is given by [6,15,16] …”

“…∇ r is the spatial gradient, A(r) is the vector potential, and B = curlA is the magnetic field. m(E, r) and g(E, r) are the energy-and position-dependent electron effective mass [6,15,16].…”

“…Nowadays, advanced fabrication technology has allowed us to fabricate the coupled nanostructures, "artificial molecules"; in particular, the vertically coupled quantum dots (VCQDs) and rings [7][8][9][10][11][12][13][14][15][16][17]. They possess structure-to-structure interaction, electronic entanglement, and charge transferability [9][10][11].…”

“…The magnetization and the magnetic susceptibility of nanoscale InAs/GaAs VCQRs under applied magnetic fields is for the first time investigated using a 3D approach [15,16]. The model considers a 3D effective one-electronic-band Hamiltonian with the positionand energy-dependent effective mass, the finite hardwall confinement potential, and the Ben Daniel-Duke boundary condition.…”

“…The model considers a 3D effective one-electronic-band Hamiltonian with the positionand energy-dependent effective mass, the finite hardwall confinement potential, and the Ben Daniel-Duke boundary condition. For the structure of VCQRs with the disk-shaped quantum rings, the corresponding nonlinear Schrödinger equation is solved with the nonlinear iterative method [6,15,16]. For the structure with the fixed height and inner radius, effects of inter-distance (d), radius of ring (R), and the magnetic field (B) on the electronic structure of VCQRs are investigated.…”