O. Voskoboynikov

Computer simulation of electron energy levels for different shape InAs/GaAs semiconductor quantum dots

Abstract A computational technique for the energy levels calculation of an electron confined by a 3D InAs quantum dot (QD) embedded in GaAs semiconductor matrix is presented. Based on the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, a finite height hard-wall 3D confinement potential, and the Ben Daniel–Duke boundary conditions, the problem is formulated and solved for the disk, ellipsoid, and conical-shaped InAs/GaAs QDs. To calculate the ground state and first excited state energy levels, the nonlinear 3D Schrodinger is solved with a developed nonlinear iterative algorithm to obtain the final self-consistent solutions. In the iteration loops, the Schrodinger equation is discretized with a nonuniform mesh finite difference method, and the corresponding matrix eigenvalue problem is solved with the balanced and shifted QR method. The proposed computational method has a monotonically convergent property for all simulation cases. The computed results show that for different quantum dot shapes, the parabolic band approximation is applicable only for relatively large dot volume. For the first excited states the non-parabolicity effect also has been found to be stronger than it at ground state. The QD model and numerical method presented here provide a novel way to calculate the energy levels of QD and it is also useful to clarify principal dependencies of QD energy states on material band parameter and QDs size for various QD shapes.

Magnetic properties of parabolic quantum dots in the presence of the spin–orbit interaction

We present a theoretical study of the effect of the spin–orbit interaction on the electron magnetization and magnetic susceptibility of small semiconductor quantum dots. Those characteristics demonstrate quite interesting behavior at low temperature. The abrupt changes of the magnetization and susceptibility at low magnetic fields are attributed to the alternative crossing between the spin–split electron levels in the energy spectrum, essentially due to the spin–orbit interaction (an analog of the general Paschen–Back effect). Detailed calculation using parameters of InAs semiconductor quantum dot demonstrates an enhancement of paramagnetism of the dots. There is an additional possibility to control the effect by external electric fields or the dot design.

Electron energy level calculations for cylindrical narrow gap semiconductor quantum dot

Three computational techniques are presented for approximation of the ground state energy and wave function of an electron confined by a disk-shaped InAs quantum dot (QD) embedded in GaAs matrix. The problem is treated with the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, and the Ben-Daniel Duke boundary conditions. To solve the three dimensional (3D) Schrodinger equation, we employ (i) the adiabatic approximation, (ii) the adiabatic approximation with averaging, and (iii) full numerical solution. It is shown that the more efficient approximations (i) and (ii) can only be used for relatively large QD sizes. The full numerical method gives qualitative as well as quantitative trends in electronic properties with various parameters.

Energy and coordinate dependent effective mass and confined electron states in quantum dots

Abstract We present a theoretical study of the electron energy states in narrow gap semiconductor quantum dots (QDs). For a finite height hard-wall 3D confinement potential the problem was solved by using of the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, and the Ben Daniel–Duke boundary condition. To solve the 3D Schrodinger equation, we employ a numerical scheme by using the finite difference method and the QR algorithm. Our results show that the parabolic band approximation is applicable only for relatively thin cylindrical QDs or for the dots with large radius. We show that the electron wave function localization plays an important role in the dependency of the energy and the electron effective mass. For the excited states, the non-parabolicity effect has been found to be stronger than it at ground state.

Dependence of energy gap on magnetic field in semiconductor nano-scale quantum rings

Abstract We study the electron and hole energy states for a complete three-dimensional (3D) model of semiconductor nano-scale quantum rings in an external magnetic field. In this study, the model formulation includes: (i) the position dependent effective mass Hamiltonian in non-parabolic approximation for electrons, (ii) the position dependent effective mass Hamiltonian in parabolic approximation for holes, (iii) the finite hard wall confinement potential, and (iv) the Ben Daniel–Duke boundary conditions. To solve this 3D non-linear problem, we apply the non-linear iterative method to obtain self-consistent solutions. We find a non-periodical oscillation of the energy band gap between the lowest electron and hole states as a function of external magnetic fields. The result is useful in describing magneto-optical properties of the nano-scale quantum rings.

Calculation of induced electron states in three-dimensional semiconductor artificial molecules

The energy levels calculation of electrons confined in small three-dimensional (3D) coupled quantum In x Ga 1-x As dots embedded in GaAs semiconductor matrix is presented. The quantum dots have disk shapes and are separated (in the disk symmetry axis direction) by a certain distance. Based on the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, a finite height hard-wall 3D confinement potential, and the Ben Daniel-Duke boundary conditions, the problem is formulated and solved for the disk-shaped coupled quantum dots. To calculate the ground and induced state energy levels, the nonlinear 3D Schrodinger equation (SE) is solved with a developed nonlinear iterative method to obtain the final self-consistent solutions. In the iteration loops, the Schrodinger equation is discretized with a nonuniform mesh finite difference method, and the matrix eigenvalue problem is solved with the balanced and shifted QR method. Our complete 3D approach demonstrates a principal possibility that the number of bound electronic states in the system can be changed when the interdot (vertical) distance is modified. However, it is impossible to produce an additional possibility to manipulate the system electronic properties within only a two-dimensional (2D) simulation.

Spin-dependent delay time in electronic resonant tunneling at zero magnetic field

Abstract The dependence of the phase tunneling time on electronic spin polarization in symmetric and asymmetric double-barrier semiconductor heterostructures is studied theoretically. The effective one-band Hamiltonian approximation and spin-dependent boundary conditions are used for theoretical investigation of the electron spin influence on the delay time in tunneling processes. It is shown that the spin–orbit splitting in the dispersion relation for the electrons can provide a dependence of the delay time on the electron spin polarization without additional magnetic field. This dependence can be controlled by an external electric field and can be very pronounced for realistic double-barrier semiconductor heterostructures.

Time-resolved spin filtering in semiconductor symmetric resonant barrier structures

Spin-dependent tunneling in semiconductor symmetric double barrier structures is studied theoretically. Our calculation is based on the effective one-band Hamiltonian and Dresselhaus spin-orbit coupling. We demonstrate that the ratio of the tunneling times of electrons with opposite spin orientations can vary over a few orders in magnitude. The large and tunable ratio of the tunneling times can serve as the basis in the development of all-semiconductor dynamic spin filters.

Effect of Shape and Size on Electron Transition Energies of InAs Semiconductor Quantum Dots

We present a theoretical study of the electron energy states in three-dimensional narrow gap semiconductor quantum dots with different shapes under an external magnetic field. The problem is solved by using the effective one-electronic-band Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the Ben Daniel-Duke boundary condition. We investigate small InAs/GaAs quantum dots with disk, lenticular, and conical shapes. Electron energy dependence on volume is expressed as V-γ where the exponent γ depends on the dot shapes and can vary over a wide range. The most stable against the dot size deviations (among dots of the same base radius) is the energy spectra of the conical dots. In addition, this type of dot also has the weakest diamagnetic shift. Contrarily, quantum dots with cylindrical shapes show a wide deviation in energy and a relatively strong diamagnetic shift.

Spin-orbit interaction and energy states in semiconductor quantum dots

Abstract We present a theoretical study of the impact of the spin–orbit interaction on electron energy states in small cylindrical quantum dots. In our calculations, we use the effective one electronic band Hamiltonian and the spin dependent boundary conditions. It has been found that the spin–orbit interaction can modify the energy spectrum of narrow gap semiconductor quantum dots. The modification consists of the energy state spin splitting that strongly depends on the dot size. The spin splitting demonstrates a non-monotonic dependence on the dot size and can provide a situation when only the lower spin split states with angular quantum number | l |=1 are bound in the dot.