Modeling ofInAs∕GaAsquantum ring capacitance spectroscopy in the nonparabolic approximation

Abstract

A three-dimensional model of InAs/ GaAs quantum rings based on a single sub-band approach with an energy dependence of the electron effective mass is used to describe the capacitance-voltage spectroscopy by Lorke et al. ͓Phys. Rev. Lett. 84, 2223 ͑2000͔͒. The confinement states energy problem is solved numerically using the finite elements method. Observed deviation of an electron effective mass from the bulk value is explained by the nonparabolic effect. Additional energy of the election ground state due to an external magnetic field is estimated and compared with the capacitance-voltage data. The model is also applied to describe the far-infrared measurements.

<I>C</I>–<I>V</I> Data and Geometry Parameters of Self-Assembled InAs/GaAs Quantum Rings

“…[2] the V s value of 0.31 eV was used in Ref. [7] for the conduction band. The BenDaniel-Duke boundary conditions are used on the interface of the material of QR and substrate.…”

Quantum Dots and Quantum Rings: Real Low Dimensional Systems

“…The strength parameter of the effective potential, in the case of the Geometry 2, was chosen to be 0.382 eV, which is close to that for QD from, 36 where V s =0.31 eV. The difference is explained by the topology dependence of the effective potentials (see section above and also 20 ).…”

“…In the figure, the confinement potential of the simulation model with effective potential V s is denoted as "strained". 20 The band gap potential for the conduction band (valence band) can be determin as V c =0.594 eV (V c =0.506 eV). The magnitude of the effective potential can be chosen to reproduce experimental data.…”

Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

“…The convergence of eigenenergies E t vs number j max of basis functions for oblate and prolate spheroidal QDs, and for spherical QD is shown on Tables I and II Tables I and II show that the expansions in basis functions (12) and (13) in cylindrical coordinates have better rate of convergence in the adiabatic Fast and slow variables x f = z and x s = ρ (oblate SQD and spherical QD), number of nodes i = (n zo = n o − 1, n ρo ), * notes diagonal approximation at j = 2 j max a = 2.5, c = 0.5 a = 2.5, c = 2.5…”

“…Electronic, kinetic, optical and other properties of QDs have been investigated experimentally and theoretically in many papers [4][5][6][7][8][9][10][11][12][13]. Particularly, the optical absorption characteristics of QDs have been shown to be strongly correlated with their geometry, on one hand, and with their physical-chemical properties, on the other hand.…”