A Tight Binding Study of Strain-Reduced Confinement Potentials in Identical and Non-Identical InAs/GaAs Vertically Stacked Quantum Dots

Abstract

Strain and electronic structure of InAs/GaAs quantum dot molecules made up of identical and non-identical vertically stacked quantum dots are compared using the sp 3 d 5 s* nearest neighbor empirical tight binding model. Hydrostatic and biaxial strain profiles strongly impact the local band edges and electronic structure for both identical and non-identical dots. Strain in the lower dot is significantly different as compared to the upper dot in the non-identical system in contrast to the identical system where it is almost the same in both dots. Therefore structural detailed differences are of critical importance and cannot be neglected. Qualitatively, the electronic structure is similar in identical and non-identical dot systems for small separations (below 6nm) and it is significantly different for large separations. The molecular orbitals convert to the dot-localized atomic orbitals at large dot separations in the non-identical system. Non-idealities such as strain and size variations induce an energy splitting in the considered dot ground states. Larger dissimilarity of dots increases e1-e2 and decreases the optical gap of system. This favors the possible use of such system in the construction of the long wavelength optical laser. I -INTRODUCTION AND METHODFor quite some time, InAs/GaAs quantum dot (QD) and coupled quantum dot systems have attracted attention for various optical [1] and quantum computing applications [2]. Due to the strain, originating from the assembly of latticemismatched semiconductors the quantum dot arrays tend to stack in the vertical direction [3,4] with upper dots slightly larger in size [4]. Such systems are inhomogeneous in material composition and strain. The simulation domain needs to contain 5-50 million atoms in total, where crystal symmetry and atomistic details of interfaces are extremely important [5,6]. Most of the work previously done [5,7] to analyze such closely coupled systems used continuum models such as effective mass and k•p which ignore such crystal symmetry and atomistic resolution. Only recently, an atomistic approach and pseudo-potential method for identical [8,9,11] and nonidentical dots have been used [10,11].In this paper, a detailed description of strain and electronic structure of closely coupled identical and nonidentical quantum dot systems is presented using NEMO 3-D [12]. NEMO 3-D can atomistically simulate realistic systems as large as containing up to 52 million atoms [13,14]. The electronic structure is calculated using a twenty band sp 3 d 5 s* nearest neighbor empirical tight binding model [15] and the strain with an atomistic valence force field (VFF) method [16].In the past, the NEMO 3-D basis set and approach have been validated through experimentally verified: 1) high bias, high current, quantitative resonant tunneling diode modeling [17], 2) photoluminescence in InAs nanoparticles [18], 3) modeling of the Stark effect of single P impurities in Si [19], 4) the valley splitting in miscut Si quantum wells on SiGe substrate [20], and 5) the strain ...

Experimental and theoretical study of polarization-dependent optical transitions in InAs quantum dots at telecommunication-wavelengths (1300-1500 nm)

“…31 Strain due to the upper QD tends to increase the energy of the seed QD energy levels, and thus the lowest electron and highest hole energy levels are confined in the upper QD. 32 Due to a large separation between the QD layers (10 nm), the electron and hole wave functions do not form hybridized molecular states. Such hybridized states can be observed for closely stacked QDs, separated by $6 nm or less, 26,32 and they also can be observed by applying an external electric field.…”

“…32 Due to a large separation between the QD layers (10 nm), the electron and hole wave functions do not form hybridized molecular states. Such hybridized states can be observed for closely stacked QDs, separated by $6 nm or less, 26,32 and they also can be observed by applying an external electric field. 26,33 In both of our bilayers, the first three electron and hole energy levels are confined to the upper QD.…”

Quantitative excited state spectroscopy of a single InGaAs quantum dot molecule through multi-million-atom electronic structure calculations

“…A comprehensive spectroscopy of the energy levels for the electrical fields spanning zero to 21kV/cm range is presented in figure 3. [22,36,38]. The reference for the electrical field shift "lever arm" is set to the top most valence band energy level H 1 to keep it fixed at its zero electrical field value.…”

In-plane polarization anisotropy of ground state optical intensity in InAs/GaAs quantum dots

“…This is because the stronger strain interaction of the larger QDs will push the energy levels of the smaller QDs to higher values. 27,28 As a result, QDs in the upper layers will be optically active; the lower layers of the QDs will not contribute a)…”