Toward weak confinement regime in epitaxial nanostructures: Interdependence of spatial character of quantum confinement and wave function extension in large and elongated quantum dots

Abstract

In this paper we present a comprehensive and detailed analysis of carrier/exciton wave function extension in large low-strain In 0.3 Ga 0.7 As quantum dots (QDs). They exhibit rather shallow confinement potential with electron/hole localization energy below 30 meV and confinement strength substantially weakened in comparison to typical epitaxial quasi-zero-dimensional semiconductor nanostructures. The aim of this study is to investigate the influence of different factors on the wave function (probability density distribution) for carriers or excitons in this regime, i.e., object shape anisotropy as well as strain, piezoelectricity, and Coulomb interactions, and to identify the physical mechanisms determining the properties of optical emission. To probe the wave function symmetry, polarization-resolved photoluminescence has been performed, and the spatial extensions of the corresponding probability densities have been verified in magneto-optical measurements. The observed diamagnetic coefficients in the range of (15-31) μeV/T 2 reflect large in-plane QD size. These studies also enable us to investigate the importance of light hole states admixture to the valence band ground state in such nanostructures, which can be addressed via the degree of linear polarization of emission as well as the exciton g X factor. The linear-polarization-resolved measurements revealed an exceptionally low exciton fine structure splitting of 5 μeV on average as well as a low emission polarization degree of −0.05, with the polarization perpendicular to the QD elongation direction dominating. The increased light hole contribution to the lowest energy hole level is reflected in the decreased exciton g X factor (in the range of 0-1) and is consistent with the results of the eight-band k·p modelling. Based on the temperature dependence of the diamagnetic coefficient, the problem of individual QD uniformity has additionally been discussed. To evaluate the impact of the confinment potential and the structure geometry on the optical properties of the QDs, a comparison between the investigated dots and InAs/InGaAlAs/InP quantum dashes exhibiting a much deeper confining potential is presented.

Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities

“…Even though the achievable Purcell factor might be overestimated due to operation conditions very close to the strong coupling regime [38], there are also physical effects lowering the Purcell factor, in particular, spatial mismatch between the QD position in the cavity and the maximum of the electromagnetic field distribution of the fundamental mode and dipole orientation mismatch between the QD and the cavity mode reducing the coupling strength. It is well established that in the case of the investigated structure the QD polarization axes are mostly oriented along [1][2][3][4][5][6][7][8][9][10] and the [110] crystallographic direction [39], whereas the deformation of the nominally circular in cross-section micropillars leads to linear polarization of the cavity modes along the [100] and [010] directions [32] which means that the respective dipoles are oriented at a 45 • angle which can additionally lower the achievable Purcell factor by a factor of 2 [40].…”

Compensation of phonon-induced renormalization of vacuum Rabi splitting in large quantum dots: Towards temperature-stable strong coupling in the solid state with quantum dot-micropillars

“…As discussed above, the mode volume is not altered significantly with temperature, but the oscillator strength which is determined by the overlap of the electron and hole wave functions as well as the wave function extension [40] might in principle be temperature dependent. In fact, a previous study on larger QDs in the same material system In 0.3 Ga 0.7 As/GaAs proved that the wave function extension of the state from which the emission takes place can actually undergo changes [29] that can be attributed to a temperature-induced carrier redistribution within the closely spaced electronic sublevels related to possible confining potential fluctuations within large QDs. Similar effects have been observed in the case of quantum dashes [41] featuring an even larger nanostructure volume in the range of 4.5 × 20−30 × 100−150 nm 3 .…”

“…Similar effects have been observed in the case of quantum dashes [41] featuring an even larger nanostructure volume in the range of 4.5 × 20−30 × 100−150 nm 3 . The strength of this effect can be estimated based on available magneto-optical experimental data [29]. As the QDs in the above reference are larger than the ones investigated in this work, this estimation will constitute an upper limit of the expected changes.…”

“…Therefore, the question arises how strongly the In concentration varies within the ensemble of QDs under study. For the structures used here the emission energy can be used as an indicator for the In concentration, because it has been shown that a variation of the In content leads to a significant change of the QD transition energy [29], which can even overcome the influence of the variation in QD height. Most importantly, this means that the OS and light-matter coupling strength is expected to be similar for all studied QDs.…”

“…To differentiate the QDs investigated here from typical strongly confined QDs we refer to them as "large" QDs. The typical dimensions of these nanostructures are: (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) nm in width, (20-50) nm in length, and (5-7) nm in the vertical direction (including wetting layer). The increase in the lateral size in the strain-based Stranski-Krastanow growth mode was possible due to lowering the strain via decreasing the amount of indium in the InGaAs alloy compound [26].…”