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

Abstract

Atomistic electronic structure calculations are performed to study the coherent inter-dot couplings of the electronic states in a single InGaAs quantum dot molecule. The experimentally observed excitonic spectrum by H. Krenner et al. [12] is quantitatively reproduced, and the correct energy states are identified based on a previously validated atomistic tight binding model. The extended devices are represented explicitly in space with 15 million atom structures. An excited state spectroscopy technique is applied where the externally applied electric field is swept to probe the ladder of the electronic energy levels (electron or hole) of one quantum dot through anti-crossings with the energy levels of the other quantum dot in a two quantum dot molecule. This technique can be used to estimate the spatial electron-hole spacing inside the quantum dot molecule as well as to reverse engineer quantum dot geometry parameters such as the quantum dot separation. Crystal deformation induced piezoelectric effects have been discussed in the literature as minor perturbations lifting degeneracies of the electron excited (P and D) states, thus affecting polarization alignment of wave function lobes for III-V Heterostructures such as single InAs/GaAs quantum dots. In contrast this work demonstrates the crucial importance of piezoelectricity to resolve the symmetries and energies of the excited states through matching the experimentally measured spectrum in an InGaAs quantum dot molecule under the influence of an electric field. Both linear and quadratic piezoelectric effects are studied for the first time for a quantum dot molecule and demonstrated to be indeed important. The net piezoelectric contribution is found to be critical in determining the correct energy spectrum, which is in contrast to recent studies reporting vanishing net piezoelectric contributions.

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

“…1(c)-1(e). The close agreement between the calculations and the experimental results obtained, without adjusting any published parameter, highlights the transferability of the empirical VFF and tight binding parameters, similar to previous work on InAs/ GaAs quantum dots 13,26 and SiGe. 30 …”

“…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.…”

“…24 Strain is calculated using an atomistic valence force field (VFF) model, with the Keating potential modified to include anharmonic corrections. 25 Both linear and quadratic piezoelectric potentials 14,26 are included. The inter-band optical transition strengths are calculated using Fermi's golden rule as the squared magnitude of the momentum matrix elements summed over the spin degenerate states.…”

“…The inter-band optical transition strengths are calculated using Fermi's golden rule as the squared magnitude of the momentum matrix elements summed over the spin degenerate states. 26 We have used large strain domains in order to fully incorporate the long range impacts of strain and piezoelectric fields. For the bilayers, the strain buffer is 70 nm  70 nm  66 nm in size, containing approximately 20  10 6 atoms.…”

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

“…The atoms at the surface are passivated according to our published approach. 36 The inter-band optical transition strengths between the electron-hole energy states are computed using Fermi's golden rule by squared absolute value of the momentum matrix elements summed over spin degenerate states: 41,52 …”