Electromechanical field effects in InAs/GaAs quantum dots based on continuum (k)over-right-arrow . (p)over-right-arrow and atomistic tight-binding methods

A comparison between (k) over right arrow . (p) over right arrow and tight-binding methods for the analysis of InAs/GaAs quantum dot bandstructures is presented based on a fully coupled computation of electromechanical effects. Electromechanical effects are addressed using a continuum elastic model for the (k) over right arrow . (p) over right arrow method and a pre-conditioned Valence Force Field algorithm for the tight-binding atomistic calculations. The Valence Force Field method allows the direct identification of the impact of internal strain. Results to ensure model parameter consistency between the two methods are also given by comparing bulk and unstrained quantum-well dispersion relations. The quantum dot size dependence of the bandstructure is investigated based on the models including electromechanical fields. Additionally, the effect of the electromechanical fields is studied for a specific dot size by comparing results with and without electromechanical fields. Good agreement is found for the confined energy levels but model differences show up in the symmetry of probability densities mainly due to the underlying crystal structure details taken into account by the tight-binding method but lacking in the (k) over right arrow . (p) over right arrow formalism. The latter follows from not including bulk inversion-asymmetry effects in the (k) over right arrow . (p) over right arrow method. Inclusion of piezoelectric field effects in the (k) over right arrow . (p) over right arrow method, however, restores the correct symmetry in the (k) over right arrow . (p) over right arrow model (in agreement with the tight-binding symmetry). Results are also given for oscillator strengths where both quantitative and qualitative differences are found in the comparison of (k) over right arrow . (p) over right arrow and tight-binding models.

Automated summary

This study compares the (k) over right arrow . (p) over right arrow and tight-binding methods for the analysis of InAs/GaAs quantum dot bandstructures based on a fully coupled computation of electromechanical effects. While the Valence Force Field algorithm in the tight-binding method allows direct identification of internal strain impacts, the lack of consideration for crystal structure details in the (k) over right arrow . (p) over right arrow formalism leads to differences in the symmetry of probability densities. Including piezoelectric field effects in the (k) over right arrow . (p) over right arrow method restores correct symmetry in the model, in agreement with the tight-binding method.