Magnetic and Magneto-Optical Properties of Dispersive Ensembles of Semiconductor Nano-Objects
Current demand for multiband and multifunctional nano-based semiconductor devices stimulates the development of novel nano-scale semiconductor components (nano-objects). Impressive progress in semiconductor technologies makes it possible to fabricate semiconductor nano-objects with very sophisticated shapes and material compositions: quantum dots, quantum dot molecules, quantum dot posts, and quantum rings, etc. The semiconductor nano-objects demonstrate unique properties those are very promising for modern optics, optoelectronics, quantum information processing, bio and medical imaging, etc. Unfortunately, the inherent dispersion of parameters (shape, size, material composition) leads to fluctuations (some time almost uncontrollable) of the physical properties of macro-systems combined from the nano-objects. To achieve a proper quantitative description and address the controllably of macro characteristics of ensembles of the semiconductor nano-objects in this study we have proposed and developed a general theoretical description of the physical response of dispersive ensembles made from the semiconductor nano-objects of complex geometries and material compositions. The description is based on the multivariate distribution function, which cumulatively reproduces variations of the objects’ parameters.In this report we present and discuss our method of multivariate simulation of physical properties of ensembles of semiconductor nano-objects with dispersion in geometry, material parameters, and spatial distributions. Using the mapping method (recently derived by us) we are able to very efficiently compute energy states and wave functions of electrons and holes confined in the nano-objects within a wide range of sizes, shapes, and compositions. Thus, using the hybrid multiscale (hierarchical) method we are able to simulate ensembles of nano-objects with multiparametric (multivariate) distributions. To demonstrate our method efficiency we simulated the absorption cross section of ensembles of ZnTe/CdSe core/shell quantum dots and the unusual diamagnetic response (magnetic susceptibility) of ensembles of wobbled InAs/GaAs quantum rings. We have theoretically obtained the actual optical spectra and magnetic susceptibility in a very good agreement with experimental data. We have proven that our multivariate statistical approach can be useful for optimization of the averaged physical characteristics of the dispersive ensembles of nano-objects.