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Modulating energy absorption in quantum dot

The fundamental feature of electronic materials that is used in optoelectronics, bioscience, or solar energy materials is the confinement of electrons or holes. Confinement of electrons or holes originates from the geometric features of the object that imposes mathematical constraints on the expansion of electronic wave functions. Unlike traditional efforts, which focus on using strain and structural  heterogeneity as a design variable to tune the electronic energy levels or confinement characteristics, we propose using atomic heterogeneity to modulate the energy levels of nanostructures as an additional variable in the design space. Remarkably, we find, employing a multi-scale framework (connecting DFT, k.p and the Finite Element Method), that disorder and strain indeed induce enhanced electron localization and makes much larger size Si/Si1-xGex QDs (that are usually disregarded because of their size) function as smaller QDs! 

Fig. Strain and composition field induced localization of electrons

                  Fig. Confinement of p-electron at the apex of a SiGe Quantum dot grown on top of a Si substrate, incurred due to the inhomogeneity in strain- and composition-fields

Where, the Schrodinger equation and the components of the Hamiltonian, describing the electronic states in an axisymmetric structure, are derived to follow the following relations [2]:

Further reading  [1] Enhanced quantum confinement due to nonuniform composition in alloy quantum dots (pdf, doi)
                      M. Z. Hossain, N. V. Medhekar, V. B. Shenoy, and H. T. Johnson, Nanotechnology 21, 095401 (2010)

                [2] Mathematical derivation of the Schrodinger equation for axisymmetric quantum dots
M. Z. Hossain, Research notes (multiscale-QD), imacMZH