Abstract:We report on a three-month undergraduate research project to compute energy levels and their corresponding wavefunctions of an electron confined in a tetrahedral-shaped quantum dot heterostructure. A typical example of such a quantum system is an InAs tetrahedral-shaped quantum dot embedded in a cuboid GaAs matrix. For the simulation we used the Schrödinger equation in three-dimensional Cartesian space. After discretizing the Schrödinger equation by using the finite volume method, the resulting large-scale eig… Show more
The dispersion in the dot size, shape, and composition leads to a difficult comparison with experimental spectroscopy and transport data even if the growth conditions are similar. In this work, an extensive analysis of the influence of the dot size and shape on the electron and hole energy states and on transition energies is carried out using a unified model of the semiconductor band structure. In this study we obtain the electron energy spectra for three-dimensional small InAs∕GaAs quantum dots of several different truncated shapes described in the literature: tetrahedral, pyramidal with base of different geometry, etc. Also, in order to give an idea of the flexibility of the method, the icosahedral geometry is analyzed. The combination of theoretical results using a unified model for all the geometries with structural techniques will allow a more precise analysis of experimental samples.
The dispersion in the dot size, shape, and composition leads to a difficult comparison with experimental spectroscopy and transport data even if the growth conditions are similar. In this work, an extensive analysis of the influence of the dot size and shape on the electron and hole energy states and on transition energies is carried out using a unified model of the semiconductor band structure. In this study we obtain the electron energy spectra for three-dimensional small InAs∕GaAs quantum dots of several different truncated shapes described in the literature: tetrahedral, pyramidal with base of different geometry, etc. Also, in order to give an idea of the flexibility of the method, the icosahedral geometry is analyzed. The combination of theoretical results using a unified model for all the geometries with structural techniques will allow a more precise analysis of experimental samples.
In more elaborate schemes, an electron’s effective mass in a heterostructure semiconductor quantum dot (QD) depends on both its position and its energy. However, the electron’s effective mass can be simply modeled by a parabolic band approximation — the electron’s effective mass inside the QD — which is assumed to be constant and differs from the one outside the QD, which is also assumed to be constant. The governing equation to be solved for the electron’s energy levels inside the QD is the nonlinear Schrödinger equation. With the approximation, the nonlinear Schrödinger equation for a tetrahedral-shaped QD is discretized by using the finite-volume method. The discretized nonlinear Schrödinger equation is solved for the electron energy levels by a computer program. It is noted that the resulting energy levels for the parabolic mass model are nondegenerate due to the mass-gradient term at the corners, edges, and surfaces of the tetrahedral-shaped QD.PACS Nos.: 02.60.Cb, 03.65.Ge, 81.07.Ta
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.