Computational modeling of quantum confinement in alloy quantum dot-substrate heterostructures

Hossain, M. ZubaerThe efficiency of the first and second generations of solar cell has hardly seen dramatically increase over the years, in which most PV cells cannot use about 55% of the energy of sunlight because a single material cannot capture the entire spectrum of sunlight. To achieve the objective of higher efficiency and low production cost, the third generations solar cells are still under investigation. Although one of the best known multi-junction solar cells could overcome Shockley-Queisser limit with a stacking number of solar cells, the market of which is obstructed by the high cost as well as non-abundant material. For the fact that each bandgap of a single solar cell is fixed, it is advancing a technology called quantum dot solar cell that could manipulate quantized energy levels to absorb sunlight by varying quantum dot's parameters. Unlike the existing researches on size or shape of quantum dots (QDs), it is of great significance to understand the electronic coupling between QDs and the substrate on which they are grown. By using the finite element method, Time-Independent Schrödinger Equation (TISE) is solved for studying three-dimensional electron confinements, including normalized wave functions and the corresponding values of energy levels. ☐ The model has been verified with known analytical solutions for simple quantum mechanical problems. The weak formulation of TISE is derived and solved for the QD-substrate system, upon conducting convergence study on mesh-size and type of shape functions for particle in a box and hydrogen atom problems. Moreover, an "efficient meshing scheme" is developed and verified in the Cartesian frame to overcome the limitations of time-consuming adaptive meshing techniques. In this scheme, site-dependent meshing is applied based on the localization of the wave functions in the domain. ☐ Applying this scheme, the electron confinement within InAs self-assembled QD on a substrate with different linear and nonlinear functions for the confining potential has been examined. It is found that the degree of nonlinearity has a strong influence on electron confinement energies in the QD, but the localization of wave-functions remains mostly unaffected. Furthermore, for InGaAs alloy QD-substrate heterostructures, it is revealed that composition maps affect both confinement energies and electron localization within heterogeneous alloy QDs, and this observation is consistent with experimental findings. Additionally, the effect of location of the alloy QD relative to the confining potential profiles is investigated. It is found that the heterogeneity of alloy QDs brought other degrees of freedom, and the substrate has a significant effect on the overall electron confinement. ☐ To summarize, This thesis research develops a computational framework to investigate the effect of size, shape, composition, material type on quantum confinement in alloy QD-substrate heterostructures. The insights obtained from this research are expected to find important applications in thin-film photovoltaics, nanoelectronics, and spintronics.University of Delaware, Department of Mechanical EngineeringM.S.M.E