Spurious Solutions in the Multiband Effective Mass Theory Applied to Low Dimensional Nanostructures

In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem.We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi-cients to small k components would lead to the appearance of non-physical solutions.We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution.This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures.Finally,based on the above requirement of small k,we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.

Computational Methods for Electromechanical Fields in Self-Assembled Quantum Dots

A detailed comparison of continuum and valence force field strain calculations in quantum-dot structures is presented with particular emphasis to boundary conditions,their implementation in the finite-elementmethod,and associated implications for electronic states.The first part of this work provides the equation framework for the elastic continuum model including piezoelectric effects in crystal structures as well as detailing the Keating model equations used in the atomistic valence force field calculations.Given the variety of possible structure shapes,a choice of pyramidal,spherical and cubic-dot shapes is made having in mind their pronounced shape differences and practical relevance.In this part boundary conditions are also considered;in particular the relevance of imposing different types of boundary conditions is highlighted and discussed.In the final part,quantum dots with inhomogeneous indium concentration profiles are studied in order to highlight the importance of taking into account the exact In concentration profile for real quantum dots.The influence of strain,electric-field distributions,and material inhomogeneity of spherical quantum dots on electronic wavefunctions is briefly discussed.

Dynamic Modeling of Phase Crossings in Two-Phase Flow

Two-phase flow and heat transfer,such as boiling and condensing flows,are complicated physical phenomena that generally prohibit an exact solution and even pose severe challenges for numerical approaches.If numerical solution time is also an issue the challenge increases even further.We present here a numerical implementation and novel study of a fully distributed dynamic one-dimensional model of twophase flow in a tube,including pressure drop,heat transfer,and variations in tube cross-section.The model is based on a homogeneous formulation of the governing equations,discretized by a high resolution finite difference scheme due to Kurganov and Tadmore.The homogeneous formulation requires a set of thermodynamic relations to cover the entire range from liquid to gas state.This leads a number of numerical challenges since these relations introduce discontinuities in the derivative of the variables and are usually very slow to evaluate.To overcome these challenges,we use an interpolation scheme with local refinement.The simulations show that the method handles crossing of the saturation lines for both liquid to two-phase and two-phase to gas regions.Furthermore,a novel result obtained in this work,the method is stable towards dynamic transitions of the inlet/outlet boundaries across the saturation lines.Results for these cases are presented along with a numerical demonstration of conservation of mass under dynamically varying boundary conditions.Finally we present results for the stability of the code in a case of a tube with a narrow section.