A Multi-Scale Approach to Wavefunction Engineering of Subdimensional Quantum Semiconductor Structures
With on going reduction in dimension of nano-devices it becomes imperative to include interface and structure boundaries accounting for complex, mixed boundary conditions. A Lagrangian approach to the physics provides the natural framework for such calculations, with computational work based on the finite element method. This variational approach has led to the design of mid-IR cascade lasers and the solution of the Schrödinger-Poisson self-consistency in arbitrary layered structures. Applications of this methodology lead to the solution for energy levels in a magnetic field in the Voigt geometry. The effect of surface proximity on binding energy for impurity states in nanowires and the beautiful physics of complex topological surfaces such as a Mobius ring are displayed as further examples of the issues addressable through multi-scale parallel computing within this variational framework.
KeywordsLagrangians Finite elements Wavefunction engineering Design of semiconductor heterostructures
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This report was written while on sabbatical leave at the Naval Research Laboratory, and I thank Dr. Fritz Kub for his hospitality. I wish to thank J. Albrecht, Z. Li, and K. H. Yoo for discussions. I also thank Quantum Semiconductor Algorithms, Inc., for the use of their finite element and sparse matrix analysis software.
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