Transmission and Bound States in 2-D Quantum Superlattices
Abstract
In this project I solve the quantum-mechanical transmission problem for an electron in a "quantum wire," a two-dimensional system whose transverse dimension is of the order of the electron de Broglie wavelength. I find exact solutions of two- dimensional bound state and transmission and reflection problems for various quantum structure geometries. The bound state for a 90 degree corner structure using multiple modes is found using a mode matching technique. Also, transmission and reflection properties of a single 90 degree corner for varying modes on a spectrum of energies are found. We also solved these problems for the "quantum dot," a rectangular cell separated by narrow entrance and exit channels. A multiple mode solution to the bound state for a single dot is found. A transfer matrix method is used to solve for the transmission and reflection properties for an electron traveling through any number of quantum dots in sequence, for varying incoming modes and various ranges of energies. We studied the origin of the band structure which arises when periodic series of quantum dots are assembled.
- Publication:
-
APS Division of Nuclear Physics Meeting Abstracts
- Pub Date:
- October 2000
- Bibcode:
- 2000APS..DNP.AS058P