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Quantum Ballistic Transport in Semiconductor Heterostructures

By Michael McLennan

Purdue University

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The development of epitaxial growth techniques has sparked a growing interest in an entirely quantum mechanical description of carrier transport. Fabrication methods, such as molecular beam epitaxy (MBE), allow for growth of ultra-thin layers of differing material compositions. Structures can be designed to exploit the wave nature of carriers, broadening the possibilities of device design. This thesis represents the first step in the development of a quantum mechanical transport theory. Wave phenomena exhibited by electrons are discussed, and applications in proposed devices are presented. A theory of quantum ballistic transport is developed, emphasizing concerns for a numerical implementation of the analysis. Finally, example calculations are presented, illustrating quantitatively the physics of quantum transport.

This work restricts its focus to electrons in the conduction band of a direct-gap material. It assumes ballistic transport near equilibrium and treats electrons with an effective mass. It is found that the electrostatic potential has a huge effect on the results of these calculations, so computing a proper, self-consistent electrostatic potential is an essential step in obtaining correct results for any device. Obtaining convergence in the self-consistent potential is difficult, but this thesis establishes a method that works quite well.

Gerhard Klimeck later showed that bandstructure effects are also an important component of any analysis. Supriyo Datta generalized this work into his theory of Non-Equilibrium Green's Functions (NEGF).

Tags, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.