Electrostatic simulations of interactions between a scanning probe and quantum Hall liquid

In this thesis we modelled interactions between metal probe and quantum Hall liquid. The setup geometries were similar to those met in scanning capacitance microscopy experiments carried out by Ashoori's group [1]. The main interest was to explore the 2DEG charge densities for a different system geometries, magnetic field applied, and tip voltages. We modelled quantum bubble formation under the metal probe, incompressible strip formation beneath the edge of the metal gate, and 2DEG density profile under the influence of donors in magnetic field. In order to model complex geometry systems, but also optimize running times and memory allocation we developed two electrostatic simulators one for cylindrically symmetric and second for arbitrary 3D geometries. Our electrostatic solver was based on successive over relaxation algorithm, but it was optimized for better stability and faster convergence times.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Spasojevic, Nemanja Ljuban

Advisor dc:contributor.advisor

• Raymond Ashoori and Gary Steele.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/35050

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/35050