Computer Modelling of Transport in Electron Waveguides With Application to Realistic Quantum Point Contacts

Laughton, Michael John (1992) Computer Modelling of Transport in Electron Waveguides With Application to Realistic Quantum Point Contacts. PhD thesis, University of Glasgow.

Abstract

This thesis describes a numerical study of the electron transport through a quantum point contact in the ballistic limit. In the initial part of this study a time-dependent model was developed. This provided a qualitative analysis of the transport and highlighted the complex scattering processes at the contact-channel interface and the modal nature of the transport in the channel region of the quantum point contact. To study the transport in more detail a coupled-mode time-independent analysis was developed and applied to various models of a quantum point contact with different approximations to the confining potential. This included an analysis of the transport through the disordered quantum point contact, which included the potential of the randomly distributed ionized donors in the calculation of the confining potential. This study shows that the random potential in a quantum point contact leads to rapid intermode scattering. The adiabatic approximation fails badly, but conductance can still be quantized through the less stringent conditions of 'compensated' scattering. This intermode scattering was found to reduce the sensitivity of the quantum point contact to the channel-contact coupling. The lack of adiabaticity in the transport can compensate for poor interface coupling of the channel modes through a process of forward intermode scattering. This non-adiabatic process can lead to the full occupancy of the lower conducting modes even when their initial coupling is poor. The forward intermode scattering length in the disordered quantum point contact was found to be approximately 100 nm, which was in good agreement with the analytical scattering length based on the Born Approximation. However, an efficient three-stage indirect back-scattering process has been identified which cannot be described within the usual Born Approximation. If this represents the dominant back-scattering process in quasi-one-dimensional systems, then the mobilities calculated using the Born Approximation will be overstated. If electron devices analogous to those of electromagnetic waveguides are to be produced, these scattering mechanisms must be eliminated. This represents a considerable engineering challenge.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Condensed matter physics, Quantum physics, Electromagnetics
• Date of Award: 1992
• Depositing User: Enlighten Team
• Unique ID: glathesis:1992-78408
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 28 Feb 2020 12:09
• Last Modified: 28 Feb 2020 12:09
• URI: https://theses.gla.ac.uk/id/eprint/78408