Hardwick, David Peter Andrew (2007) *Quantum and semiclassical calculations of electron transport through a stochastic system.* PhD thesis, University of Nottingham.

## Abstract

In this thesis, I present a semiclassical and quantum mechanical study of a biased superlattice with a tilted magnetic field applied. This system exhibits non-KAM chaotic behaviour which can be controlled by the ratio between the cyclotron and Bloch frequencies. I will use a semiclassical model to show that electron trajectories become unbounded when this ratio takes an integer value. These extended electron trajectories cause peaks in the electron drift-velocity, which lead to current enhancements calculated using a drift-diffusion model. Furthermore, I will explain this current enhancement with reference to the electric field and charge carrier density across the superlattice. These results will then be compared to experimentally measured current-voltage characteristics.

A second superlattice is also studied, which has a high probability of interminiband tunnelling. I will outline several theoretical models to account for interminiband tunnelling and will ultimately use an empirical method. The current-voltage results obtained via this method will then be compared to experimental data.

Finally, I will use a quantum mechanical model to determine the electron eigenstates for the first superlattice. These quantum mechanical eigenstates will be compared to the semiclassical results to determine the degree of correspondence between the two models. Furthermore, I will use the eigenstates to calculate the energy level structure of the system and investigate how this varies for different applied field strengths. Ultimately, I will suggest a combined band transport plus scattering model to explain experimental current-voltage data obtained for high magnetic fields.

Item Type: | Thesis (PhD) |
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Supervisors: | Fromhold, M. |
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Uncontrolled Keywords: | Quantum chaos, stochastic transport, superlattices |
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Faculties/Schools: | UK Campuses > Faculty of Science > School of Physics and Astronomy |
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ID Code: | 389 |
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Deposited By: | David Hardwick |
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Deposited On: | 23 Jan 2008 |
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Last Modified: | 06 Feb 2009 14:43 |
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