Mathematical Modelling of Quantum Transport in Nanoscale Structures

Abstract

Molecular electronics is a versatile test bed for investigating nanoscale thermoelectricity and for contributing to the design of new low-cost and eco-friendly organic thermoelectric materials. This thesis presents theoretical results which aid this design process, firstly through demonstrating the optimisation of thermopower in self assembled monolayers based on the pressure applied to the molecules, and secondly through a novel method of predicting thermoelectric properties based on experimental 𝐼−𝑉 curves. This thesis provides a brief introduction to the theoretical tools used, starting in chapter 2 with density functional theory and its implementation in the SIESTA code, which enables Hamiltonians and ground state wavefunctions for molecules and junction interfaces to be found. Subsequently in chapter 3 the theoretical basis for calculating electronic and heat transport is described, including Green’s function methods for obtaining the transmission coefficient of semi-infinite leads connected to a scattering region. The second tool is the quantum transport code GOLLUM. To introduce this approach, in chapter 3 I present solutions of Green’s functions for infinite and semi-infinite chains and the transmission coefficient equation which forms the theoretical basis of this code. Chapter 4 is the first results chapter in this thesis, which demonstrates a major potential advantage of creating thermoelectric devices using self-assembled monolayers (SAMs). Two anthracene based SAMs terminated with thioacetate are investigated: 9,10- di(4-(ethynyl)phenylthioacetate), and 1,5- di(4-(ethynyl)phenylthioacetate. I demonstrate that the thermoelectric properties of such molecular devices can be controlled by taking advantage of their mechanical flexibility, more specifically by tuning the optimum power via the applied pressure which alters the molecules’ tilt angle 𝜃. Through v systematic theoretical simulations, I show how varying 𝜃 increases the conductance 𝐺 while decreasing thermopower 𝑆, ultimately achieving the optimum power 𝑃=𝐺 S2 at 𝜃 ≈ 65. Excellent agreement has been obtained between my simulations and experimental measurements using conductive Atomic Force Microscopy (AFM) for both SAMs. The thermoelectric properties of SAMs fabricated from thiol terminated molecules were measured by my collaborators, with a modified AFM system, and the conformation of the SAMs was controlled by regulating the loading force between the organic thin film and the probe, which changes the tilt angle at the metal-molecule interface. The thermopower shift versus the tilt angle of the SAM was tracked and showed that changes in both the electrical conductivity and Seebeck coefficient combine to optimise the power factor 𝑃 at a specific tilt angle. This optimisation of thermoelectric performance via applied pressure is confirmed through the use of my theoretical calculations and is expected to be a general method for optimising the power factor of SAMs. In chapter 5, I address the question of whether the Seebeck coefficient of a single molecule or SAM can be predicted from a measurement of 𝐼−𝑉 curves. If so, then the experimentally more difficult task of creating a set-up to measure their thermoelectric properties could be avoided, thus saving a significant amount of cost and effort. My theoretical approach begins by making a fit to measured 𝐺−𝑉 curves using three fitting parameters, denoted 𝑎,𝑏 and 𝑐, hence I refer to this method as ‘ABC’ theory. Then predicts a maximum value for the magnitude of the corresponding Seebeck coefficient. This is a useful material parameter, because if the predicted upper bound is large, then the material would warrant further investigation using a full Seebeck measurement setup. On the other hand, if the upper bound is small, then the material would not be vi promising and this much more technica