Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Block copolymer self-assembly based device structures

This thesis investigated the block copolymer (BCP) thin film characteristics and pattern formation using a set of predetermined molecular weights of PS-b-PMMA and PS-b-PDMS. Post BCP pattern fabrication on the required base substrate a dry plasma etch process was utilised for successful pattern transfer of the BCP resist onto underlying substrate. The resultant sub-10 nm device features were used in front end of line (FEoL) fabrication of active device components in integrated circuits (IC). The potential use of BCP templates were further extended to metal and metal-oxide nanowire fabrication. These nanowires were further investigated in real-time applications as novel sensors and supercapacitors.

Development of block copolymer lithography for device structure fabrication

This thesis investigated well-ordered block copolymer (BCP) thin film characteristics and their use for nanoscale pattern formation using a series of polystyrene-block-polymethylmethacrylate (PS-b-PMMA), polystyrene-blockpolydimethylsiloxane (PS-b-PDMS) and polystyrene-block-poly(ethylene oxide) (PS-b-PEO) systems of various molecular weights. BCP thin films, which act as an ‘on-chip’ etch mask and material templates, are highly promising self-assembling process for future scalable nanolithography. Unlike conventional BCP processing methods, the work in this thesis demonstrates that well-ordered patterns can be achieved in a few seconds compared to several hours by use of a non-conventional microwave assisted technique. As a result, well-ordered BCP nanoscale structures can be developed in industry appropriate periods facilitating their incorporation into current technologies. An optimised and controlled plasma dry etch process was used for successful pattern transfer to the underlying silicon substrate. Long range ordered BCP templates were further modified by selective metal inclusion technique to form a hard mask template towards fabrication of high aspect ratio nanopillars and nanowires. The work described here is centred on how these templates might be used to generate function at substrate surfaces. Herein we describe a number of innovations which might allow their successful uptake in a number of applications.

Formation of sub-7 nm feature size PS-b-P4VP block copolymer structures by solvent vapour process

The nanometer range structure produced by thin films of diblock copolymers makes them a great of interest as templates for the microelectronics industry. We investigated the effect of annealing solvents and/or mixture of the solvents in case of symmetric Poly (styrene-block-4vinylpyridine) (PS-b-P4VP) diblock copolymer to get the desired line patterns. In this paper, we used different molecular weights PS-b-P4VP to demonstrate the scalability of such high χ BCP system which requires precise fine-tuning of interfacial energies achieved by surface treatment and that improves the wetting property, ordering, and minimizes defect densities. Bare Silicon Substrates were also modified with polystyrene brush and ethylene glycol self-assembled monolayer in a simple quick reproducible way. Also, a novel and simple in situ hard mask technique was used to generate sub-7nm Iron oxide nanowires with a high aspect ratio on Silicon substrate, which can be used to develop silicon nanowires post pattern transfer.

Electron beam lithography assisted high-resolution pattern generation

This thesis details the top-down fabrication of nanostructures on Si and Ge substrates by electron beam lithography (EBL). Various polymeric resist materials were used to create nanopatterns by EBL and Chapter 1 discusses the development characteristics of these resists. Chapter 3 describes the processing parameters, resolution and topographical and structural changes of a new EBL resist known as ‘SML’. A comparison between SML and the standard resists PMMA and ZEP520A was undertaken to determine the suitability of SML as an EBL resist. It was established that SML is capable of high-resolution patterning and showed good pattern transfer capabilities. Germanium is a desirable material for use in microelectronic applications due to a number of superior qualities over silicon. EBL patterning of Ge with high-resolution hydrogen silsesquioxane (HSQ) resist is however difficult due to the presence of native surface oxides. Thus, to combat this problem a new technique for passivating Ge surfaces prior to EBL processes is detailed in Chapter 4. The surface passivation was carried out using simple acids like citric acid and acetic acid. The acids were gentle on the surface and enabled the formation of high-resolution arrays of Ge nanowires using HSQ resist. Chapter 5 details the directed self-assembly (DSA) of block copolymers (BCPs) on EBL patterned Si and, for the very first time, Ge surfaces. DSA of BCPs on template substrates is a promising technology for high volume and cost effective nanofabrication. The BCP employed for this study was poly (styrene-b-ethylene oxide) and the substrates were pre-defined by HSQ templates produced by EBL. The DSA technique resulted into pattern rectification (ordering in BCP) and in pattern multiplication within smaller areas.