The formation of nanotubes and nanocoils of molybdenum disulphide

This work reports the successful realization of MoS2 nanotubes by a novel intercalation chemistry and hydrothermal treatment. An inorganic-organic precursor of hexadecylamine (HDA) and molybdenum disulphide (MoS2) were used in synthesizing the nanocomposite comprising laminar MoS2 with HDA intercalated in the interlaminar spacing. The formation of MoS2 nanotubes occurred during hydrothermal treatment (HT) by a self-organized rolling mechanism. The nanotubes were observed to have dimensions 2-12 µm in length and inner diameters typically in the range of 25-100 nm. We also report the formation of amorphous nanocoils of MoS2 obtained during similar procedures.

Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Low power predictable memory and processing architectures

Great demand in power optimized devices shows promising economic potential and draws lots of attention in industry and research area. Due to the continuously shrinking CMOS process, not only dynamic power but also static power has emerged as a big concern in power reduction. Other than power optimization, average-case power estimation is quite significant for power budget allocation but also challenging in terms of time and effort. In this thesis, we will introduce a methodology to support modular quantitative analysis in order to estimate average power of circuits, on the basis of two concepts named Random Bag Preserving and Linear Compositionality. It can shorten simulation time and sustain high accuracy, resulting in increasing the feasibility of power estimation of big systems. For power saving, firstly, we take advantages of the low power characteristic of adiabatic logic and asynchronous logic to achieve ultra-low dynamic and static power. We will propose two memory cells, which could run in adiabatic and non-adiabatic mode. About 90% dynamic power can be saved in adiabatic mode when compared to other up-to-date designs. About 90% leakage power is saved. Secondly, a novel logic, named Asynchronous Charge Sharing Logic (ACSL), will be introduced. The realization of completion detection is simplified considerably. Not just the power reduction improvement, ACSL brings another promising feature in average power estimation called data-independency where this characteristic would make power estimation effortless and be meaningful for modular quantitative average case analysis. Finally, a new asynchronous Arithmetic Logic Unit (ALU) with a ripple carry adder implemented using the logically reversible/bidirectional characteristic exhibiting ultra-low power dissipation with sub-threshold region operating point will be presented. The proposed adder is able to operate multi-functionally.

Novel processes, test structures and characterisation for future germanium technologies

In order to widely use Ge and III-V materials instead of Si in advanced CMOS technology, the process and integration of these materials has to be well established so that their high mobility benefit is not swamped by imperfect manufacturing procedures. In this dissertation number of key bottlenecks in realization of Ge devices are investigated; We address the challenge of the formation of low resistivity contacts on n-type Ge, comparing conventional and advanced rapid thermal annealing (RTA) and laser thermal annealing (LTA) techniques respectively. LTA appears to be a feasible approach for realization of low resistivity contacts with an incredibly sharp germanide-substrate interface and contact resistivity in the order of 10 -7 Ω.cm2. Furthermore the influence of RTA and LTA on dopant activation and leakage current suppression in n+/p Ge junction were compared. Providing very high active carrier concentration > 1020 cm-3, LTA resulted in higher leakage current compared to RTA which provided lower carrier concentration ~1019 cm-3. This is an indication of a trade-off between high activation level and junction leakage current. High ION/IOFF ratio ~ 107 was obtained, which to the best of our knowledge is the best reported value for n-type Ge so far. Simulations were carried out to investigate how target sputtering, dose retention, and damage formation is generated in thin-body semiconductors by means of energetic ion impacts and how they are dependent on the target physical material properties. Solid phase epitaxy studies in wide and thin Ge fins confirmed the formation of twin boundary defects and random nucleation growth, like in Si, but here 600 °C annealing temperature was found to be effective to reduce these defects. Finally, a non-destructive doping technique was successfully implemented to dope Ge nanowires, where nanowire resistivity was reduced by 5 orders of magnitude using PH3 based in-diffusion process.