X-ray propagation in carbon nanotubes

The maintenance of the growth of the multibillion-dollar semiconductor industry requires the development of techniques for the fabrication and characterisation of nanoscale devices. Consequently, there is great interest in photolithography techniques such as extreme UV and x-ray. Both of these techniques are extremely expensive and technologically very demanding. In this paper we describe research on the feasibility of exploiting x-ray propagation within carbon nanotubes (CNT's) for the fabrication and characterisation of nanoscale devices. This work discusses the parameters determining the design space available. To demonstrate experimentally the feasibility of x-ray propagation, arrays of carbon nanotubes have been grown on silicon membranes. The latter are required to provide structural support for the CNT's while minimising energy loss. To form a waveguide metal is deposited between the nanotubes to block x-ray transmission in this region at the same time as cladding the CNT's. The major challenge has been to fill the spaces between the CNT's with material of sufficient thickness to block x-ray transmission while maintaining the structural integrity of the CNT's. Various techniques have been employed to fill the gaps between the nanotubes including electroplating, sputtering and evaporation. This work highlights challenges encountered in optimising the process.

Random function priors for exchangeable arrays with applications to graphs and relational data

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlying relations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.