Missing observations and restrictions on randomization in nanomanufacturing experimentation

by 1977- Acharya, Navin N.

In recent years, scientists have discovered various techniques for building nanostructures, but they have only just begun to investigate their properties and potential applications. Moreover, to translate scientific discoveries from the laboratory to commercial products, it is imperative to address some of the fundamental scientific barriers to nanomanufacturing, in addition to the ongoing research in the field of nanotechnology. This thesis suggests that some of the above challenges can be addressed using experimental designs tailored to specific concerns. An instance of such a scenario is considered that involves a series of gas-phase nano-scale lubrication experiments for micro-electro-mechanical systems (MEMS) devices. Due to the physical unavailability of some of the C-6 alcohol molecules in the experiments, the experimenter is forced to deal with a design having one or more missing observations. In this study, new Bayesian algorithms are proposed that combine information from the traditional Bayesian screening algorithm used for identifying active factors and three existing algorithms for missing observations. The criterion used for estimating the missing observations is predictive ability in addition to minimization of residual sum of squares (RSS). These new algorithms are applied to simulated data sets that resemble the setup of the nano-scale lubrication experiment assuming one and two missing observations. The performance of the Bayesian algorithms are compared to the three existing algorithms that have minimal RSS as the only criterion with an appropriate performance measure, PRESSDiff. A comparison of the algorithms over the different positions of the iv missing observations reveals that in all the cases, the Bayesian algorithms perform significantly better than the non-Bayesian algorithms. In the study the robustness of the proposed algorithms to the initial model specified by the Bayesian screening method, various mismatches of active factors were considered. In all the mismatches considered for one and two missing observations, the results indicate that the Bayesian algorithms still outperform the respective non-Bayesian ones. Finally, judging from the studies performed, the Bayesian Complete RSS minimization algorithm seems to yield the closest estimates of the missing observations, while yielding the maximum predictive ability. In some nanomanufacturing situations, due to the physical constraints in the process, it is impracticable to execute a full or fractional factorial experiment. In such cases, restriction on randomization is imposed and the experimenter is forced to resort to a split-plot design or some of its variants. Many processes in nanomanufacturing are conducted over a series of stages. Additionally, some of the process variables in some of the stages might be difficult or hard to change in terms of time, limited resources, or – in many cases – money. Specifically, a polymerization process for the fabrication of nano-films is investigated, where the fabrication is carried out over three stages. To execute efficient experimentation and fully understand the intricacies at the nano-scale, split-plot designs that can be applied effectively over multiple stages are proposed with the aim of reducing the cost of experimentation, and their characteristics examined. General expressions for some of the properties of these designs and analysis are developed. As common design ranking criteria such as resolution and minimum aberration do not provide the “best” v designs in all cases, two new design optimality criteria are proposed. Catalogs of splitplot designs for three and four stages are created and ranked according to the proposed criteria. vi