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This thesis investigates advanced silicon devices fabricated using phosphorous ion implantation. The novel devices presented are the silicon quantum cellular automata cell and the few-donor device implanted with controlled numbers of phosphorous donors. In addition, the thesis presents novel measurements of a phosphorous implanted silicon double-dot device, a crucial building block of a quantum cellular automata cell. The devices were fabricated using standard lithographic techniques and, in the case of few-donor devices, a new method of controlled single ion implantation using on-chip detector electrodes. The positional accuracy of the implanted ions was achieved using a resist mask defined by electron beam lithography. A series of subsequent process steps has also been developed to repair the substrate implantation damage, define surface control gates, and to define single electron transistors used for readout via the detection of sub-electron charge transfer signals in the device. The device operations were achieved at mK-temperatures using various measurement techniques. In the case of quantum cellular automata cells, the device operation was demonstrated directly by switching the polarization of the cells from one logic state to another and detecting the corresponding change in the electrostatic environment using single-electron transistors. The control gate limits necessary for stable QCA cell operation were also determined, indirectly demonstrating QCA logic state switching. The double-dot device operation was demonstrated using SET detection in both linear and for the first time in non-linear regimes. In addition, source-drain conductance detection of charge states, simultaneous detection using single-electron transistors and source-drain conductance, and source-drain bias spectroscopy measurements of these systems were also achieved. In the case of few-donor implanted devices, isolated charge transfers were detected in both MOS and PIN based devices. The signals corresponded to between 0.01 and 0.05 of a single electron charge, induced on the islands of the SETs. The magnetic field dependence of the charge transfers detected in few-donor implanted devices was also investigated, along with basic phosphorous donor ionization experiments. The devices were also measured using SETs operated in rf mode, yielding consistent results. The work presented in this thesis is a step towards realizing a silicon charge-based quantum computer and other advanced single-electron devices based on phosphorous ion-implantation in silicon.

Thesis (M.S.)--Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (leaves 119-137).

Thesis (PhD)--Montana State University--Bozeman, 2008. / Typescript. Chairperson, Graduate Committee: Philip S. Stewart. Includes bibliographical references.

We consider the problem of decontaminating a network where all nodes are infected by a virus. The decontamination strategy is performed using a Cellular Automata (CA) model in which each node of the network is represented by the automata cell and thus, the network host status is also mapped to the CA state (contaminated, decontaminating, decontaminated). All hosts are assumed to be initially contaminated and the status of each cell is synchronously updated according to a set of local rules, based on the state of its neighbourhood. Our goal is to find the set of local rules that will accomplish the decontamination in an optimal way. The metrics used to define optimality is the minimization of three metrics: the maximum number of decontaminating cells at each step, the required value of the immunity time of each cell and the number of steps to complete the sanitization algorithm. In our research, we explore the designing of these local decontamination rules by refining the concept of the neighbourhood radius of CA with the addition of two new dimensions: Visibility Hop and Contamination Distance. Additionally, a research tool that help us manage our study have been developed.

Network decontamination is a well known mobile agent problem with many applications. We assume that all nodes of a network are contaminated (e.g., by a virus) and a set of agents is deployed to decontaminate them. An agent passing by a node decontaminates it, however a decontaminated node can be recontaminated if any of its neighbours is contaminated. In the vast literature a variety of models are considered and different assumptions are made on the power of the agents. In this thesis we study variation of the decontamination problem in mesh and tori topologies, under the assumption that when a node is decontaminated, it is immune to recontamination for a predefined amount of time t (called immunity time). After the immunity time is elapsed, recontamination can occur. We focus on three different models: mobile agents (MA), cellular automata (CA), and mobile cellular automata (MCA). The first two models are commonly studied and employed in several other contexts, the third model is introduced in this thesis for the first time. In each model we study the temporal decontamination problem (adapted to the particular setting) under a variety of assumptions on the capabilities of the decontaminating elements (agents for MA and MCA, decontaminating cells for CA). Some of the parameters we consider in this study are: visibility of the active elements, their ability to make copies of themselves, their ability to communicate, and the possibility to remember their past actions (memory). We describe several solutions in the various scenarios and we analyze their complexity. Efficiency is evaluated slightly differently in each model, but essentially the effort is in the minimization of the number of simultaneous decontaminating elements active in the system while performing the decontamination with a given immunity time.

Cellular automata are systems of interconnected cells which are discrete in space, time and state. Cell states are updated synchronously according to a local rule which is dependent upon the current state of the given cell and those of its neighbours in a pre-defined neighbourhood. The local rule is common to all cells. Fuzzy cellular automata extend this notion to systems which are discrete in space and time but not state. In this thesis, we explore fuzzy cellular automata which are created from the extension of Boolean rules in disjunctive normal form to continuous functions. Motivated by recent results on the classification of these rules from empirical evidence, we set out first to show that fuzzy cellular automata can shed some light on classical cellular automata and then to prove that the observed results are mathematically correct. The main results of this thesis can be divided into two categories. We first investigate the links between fuzzy cellular automata and their Boolean counter-parts. We prove that number conservation is preserved by this transformation. We further show that Boolean additive cellular automata have a definable property in their fuzzy form which we call self-oscillation. We then give a probabilistic interpretation of fuzzy cellular automata and show that homogeneous asymptotic states are equivalent to mean field approximations of Boolean cellular automata. We then turn our attention the asymptotic behaviour of fuzzy cellular automata. In the second half of the thesis we investigate the observed behaviours of the fuzzy cellular automata derived from balanced Boolean rules. We show that the empirical results of asymptotic behaviour are correct. In fuzzy form, the balanced rules can be categorized as one of three types: weighted average rules, self-averaging rules, and local majority rules. Each type is analyzed in a variety of ways using a range of tools to explain their behaviours.

Network decontamination is a well known mobile agent problem with many applications. We assume that all nodes of a network are contaminated (e.g., by a virus) and a set of agents is deployed to decontaminate them. An agent passing by a node decontaminates it, however a decontaminated node can be recontaminated if any of its neighbours is contaminated. In the vast literature a variety of models are considered and different assumptions are made on the power of the agents. In this thesis we study variation of the decontamination problem in mesh and tori topologies, under the assumption that when a node is decontaminated, it is immune to recontamination for a predefined amount of time t (called immunity time). After the immunity time is elapsed, recontamination can occur. We focus on three different models: mobile agents (MA), cellular automata (CA), and mobile cellular automata (MCA). The first two models are commonly studied and employed in several other contexts, the third model is introduced in this thesis for the first time. In each model we study the temporal decontamination problem (adapted to the particular setting) under a variety of assumptions on the capabilities of the decontaminating elements (agents for MA and MCA, decontaminating cells for CA). Some of the parameters we consider in this study are: visibility of the active elements, their ability to make copies of themselves, their ability to communicate, and the possibility to remember their past actions (memory). We describe several solutions in the various scenarios and we analyze their complexity. Efficiency is evaluated slightly differently in each model, but essentially the effort is in the minimization of the number of simultaneous decontaminating elements active in the system while performing the decontamination with a given immunity time.

Network decontamination is a well known mobile agent problem with many applications. We assume that all nodes of a network are contaminated (e.g., by a virus) and a set of agents is deployed to decontaminate them. An agent passing by a node decontaminates it, however a decontaminated node can be recontaminated if any of its neighbours is contaminated. In the vast literature a variety of models are considered and different assumptions are made on the power of the agents. In this thesis we study variation of the decontamination problem in mesh and tori topologies, under the assumption that when a node is decontaminated, it is immune to recontamination for a predefined amount of time t (called immunity time). After the immunity time is elapsed, recontamination can occur. We focus on three different models: mobile agents (MA), cellular automata (CA), and mobile cellular automata (MCA). The first two models are commonly studied and employed in several other contexts, the third model is introduced in this thesis for the first time. In each model we study the temporal decontamination problem (adapted to the particular setting) under a variety of assumptions on the capabilities of the decontaminating elements (agents for MA and MCA, decontaminating cells for CA). Some of the parameters we consider in this study are: visibility of the active elements, their ability to make copies of themselves, their ability to communicate, and the possibility to remember their past actions (memory). We describe several solutions in the various scenarios and we analyze their complexity. Efficiency is evaluated slightly differently in each model, but essentially the effort is in the minimization of the number of simultaneous decontaminating elements active in the system while performing the decontamination with a given immunity time.

Cellular automata are systems of interconnected cells which are discrete in space, time and state. Cell states are updated synchronously according to a local rule which is dependent upon the current state of the given cell and those of its neighbours in a pre-defined neighbourhood. The local rule is common to all cells. Fuzzy cellular automata extend this notion to systems which are discrete in space and time but not state. In this thesis, we explore fuzzy cellular automata which are created from the extension of Boolean rules in disjunctive normal form to continuous functions. Motivated by recent results on the classification of these rules from empirical evidence, we set out first to show that fuzzy cellular automata can shed some light on classical cellular automata and then to prove that the observed results are mathematically correct. The main results of this thesis can be divided into two categories. We first investigate the links between fuzzy cellular automata and their Boolean counter-parts. We prove that number conservation is preserved by this transformation. We further show that Boolean additive cellular automata have a definable property in their fuzzy form which we call self-oscillation. We then give a probabilistic interpretation of fuzzy cellular automata and show that homogeneous asymptotic states are equivalent to mean field approximations of Boolean cellular automata. We then turn our attention the asymptotic behaviour of fuzzy cellular automata. In the second half of the thesis we investigate the observed behaviours of the fuzzy cellular automata derived from balanced Boolean rules. We show that the empirical results of asymptotic behaviour are correct. In fuzzy form, the balanced rules can be categorized as one of three types: weighted average rules, self-averaging rules, and local majority rules. Each type is analyzed in a variety of ways using a range of tools to explain their behaviours.