Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

High Precision Plasma Etch for Pattern Transfer: Towards Fluorocarbon Based Atomic Layer Etching

A basic requirement of a plasma etching process is fidelity of the patterned organic materials. In photolithography, a He plasma pretreatment (PPT) based on high ultraviolet and vacuum ultraviolet (UV/VUV) exposure was shown to be successful for roughness reduction of 193nm photoresist (PR). Typical multilayer masks consist of many other organic masking materials in addition to 193nm PR. These materials vary significantly in UV/VUV sensitivity and show, therefore, a different response to the He PPT. A delamination of the nanometer-thin, ion-induced dense amorphous carbon (DAC) layer was observed. Extensive He PPT exposure produces volatile species through UV/VUV induced scissioning. These species are trapped underneath the DAC layer in a subsequent plasma etch (PE), causing a loss of adhesion. Next to stabilizing organic materials, the major goals of this work included to establish and evaluate a cyclic fluorocarbon (FC) based approach for atomic layer etching (ALE) of SiO2 and Si; to characterize the mechanisms involved; and to evaluate the impact of processing parameters. Periodic, short precursor injections allow precise deposition of thin FC films. These films limit the amount of available chemical etchant during subsequent low energy, plasma-based Ar+ ion bombardment, resulting in strongly time-dependent etch rates. In situ ellipsometry showcased the self-limited etching. X-ray photoelectron spectroscopy (XPS) confirms FC film deposition and mixing with the substrate. The cyclic ALE approach is also able to precisely etch Si substrates. A reduced time-dependent etching is seen for Si, likely based on a lower physical sputtering energy threshold. A fluorinated, oxidized surface layer is present during ALE of Si and greatly influences the etch behavior. A reaction of the precursor with the fluorinated substrate upon precursor injection was observed and characterized. The cyclic ALE approach is transferred to a manufacturing scale reactor at IBM Research. Ensuring the transferability to industrial device patterning is crucial for the application of ALE. In addition to device patterning, the cyclic ALE process is employed for oxide removal from Si and SiGe surfaces with the goal of minimal substrate damage and surface residues. The ALE process developed for SiO2 and Si etching did not remove native oxide at the level required. Optimizing the process enabled strong O removal from the surface. Subsequent 90% H2/Ar plasma allow for removal of C and F residues.

Self-Organizing Map Neural Architectures Based on Limit Cycle Attractors

Recent efforts to develop large-scale neural architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason is that most conventional SOMs use a static encoding representation: Each input is typically represented by the fixed activation of a single node in the map layer. This not only carries information in an inefficient and unreliable way that impedes building robust multi-SOM neural architectures, but it is also inconsistent with rhythmic oscillations in biological neural networks. Here I develop and study an alternative encoding scheme that instead uses limit cycle attractors of multi-focal activity patterns to represent input patterns/sequences. Such a fundamental change in representation raises several questions: Can this be done effectively and reliably? If so, will map formation still occur? What properties would limit cycle SOMs exhibit? Could multiple such SOMs interact effectively? Could robust architectures based on such SOMs be built for practical applications? The principal results of examining these questions are as follows. First, conditions are established for limit cycle attractors to emerge in a SOM through self-organization when encoding both static and temporal sequence inputs. It is found that under appropriate conditions a set of learned limit cycles are stable, unique, and preserve input relationships. In spite of the continually changing activity in a limit cycle SOM, map formation continues to occur reliably. Next, associations between limit cycles in different SOMs are learned. It is shown that limit cycles in one SOM can be successfully retrieved by another SOM’s limit cycle activity. Control timings can be set quite arbitrarily during both training and activation. Importantly, the learned associations generalize to new inputs that have never been seen during training. Finally, a complete neural architecture based on multiple limit cycle SOMs is presented for robotic arm control. This architecture combines open-loop and closed-loop methods to achieve high accuracy and fast movements through smooth trajectories. The architecture is robust in that disrupting or damaging the system in a variety of ways does not completely destroy the system. I conclude that limit cycle SOMs have great potentials for use in constructing robust neural architectures.

Improved Venting for Flammability Limit Testing Using ASTM E681 Apparatus

The literature on the determination of flammability limits was reviewed and experts on the ASTM E681 standard were interviewed to identify new means of improving the reproducibility of the ASTM E681 test. Venting was identified as a variable of flammability limits not yet addressed. Limitations of the current system for sealing and venting (a rubber stopper) were identified and addressed by the development of a custom burst disc. The burst disc was evaluated for its ability to hold and maintain a vacuum, its ability to vent at pressures of interest, and for its venting phenomena. The burst disc was deemed to be a satisfactory alternative to the rubber stopper and is recommended to be included in the ASTM E681 standard.