The Asymptotic Cone of Teichm\"uller Space: Thickness and Divergence

We study the Asymptotic Cone of Teichm\"uller space equipped with the Weil-Petersson metric. In particular, we provide a characterization of the canonical finest pieces in the tree-graded structure of the asymptotic cone of Teichm\"uller space along the same lines as a similar characterization for right angled Artin groups by Behrstock-Charney and for mapping class groups by Behrstock-Kleiner-Minksy-Mosher. As a corollary of the characterization, we complete the thickness classification of Teichm\"uller spaces for all surfaces of finite type, thereby answering questions of Behrstock-Drutu, Behrstock-Drutu-Mosher, and Brock-Masur. In particular, we prove that Teichm\"uller space of the genus two surface with one boundary component (or puncture) can be uniquely characterized in the following two senses: it is thick of order two, and it has superquadratic yet at most cubic divergence. In addition, we characterize strongly contracting quasi-geodesics in Teichm\"uller space, generalizing results of Brock-Masur-Minsky. As a tool, we develop a complex of separating multicurves, which may be of independent interest.Comment: This paper comprises the main portion of the author's doctoral thesis, 54 page

Contracting Boundaries of CAT(0) Spaces

As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well-defined since quasi-isometric CAT(0) spaces can have non-homeomorphic boundaries. We introduce a new type of boundary for a CAT(0) space, called the contracting boundary, made up rays satisfying one of five hyperbolic-like properties. We prove that these properties are all equivalent and that the contracting boundary is a quasi-isometry invariant. We use this invariant to distinguish the quasi-isometry classes of certain right-angled Coxeter groups.Comment: 27 pages, 8 figure

Top-down fabricated ZnO nanowire transistors for application in biosensors

Top-down ZnO nanowire FETs have been fabricated using mature photolithography, ZnO atomic layer deposition (ALD) and plasma etching. This paper investigates the effects of oxygen adsorption by measuring FET characteristics at different gate bias sweep rates and by characterizing hysteresis effects. Unpassivated devices exhibit a low threshold voltage shift of 5.4 V when the gate bias sweep rate is varied from 2500 V/s to 1.2 V/s and a low hysteresis width of less than 1.5 V. These results are considerably better than the state of the art for bottom-up as-fabricated ZnO nanowire FETs and demonstrate the suitability of this top-down technology for biosensor applications

Electrical characteristics of top-down ZnO nanowire transistors using remote plasma ALD

Top-down fabrication is used to produce ZnO nanowires by remote plasma atomic layer deposition over a SiO2 pillar and anisotropic dry etching. Nanowire field-effect transistors (FETs), with channel lengths in the range of 1.3–18.6 µm, are then fabricated using these 80 nm × 40 nm nanowires. Measured electrical results show n-type enhancement behavior and a breakdown voltage ~75 V at all channel lengths. This is the first report of high-voltage operation for ZnO nanowire FETs. Reproducible well-behaved electrical characteristics are obtained, and the drain current scales with 1/L, as expected for long-channel FETs. A respectable ION/IOFF ratio of 2 × 106 is obtained