Hole-defect chaos in the one-dimensional complex Ginzburg-Landau equation

We study the spatiotemporally chaotic dynamics of holes and defects in the 1D complex Ginzburg--Landau equation (CGLE). We focus particularly on the self--disordering dynamics of holes and on the variation in defect profiles. By enforcing identical defect profiles and/or smooth plane wave backgrounds, we are able to sensitively probe the causes of the spatiotemporal chaos. We show that the coupling of the holes to a self--disordered background is the dominant mechanism. We analyze a lattice model for the 1D CGLE, incorporating this self--disordering. Despite its simplicity, we show that the model retains the essential spatiotemporally chaotic behavior of the full CGLE.Comment: 8 pages, 10 figures; revised and shortened; extra discussion of self-disordering dynamic

Capacitive MEMS-based sensors : thermo-mechanical stability and charge trapping

Micro-Electro Mechanical Systems (MEMS) are generally characterized as miniaturized systems with electrostatically driven moving parts. In many cases, the electrodes are capacitively coupled. This basic scheme allows for a plethora of specifications and functionality. This technology has presently matured and is widely employed in industry. \ud A voltage across the electrodes will attract the movable part. This relation between electric field and separation (or capacitance) can be conveniently employed to sense tiny displacements (less than 1 pm) or for example as a through sensor for electromagnetic power through a coplanar waveguide (CPW).\ud The design involves often dielectric layers, whether accidental (native oxide) or intentional. During fabrication and / or operation of the device, trapped charge can uncontrollably accumulate and decumulate in these layers, causing parasitic forces on the device. These parasitic forces can influence the device beyond acceptable limits. The research described in this thesis approaches this phenomenon in two ways: a) device level and b) fundamental level. \ud a) Device level: Complete MEMS structures. The thesis contains theory of capacitive MEMS, including amongst others pull-in voltage, electrostatically loaded clamped-clamped beams, and electro-mechanical resonance, as well as the origin, dynamics and influence of trapped charges, in conjunction with built-in voltage. A cryogenic experimental study has been done on the effect of charge trapping on two types of MEMS-based RF power sensors. New structures have been realized with far better thermo-mechanical immunity. These structures are the first to involve double beam springs, which are fabricated by wet KOH etching of silicon. It is demonstrated that even an ultrathin aluminum oxide (native, ~ 2 nm) can harbor significant charge trapping. The dynamics are found to slow down considerably at cryogenic temperatures. At last, a study is done on when charge trapping actually limit the performance of real MEMS devices: a gravity gradiometer and an RF power sensor. \ud b) Fundamental level. Existing measurements and imaging of local trapped charges by conducting atomic force microscopy (AFM) are reinterpreted by a new model. This multi mirror model calculates the electrostatic interaction (force, gradient and contact potential difference) between the sample surface containing the trapped charge and the tip of the AFM, represented by a conducting sphere. This model improves drastically over existing calculations. Some interesting theoretical approximations of quantities describing this interaction have been found