Development of nano-patterned sapphire substrates for deposition of AlGaInN semiconductors by molecular beam epitaxy

Thesis (M.Sc.Eng.)This research addressed the design and fabrication of nano-patterned sapphire substrates (NPSS) as well as the growth by molecular-beam epitaxy (MBE) on such substrates of AlGaN and InGaN multiple quantum wells (MQWs). In recent years a number of LED manufacturers are developing nitride LED devices emitting in the visible part of the electromagnetic spectrum on micron-patterned sapphire substrate (MPSS). These devices are reported to have lower threading dislocation densities, resulting in improvement of the LED internal quantum efficiency (IQE). Furthermore, the LED devices fabricated on MPSS were also found to have improved light extraction efficiency (LEE), due to light scattering by the patterned substrate. My research focuses on the development of nano-patterned sapphire substrate aiming to improve the performance of LEDs grown by MBE and emitting at the deep ultraviolet region of the electromagnetic spectrum. In order to optimize the nano-patterning of the sapphire substrates for maximum light-extraction, the Finite-Difference Time-Domain (FDTD) simulation method was employed. The LEE enhancement was calculated as a function of the diameter, height and perion of the pattern. The calculations were performed only at a single wavelength, corresponding to the maximum of the emitted LED spectrum, which was taken to be 280 nm. These calculations have shown that the best sapphire substrate patterning strategy for this wavelength is the cone shape pattern in hexagonal array structure. Based on limited number of calculations I found that the optimum period, diameter and height of this cone shaped pattern are 400nm 375nm and 375nm respectively. Experimentally, nano patterned substrates were fabricated through natural and nano-imprint lithography. In natural lithography the first step for the definition of the nano-pattern consists of coating the sapphire substrate with photoresist (PMMA) followed by depositing a monolayer of polystyrene nanospheres, 400nm in diameter, using the Langmuir–Blodgett method. These spheres assemble on the substrate and form a closed packed hexagonal array pattern. Following this step the size of the spheres was slightly reduced using reactive-ion etching (RIE) in oxygen plasma. This was followed by the deposition a chromium film, lift-off to remove the polystyrene spheres and RIE to remove the PMMA from the footprints of the spheres. The substrate was then coated with a nickel or chromium films followed by another lift-off which defines the final mask for the formation of cone shaped features by RIE in a CHF3 plasma. An alternative method for pattern definition was the nanoimprint lithography; the stamp for this method (2 mm2 in size) was formed on Silicon substrate using e-beam lithography. NPSS with high quality pillar shape was also fabricated by this method, however, this method can produce only small size patterns. AlGaN films and GaN/InGaN MQWs were deposited on the NPSS by MBE, and characterized by Scanning electron microscopy and photoluminescence and cathodoluminescence measurements. The cathodoluminescence and photoluminescence spectra show that films grown on NPSS has much stronger luminescence than the films grown on flat sapphire substrate, consistent with enhanced light extraction efficiency

Scalable string reconciliation by recursive content-dependent shingling

We consider the problem of reconciling similar strings in a distributed system. Specifically, we are interested in performing this reconciliation in an efficient manner, minimizing the communication cost. Our problem applies to several types of large-scale distributed networks, file synchronization utilities, and any system that manages the consistency of string encoded ordered data. We present the novel Recursive Content-Dependent Shingling (RCDS) protocol that can handle large strings and has the communication complexity that scales with the edit distance between the reconciling strings. Also, we provide analysis, experimental results, and comparisons to existing synchronization software such as the Rsync utility with an implementation of our protocol.2019-12-03T00:00:00

Inversely Unstable Solutions of Two-Dimensional Systems on Genus-p Surfaces and the Topology of Knotted Attractors

In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins, 2004] and give conditions under which these invariant sets are not homeomorphic to a circle individually, which implies the existence of chaotic behaviour. This is achieved by studying the appearance of inversely unstable solutions within each invariant set.Comment: 19 pages with 20 figures, AMS La-TeX, to be published in International Journal of Bifurcation and Chao

Local transformations of superpositions of entangled states

Suppose that we have two entangled states $\ket {\phi_1}$, $\ket{\psi_1}$ that cannot be converted to any of other two states $\ket{\phi_2}$, $\ket{\psi_2}$ by local operations and classical communication. We analyze the possibility of locally transforming a superposition of $\ket{\phi_1}$ and $\ket{\psi_1}$ into a superposition of $\ket{\phi_2}$ and $\ket{\psi_2}$. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed