Partial regularity for Lipschitz solutions to the minimal surface system

In this paper, we study the regularity of several notions of Lipschitz solutions to the minimal surface system with an emphasis on partial regularity results. These include stationary solutions, integral weak solutions, and viscosity solutions. We also prove an interior gradient estimate for classical solutions to the system using the maximum principle, assuming the area-decreasing condition and that all but one component have small infinity norm.Comment: 30 pages. Submitted to Calc. Var. Partial Differential Equation

Experiences of a Novice Modeler Navigating the Alternative Certification Process

Interactive Engagement methods of instruction have proven more effective than Traditional instruction in terms of conceptual learning in introductory physics classrooms. Modeling instruction is one type of Interactive Engagement methodology used in introductory physics at the secondary and collegiate level. This study compares the conceptual gains of students taught by an experienced traditional instructor to the conceptual gains of students taught by a novice, alternatively certified instructor who employs the Modeling methodology in physics classes at a large suburban high school. Pre-tests and post-tests were administered to all groups using validated physics conceptual inventories and a scientific reasoning assessment. AP Physics B mock exam scores were also compiled and analyzed to determine the impact of Modeling instruction on students’ problem solving abilities. Additional analyses were conducted to verify the impact of scientific reasoning skills on conceptual learning gains, and to examine whether Modeling instruction closed the “gender gap” in physics. Furthermore, a post hoc analysis was performed comparing the conceptual gains of general physics students taught by a novice teacher using traditional instructional methods to the conceptual gains of general physics students taught by the same teacher after completion of a Modeling Workshop. The results indicate that the Modeling methodology is an effective way to increase conceptual understanding of forces and motion in introductory high school physics. The results also support the Modeling Workshop to be an effective and efficient way to train a new, alternatively certified physics teacher

Simple Monte Carlo Simulator for modelling Linear Mode and Geiger Mode Avalanche Photodiodes in C++

Linear mode and Geiger mode Avalanche Photodiodes are widely used to detect weak optical signals, with the latter able to detect a single photon at a time. Practical simulators for these devices should accurately produce relevant device characteristics and not be overly computationally intensive. The Simple Monte Carlo Simulator, written in C++, offers such a combination and can simulate avalanche photodiodes made with Silicon, Gallium Arsenide and Indium Gallium Phosphide, with the potential to include other semiconductor materials. The software is available on The University of Sheffield Research Data Catalogue and Repository at https://doi.org/10.15131/shef.data.5683939 and on GitHub at https://github.com/jdpetticrew/Simple-Monte-Carlo-Simulator

A theoretical comparison of the breakdown behavior of In0.52Al0.48As and InP near-infrared single-photon avalanche photodiodes

We study the breakdown characteristics and timing statistics of InP and In0.52Al0.48As single-photon avalanche photodiodes (SPADs) with avalanche widths ranging from 0.2 to 1.0 mu m at room temperature using a random ionization path-length model. Our results show that, for a given avalanche width, the breakdown probability of In0.52Al0.48As SPADs increases faster with overbias than InP SPADs. When we compared their timing statistics, we observed that, for a given breakdown probability, InP requires a shorter time to reach breakdown and exhibits a smaller timing jitter than In0.52Al0.48As. However, due to the lower dark count probability and faster rise in breakdown probability with overbias, In0.52Al0.48As SPADs with avalanche widths <= 0.5 mu m are more suitable for single-photon detection at telecommunication wavelengths than InP SPADs. Moreover, we predict that, in InP SPADs with avalanche widths <= 0.3 mu m and In0.52Al0.48As SPADs with avalanche widths <= 0.2 mu m, the dark count probability is higher than the photon count probability for all applied biases

Thin GaAsSb Diodes With Low Excess Noise

Thin avalanche layers have been adopted to achieve low excess noise and high gain bandwidth products in InP and InAlAs avalanche photodiodes. In this work we report the excess noise characterization in a series of Al1-xGaxAs0.56Sb0.44 (x = 0, 0.05, 0.1, 0.15) diodes with avalanche layer thickness of 110-116 nm. These alloys, lattice matched to InP, showed lower excess noise than InP and InAlAs. Dark current, most probably originating from surface leakage, was observed to be lower in composition with higher Ga concentration. Avalanche gain and excess noise measurements using lasers of 543 and 633 nm wavelengths indicated that at a given electric field, the electron ionization coefficient is larger than the hole ionization coefficient. Using the 543 nm laser, low excess noise data corresponding to an effective ionization coefficient ratio of k = 0.1 in the conventional excess noise theory was measured in Al1-xGaxAs0.56Sb0.44 (x = 0.05, 0.1, 0.15), although pure electron injection was not achieved. Our results demonstrated the potential of using Al1-xGaxAs0.56Sb0.44 (x = 0.05, 0.1, 0.15) as replacement for InP and InAlAs for high speed and low excess noise avalanche photodiodes. The data reported in this paper is available from the ORDA digital repository (https://doi.org/10.15131/shef.data.5155822)

Avalanche Breakdown Timing Statistics for Silicon Single Photon Avalanche Diodes

CCBY Silicon-based Single Photon Avalanche Diodes (SPADs) are widely used as single photon detectors of visible and near infrared photons. There has however been a lack of models accurately interpreting the physics of impact ionization (the mechanism behind avalanche breakdown) for these devices. In this work, we present a statistical simulation model for silicon SPADs that is capable of predicting breakdown probability, mean time to breakdown and timing jitter. Our model inherently incorporates carriers & #x0027; dead space due to phonon scattering and allows for non-uniform electric fields. Model validation included avalanche gain, excess noise factor, breakdown voltage, breakdown probability, and timing statistics. Simulating an n on-p and a p-on-n SPAD design using our model, we found that the n-on-p design offers significantly improved mean time to breakdown and timing jitter characteristics. For a breakdown probability of 0.5, mean time to breakdown and timing jitter from the n-on-p design were 3 and 4 times smaller compared to those from the p on n design. The data reported in this paper is available from the ORDA digital repository (DOI: 10.15131/shef.data.4823248)

Effects of carrier injection profile on low noise thin Al0.85Ga0.15As0.56Sb0.44 avalanche photodiodes

Avalanche photodiodes (APDs) with thin avalanche regions have shown low excess noise characteristics and high gain-bandwidth products, so they are suited for long-haul optical communications. In this work, we investigated how carrier injection profile affects the avalanche gain and excess noise factors of Al0.85Ga0.15As0.56Sb0.44 (lattice-matched to InP substrates) p-i-n and n-i-p diodes with total depletion widths of 145-240 nm. Different carrier injection profiles were achieved by using light with wavelengths of 420, 543 and 633nm. For p-i-n diodes, shorter wavelength light produces higher avalanche gains for a given reverse bias and lower excess noise factors at a given gain, compared to longer wavelength light. Thus, using 420 nm light on the p-i-n diodes, corresponding to pure electron injection conditions, gave the highest gain and lowest excess noise. In n-i-p diodes, pure hole injection yields significantly lower gain and higher excess noise, compared to mixed carrier injection. These show that the electron ionization coefficient, α, is higher than the hole ionization coefficient, β. Using pure electron injection, excess noise factor characteristics with effective ionization ratios, keff, of 0.08-0.1 were obtained. This is significantly lower than those of InP and In0.52Al0.48As, the commonly used avalanche materials combined with In0.53Ga0.47As absorber. The data reported in this paper is available from the ORDA digital repository (DOI: 10.15131/shef. DATA: 5787318)

Modeling temperature dependent avalanche characteristics of InP

Avalanche photodiodes (APDs), and single photon avalanche diodes (SPADs), with InP avalanche regions and InGaAs absorption regions, are used for detecting weak infrared light at ~ 1.55 μm wavelength. These devices are often cooled to below room temperature during operation yet both validated simulation models and impact ionization coefficients that accurately describe the avalanche characteristics of InP are lacking in the temperature range of interest (200 K to room temperature). In this paper we present an accessible, validated temperature dependent simulation model for InP APDs/SPADs. The model is capable of simulating avalanche gain, excess noise, breakdown voltage, and impulse current at 150 - 300 K. Temperature dependent ionization coefficients in InP, which may be used with other APD/SPAD simulation models, are also presented. The data reported in this paper is available from the ORDA digital repository (DOI: 10.15131/shef.data.c.4373006)

Effects of carrier injection profile on low noise thin Al0.85Ga0.15As0.56Sb0.44 avalanche photodiodes

Avalanche photodiodes (APDs) with thin avalanche regions have shown low excess noise characteristics and high gain-bandwidth products, so they are suited for long-haul optical communications. In this work, we investigated how carrier injection profile affects the avalanche gain and excess noise factors of Al0.85Ga0.15As0.56Sb0.44 (lattice-matched to InP substrates) p-i-n and n-i-p diodes with total depletion widths of 145-240 nm. Different carrier injection profiles were achieved by using light with wavelengths of 420, 543 and 633nm. For p-i-n diodes, shorter wavelength light produces higher avalanche gains for a given reverse bias and lower excess noise factors at a given gain, compared to longer wavelength light. Thus, using 420 nm light on the p-i-n diodes, corresponding to pure electron injection conditions, gave the highest gain and lowest excess noise. In n-i-p diodes, pure hole injection yields significantly lower gain and higher excess noise, compared to mixed carrier injection. These show that the electron ionization coefficient, α, is higher than the hole ionization coefficient, β. Using pure electron injection, excess noise factor characteristics with effective ionization ratios, keff, of 0.08-0.1 were obtained. This is significantly lower than those of InP and In0.52Al0.48As, the commonly used avalanche materials combined with In0.53Ga0.47As absorber. The data reported in this paper is available from the ORDA digital repository (DOI: 10.15131/shef. DATA: 5787318)