Energy Models for One-Carrier Transport in Semiconductor Devices

Moment models of carrier transport, derived from the Boltzmann equation, made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It was found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime required empirical modification of this law, or nonstandard choices. Simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, are presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms. Some mathematical results are presented and contrasted with the highly developed state of the drift-diffusion model

Mathematics Course Placement Using Holistic Measures: Possibilities for Community College Students.

Background/Context: Most community colleges across the country use a placement test to determine students’ readiness for college-level coursework, yet these tests are admittedly imperfect instruments. Researchers have documented significant problems stemming from overreliance on placement testing, including placement error and misdiagnosis of remediation needs. They have also described significant consequences of misplacement, which can hinder the educational progression and attainment of community college students. Purpose/Objective/Research Question/Focus of Study: We explore possibilities for placing community college students in mathematics courses using a holistic approach that considers measures beyond placement test scores. This includes academic background measures, such as high school GPA and math courses taken, and indicators of noncognitive constructs, such as motivation, time use, and social support. Setting: The study draws upon administrative data from a large urban community college district in California that serves over 100,000 students each semester. The data enable us to link students’ placement testing results, survey data, background information, and transcript records. Research Design: We first use the supplemental survey data gathered during routine placement testing to conduct predictive exercises that identify severe placement errors under existing placement practices. We then move beyond prediction and evaluate student outcomes in two colleges where noncognitive indicators were directly factored into placement algorithms. Findings/Results: Using high school background information and noncognitive indicators to predict success reveals as many as one quarter of students may be misassigned to their math courses by status quo practices. In our subsequent analysis we find that students placed under a holistic approach that considered noncognitive indicators in addition to placement test scores performed no differently from higher scoring peers in the same course. Conclusions/Recommendations: The findings suggest a holistic approach to mathematics course placement may improve placement accuracy and provide access to higher level mathematics courses for community college students without compromising their likelihood of success

Strong Analytic Controllability for Hydrogen Control Systems

The realization and representation of so(4,2) associated with the hydrogen atom Hamiltonian are derived. By choosing operators from the realization of so(4,2) as interacting Hamiltonians, a hydrogen atom control system is constructed, and it is proved that this control system is strongly analytically controllable based on a time-dependent strong analytic controllability theorem.Comment: 6 pages; corrected typo; added equations in section III for representation states of so(4,2). accepted by CDC 200

Photovoltage Detection of Edge Magnetoplasmon Oscillations and Giant Magnetoplasmon Resonances in A Two-Dimensional Hole System

In our high mobility p-type AlGaAs/GaAs two-dimensional hole samples, we originally observe the B-periodic oscillation induced by microwave (MW) in photovoltage (PV) measurements. In the frequency range of our measurements (5 - 40 GHz), the period ({\Delta}B) is inversely proportional to the microwave frequency (f). The distinct oscillations come from the edge magnetoplasmon (EMP) in the high quality heavy hole system. In our hole sample with a very large effective mass, the observation of the EMP oscillations is in neither the low frequency limit nor the high frequency limit, and the damping of the EMP oscillations is very weak under high magnetic fields. Simultaneously, we observe the giant plasmon resonance signals in our measurements on the shallow two-dimensional hole system (2DHS)