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Non-Equilibrium Carrier Concentrations
ECE 531 Semiconductor Devices Lecture Notes { 06 Dr. Andre Zeumault Outline 1 Overview 1 2 Revisiting Equilibrium Considerations1 2.1 What is Meant by Thermal Equilibrium?........................1 2.2 Non-Equilibrium Carrier Concentrations.........................3 3 Recombination and Generation3 3.1 Generation.........................................3 4 Continuity Equations5 4.1 Minority Carrier Diffusion Equations...........................5 5 Quasi-Fermi Levels8 1 Overview So far, we have only discussed charge carrier concentrations under equilibrium conditions. Since no current can flow in thermal equilibrium, this particular case isn't much interest to us in trying to create electronic devices. Therefore, in this lecture, we discuss the situations and governing equations in which a charge carrier responds under non-equilibrium conditions. Topics to be covered include: • Recombination and Generation: An increase (generation) or decrease (recombination) in charge carrier concentrations away from or towards equilibrium. (e.g. due to absorption of light) • Current Continuity: Charge conservation, applied in the context of drift/diffusion. • Minority Carrier Diffusion Equations: Minority carrier diffusion in the presence of a large majority carrier concentration. • Quasi-Fermi Levels: Treating carrier densities under non-equilibrium conditions. 2 Revisiting Equilibrium Considerations 2.1 What is Meant by Thermal Equilibrium? When we discussed equilibrium charge carrier concentrations, it was argued that the production of charge carriers was thermally activated. This was shown to be true regardless of whether or not the semiconductor was intrinsic or extrinsic. When a semiconductor is intrinsic, the thermal energy necessary for charge carrier production is the bandgap energy EG, which corresponds to the energy needed to break a Silicon-Silicon covalent bond. -
Gold Nanoarray Deposited Using Alternating Current for Emission Rate
Xue et al. Nanoscale Research Letters 2013, 8:295 http://www.nanoscalereslett.com/content/8/1/295 NANO EXPRESS Open Access Gold nanoarray deposited using alternating current for emission rate-manipulating nanoantenna Jiancai Xue1, Qiangzhong Zhu1, Jiaming Liu1, Yinyin Li2, Zhang-Kai Zhou1*, Zhaoyong Lin1, Jiahao Yan1, Juntao Li1 and Xue-Hua Wang1* Abstract We have proposed an easy and controllable method to prepare highly ordered Au nanoarray by pulse alternating current deposition in anodic aluminum oxide template. Using the ultraviolet–visible-near-infrared region spectrophotometer, finite difference time domain, and Green function method, we experimentally and theoretically investigated the surface plasmon resonance, electric field distribution, and local density of states enhancement of the uniform Au nanoarray system. The time-resolved photoluminescence spectra of quantum dots show that the emission rate increased from 0.0429 to 0.5 ns−1 (10.7 times larger) by the existence of the Au nanoarray. Our findings not only suggest a convenient method for ordered nanoarray growth but also prove the utilization of the Au nanoarray for light emission-manipulating antennas, which can help build various functional plasmonic nanodevices. Keywords: Anodic aluminum oxide template, Au nanoarray, Emission rate, Nanoantenna, Surface plasmon PACS: 82.45.Yz, 78.47.jd, 62.23.Pq Background Owing to the self-organized hexagonal arrays of Excited by an incident photon beam and provoking a uniform parallel nanochannels, anodic aluminum oxide collective oscillation of free electron gas, plasmonic (AAO) film has been widely used as the template for materials gain the ability to manipulate electromagnetic nanoarray growth [26-29]. Many distinctive discoveries field at a deep-subwavelength scale, making them play a have been made in the nanosystems fabricated in AAO major role in current nanoscience [1-5]. -
Bringing Optical Metamaterials to Reality
UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Bringing Optical Metamaterials to Reality Permalink https://escholarship.org/uc/item/5d37803w Author Valentine, Jason Gage Publication Date 2010 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Bringing Optical Metamaterials to Reality By Jason Gage Valentine A dissertation in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering – Mechanical Engineering in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Xiang Zhang, Chair Professor Costas Grigoropoulos Professor Liwei Lin Professor Ming Wu Fall 2010 Bringing Optical Metamaterials to Reality © 2010 By Jason Gage Valentine Abstract Bringing Optical Metamaterials to Reality by Jason Gage Valentine Doctor of Philosophy in Mechanical Engineering University of California, Berkeley Professor Xiang Zhang, Chair Metamaterials, which are artificially engineered composites, have been shown to exhibit electromagnetic properties not attainable with naturally occurring materials. The use of such materials has been proposed for numerous applications including sub-diffraction limit imaging and electromagnetic cloaking. While these materials were first developed to work at microwave frequencies, scaling them to optical wavelengths has involved both fundamental and engineering challenges. Among these challenges, optical metamaterials tend to absorb a large amount of the incident light and furthermore, achieving devices with such materials has been difficult due to fabrication constraints associated with their nanoscale architectures. The objective of this dissertation is to describe the progress that I have made in overcoming these challenges in achieving low loss optical metamaterials and associated devices. The first part of the dissertation details the development of the first bulk optical metamaterial with a negative index of refraction. -
How to Introduce the Magnetic Dipole Moment
IOP PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 33 (2012) 1313–1320 doi:10.1088/0143-0807/33/5/1313 How to introduce the magnetic dipole moment M Bezerra, W J M Kort-Kamp, M V Cougo-Pinto and C Farina Instituto de F´ısica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, CEP 21941-972, Rio de Janeiro, Brazil E-mail: [email protected] Received 17 May 2012, in final form 26 June 2012 Published 19 July 2012 Online at stacks.iop.org/EJP/33/1313 Abstract We show how the concept of the magnetic dipole moment can be introduced in the same way as the concept of the electric dipole moment in introductory courses on electromagnetism. Considering a localized steady current distribution, we make a Taylor expansion directly in the Biot–Savart law to obtain, explicitly, the dominant contribution of the magnetic field at distant points, identifying the magnetic dipole moment of the distribution. We also present a simple but general demonstration of the torque exerted by a uniform magnetic field on a current loop of general form, not necessarily planar. For pedagogical reasons we start by reviewing briefly the concept of the electric dipole moment. 1. Introduction The general concepts of electric and magnetic dipole moments are commonly found in our daily life. For instance, it is not rare to refer to polar molecules as those possessing a permanent electric dipole moment. Concerning magnetic dipole moments, it is difficult to find someone who has never heard about magnetic resonance imaging (or has never had such an examination). -
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions. -
Gauss' Theorem (See History for Rea- Son)
Gauss’ Law Contents 1 Gauss’s law 1 1.1 Qualitative description ......................................... 1 1.2 Equation involving E field ....................................... 1 1.2.1 Integral form ......................................... 1 1.2.2 Differential form ....................................... 2 1.2.3 Equivalence of integral and differential forms ........................ 2 1.3 Equation involving D field ....................................... 2 1.3.1 Free, bound, and total charge ................................. 2 1.3.2 Integral form ......................................... 2 1.3.3 Differential form ....................................... 2 1.4 Equivalence of total and free charge statements ............................ 2 1.5 Equation for linear materials ...................................... 2 1.6 Relation to Coulomb’s law ....................................... 3 1.6.1 Deriving Gauss’s law from Coulomb’s law .......................... 3 1.6.2 Deriving Coulomb’s law from Gauss’s law .......................... 3 1.7 See also ................................................ 3 1.8 Notes ................................................. 3 1.9 References ............................................... 3 1.10 External links ............................................. 3 2 Electric flux 4 2.1 See also ................................................ 4 2.2 References ............................................... 4 2.3 External links ............................................. 4 3 Ampère’s circuital law 5 3.1 Ampère’s original -
Temporal Analysis of Radiating Current Densities
Temporal analysis of radiating current densities Wei Guoa aP. O. Box 470011, Charlotte, North Carolina 28247, USA ARTICLE HISTORY Compiled August 10, 2021 ABSTRACT From electromagnetic wave equations, it is first found that, mathematically, any current density that emits an electromagnetic wave into the far-field region has to be differentiable in time infinitely, and that while the odd-order time derivatives of the current density are built in the emitted electric field, the even-order deriva- tives are built in the emitted magnetic field. With the help of Faraday’s law and Amp`ere’s law, light propagation is then explained as a process involving alternate creation of electric and magnetic fields. From this explanation, the preceding math- ematical result is demonstrated to be physically sound. It is also explained why the conventional retarded solutions to the wave equations fail to describe the emitted fields. KEYWORDS Light emission; electromagnetic wave equations; current density In electrodynamics [1–3], a time-dependent current density ~j(~r, t) and a time- dependent charge density ρ(~r, t), all evaluated at position ~r and time t, are known to be the sources of an emitted electric field E~ and an emitted magnetic field B~ : 1 ∂2 4π ∂ ∇2E~ − E~ = ~j + 4π∇ρ, (1) c2 ∂t2 c2 ∂t and 1 ∂2 4π ∇2B~ − B~ = − ∇× ~j, (2) c2 ∂t2 c2 where c is the speed of these emitted fields in vacuum. See Refs. [3,4] for derivation of these equations. (In some theories [5], on the other hand, ρ and ~j are argued to arXiv:2108.04069v1 [physics.class-ph] 6 Aug 2021 be responsible for instantaneous action-at-a-distance fields, not for fields propagating with speed c.) Note that when the fields are observed in the far-field region, the contribution to E~ from ρ can be practically ignored [6], meaning that, in that region, Eq. -
Oct. 30, 1923. 1,472,583 W
Oct. 30, 1923. 1,472,583 W. G. CADY . METHOD OF MAINTAINING ELECTRIC CURRENTS OF CONSTANT FREQUENCY Filed May 28. 1921 Patented Oct. 30, 1923. 1,472,583 UNITED STATES PATENT OFFICE, WALTER GUYTON CADY, OF MIDDLETowN, connECTICUT. METHOD OF MAINTAINING ELECTRIC CURRENTS OF CONSTANT FREQUENCY, To all whom it may concern:Application filed May 28, 1921. Serial No. 473,434. REISSUED Be it known that I, WALTER G. CADY, a tric resonator that I take advantage of for citizen of the United States of America, my present purpose are-first: that prop residing at Middletown, in the county of erty by virtue of which such a resonator, 5 Middlesex, State of Connecticut, have in whose vibrations are maintained by im vented certain new and useful Improve pulses; received from one electric circuit, ments in Method of Maintaining Electric may be used to transmit energy in the form B) Currents of Constant Frequency, of which of an alternating current into another cir the following is a full, clear, and exact de cuit; second, that property which it posses 0 scription. ses of modifying by its reactions the alter The invention which forms the subject nating current of a particular frequency or of my present application for Letters Patent frequencies flowing to it; and third, the fact that the effective capacity of the resonator andis an maintainingimprovement alternatingin the art ofcurrents producing of depends, in a manner which will more fully 5 constant frequency. It is well known that hereinafter appear, upon the frequency of heretofore the development of such currents the current in the circuit with which it may to any very high degree of precision has be connected. -
Alternating Current Principles
Basic Electrical Theory Power Principles and Phase Angle PJM State & Member Training Dept. PJM©2014 10/24/2013 Objectives • At the end of this presentation the learner will be able to; • Identify the characteristics of Sine Waves • Discuss the principles of AC Voltage, Current, and Phase Relations • Compute the Energy and Power on AC Systems • Identify Three-Phase Power and its configurations PJM©2014 10/24/2013 Sine Waves PJM©2014 10/24/2013 Sine Waves • Generator operation is based on the principles of electromagnetic induction which states: When a conductor moves, cuts, or passes through a magnetic field, or vice versa, a voltage is induced in the conductor • When a generator shaft rotates, a conductor loop is forced through a magnetic field inducing a voltage PJM©2014 10/24/2013 Sine Waves • The magnitude of the induced voltage is dependant upon: • Strength of the magnetic field • Position of the conductor loop in reference to the magnetic lines of force • As the conductor rotates through the magnetic field, the shape produced by the changing magnitude of the voltage is a sine wave • http://micro.magnet.fsu.edu/electromag/java/generator/ac.html PJM©2014 10/24/2013 Sine Waves PJM©2014 10/24/2013 Sine Waves RMS PJM©2014 10/24/2013 Sine Waves • A cycle is the part of a sine wave that does not repeat or duplicate itself • A period (T) is the time required to complete one cycle • Frequency (f) is the rate at which cycles are produced • Frequency is measured in hertz (Hz), One hertz equals one cycle per second PJM©2014 10/24/2013 Sine Waves -
Application Note No. 034 Carrier Lifetime and Forward Resistance in RF PIN-Diodes
Application Note, Rev. 2.0, Oct. 2006 Application Note No. 034 Carrier Lifetime and Forward Resistance in RF PIN-Diodes RF & Protection Devices Edition 2006-10-20 Published by Infineon Technologies AG 81726 München, Germany © Infineon Technologies AG 2009. All Rights Reserved. LEGAL DISCLAIMER THE INFORMATION GIVEN IN THIS APPLICATION NOTE IS GIVEN AS A HINT FOR THE IMPLEMENTATION OF THE INFINEON TECHNOLOGIES COMPONENT ONLY AND SHALL NOT BE REGARDED AS ANY DESCRIPTION OR WARRANTY OF A CERTAIN FUNCTIONALITY, CONDITION OR QUALITY OF THE INFINEON TECHNOLOGIES COMPONENT. THE RECIPIENT OF THIS APPLICATION NOTE MUST VERIFY ANY FUNCTION DESCRIBED HEREIN IN THE REAL APPLICATION. INFINEON TECHNOLOGIES HEREBY DISCLAIMS ANY AND ALL WARRANTIES AND LIABILITIES OF ANY KIND (INCLUDING WITHOUT LIMITATION WARRANTIES OF NON-INFRINGEMENT OF INTELLECTUAL PROPERTY RIGHTS OF ANY THIRD PARTY) WITH RESPECT TO ANY AND ALL INFORMATION GIVEN IN THIS APPLICATION NOTE. Information For further information on technology, delivery terms and conditions and prices please contact your nearest Infineon Technologies Office (www.infineon.com). Warnings Due to technical requirements components may contain dangerous substances. For information on the types in question please contact your nearest Infineon Technologies Office. Infineon Technologies Components may only be used in life-support devices or systems with the express written approval of Infineon Technologies, if a failure of such components can reasonably be expected to cause the failure of that life-support device or system, or to affect the safety or effectiveness of that device or system. Life support devices or systems are intended to be implanted in the human body, or to support and/or maintain and sustain and/or protect human life. -
Electric Current and Power
Chapter 10: Electric Current and Power Chapter Learning Objectives: After completing this chapter the student will be able to: Calculate a line integral Calculate the total current flowing through a surface given the current density. Calculate the resistance, current, electric field, and current density in a material knowing the material composition, geometry, and applied voltage. Calculate the power density and total power when given the current density and electric field. You can watch the video associated with this chapter at the following link: Historical Perspective: André-Marie Ampère (1775-1836) was a French physicist and mathematician who did ground-breaking work in electromagnetism. He was equally skilled as an experimentalist and as a theorist. He invented both the solenoid and the telegraph. The SI unit for current, the Ampere (or Amp) is named after him, as well as Ampere’s Law, which is one of the four equations that form the foundation of electromagnetic field theory. Photo credit: https://commons.wikimedia.org/wiki/File:Ampere_Andre_1825.jpg, [Public domain], via Wikimedia Commons. 1 10.1 Mathematical Prelude: Line Integrals As we saw in section 5.1, a surface integral requires that we take the dot product of a vector field with a vector that is perpendicular to a specified surface at every point along the surface, and then to integrate the resulting dot product over the surface. Surface integrals must always be a double integral, since they must involve an integral over a two-dimensional surface. We also have a special symbol for a surface integral over a closed surface, such as a sphere or a cube: (Copies of Equations 5.1 and 5.2) While a surface integral requires a double integral to be taken of a dot product over a surface, a line integral requires a single integral to be taken of a dot product over a linear path. -
Unit I Microwave Transmission Lines
UNIT I MICROWAVE TRANSMISSION LINES INTRODUCTION Microwaves are electromagnetic waves with wavelengths ranging from 1 mm to 1 m, or frequencies between 300 MHz and 300 GHz. Apparatus and techniques may be described qualitatively as "microwave" when the wavelengths of signals are roughly the same as the dimensions of the equipment, so that lumped-element circuit theory is inaccurate. As a consequence, practical microwave technique tends to move away from the discrete resistors, capacitors, and inductors used with lower frequency radio waves. Instead, distributed circuit elements and transmission-line theory are more useful methods for design, analysis. Open-wire and coaxial transmission lines give way to waveguides, and lumped-element tuned circuits are replaced by cavity resonators or resonant lines. Effects of reflection, polarization, scattering, diffraction, and atmospheric absorption usually associated with visible light are of practical significance in the study of microwave propagation. The same equations of electromagnetic theory apply at all frequencies. While the name may suggest a micrometer wavelength, it is better understood as indicating wavelengths very much smaller than those used in radio broadcasting. The boundaries between far infrared light, terahertz radiation, microwaves, and ultra-high-frequency radio waves are fairly arbitrary and are used variously between different fields of study. The term microwave generally refers to "alternating current signals with frequencies between 300 MHz (3×108 Hz) and 300 GHz (3×1011 Hz)."[1] Both IEC standard 60050 and IEEE standard 100 define "microwave" frequencies starting at 1 GHz (30 cm wavelength). Electromagnetic waves longer (lower frequency) than microwaves are called "radio waves". Electromagnetic radiation with shorter wavelengths may be called "millimeter waves", terahertz radiation or even T-rays.