Electrons and Holes in Semiconductors
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Lecture Notes: BCS Theory of Superconductivity
Lecture Notes: BCS theory of superconductivity Prof. Rafael M. Fernandes Here we will discuss a new ground state of the interacting electron gas: the superconducting state. In this macroscopic quantum state, the electrons form coherent bound states called Cooper pairs, which dramatically change the macroscopic properties of the system, giving rise to perfect conductivity and perfect diamagnetism. We will mostly focus on conventional superconductors, where the Cooper pairs originate from a small attractive electron-electron interaction mediated by phonons. However, in the so- called unconventional superconductors - a topic of intense research in current solid state physics - the pairing can originate even from purely repulsive interactions. 1 Phenomenology Superconductivity was discovered by Kamerlingh-Onnes in 1911, when he was studying the transport properties of Hg (mercury) at low temperatures. He found that below the liquifying temperature of helium, at around 4:2 K, the resistivity of Hg would suddenly drop to zero. Although at the time there was not a well established model for the low-temperature behavior of transport in metals, the result was quite surprising, as the expectations were that the resistivity would either go to zero or diverge at T = 0, but not vanish at a finite temperature. In a metal the resistivity at low temperatures has a constant contribution from impurity scattering, a T 2 contribution from electron-electron scattering, and a T 5 contribution from phonon scattering. Thus, the vanishing of the resistivity at low temperatures is a clear indication of a new ground state. Another key property of the superconductor was discovered in 1933 by Meissner. -
Concepts of Condensed Matter Physics Spring 2015 Exercise #1
Concepts of condensed matter physics Spring 2015 Exercise #1 Due date: 21/04/2015 1. Adding long range hopping terms In class we have shown that at low energies (near half-filling) electrons in graphene have a doubly degenerate Dirac spectrum located at two points in the Brillouin zone. An important feature of this dispersion relation is the absence of an energy gap between the upper and lower bands. However, in our analysis we have restricted ourselves to the case of nearest neighbor hopping terms, and it is not clear if the above features survive the addition of more general terms. Write down the Bloch-Hamiltonian when next nearest neighbor and next-next nearest neighbor terms are included (with amplitudes 푡’ and 푡’’ respectively). Draw the spectrum for the case 푡 = 1, 푡′ = 0.4, 푡′′ = 0.2. Show that the Dirac cones survive the addition of higher order terms, and find the corresponding low-energy Hamiltonian. In the next question, you will study under which circumstances the Dirac cones remain stable. 2. The robustness of Dirac fermions in graphene –We know that the lattice structure of graphene has unique symmetries (e.g. 3-fold rotational symmetry of the honeycomb lattice). The question is: What protects the Dirac spectrum? Namely, what inherent symmetry in graphene we need to violate in order to destroy the massless Dirac spectrum of the electrons at low energies (i.e. open a band gap). In this question, consider only nearest neighbor terms. a. Stretching the graphene lattice - one way to reduce the symmetry of graphene is to stretch its lattice in one direction. -
Chips for Discovering the Higgs Boson and Other Particles at CERN: Present and Future
Chips for discovering the Higgs boson and other particles at CERN: present and future W. Snoeys CERN PH-ESE-ME, Geneva, Switzerland [email protected] Abstract – Integrated circuits and devices revolutionized particle physics experiments, and have been essential in the recent discovery of the Higgs boson by the ATLAS and CMS experiments at the Large Hadron Collider at CERN [1,2]. Particles are accelerated and brought into collision at specific interaction points where detectors, giant cameras of about 40 m long by 20 m in diameter, take pictures of the collision products as they fly away from the collision point. These detectors contain millions of channels, often implemented as reverse biased silicon pin diode arrays covering areas of up to 200 m2 in the center of the experiment, generating a small (~1fC) electric charge upon particle traversals. Integrated circuits provide the readout, and accept collision rates of about 40 MHz with on-line selection of potentially interesting events before data storage. Important limitations are power consumption, radiation tolerance, data rates, and system issues like robustness, redundancy, channel-to-channel uniformity, timing distribution and safety. The already predominant role of Figure 1. Aerial view of CERN indicating the location of the 27 silicon devices and integrated circuits in these detectors km LHC ring with the position of the main experimental areas the is only expected to increase in the future. ring. The city of Geneva, its airport, the lake and Mont Blanc are visible © 2015 CERN. Keywords-particle detection; silicon pin diodes; charge sensitive readout II. MAIN CONSTRAINTS AND LIMITATIONS I. -
First Line of Title
GALLIUM NITRIDE AND INDIUM GALLIUM NITRIDE BASED PHOTOANODES IN PHOTOELECTROCHEMICAL CELLS by John D. Clinger A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Science with a major in Electrical and Computer Engineering Winter 2010 Copyright 2010 John D. Clinger All Rights Reserved GALLIUM NITRIDE AND INDIUM GALLIUM NITRIDE BASED PHOTOANODES IN PHOTOELECTROCHEMICAL CELLS by John D. Clinger Approved: __________________________________________________________ Robert L. Opila, Ph.D. Professor in charge of thesis on behalf of the Advisory Committee Approved: __________________________________________________________ James Kolodzey, Ph.D. Professor in charge of thesis on behalf of the Advisory Committee Approved: __________________________________________________________ Kenneth E. Barner, Ph.D. Chair of the Department of Electrical and Computer Engineering Approved: __________________________________________________________ Michael J. Chajes, Ph.D. Dean of the College of Engineering Approved: __________________________________________________________ Debra Hess Norris, M.S. Vice Provost for Graduate and Professional Education ACKNOWLEDGMENTS I would first like to thank my advisors Dr. Robert Opila and Dr. James Kolodzey as well as my former advisor Dr. Christiana Honsberg. Their guidance was invaluable and I learned a great deal professionally and academically while working with them. Meghan Schulz and Inci Ruzybayev taught me how to use the PEC cell setup and gave me excellent ideas on preparing samples and I am very grateful for their help. A special thanks to Dr. C.P. Huang and Dr. Ismat Shah for arrangements that allowed me to use the lab and electrochemical equipment to gather my results. Thanks to Balakrishnam Jampana and Dr. Ian Ferguson at Georgia Tech for growing my samples, my research would not have been possible without their support. -
Chapter1: Semiconductor Diode
Chapter1: Semiconductor Diode. Electronics I Discussion Eng.Abdo Salah Theoretical Background: • The semiconductor diode is formed by doping P-type impurity in one side and N-type of impurity in another side of the semiconductor crystal forming a p-n junction as shown in the following figure. At the junction initially free charge carriers from both side recombine forming negatively c harged ions in P side of junction(an atom in P -side accept electron and be comes negatively c harged ion) and po sitive ly c harged ion on n side (an atom in n-side accepts hole i.e. donates electron and becomes positively charged ion)region. This region deplete of any type of free charge carrier is called as depletion region. Further recombination of free carrier on both side is prevented because of the depletion voltage generated due to charge carriers kept at distance by depletion (acts as a sort of insulation) layer as shown dotted in the above figure. Working principle: When voltage is not app lied acros s the diode , de pletion region for ms as shown in the above figure. When the voltage is applied be tween the two terminals of the diode (anode and cathode) two possibilities arises depending o n polarity of DC supply. [1] Forward-Bias Condition: When the +Ve terminal of the battery is connected to P-type material & -Ve terminal to N-type terminal as shown in the circuit diagram, the diode is said to be forward biased. The application of forward bias voltage will force electrons in N-type and holes in P -type material to recombine with the ions near boundary and to flow crossing junction. -
Phonon Spectroscopy of the Electron-Hole-Liquid W
PHONON SPECTROSCOPY OF THE ELECTRON-HOLE-LIQUID W. Dietsche, S. Kirch, J. Wolfe To cite this version: W. Dietsche, S. Kirch, J. Wolfe. PHONON SPECTROSCOPY OF THE ELECTRON- HOLE-LIQUID. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-447-C6-449. 10.1051/jphyscol:19816129. jpa-00221192 HAL Id: jpa-00221192 https://hal.archives-ouvertes.fr/jpa-00221192 Submitted on 1 Jan 1981 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAI, DE PHYSIQUE CoZZoque C6, suppZe'ment au nOl2, Tome 42, de'cembre 1981 page C6-447 PHONON SPECTROSCOPY OF THE ELECTRON-HOLE-LIQUID W. ~ietschejS.J. Kirch and J.P. Wolfe Physics Department and Materials Research ihboratory, University of IZZinois at Urbana-Champaign, Urbana, IL. 61 801, U. S. A. Abstract.-We have observed the 2kF cut-off in the phonon absorption of electron-hole droplets in Ge and measured the deformation potential. Photoexcited carriers in Ge at low temperatures condense into metallic drop- lets of electron-hole liquid (EHL).' These droplets provide a unique, tailorable system for studying the electron-phonon interaction in a Fermi liquid. The inter- 2 action of phonons with EHL was considered theoretically by Keldysh and has been studied experimentally using heat In contrast, we have employed mono- chromatic phonons5 to examine the frequency dependence of the absorption over the range of 150 - 500 GHz. -
Quantum Mechanics Electromotive Force
Quantum Mechanics_Electromotive force . Electromotive force, also called emf[1] (denoted and measured in volts), is the voltage developed by any source of electrical energy such as a batteryor dynamo.[2] The word "force" in this case is not used to mean mechanical force, measured in newtons, but a potential, or energy per unit of charge, measured involts. In electromagnetic induction, emf can be defined around a closed loop as the electromagnetic workthat would be transferred to a unit of charge if it travels once around that loop.[3] (While the charge travels around the loop, it can simultaneously lose the energy via resistance into thermal energy.) For a time-varying magnetic flux impinging a loop, theElectric potential scalar field is not defined due to circulating electric vector field, but nevertheless an emf does work that can be measured as a virtual electric potential around that loop.[4] In a two-terminal device (such as an electrochemical cell or electromagnetic generator), the emf can be measured as the open-circuit potential difference across the two terminals. The potential difference thus created drives current flow if an external circuit is attached to the source of emf. When current flows, however, the potential difference across the terminals is no longer equal to the emf, but will be smaller because of the voltage drop within the device due to its internal resistance. Devices that can provide emf includeelectrochemical cells, thermoelectric devices, solar cells and photodiodes, electrical generators,transformers, and even Van de Graaff generators.[4][5] In nature, emf is generated whenever magnetic field fluctuations occur through a surface. -
Junction Analysis and Temperature Effects in Semi-Conductor
Junction analysis and temperature effects in semi-conductor heterojunctions by Naresh Tandan A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Electrical Engineering Montana State University © Copyright by Naresh Tandan (1974) Abstract: A new classification for semiconductor heterojunctions has been formulated by considering the different mutual positions of conduction-band and valence-band edges. To the nine different classes of semiconductor heterojunction thus obtained, effects of different work functions, different effective masses of carriers and types of semiconductors are incorporated in the classification. General expressions for the built-in voltages in thermal equilibrium have been obtained considering only nondegenerate semiconductors. Built-in voltage at the heterojunction is analyzed. The approximate distribution of carriers near the boundary plane of an abrupt n-p heterojunction in equilibrium is plotted. In the case of a p-n heterojunction, considering diffusion of impurities from one semiconductor to the other, a practical model is proposed and analyzed. The effect of temperature on built-in voltage leads to the conclusion that built-in voltage in a heterojunction can change its sign, in some cases twice, with the choice of an appropriate doping level. The total change of energy discontinuities (&ΔEc + ΔEv) with increasing temperature has been studied, and it is found that this change depends on an empirical constant and the 0°K Debye temperature of the two semiconductors. The total change of energy discontinuity can increase or decrease with the temperature. Intrinsic semiconductor-heterojunction devices are studied? band gaps of value less than 0.7 eV. -
CHAPTER 8: Diffusion
1 Chapter 8 CHAPTER 8: Diffusion Diffusion and ion implantation are the two key processes to introduce a controlled amount of dopants into semiconductors and to alter the conductivity type. Figure 8.1 compares these two techniques and the resulting dopant profiles. In the diffusion process, the dopant atoms are introduced from the gas phase of by using doped-oxide sources. The doping concentration decreases monotonically from the surface, and the in-depth distribution of the dopant is determined mainly by the temperature and diffusion time. Figure 8.1b reveals the ion implantation process, which will be discussed in Chapter 9. Generally speaking, diffusion and ion implantation complement each other. For instance, diffusion is used to form a deep junction, such as an n-tub in a CMOS device, while ion implantation is utilized to form a shallow junction, like a source / drain junction of a MOSFET. Boron is the most common p-type impurity in silicon, whereas arsenic and phosphorus are used extensively as n-type dopants. These three elements are highly soluble in silicon with solubilities exceeding 5 x 1020 atoms / cm3 in the diffusion temperature range (between 800oC and 1200oC). These dopants can be introduced via several means, including solid sources (BN for B, As2O3 for As, and P2O5 for P), liquid sources (BBr3, AsCl3, and POCl3), and gaseous sources (B2H6, AsH3, and PH3). Usually, the gaseous source is transported to the semiconductor surface by an inert gas (e.g. N2) and is then reduced at the surface. 2 Chapter 8 Figure 8.1: Comparison of (a) diffusion and (b) ion implantation for the selective introduction of dopants into a semiconductor substrate. -
Which Pnictogen Is Best?† Cite This: New J
NJC PAPER Pnictogen bonding with alkoxide cages: which pnictogen is best?† Cite this: New J. Chem., 2019, 43,14305 Henry J. Trubenstein, ‡ Shiva Moaven, ‡ Maythe Vega, Daniel K. Unruh and Anthony F. Cozzolino * Pnictogen bonding is beginning to emerge as a useful supramolecular interaction. The design strategies for these systems are still in the early stages of development and much attention has been focused on the lighter pnictogens. Pnictogen bond donors can have up to three independent sites for binding which can result in triple pnictogen bonding. This has been observed in the self-assembly of antimony alkoxide cages, but not with the lighter congeners. This work reports structural characterization of an analogous arsenic alkoxide cage that engages in a single pnictogen bond and synthetic explorations of Received 14th July 2019, the bismuth congener. DFT calculations are used to evaluate the differences between the structures. Accepted 13th August 2019 Ultimately the partial charge on the pnictogen and the energy of the pnictogen lone pair dictate the DOI: 10.1039/c9nj03648b strength, orientation and number of pnictogen bonds that these cages form. Antimony cages strike the best balance between strength and directionality, allowing them to achieve triple pnictogen bonding rsc.li/njc where the other congeners do not. Introduction or bismuth.15–23 Recently, antimony centred PnBs have been purposefully designed into molecules to actively direct the self- A pnictogen bond (PnB), in analogy to a halogen or chalcogen assembly of reversed bilayer vesicles,24 enable anion binding bond (XB/HaB or ChB), is ‘‘the net attractive interaction between with applications in sensing and transport,25–28 self-assembly an electrophilic region associated with a [pnictogen] atom in a complex architectures through triple pnictogen bonding29 and molecular entity [the PnB donor] and a nucleophilic region in allow for supramolecular catalysis.30 These applications rely on another, or the same, molecular entity [the PnB acceptor].’’1 the predictable formation of PnBs. -
Introduction to Semiconductor
Introduction to semiconductor Semiconductors: A semiconductor material is one whose electrical properties lie in between those of insulators and good conductors. Examples are: germanium and silicon. In terms of energy bands, semiconductors can be defined as those materials which have almost an empty conduction band and almost filled valence band with a very narrow energy gap (of the order of 1 eV) separating the two. Types of Semiconductors: Semiconductor may be classified as under: a. Intrinsic Semiconductors An intrinsic semiconductor is one which is made of the semiconductor material in its extremely pure form. Examples of such semiconductors are: pure germanium and silicon which have forbidden energy gaps of 0.72 eV and 1.1 eV respectively. The energy gap is so small that even at ordinary room temperature; there are many electrons which possess sufficient energy to jump across the small energy gap between the valence and the conduction bands. 1 Alternatively, an intrinsic semiconductor may be defined as one in which the number of conduction electrons is equal to the number of holes. Schematic energy band diagram of an intrinsic semiconductor at room temperature is shown in Fig. below. b. Extrinsic Semiconductors: Those intrinsic semiconductors to which some suitable impurity or doping agent or doping has been added in extremely small amounts (about 1 part in 108) are called extrinsic or impurity semiconductors. Depending on the type of doping material used, extrinsic semiconductors can be sub-divided into two classes: (i) N-type semiconductors and (ii) P-type semiconductors. 2 (i) N-type Extrinsic Semiconductor: This type of semiconductor is obtained when a pentavalent material like antimonty (Sb) is added to pure germanium crystal. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S.