PHY 481/581 Intro Nano- MSE: Applying Simple Quantum Mechanics to Nanoscience Problems, Part I
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Accomplishments in Nanotechnology
U.S. Department of Commerce Carlos M. Gutierrez, Secretaiy Technology Administration Robert Cresanti, Under Secretaiy of Commerce for Technology National Institute ofStandards and Technolog}' William Jeffrey, Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment used are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publication 1052 Natl. Inst. Stand. Technol. Spec. Publ. 1052, 186 pages (August 2006) CODEN: NSPUE2 NIST Special Publication 1052 Accomplishments in Nanoteciinology Compiled and Edited by: Michael T. Postek, Assistant to the Director for Nanotechnology, Manufacturing Engineering Laboratory Joseph Kopanski, Program Office and David Wollman, Electronics and Electrical Engineering Laboratory U. S. Department of Commerce Technology Administration National Institute of Standards and Technology Gaithersburg, MD 20899 August 2006 National Institute of Standards and Teclinology • Technology Administration • U.S. Department of Commerce Acknowledgments Thanks go to the NIST technical staff for providing the information outlined on this report. Each of the investigators is identified with their contribution. Contact information can be obtained by going to: http ://www. nist.gov Acknowledged as well, -
Quantum Well Devices: Applications of the PIAB
Quantum Well Devices: Applications of the PIAB. H2A Real World Friday What is a semiconductor? no e- Conduction Band Empty e levels a few e- Empty e levels lots of e- Empty e levels Filled e levels Filled e levels Filled e levels Insulator Semiconductor Metal Electrons in the conduction band of semiconductors like Si or GaAs can move about freely. Conduction band a few e- Eg = hν Energy Bandgap in Valence band Filled e levels Semiconductors We can get electrons into the conduction band by either thermal excitation or light excitation (photons). Solar cells use semiconductors to convert photons to electrons. A "quantum well" structure made from AlGaAs-GaAs-AlGaAs creates a potential well for conduction electrons. 10-20 nm! A conduction electron that get trapped in a quantum well acts like a PIAB. A conduction electron that get trapped in a quantum well acts like a PIAB. Quantum Wells are used to make Laser Diodes Quantum Well Laser Diodes Quantum Wells are used to make Laser Diodes Quantum Well Laser Diodes Multiple Quantum Wells work even better. Multiple Quantum Well Laser Diodes Multiple Quantum Wells work even better. Multiple Quantum Well LEDs Multiple Quantum Wells work even better. Multiple Quantum Well Laser Diodes Multiple Quantum Wells also are used to make high efficiency Solar Cells. Quantum Well Solar Cells Multiple Quantum Wells also are used to make high efficiency Solar Cells. The most common approach to high efficiency photovoltaic power conversion is to partition the solar spectrum into separate bands and each absorbed by a cell specially tailored for that spectral band. -
Federico Capasso “Physics by Design: Engineering Our Way out of the Thz Gap” Peter H
6 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 1, JANUARY 2013 Terahertz Pioneer: Federico Capasso “Physics by Design: Engineering Our Way Out of the THz Gap” Peter H. Siegel, Fellow, IEEE EDERICO CAPASSO1credits his father, an economist F and business man, for nourishing his early interest in science, and his mother for making sure he stuck it out, despite some tough moments. However, he confesses his real attraction to science came from a well read children’s book—Our Friend the Atom [1], which he received at the age of 7, and recalls fondly to this day. I read it myself, but it did not do me nearly as much good as it seems to have done for Federico! Capasso grew up in Rome, Italy, and appropriately studied Latin and Greek in his pre-university days. He recalls that his father wisely insisted that he and his sister become fluent in English at an early age, noting that this would be a more im- portant opportunity builder in later years. In the 1950s and early 1960s, Capasso remembers that for his family of friends at least, physics was the king of sciences in Italy. There was a strong push into nuclear energy, and Italy had a revered first son in En- rico Fermi. When Capasso enrolled at University of Rome in FREDERICO CAPASSO 1969, it was with the intent of becoming a nuclear physicist. The first two years were extremely difficult. University of exams, lack of grade inflation and rigorous course load, had Rome had very high standards—there were at least three faculty Capasso rethinking his career choice after two years. -
Dephasing in an Electronic Mach-Zehnder Interferometer,” Phys
Dephasing and Quantum Noise in an electronic Mach-Zehnder Interferometer Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr. rer. nat.) der Fakultät für Physik der Universität Regensburg vorgelegt von Andreas Helzel aus Kelheim Dezember 2012 ii Promotionsgesuch eingereicht am: 22.11.2012 Die Arbeit wurde angeleitet von: Prof. Dr. Christoph Strunk Prüfungsausschuss: Prof. Dr. G. Bali (Vorsitzender) Prof. Dr. Ch. Strunk (1. Gutachter) Dr. F. Pierre (2. Gutachter) Prof. Dr. F. Gießibl (weiterer Prüfer) iii In Gedenken an Maria Höpfl. Sie war die erste Taxifahrerin von Kelheim und wurde 100 Jahre alt. Contents 1. Introduction1 2. Basics 5 2.1. The two dimensional electron gas....................5 2.2. The quantum Hall effect - Quantized Landau levels...........8 2.3. Transport in the quantum Hall regime.................. 10 2.3.1. Quantum Hall edge states and Landauer-Büttiker formalism.. 10 2.3.2. Compressible and incompressible strips............. 14 2.3.3. Luttinger liquid in the QH regime at filling factor 2....... 16 2.4. Non-equilibrium fluctuations of a QPC.................. 24 2.5. Aharonov-Bohm Interferometry..................... 28 2.6. The electronic Mach-Zehnder interferometer............... 30 3. Measurement techniques 37 3.1. Cryostat and devices........................... 37 3.2. Measurement approach.......................... 39 4. Sample fabrication and characterization 43 4.1. Fabrication................................ 43 4.1.1. Material.............................. 43 4.1.2. Lithography............................ 44 4.1.3. Gold air bridges.......................... 45 4.1.4. Sample Design.......................... 46 4.2. Characterization.............................. 47 4.2.1. Filling factor........................... 47 4.2.2. Quantum point contacts..................... 49 4.2.3. Gate setting............................ 50 5. Characteristics of a MZI 51 5.1. -
Further Quantum Physics
Further Quantum Physics Concepts in quantum physics and the structure of hydrogen and helium atoms Prof Andrew Steane January 18, 2005 2 Contents 1 Introduction 7 1.1 Quantum physics and atoms . 7 1.1.1 The role of classical and quantum mechanics . 9 1.2 Atomic physics—some preliminaries . .... 9 1.2.1 Textbooks...................................... 10 2 The 1-dimensional projectile: an example for revision 11 2.1 Classicaltreatment................................. ..... 11 2.2 Quantum treatment . 13 2.2.1 Mainfeatures..................................... 13 2.2.2 Precise quantum analysis . 13 3 Hydrogen 17 3.1 Some semi-classical estimates . 17 3.2 2-body system: reduced mass . 18 3.2.1 Reduced mass in quantum 2-body problem . 19 3.3 Solution of Schr¨odinger equation for hydrogen . ..... 20 3.3.1 General features of the radial solution . 21 3.3.2 Precisesolution.................................. 21 3.3.3 Meanradius...................................... 25 3.3.4 How to remember hydrogen . 25 3.3.5 Mainpoints.................................... 25 3.3.6 Appendix on series solution of hydrogen equation, off syllabus . 26 3 4 CONTENTS 4 Hydrogen-like systems and spectra 27 4.1 Hydrogen-like systems . 27 4.2 Spectroscopy ........................................ 29 4.2.1 Main points for use of grating spectrograph . ...... 29 4.2.2 Resolution...................................... 30 4.2.3 Usefulness of both emission and absorption methods . 30 4.3 The spectrum for hydrogen . 31 5 Introduction to fine structure and spin 33 5.1 Experimental observation of fine structure . ..... 33 5.2 TheDiracresult ..................................... 34 5.3 Schr¨odinger method to account for fine structure . 35 5.4 Physical nature of orbital and spin angular momenta . -
Quantum Mechanics C (Physics 130C) Winter 2015 Assignment 2
University of California at San Diego { Department of Physics { Prof. John McGreevy Quantum Mechanics C (Physics 130C) Winter 2015 Assignment 2 Posted January 14, 2015 Due 11am Thursday, January 22, 2015 Please remember to put your name at the top of your homework. Go look at the Physics 130C web site; there might be something new and interesting there. Reading: Preskill's Quantum Information Notes, Chapter 2.1, 2.2. 1. More linear algebra exercises. (a) Show that an operator with matrix representation 1 1 1 P = 2 1 1 is a projector. (b) Show that a projector with no kernel is the identity operator. 2. Complete sets of commuting operators. In the orthonormal basis fjnign=1;2;3, the Hermitian operators A^ and B^ are represented by the matrices A and B: 0a 0 0 1 0 0 ib 01 A = @0 a 0 A ;B = @−ib 0 0A ; 0 0 −a 0 0 b with a; b real. (a) Determine the eigenvalues of B^. Indicate whether its spectrum is degenerate or not. (b) Check that A and B commute. Use this to show that A^ and B^ do so also. (c) Find an orthonormal basis of eigenvectors common to A and B (and thus to A^ and B^) and specify the eigenvalues for each eigenvector. (d) Which of the following six sets form a complete set of commuting operators for this Hilbert space? (Recall that a complete set of commuting operators allow us to specify an orthonormal basis by their eigenvalues.) fA^g; fB^g; fA;^ B^g; fA^2; B^g; fA;^ B^2g; fA^2; B^2g: 1 3.A positive operator is one whose eigenvalues are all positive. -
On the Symmetry of the Quantum-Mechanical Particle in a Cubic Box Arxiv:1310.5136 [Quant-Ph] [9] Hern´Andez-Castillo a O and Lemus R 2013 J
On the symmetry of the quantum-mechanical particle in a cubic box Francisco M. Fern´andez INIFTA (UNLP, CCT La Plata-CONICET), Blvd. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina E-mail: [email protected] arXiv:1310.5136v2 [quant-ph] 25 Dec 2014 Particle in a cubic box 2 Abstract. In this paper we show that the point-group (geometrical) symmetry is insufficient to account for the degeneracy of the energy levels of the particle in a cubic box. The discrepancy is due to hidden (dynamical symmetry). We obtain the operators that commute with the Hamiltonian one and connect eigenfunctions of different symmetries. We also show that the addition of a suitable potential inside the box breaks the dynamical symmetry but preserves the geometrical one.The resulting degeneracy is that predicted by point-group symmetry. 1. Introduction The particle in a one-dimensional box with impenetrable walls is one of the first models discussed in most introductory books on quantum mechanics and quantum chemistry [1, 2]. It is suitable for showing how energy quantization appears as a result of certain boundary conditions. Once we have the eigenvalues and eigenfunctions for this model one can proceed to two-dimensional boxes and discuss the conditions that render the Schr¨odinger equation separable [1]. The particular case of a square box is suitable for discussing the concept of degeneracy [1]. The next step is the discussion of a particle in a three-dimensional box and in particular the cubic box as a representative of a quantum-mechanical model with high symmetry [2]. -
Molecular Energy Levels
MOLECULAR ENERGY LEVELS DR IMRANA ASHRAF OUTLINE q MOLECULE q MOLECULAR ORBITAL THEORY q MOLECULAR TRANSITIONS q INTERACTION OF RADIATION WITH MATTER q TYPES OF MOLECULAR ENERGY LEVELS q MOLECULE q In nature there exist 92 different elements that correspond to stable atoms. q These atoms can form larger entities- called molecules. q The number of atoms in a molecule vary from two - as in N2 - to many thousand as in DNA, protiens etc. q Molecules form when the total energy of the electrons is lower in the molecule than in individual atoms. q The reason comes from the Aufbau principle - to put electrons into the lowest energy configuration in atoms. q The same principle goes for molecules. q MOLECULE q Properties of molecules depend on: § The specific kind of atoms they are composed of. § The spatial structure of the molecules - the way in which the atoms are arranged within the molecule. § The binding energy of atoms or atomic groups in the molecule. TYPES OF MOLECULES q MONOATOMIC MOLECULES § The elements that do not have tendency to form molecules. § Elements which are stable single atom molecules are the noble gases : helium, neon, argon, krypton, xenon and radon. q DIATOMIC MOLECULES § Diatomic molecules are composed of only two atoms - of the same or different elements. § Examples: hydrogen (H2), oxygen (O2), carbon monoxide (CO), nitric oxide (NO) q POLYATOMIC MOLECULES § Polyatomic molecules consist of a stable system comprising three or more atoms. TYPES OF MOLECULES q Empirical, Molecular And Structural Formulas q Empirical formula: Indicates the simplest whole number ratio of all the atoms in a molecule. -
Statistical Mechanics, Lecture Notes Part2
4. Two-level systems 4.1 Introduction Two-level systems, that is systems with essentially only two energy levels are important kind of systems, as at low enough temperatures, only the two lowest energy levels will be involved. Especially important are solids where each atom has two levels with different energies depending on whether the electron of the atom has spin up or down. We consider a set of N distinguishable ”atoms” each with two energy levels. The atoms in a solid are of course identical but we can distinguish them, as they are located in fixed places in the crystal lattice. The energy of these two levels are ε and ε . It is easy to write down the partition function for an atom 0 1 −ε0 / kB T −ε1 / kBT −ε 0 / k BT −ε / kB T Z = e + e = e (1+ e ) = Z0 ⋅ Zterm where ε is the energy difference between the two levels. We have written the partition sum as a product of a zero-point factor and a “thermal” factor. This is handy as in most physical connections we will have the logarithm of the partition sum and we will then get a sum of two terms: one giving the zero- point contribution, the other giving the thermal contribution. At thermal dynamical equilibrium we then have the occupation numbers in the two levels N −ε 0/kBT N n0 = e = Z 1+ e−ε /k BT −ε /k BT N −ε 1 /k BT Ne n1 = e = Z 1 + e−ε /k BT We see that at very low temperatures almost all the particles are in the ground state while at high temperatures there is essentially the same number of particles in the two levels. -
Electronic Supplementary Information: Low Ensemble Disorder in Quantum Well Tube Nanowires
Electronic Supplementary Material (ESI) for Nanoscale. This journal is © The Royal Society of Chemistry 2015 Electronic Supplementary Information: Low Ensemble Disorder in Quantum Well Tube Nanowires Christopher L. Davies,∗a Patrick Parkinson,b Nian Jiang,c Jessica L. Boland,a Sonia Conesa-Boj,a H. Hoe Tan,c Chennupati Jagadish,c Laura M. Herz,a and Michael B. Johnston.a‡ (a) 3.950 nm (b) GaAs-QW 2.026 nm 2.181 nm 4.0 nm 3.962 nm 50 nm 20 nm GaAs-core Fig. S1 TEM image of top of B50 sample Fig. S2 TEM image of bottom of B50 sample S1 TEM Figure S1(a) corresponds to a low magnification bright field TEM image of a representative cross-section of the sample B50. The thickness of the GaAs QW has been measured in different regions. S2 1D Finite Square Well Model The variations in thickness are found to be around 4 nm and 2 For a semiconductor the Fermi-Dirac distribution for electrons in nm in the edges and in the facets, respectively, confirming the the conduction band and holes in the valence band is given by, disorder in the GaAs QW. In the HR-TEM image performed in 1 one of the edges of the nanowire cross section, figure S1(b), the f = ; (1) e,h exp((E − Ec,v) ) + 1 variation in the QW thickness (marked by white dashed lines) f b between the edge and the facets is clearly visible. c,v where b = 1=kBT, T is the electron temperature and Ef is the Figures S2 and S3 are additional TEM images of sample B50 Fermi energies of the electrons and holes. -
Modeling Multiple Quantum Well and Superlattice Solar Cells
Natural Resources, 2013, 4, 235-245 235 http://dx.doi.org/10.4236/nr.2013.43030 Published Online July 2013 (http://www.scirp.org/journal/nr) Modeling Multiple Quantum Well and Superlattice Solar Cells Carlos I. Cabrera1, Julio C. Rimada2, Maykel Courel2,3, Luis Hernandez4,5, James P. Connolly6, Agustín Enciso4, David A. Contreras-Solorio4 1Department of Physics, University of Pinar del Río, Pinar del Río, Cuba; 2Solar Cell Laboratory, Institute of Materials Science and Technology (IMRE), University of Havana, Havana, Cuba; 3Higher School in Physics and Mathematics, National Polytechnic Insti- tute, Mexico City, Mexico; 4Academic Unit of Physics, Autonomous University of Zacatecas, Zacatecas, México; 5Faculty of Phys- ics, University of Havana, La Habana, Cuba; 6Nanophotonics Technology Center, Universidad Politécnica de Valencia, Valencia, Spain. Email: [email protected] Received January 23rd, 2013; revised May 14th, 2013; accepted May 27th, 2013 Copyright © 2013 Carlos I. Cabrera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT The inability of a single-gap solar cell to absorb energies less than the band-gap energy is one of the intrinsic loss mechanisms which limit the conversion efficiency in photovoltaic devices. New approaches to “ultra-high” efficiency solar cells include devices such as multiple quantum wells (QW) and superlattices (SL) systems in the intrinsic region of a p-i-n cell of wider band-gap energy (barrier or host) semiconductor. These configurations are intended to extend the absorption band beyond the single gap host cell semiconductor. -
About Supersymmetric Hydrogen
About Supersymmetric Hydrogen Robin Schneider 12 supervised by Prof. Yuji Tachikawa2 Prof. Guido Festuccia1 August 31, 2017 1Theoretical Physics - Uppsala University 2Kavli IPMU - The University of Tokyo 1 Abstract The energy levels of atomic hydrogen obey an n2 degeneracy at O(α2). It is a consequence of an so(4) symmetry, which is broken by relativistic effects such as the fine or hyperfine structure, which have an explicit angular momentum and spin dependence at higher order in α. The energy spectra of hydrogenlike bound states with underlying supersym- metry show some interesting properties. For example, in a theory with N = 1, the hyperfine splitting disappears and the spectrum is described by supermul- tiplets with energies solely determined by the super spin j and main quantum number n [1, 2]. Adding more supercharges appears to simplify the spectrum even more. For a given excitation Vl, the spectrum is then described by a single multiplet for which the energy depends only on the angular momentum l and n. In 2015 Caron-Huot and Henn showed that hydrogenlike bound states in N = 4 super Yang Mills theory preserve the n2 degeneracy of hydrogen for relativistic corrections up to O(α3) [3]. Their investigations are based on the dual super conformal symmetry of N = 4 super Yang Mills. It is expected that this result also holds for higher orders in α. The goal of this thesis is to classify the different energy spectra of super- symmetric hydrogen, and then reproduce the results found in [3] by means of conventional quantum field theory. Unfortunately, it turns out that the tech- niques used for hydrogen in (S)QED are not suitable to determine the energy corrections in a model where the photon has a massless scalar superpartner.