SEMICONDUCTOR I: Doping, semiconductor statistics (REF: Sze, McKelvey, and Kittel)


 Sabrina McGee
 1 years ago
 Views:
Transcription
1 SEMICONDUCTOR I: Doping, semiconductor statistics (REF: Sze, McKelvey, and Kittel) Introduction Based on known band structures of Si, Ge, and GaAs, we will begin to focus on specific properties of semiconductors, including the doping problem, electron and hole population calculation, and other problems related to statistics. These are necessary tools for understanding semiconductor devices. I expect you to get familiar with the equations in the first chapter of Sze s bible (Physics of semiconductor devices, nd Ed.): knowing how to derive each equation and their physical meanings. Following this section, we will begin to explore the semiconductor transport properties, optical properties, and magnetic properties. A Bohr atom in vacuum and an impurity atom in semiconductors For a typical hydrogen atom, an electron with charge (e) and mass (m o ) is moving in free space in the presence of an attractive potential e /r at the nuclear, with r the spacing between the proton and the electron. The Bohr radius a o = h /(me ). Putting a positive ion in Si will give a very similar situation, except that now the electric field is screened to be e /(ǫr), and the electron will sense that it is in silicon and thus has an effective mass m. Here, ǫ is the dielectric constant of the host material. As a result, the radius of the ground state of the ionized impurityelectron atom will be a o ǫ/m, that is, the size is scaled by ǫ/m. The ground state binding energy (the energy it takes to ionize the impurity) also becomes 3.6eV m /ǫ. (E ionization of a hydrogen atom is m o e 4 /3π ǫ h = 3.6 ev in vacuum.) For common values of ǫ (Si:.9, Ge: 6, and GaAs: 3.) and m (in unit of m o, Si: 0.98 and 0.6, Ge: 0.04 and.64, and GaAs: 0.067), the radius of the impurity atom (when the electron is still bound to the ion) will be around 00 Å. The ionization energy is also scaled to be 3.6eV 0./0, about 00 times smaller. This is a consistent story: the size of the impurity atom must be several times larger than the lattice constant to make the screening argument justified. Let s use an example: As in Si. Initially, an electron is bound to As +, and the As atom is neutral. The ionization energy is found to be 54 mev. (Page of Sze lists many ionization energies for commonly observed elements in Si, Ge, and GaAs.) That is to say, if the electron can get 54 mev, it is able to travel free in Si and become, in the band structure language, an electron in the conduction band. When the electron is set free, the As will carry one positive charge, and there is a possibility for this ion to capture an electron and become neutral again. Since, in this example, 54 mev is the ionization energy, we therefore plot the donor energy at 54 mev below the conduction band minimum on the band structure. The position of the impurity states is only to follow the convention of Fermi statistics: the states below ǫ F is filled, and, if above, empty. By the same token, we define acceptor levels. Usually, column V (III) elements in column IV materials will become donors (acceptors). However, column IV elements in GaAs (a IIIV compound) is amphoteric. For example, Si in GaAs can be:
2 . a donor: Si Si + Ga + one electron. an acceptor : Si Si As + one hole 3. a neutral impurity: interstitial, or through compensation. Doping is of great importance to semiconductors. The impurity level is usually close to the band edges, thus by controlling the impurity concentration carrier concentration and therefore conductivity of a semiconductor sample can be tuned. This property turns out to be useful in making transistors. Bandgap change as a function of temperature Experimentally observed temperaturedependence of bandgap can be expressed as: E g (T) = E g (T = 0) [αt /(T + β)]. For Si, Ge, and GaAs, bandgap increases at low temperature. (Ref: Sze, page 5.) Carrier concentration at thermal equilibrium: INTRINSIC semiconductor (n = p = n i ) For an intrinsic semiconductor at zero temperature, all valence bands are filled and all conduction bands are empty. Free electron concentration and free hole concentration are both zero. (What is the total electron concentration?) By definition, at the conduction band, n = Ec ded(e)f(e), () where n is free electron concentration in the conduction band, Ec is the energy at conduction band minimum, D(E) is density of states, and f(e) is FermiDirac distribution function. Taken into account the anisotropic Fermi surface (ellipsoid for Si and Ge), D(E) = Mc π (E Ec) / h 3 (m m m 3 )/, () where Mc is the valley degeneracy (6 for Si, 8 for Ge, and for GaAs). Sometimes we define the density of states effective mass m de by (m m m 3 )/3. Spin degeneracy () is included in the above D(E). The effective masses (m m m 3 )/3 are along the principle axes of the ellipsoidal constant energy surface. For example, in Si, we can define m to be the longitudinal effective mass and m and m 3 to be the transverse effective mass. The FermiDirac distribution function (Ref: Kittel and many other statistical mechanics textbooks) is defined as: f(e) = + exp( E Ef kt ), (3)
3 where k is Boltzmann s constant, T the temperature, and E f the Fermi energy. (Whenever a temperature is given or FermiDirac statistics is used, it implies that the electrons are in equilibrium among themselves. If electrons and the lattice are also in equilibrium, then the lattice temperature should be the same as the electron temperature.) Homework: Derive the form of D(E) and f(e). For a simple example, volume = 4 3 πk3, energy= h k /m, i.e., k = (m E/ h ) /. Since = π dk, D(E) is then (from spin degeneracy) [ (4πk 3 /3)/ E] = 4π m 3/ E / /(π h 3 ). Finally, multiply the above result by valley degeneracy. For an ellipsoid (anisotropic effective mass), E f = h (k xf m x + k yf m y + k zf m z ). Or, = kxf (a + m x ) kyf (a + k zf m y ) (a, where a = E m z ) f / h. That is, a change in k x, k y, and k z are linked, and the dk relation is: mx = dky x m = dkz y m. Now, the Fermi ellipsoid has a volume of 4 z 3 π(k xf +kyf +kzf). When energy is increased a little bit, the change in k will be scaled by the m. So, when energy is increased, the small volume increase is 4π 3 (k xfk yf dk z + k yf k zf dk x + k zf k xf dk y ) = 4π[k m 3 yfk x zf m dk x + k xf k m m z y yf m dk x + k zf k xf x x m dk x ] = 4π x 3 d( Ef h ) [ E f h m x m y m z 3 ] = the expression in equation (). Now, putting D(E) and f(e) together, and define several new terms: dk x m x [ E f h m x m y m z 3] = 4π 3 3 n = N c π F / (E f Ec) kt, (4) where N c is the effective density of states in the conduction band and is defined as N c = ( πm dekt h ) 3/ Mc, (5) and F / is called FermiDirac integral, defined by F / (η f ) = 0 η / dη + e (η eta f ). (6) For a plot of calculated FermiDirac integral, see page 8 of Sze. Homework: Use computer to calculate this integral and plot or table the results like what shown in Fig. 0 of Sze. Numerical calculation of this FermiDirac integral is often simplified by using fitted equations. (Ref: Selberherr: Analysis and simulation of semiconductor devices, page 57.) Two asymptotic behaviors of F / are of interest to our discussion:. F / (x) π ex, for x ; 3
4 . F / (x) 3 x3/, for x. So, for nondegerate semiconductors, where in practice either the temperature is high, or the doping level is low, as an end result the Fermi level is more than several kt below the conduction band minimum, we can simplified the calculation of n (from the asymptotic value of FermiDirac integral) and get: n = N c e (Ec E f ) kt. (7) Degenerate electron gas just means that the Fermi level is close enough (about several kt) to the conduction band minimum or valence band top, therefore, we have to use the full definition in equation (?) to calculate the electron or hole concentrations. Notice that given the relatively large bandgap of Si, Ge, and GaAs, if the sample is degenerate for electrons, it will be nondegenerate for holes, and vice versa. Homework: Calculate N c for Si, and compare your result with what listed in Sze (page 850, appendix H). Similar equations holds for holes (in Si, Ge, and GaAs):. p = N v π F / (Ev E f ) kt,. N v = ( πm dhkt h ) 3/, (Mv = ), 3. m dh = (m 3/ lh + m 3/ hh ) /3, 4. p = N v e (E f Ev) kt (if nondegenerate). (lh: light hole, hh: heavy hole) For Si, N c = /cm 3 N v = /cm 3, and N i = /cm 3. For GaAs, N c = /cm 3 N v = /cm 3, and N i = /cm 3. The definition of intrinsic semiconductor is that n = p = n i. This result is coming from that all electrons in the conduction band must be excited from valence band. Therefore, there is equal number of electrons and holes in the semiconductor, and we just further define their concentration to be n i. (By the way, intrinsic semiconductors are, by definition, nondegenerate.) The Fermi level of an intrinsic semiconductor is called E i. We here list some basic relations for intrinsic semiconductors:. n = N c e (Ec E f ) kt ;. p = N v e (E f Ev) kt ; 4
5 3. n = p = n i np = n i n i = N c N v e Eg/kT ; 4. n = p E i = E f intrinsic = (Ec+Ev) + kt ln(nv N c ) = (Ec+Ev) + 3kT 4 ln(m dh m de ). Homework: Calculate n i as a function of temperature for Si, Ge, and GaAs, and plot the results like what shown in Fig. of Sze. Homework: For intrinsic Si, at what temperature would n = 0 7 /cm 3? Homework: Does E i have temperature dependence? If so, where is it from? (What is the physics involved?) DOPED SEMICONDUCTOR: calculation of n, p, and E f for all cases (to be more specific, both degenerate and nondegenerate) (Ref: Page 70 of McKelvey) Charge neutrality We will derive relations for a very generalized case, where in a semiconductor there are free electrons, free holes, ionized donors, unionized donors, ionized acceptors, and unionized acceptors. At thermal equilibrium, the net charge density should be zero, and the Fermi level is flat everywhere. The charge neutrality rule is based on the physical consideration that air molecules can neutralize the sample. And, the Fermi level must be flat in the sample, otherwise there is current flowing which indicates a nonequilibrium state. So, we have contributions from various terms, and each one deserves a detailed look. n + n d + N a = p + p a + N d, (8) where the definition of the terms are listed below:. n is free electron concentration in the conduction band, n = up E c ded e (E)f(E); 5
6 . n d is (bound) electron concentration at the donor cites, n d =, g= (due to spin, please refer to page 70 in J. McKelvey for a derivation); N d + g ee d E f /kt 3. N a is the concentration of acceptors, a known value when the sample is prepred; 4. p is free hole concentration in the valence band, p = down E v ded h (E)f(E); 5. p a is (bound) hole concentration at the acceptor cites; p a = N a N a = N a + g e(e f Ea)/kT, g=4 (due to spin and the additional hh/lh degeneracy). 6. N d is the concentration of donors, a known value when the sample is prepred. Also, N a is the concentration of (access) electrons at acceptors. So, N a = N a For the same reason, the concentration of ionized donors will be N + d + e(e d E f )/kt ). +4e (Ea E f )/kt. = N d n d = N d ( Using the graphic solution shown in page 4 of Sze, we can then calculate n(t), p(t), and E f (T). (Ref: page 4 of Sze) We are also interested to get analytical equations. In the following, we will discuss several useful limits. 6
Semiconductor Physics
10p PhD Course Semiconductor Physics 18 Lectures NovDec 2011 and Jan Feb 2012 Literature Semiconductor Physics K. Seeger The Physics of Semiconductors Grundmann Basic Semiconductors Physics  Hamaguchi
More informationModule 6 : PHYSICS OF SEMICONDUCTOR DEVICES Lecture 34 : Intrinsic Semiconductors
Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES Lecture 34 : Intrinsic Semiconductors Objectives In this course you will learn the following Intrinsic and extrinsic semiconductors. Fermi level in a semiconductor.
More informationDoped Semiconductors. Dr. Katarzyna Skorupska
Doped Semiconductors Dr. Katarzyna Skorupska 1 Doped semiconductors Increasing the conductivity of semiconductors by incorporation of foreign atoms requires increase of the concentration of mobile charge
More informationFirst Time User Guide to Carrier Statistics Lab on nanohub.org Ver. 2
Network for Computational Nanotechnology (NCN) UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP First Time User Guide to Carrier Statistics Lab on nanohub.org Ver. 2,Saumitra Raj
More informationIntrinsic and Extrinsic Semiconductors, FermiDirac Distribution Function, the Fermi level and carrier concentrations
ENEE 33, Spr. 09 Supplement I Intrinsic and Extrinsic Semiconductors, FermiDirac Distribution Function, the Fermi level and carrier concentrations Zeynep Dilli, Oct. 2008, rev. Mar 2009 This is a supplement
More informationApplied Quantum Mechanics for Electrical Engineers Workshop II Energy Band Model and Doping
Applied Quantum Mechanics for Electrical Engineers Workshop II Energy Band Model and Doping 95 pts Objective: Explore the effect of doping on the energy band diagram and the carrier concentration. Instructions:
More informationThis is the 11th lecture of this course and the last lecture on the topic of Equilibrium Carrier Concentration.
Solid State Devices Dr. S. Karmalkar Department of Electronics and Communication Engineering Indian Institute of Technology, Madras Lecture  11 Equilibrium Carrier Concentration (Contd.) This is the 11th
More informationLecture 3: Electron statistics in a solid
Lecture 3: Electron statistics in a solid Contents Density of states. DOS in a 3D uniform solid.................... 3.2 DOS for a 2D solid........................ 4.3 DOS for a D solid........................
More informationFYS3410  Vår 2015 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v15/index.html
FYS3410  Vår 015 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v15/index.html Pensum: Introduction to Solid State Physics by Charles Kittel (Chapters 19 and 17, 18, 0,
More informationSolid State Detectors = SemiConductor based Detectors
Solid State Detectors = SemiConductor based Detectors Materials and their properties Energy bands and electronic structure Charge transport and conductivity Boundaries: the pn junction Charge collection
More informationChapter 5. Second Edition ( 2001 McGrawHill) 5.6 Doped GaAs. Solution
Chapter 5 5.6 Doped GaAs Consider the GaAs crystal at 300 K. a. Calculate the intrinsic conductivity and resistivity. Second Edition ( 2001 McGrawHill) b. In a sample containing only 10 15 cm 3 ionized
More informationLecture 8: Extrinsic semiconductors  mobility
Lecture 8: Extrinsic semiconductors  mobility Contents Carrier mobility. Lattice scattering......................... 2.2 Impurity scattering........................ 3.3 Conductivity in extrinsic semiconductors............
More informationMCEN Fall 2003.
Basic types of solid materials. Overview The theory of bands provides a basis for understanding the classification and physical properties of solid materials such as electrical conductivity, optical behavior
More information1.5 Light absorption by solids
1.5 Light absorption by solids BlochBrilloin model L e + + + + + allowed energy bands band gaps p x In a unidimensional approximation, electrons in a solid experience a periodic potential due to the positively
More informationLecture 2 Semiconductor Physics (I)
Lecture 2 Semiconductor Physics (I) Outline Intrinsic bond model : electrons and holes Generation and recombination Intrinsic semiconductor Doping: Extrinsic semiconductor Charge Neutrality Reading Assignment:
More informationLecture 2  Semiconductor Physics (I) September 13, 2005
6.012  Microelectronic Devices and Circuits  Fall 2005 Lecture 21 Lecture 2  Semiconductor Physics (I) September 13, 2005 Contents: 1. Silicon bond model: electrons and holes 2. Generation and recombination
More informationSemiconductor Detectors Calorimetry and Tracking with High Precision
Semiconductor Detectors Calorimetry and Tracking with High Precision Applications 1. Photon spectroscopy with high energy resolution. Vertex detection with high spatial resolution 3. Energy measurement
More informationAnalog & Digital Electronics Course No: PH218
Analog & Digital Electronics Course No: PH218 Lecture 1: Semiconductor Materials Course Instructors: Dr. A. P. VAJPEYI Department of Physics, Indian Institute of Technology Guwahati, India 1 Semiconductors
More informationSemiconductors Band Formation & direct and indirect gaps. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India
Semiconductors Band Formation & direct and indirect gaps 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 Review of Energy Bands (1)
More informationPhysics 551: Solid State Physics F. J. Himpsel
Physics 551: Solid State Physics F. J. Himpsel Background Most of the objects around us are in the solid state. Today s technology relies heavily on new materials, electronics is predominantly solid state.
More informationLecture Light Emitting Diodes.
Lecture 1920 Light Emitting Diodes. Today: 1. Carrier recombination in semiconductors. 2. pn junctions with carrier injection. Lightemitting diodes (LEDs). Questions you should be able to answer by
More informationINSTITUTE FOR APPLIED PHYSICS Physical Practice for Learners of Engineering sciences Hamburg University, Jungiusstraße 11
INSTITUTE FOR APPIED PHYSICS Physical Practice for earners of Engineering sciences Hamburg University, Jungiusstraße 11 Hall effect 1 Goal Characteristic data of a test semiconductor (Germanium) should
More informationFall 2004 Ali Shakouri
University of California at Santa Cruz Jack Baskin School of Engineering Electrical Engineering Department EE145L: Properties of Materials Laboratory Lab 5b: Temperature Dependence of Semiconductor Conductivity
More information thus the electrons are free to change their energies within the 3s band
Allowed and Forbidden Energy Bands  allowed energy bands associated with different atomic orbitals may overlap, as in (a)  the regions between allowed energy bands are called forbidden bands or band
More informationUniversity of Toronto Department of Electrical and Computer Engineering. ECE 330F SEMICONDUCTOR PHYSICS Eng. Annex 305
University of Toronto Department of Electrical and Computer Engineering ECE 330F SEMICONDUCTOR PHYSICS Eng. Annex 305 Experiment # 1 RESISTIVITY AND BAND GAP OF GERMANIUM TA: Iraklis Nikolalakos OBJECTIVE
More informationSemiconductors, diodes, transistors
Semiconductors, diodes, transistors (Horst Wahl, QuarkNet presentation, June 2001) Electrical conductivity! Energy bands in solids! Band structure and conductivity Semiconductors! Intrinsic semiconductors!
More informationLecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm First H/W#1 is due Sept. 10 Course Info The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model)
More informationLecture 2: Semiconductors: Introduction
Lecture 2: Semiconductors: Introduction Contents 1 Introduction 1 2 Band formation in semiconductors 2 3 Classification of semiconductors 5 4 Electron effective mass 10 1 Introduction Metals have electrical
More informationThe Physics of Energy sources Renewable sources of energy. Solar Energy
The Physics of Energy sources Renewable sources of energy Solar Energy B. Maffei Bruno.maffei@manchester.ac.uk Renewable sources 1 Solar power! There are basically two ways of using directly the radiative
More informationDO PHYSICS ONLINE. conduction band. ~ 6 ev. Fig. 1. Energy band diagram for diamond (insulator) and silicon (semiconductor).
DO PHYSIS ONLINE FROM IDEAS TO IMPLEMENTATION 9.4.3 ATOMS TO TRANSISTORS SEMIONDUTORS ENERGY BANDS Diamond is a very good insulator. The electronic configuration in the ground state is 1s 2 2s 2 2. It
More informationRules for this test. Physics 222, Winter 2012 Final Exam April 16, 2012 Instructor: Scott Bergeson
Physics 222, Winter 2012 Final Exam April 16, 2012 Instructor: Scott Bergeson Rules for this test 1. This test is open book and open notes, including our class notes page online, and your homework solutions.
More informationCHAPTER  45 SEMICONDUCTOR AND SEMICONDUCTOR DEVICES
1. f = 101 kg/m, V = 1 m CHAPTER  45 SEMCONDUCTOR AND SEMCONDUCTOR DEVCES m = fv = 101 1 = 101 kg No.of atoms = 101 10 6 10 = 64.6 10 6. a) Total no.of states = N = 64.6 10 6 = 58.5 = 5. 10 8 10 6 b)
More informationCHAPTER 1: Semiconductor Materials & Physics
Chapter 1 1 CHAPTER 1: Semiconductor Materials & Physics In this chapter, the basic properties of semiconductors and microelectronic devices are discussed. 1.1 Semiconductor Materials Solidstate materials
More informationElectrons and Holes in Semiconductors
Hu_ch01v4.fm Page 1 Thursday, February 12, 2009 10:14 AM 1 Electrons and Holes in Semiconductors CHAPTER OBJECTIVES This chapter provides the basic concepts and terminology for understanding semiconductors.
More informationFree Electron Fermi Gas (Kittel Ch. 6)
Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals  they are the glue that hold the nuclei together Types of binding (see next slide)
More information1. Degenerate Pressure
. Degenerate Pressure We next consider a Fermion gas in quite a different context: the interior of a white dwarf star. Like other stars, white dwarfs have fully ionized plasma interiors. The positively
More informationBasic laws and electrical properties of metals (I) Electrical properties. Basic laws and electrical properties of metals (II)
Electrical properties Electrical conduction How many moveable electrons are there in a material (carrier density)? How easily do they move (mobility)? Semiconductivity Electrons and holes Intrinsic and
More informationSolidState Physics: The Theory of Semiconductors (Ch. 10.610.8) SteveSekula, 30 March 2010 (created 29 March 2010)
Modern Physics (PHY 3305) Lecture Notes Modern Physics (PHY 3305) Lecture Notes SolidState Physics: The Theory of Semiconductors (Ch. 10.610.8) SteveSekula, 30 March 2010 (created 29 March 2010) Review
More informationLecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e  n( ) n' n '' n ' = 1 + Nucleus
More informationSMA5111  Compound Semiconductors Lecture 2  MetalSemiconductor Junctions  Outline Introduction
SMA5111  Compound Semiconductors Lecture 2  MetalSemiconductor Junctions  Outline Introduction Structure  What are we talking about? Behaviors: Ohmic, rectifying, neither Band picture in thermal equilibrium
More informationFUNDAMENTAL PROPERTIES OF SOLAR CELLS
FUNDAMENTAL PROPERTIES OF SOLAR CELLS January 31, 2012 The University of Toledo, Department of Physics and Astronomy SSARE, PVIC Principles and Varieties of Solar Energy (PHYS 4400) and Fundamentals of
More informationSemiconductors, Insulators and Metals
CHAPTER 2 ENERGY BANDS AND EFFECTIVE MASS Semiconductors, insulators and metals Semiconductors Insulators Metals The concept of effective mass Prof. Dr. Beşire GÖNÜL Semiconductors, Insulators and Metals
More informationProcessing of Semiconducting Materials Prof. Pallab Banerji Department of Metallurgy and Material Science Indian Institute of Technology, Kharagpur
Processing of Semiconducting Materials Prof. Pallab Banerji Department of Metallurgy and Material Science Indian Institute of Technology, Kharagpur Lecture  8 Diffusion and Ion Implantation II (Refer
More informationFigure 1: (a) Diode cross section. (b) Reverse biased diode. (c) Forward biased diode.
The Junction Diode Basic Operation The diode is fabricated of a semiconductor material, usually silicon, which is doped with two impurities. One side is doped with a donor or ntype impurity which releases
More informationCrystalline solids. A solid crystal consists of different atoms arranged in a periodic structure.
Crystalline solids A solid crystal consists of different atoms arranged in a periodic structure. Crystals can be formed via various bonding mechanisms: Ionic bonding Covalent bonding Metallic bonding Van
More informationSilicon Basics  General Overview. File: ee4494 silicon basics.ppt revised 09/11/2001 copyright james t yardley 2001 Page 1
Silicon Basics  General Overview. File: ee4494 silicon basics.ppt revised 09/11/2001 copyright james t yardley 2001 Page 1 Semiconductor Electronics: Review. File: ee4494 silicon basics.ppt revised 09/11/2001
More informationSpring 2008 Chemistry 2000 Midterm #1A / 50 marks
Spring 2008 hemistry 2000 Midterm #1A / 50 marks INSTRUTINS 1) Please read over the test carefully before beginning. You should have 5 pages of questions and a periodic table. 2) If you need extra space,
More informationElectrical Conductivity
Advanced Materials Science  Lab Intermediate Physics University of Ulm Solid State Physics Department Electrical Conductivity Translated by MichaelStefan Rill January 20, 2003 CONTENTS 1 Contents 1 Introduction
More informationELECTRONIC DEVICES MENJANA MINDA KREATIF DAN INOVATIF
INTRODUCTION TO ELECTRONIC DEVICES MENJANA MINDA KREATIF DAN INOVATIF Introduction What is Electronics? Electronic Devices? Electronic Systems? introduction Electronics: The branch of physics that deals
More informationA Program for Calculating Mobility and Carrier Density in Bulk Semiconductors
A Program for Calculating Mobility and Carrier Density in Bulk Semiconductors Dan Barrett, Electrical Engineering, University of Notre Dame Contents 1 Introduction A  1 2 Theory A  2 3 The Program A
More informationNORGES TEKNISK NATURVITENSKAPELIGE UNIVERSITET INSTITUTT FOR FYSIKK. Eksamen i Emne TFY4220 Faste Stoffers Fysikk
Page of 5 NORGES TEKNISK NATURVITENSKAPELIGE UNIVERSITET INSTITUTT FOR FYSIKK Fagleg kontakt under eksamen: Institutt for fysikk, Gløshaugen Professor Steinar Raaen, 4896758 Eksamen i Emne TFY40 Faste
More informationSemiconductor lasers and LEDs read Agrawal pp
Semiconductor lasers and LEDs read Agrawal pp. 78116 Objectives, understand the following: Stimulated emission, spontaneous emission, and absorption in semiconductors Design of an LED and laser diode:
More information3. Diodes and Diode Circuits. 3. Diodes and Diode Circuits TLT8016 Basic Analog Circuits 2005/2006 1
3. Diodes and Diode Circuits 3. Diodes and Diode Circuits TLT8016 Basic Analog Circuits 2005/2006 1 3.1 Diode Characteristics SmallSignal Diodes Diode: a semiconductor device, which conduct the current
More informationHigh Open Circuit Voltage of MQW Amorphous Silicon Photovoltaic Structures
High Open Circuit Voltage of MQW Amorphous Silicon Photovoltaic Structures ARGYRIOS C. VARONIDES Physics and EE Department University of Scranton 800 Linden Street, Scranton PA, 18510 United States Abstract:
More informationConsider a onedimensional chain of alternating positive and negative ions. Show that the potential energy of an ion in this hypothetical crystal is
Chapter 11 The Solid State. Home Wor Solutions 11.1 Problem 11.5 Consider a onedimensional chain of alternating positive and negative ions. Show that the potential energy of an ion in this hypothetical
More information1: Below you can see a computer generated image of a 2s orbital from Rutgers University website.
Quantum Mechanics of an H atom: 1: Below you can see a computer generated image of a 2s orbital from Rutgers University website. 2: Since the rest of the problems include alteration to the plot, it is
More informationCondensed Matter Physics Prof. G. Rangarajan Department of Physics Indian Institute of Technology, Madras. Lecture  36 Semiconductors
Condensed Matter Physics Prof. G. Rangarajan Department of Physics Indian Institute of Technology, Madras Lecture  36 Semiconductors We will start a discussion of semiconductors one of the most important
More informationElectrical Properties
Electrical Properties Outline of this Topic 1. Basic laws and electrical properties of metals 2. Band theory of solids: metals, semiconductors and insulators 3. Electrical properties of semiconductors
More informationDegeneracy of Electrons
Properties of Degenerated FermiGas in Astrophysics HsinYu Chen Introduction The degenerated fermigas is a dominated component in a highly dense region in Astronomy, such as the center of a white dwarf.
More informationPeriodic Table. inert gases. Columns: Similar Valence Structure. give up 1e  give up 2e  Oaccept 2e accept 1e  give up 3e 
Periodic Table give up 1e  give up 2e  give up 3e  H Li Be Na Mg K Ca Columns: Similar Valence Structure Sc Oaccept 2e accept 1e  inert gases S Se F Cl Br He Ne Ar Kr Adapted from Fig. 2.6, Callister
More informationAtomic structure of (a) silicon; (b) germanium; and (c) gallium and arsenic.
Fig. 1.3 Atomic structure of (a) silicon; (b) germanium; and (c) gallium and arsenic. 14 electrons 32 electrons 31electrons 33electrons Jalal S Al Roumy Electrical Engineering Department., The Islamic
More informationSection A5: Current Flow in Semiconductors
Section A5: Current Flow in Semiconductors Conductive behaviors in materials, defined by the parameter conductivity, are a primary factor in the development of electronic and optoelectronic devices. Electrical
More informationDefinition : Characteristics of Metals :
Metallic Bond Definition : It may be defined as, 1. The force that binds a metal ion to a number of electrons with in its sphere of influence. 2. The attractive force which holds the atoms of two or more
More informationELE2110A Electronic Circuits
Chinese University of Hong Kong Department of Electronic Engineering Second Term 07/08 ELE2110A Electronic Circuits Prof. Pun Kong Pang Email: kppun@ee.cuhk.edu.hk Lecture 011 Course Information Homepage:
More informationStudy of Impurity Photovoltaic Effect with Different Doping Materials using SCAPS Simulator
International Journal of Scientific and Research Publications, Volume 3, Issue 7, July 2013 1 Study of Impurity Photovoltaic Effect with Different Doping Materials using SCAPS Simulator Ratna Sircar*,
More informationPractice questions for Ch. 7
Name: Class: Date: ID: A Practice questions for Ch. 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. When ignited, a uranium compound burns with a green
More informationEnergy band diagrams. Single atom. Crystal. Excited electrons cannot move. Excited electrons can move (free electrons)
Energy band diagrams In the atoms, the larger the radius, the higher the electron potential energy Hence, electron position can be described either by radius or by its potential energy In the semiconductor
More information in a typical metal each atom contributes one electron to the delocalized electron gas describing the conduction electrons
Free Electrons in a Metal  in a typical metal each atom contributes one electron to the delocalized electron gas describing the conduction electrons  if these electrons would behave like an ideal gas
More informationENEE 313, Spr 09 Midterm II Solution
ENEE 313, Spr 09 Midterm II Solution PART I DRIFT AND DIFFUSION, 30 pts 1. We have a silicon sample with nonuniform doping. The sample is 200 µm long: In the figure, L = 200 µm= 0.02 cm. At the x = 0
More informationL5. P1. Lecture 5. Solids. The free electron gas
Lecture 5 Page 1 Lecture 5 L5. P1 Solids The free electron gas In a solid state, a few loosely bound valence (outermost and not in completely filled shells) elections become detached from atoms and move
More informationThe General Properties of Si, Ge, SiGe, SiO 2 and Si 3 N 4 June 2002
The neral Properties of,,, O 2 and 3 N 4 June 2002 Virginia Semiconductor 1501 Powhatan Street, Fredericksburg, VA 224014647 USA Phone: (540) 3732900, FAX (540) 3710371 www.virginiasemi.com, tech@virginiasemi.com
More informationPhysics Notes Class 12 Chapter 14 Semiconductor Electronics, Materials, Devices and Sample Circuits
1 P a g e Physics Notes Class 12 Chapter 14 Semiconductor Electronics, Materials, Devices and Sample Circuits It is the branch of science which deals with the electron flow through a vacuum, gas or semiconductor.
More informationRadiation Interactions with Matter: Energy Deposition
Radiation Interactions with Matter: Energy Deposition Biological effects are the end product of a long series of phenomena, set in motion by the passage of radiation through the medium. Image removed due
More informationUNDERSTANDING THE LIMITS OF SEMICONDUCTOR TECHNOLOGY
UNDERSTANDING THE LIMITS OF SEMICONDUCTOR TECHNOLOGY Department of Electronic Engineering UPC, Barcelona, Spain OUTLINE OF THE COURSE Introduction and motivation Limits of the technology at fundamental,
More informationProcessing of Semiconducting Materials Prof. Pallab Banerji Metallurgy and Material Science Indian Institute of Technology, Kharagpur
Processing of Semiconducting Materials Prof. Pallab Banerji Metallurgy and Material Science Indian Institute of Technology, Kharagpur Lecture  25 Carrier Transport in P  N Junction In my last lecture,
More informationChapter 1. Semiconductors
THE ELECTRON IN ELECTRIC FIELDS Semiconductors If we were to take two parallel plates and connect a voltage source across them as shown in Figure 1, an electric field would be set up between the plates.
More informationSolar Cell Parameters and Equivalent Circuit
9 Solar Cell Parameters and Equivalent Circuit 9.1 External solar cell parameters The main parameters that are used to characterise the performance of solar cells are the peak power P max, the shortcircuit
More informationMetals, Semiconductors, and Insulators
Metals, Semiconductors, and Insulators Every solid has its own characteristic energy band structure. In order for a material to be conductive, both free electrons and empty states must be available. Metals
More informationSample Exercise 12.1 Calculating Packing Efficiency
Sample Exercise 12.1 Calculating Packing Efficiency It is not possible to pack spheres together without leaving some void spaces between the spheres. Packing efficiency is the fraction of space in a crystal
More informationMMIC Design and Technology. Fabrication of MMIC
MMIC Design and Technology Fabrication of MMIC Instructor Dr. Ali Medi Substrate Process Choice Mobility & Peak Velocity: Frequency Response BandGap Energy: Breakdown Voltage (PowerHandling) Resistivity:
More informationWhite Dwarf Properties and the Degenerate Electron Gas
White Dwarf Properties and the Degenerate Electron Gas Nicholas Rowell April 10, 2008 Contents 1 Introduction 2 1.1 Discovery....................................... 2 1.2 Survey Techniques..................................
More informationAP Chemistry A. Allan Chapter 7 Notes  Atomic Structure and Periodicity
AP Chemistry A. Allan Chapter 7 Notes  Atomic Structure and Periodicity 7.1 Electromagnetic Radiation A. Types of EM Radiation (wavelengths in meters) 101 1010 108 4 to 7x107 104 101 10 10 4 gamma
More informationConduction in Semiconductors
Chapter 1 Conduction in Semiconductors 1.1 Introduction All solidstate devices, e.g. diodes and transistors, are fabricated from materials known as semiconductors. In order to understand the operation
More informationThe properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: µ >> k B T βµ >> 1,
Chapter 3 Ideal Fermi gas The properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: µ >> k B T βµ >>, which defines the degenerate Fermi gas. In
More information1 THE MAXWELLBOLTZMANN DISTRIBUTION FUNCTION
1 THE MAXWELLBOLTZMANN DISTRIBUTION FUNCTION In this exercise you will use Excel to create a spreadsheet for the MaxwellBoltzmann speed distribution and then plot the speed distribution for particles
More informationProcessing of Semiconducting Materials Prof. Pallab Banerji Material Science Centre Indian Institute of Technology, Kharagpur
Processing of Semiconducting Materials Prof. Pallab Banerji Material Science Centre Indian Institute of Technology, Kharagpur Lecture  27 Characterization II Let us define the following parameters for
More informationA Course Material on. Engineering Physics  II
A Course Material on Engineering Physics  II By Ms. I.JEENA RAJATHY Mrs.V.HEMALATHA Mr.K.PRAVEEN KUMAR Mr.P.PRAKASH Mr.M.SARAVANAN ASSISTANT PROFESSOR DEPARTMENT OF SCIENCE AND HUMANITIES PHYSICS SASURIE
More information4.1 SOLAR CELL OPERATION. Y. Baghzouz ECE Department UNLV
4.1 SOLAR CELL OPERATION Y. Baghzouz ECE Department UNLV SOLAR CELL STRUCTURE Light shining on the solar cell produces both a current and a voltage to generate electric power. This process requires a material
More informationCharacteristic curves of a solar cell
Related Topics Semiconductor, pn junction, energyband diagram, Fermi characteristic energy level, diffusion potential, internal resistance, efficiency, photoconductive effect, acceptors, donors, valence
More informationATOMS AND THE PERIODIC TABLE CHAPTER 3 PHYSICAL SCIENCE
ATOMS AND THE PERIODIC TABLE CHAPTER 3 PHYSICAL SCIENCE Chapter 3 Vocabulary Words (27 words) Nucleus Atomic number Proton Mass number Neutron Isotopes Electron Atomic mass unit (amu) Energy level Average
More informationTHE CURRENTVOLTAGE CHARACTERISTICS OF AN LED AND A MEASUREMENT OF PLANCK S CONSTANT Physics 258/259
DSH 2004 THE CURRENTVOLTAGE CHARACTERISTICS OF AN LED AND A MEASUREMENT OF PLANCK S CONSTANT Physics 258/259 I. INTRODUCTION Max Planck (18581947) was an early pioneer in the field of quantum physics.
More informationPhys 234H Practice Final Exam (Note: this practice exam contains more questions than will the final, which will have 25 multiplechoice questions.
Phys 234H Practice Final Exam (Note: this practice exam contains more questions than will the final, which will have 25 multiplechoice questions. MULTIPLE CHOICE. Choose the one alternative that best
More informationVacuum Evaporation Recap
Sputtering Vacuum Evaporation Recap Use high temperatures at high vacuum to evaporate (eject) atoms or molecules off a material surface. Use ballistic flow to transport them to a substrate and deposit.
More information2) Remember the Pauli exclusion principle. 3) Hund s rule of maximum multiplicity Energy
Building up the atoms in the periodic table 1) The Aufbau ( building up ) principle: lowest energy orbitals are filled first 1s, then 2s, then 2p, then 3s, then 3p, etc. 2) Remember the Pauli exclusion
More informationE α q 1 q 2 d. NOTE: The negative charge is the same distance from the positive charge in
During Class Invention Question: How are electrons arranged in an atom? 1. Describe the nature of the interaction between protons and electrons in an atom? Consider using some or all of the following terms
More informationThe nearlyfree electron model
Handout 3 The nearlyfree electron model 3.1 Introduction Having derived Bloch s theorem we are now at a stage where we can start introducing the concept of bandstructure. When someone refers to the bandstructure
More informationEQUATION OF STATE. e (E µ)/kt ± 1 h 3 dp,
EQUATION OF STATE Consider elementary cell in a phase space with a volume x y z p x p y p z = h 3, (st.1) where h = 6.63 1 7 erg s is the Planck constant, x y z is volume in ordinary space measured in
More informationThe Illuminated pn Junction. ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
The Illuminated pn Junction The Illuminated pn Junction Generation revisited Basic requirements Optical Generation Absorption Coefficient Optical Generation Rate The Illuminated pn Junction IV equation
More informationLecture / Tutorial (per week) 4/1 Course Credits 4.5
Institute / School Name Chitkara School of Engineering & Technology Program Name B.E.(Electronics & Communication Engineering) Course Code ECL5201 Course Name Fundamentals of Electronic Devices Lecture
More information3. What would you predict for the intensity and binding energy for the 3p orbital for that of sulfur?
PSI AP Chemistry Periodic Trends MC Review Name Periodic Law and the Quantum Model Use the PES spectrum of Phosphorus below to answer questions 13. 1. Which peak corresponds to the 1s orbital? (A) 1.06
More information