Charge carrier density in metals and semiconductors

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Charge carrier density in metals and semiconductors"

Transcription

1 Charge carrier density in metals and semiconductors 1. Introduction The Hall Effect Particles must overlap for the permutation symmetry to be relevant. We saw examples of this in the exchange energy in atoms. Does the same hold true for solids? The answer depends on the carrier concentration. Exchange energy is large in metals with large free electron densities, and small in semiconductors. The mobile carrier density can be found with the Hall Effect. This is a potential difference VV HH that appears perpendicular to the direction of current flow in an applied magnetic field, due to the Lorentz force. The drift velocity approximation, valid for small magnetic fields, adds to the forces on a charged particle moving in crossed EE and BB fields, a force due to collisions in a solid. This force is proportional to its velocity vv = μμμμ, where μμ is the mobility of the particle. The free-particle solution is not a good starting point in small magnetic fields and with high scattering rates, because charges cannot complete even a small fraction of a cyclotron orbit before being scattered (ωω cc ττ 1). We must solve the problem from the beginning. For a EE xx field, a BB zz field and an induced EE yy field (figure 1(a)) we get {nnnnee xx + II yy BB zz mm II eeττ xx = 0, nnnnee yy II xx BB zz mm ee ddpp yy dddd = 0 = eeee yy eebb zz vv xx pp yy ττ. eeττ ee II yy = 0}. Alternatively, ddpp xx dddd = 0 = eeee xx + eebb zz vv yy pp xx ττ and Setting II yy = 0 in the steady-state gives {nnnnee xx mm eeττ ee II xx = 0, nnnnee yy II xx BB zz = 0} or ρρ EE xx = mm (no effect of BB II xx ee 2 nnττ zz ), ρρ HH EE yy = BB zz, and tan φφ ee II xx nnnn HH = EE yy = BB zz eeττ EE xx mm ee The free-particle limit corresponds to ττ ee and EE yy = 0 condition. Then, nnnnee xx + II yy BB zz = 0 nnnnvv yy = II yy = nnnnee xx BB zz vv yy = EE xx BB zz and II xx BB zz = 0 II xx = 0, as expected. The Hall coefficient is defined as RR HH VV HHtt = 1, where tt is the thickness of the material. IIII nnnn Measuring VV HH (BB) with a variable applied field BB and fitting for the slope is the standard method to find the density of mobile charge carriers and the sign of their charge. For instance, the slope is much smaller in Cu than in doped Si, and its sign is different for nn doped (with electrons) and pp doped Si (with holes) because the sign of mobile charge carriers is different. Page 1

2 BB zz 1 4 EE yy (a) EE xx 2 3 (b) Fig.1: (a) Applied (EE xx, BB zz ) and induced (EE yy ) fields. (b) Geometry and contact definitions in practice. The current is injected across two contacts, and the voltage measured across two different contacts. The current flow will depend on the sample shape and current and voltage contact positions, and therefore, so will the measured resistance RR = VV II. 2. Measuring resistivity of thin films You measured the resistivity of a thin wire (B-E statistics) and a thick disk (Meissner Effect). The samples of this experiment are in the form of a thin film. How can we measure its resistivity? In ideal conditions, a thin film sample on a completely insulating substrate has a resistance RR = ρρρρ wwww, where ρρ is the resistivity of the material, ll the film length, ww and tt are the width and thickness of the film. The quantities that are not well-known are ρρ and tt. Because of this, instead of solving for ρρ, we solve for ρρ = RRRR. We can measure RR, ll, ww, but a further tt ll simplification is useful and is often chosen to make the comparison of results from different labs easier. When ww = ll, the quantity on the RHS does not depend on the in-plane physical dimensions and is called the sheet resistance R, with units of Ω/ssssssssssss. This is the intrinsic electrical transport parameter of the thin film. The sheet resistance R can be measured with four equidistant electrodes if the film is large enough so that the boundary effects are small or with four corner electrodes if the film is smaller. Then, it can be shown that R = ππ ln 2 VV 2ππ and R = II ln 2 VV, respectively (in both cases, II the result does not depend on the distance between electrodes). These standard electrode configurations are also applied in measurements on thick samples. We will use the second configuration (figure 1(b)). Page 2

3 3. Experiments In principle, measuring VV and II once would be enough in an ideal case. In practice, to account for sample shape and differences between contact placement and quality, a series of measurements is necessary. We will be using a lock-in method for higher sensitivity 3.1. Measuring the sheet resistance In this case, the current is injected between two neighboring contacts. Measure the 8 combinations RR aaaa,cccc (RR 12,34, RR 23,41, RR 34,12, RR 41,23 ) as well as the ones with contacts inverted (RR 21,43, RR 32,14, RR 43,21, RR 14,32 ). Then, average RR aaaa,cccc with RR bbbb,dddd (1 st consistency check, should be satisfied within 5%) and average RR 12,34 with RR 34,12 and RR 23,41 with RR 41,23 (reciprocity theorem, 2 nd consistency check). We end up with two resistances RR 12,34 = RR AA and RR 23,41 = RR BB, which go into the van der Pauw equation ee ππrr AA RRss + ee ππrr BB RRss = 1. It can be shown that its solution RR ss of this equation is the intrinsic sheet resistance of the film Mobile carrier density in semiconductors and metals Consistent with the Hall Effect model geometry of crossed II and VV HH directions, measurements are made across the current contacts (VV 13 and II 24 etc.). Start with a lightly-doped semiconductor (pp-doped Ge or nn doped Si wafer) that have a small carrier density and a large Hall voltage Apply the field in one direction (call this positive, PP) and measure VV 13PP with II 24. Invert both the current and voltage leads and measure VV 31PP with II 42 (the reciprocity theorem requires that these should be close, 1 st consistency check). Interchange the voltage and current leads to obtain VV 24PP with II 13 and VV 42PP with II 31. Repeat for the reversed magnetic field Calculate VV CC = VV 24PP VV 24NN, VV DD = VV 42PP VV 42NN, VV EE = VV 13PP VV 13NN, VV FF = VV 31PP VV 31NN 10 The charge carrier density is then (if holes) pp ss = 8 8 IIII qq 2(VV CC +VV DD +VV EE +VV FF ) Then, switch to the Cu thin foil, which will have a smaller voltage because of the larger carrier density A measurement of the sheet resistivity and carrier density allows finding the mobility μμ = 1 eenn ss RR ss of the charge carriers and the scattering time ττ = mm ee μμ. Find the distance between scattering events and compare to the distance between electrons obtained from their density for metals and semiconductors. Page 3

4 4. Conclusion The different mobile carrier concentrations obtained show why classical Boltzmann statistics works well for semiconductors, while quantum statistics must be used for metals. The Hall voltage VV HH 1 and the measurements are easier in thin samples because the tt current density is 1 for the same injected current II. tt The classical Hall Effect is the simplest of a family of Hall Effects that includes the anomalous Hall Effect (dependence of VV HH on sample magnetization), Integer and Fractional Quantum Hall Effects. Page 4

5 Phys-602 Quantum Mechanics Laboratory I Charge carrier density in metals and semiconductors lab report Name Date Page 5

Lecture 3 Transport in Semiconductors

Lecture 3 Transport in Semiconductors EE 471: Transport Phenomena in Solid State Devices Spring 2018 Lecture 3 Transport in Semiconductors Bryan Ackland Department of Electrical and Computer Engineering Stevens Institute of Technology Hoboken,

More information

(1) Correspondence of the density matrix to traditional method

(1) Correspondence of the density matrix to traditional method (1) Correspondence of the density matrix to traditional method New method (with the density matrix) Traditional method (from thermal physics courses) ZZ = TTTT ρρ = EE ρρ EE = dddd xx ρρ xx ii FF = UU

More information

The Bose Einstein quantum statistics

The Bose Einstein quantum statistics Page 1 The Bose Einstein quantum statistics 1. Introduction Quantized lattice vibrations Thermal lattice vibrations in a solid are sorted in classical mechanics in normal modes, special oscillation patterns

More information

Angular Momentum, Electromagnetic Waves

Angular Momentum, Electromagnetic Waves Angular Momentum, Electromagnetic Waves Lecture33: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay As before, we keep in view the four Maxwell s equations for all our discussions.

More information

Exam 2 Fall 2015

Exam 2 Fall 2015 1 95.144 Exam 2 Fall 2015 Section instructor Section number Last/First name Last 3 Digits of Student ID Number: Show all work. Show all formulas used for each problem prior to substitution of numbers.

More information

Review for Exam Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa

Review for Exam Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa Review for Exam2 11. 13. 2015 Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa Assistant Research Scientist IIHR-Hydroscience & Engineering, University

More information

Advantages / Disadvantages of semiconductor detectors

Advantages / Disadvantages of semiconductor detectors Advantages / Disadvantages of semiconductor detectors Semiconductor detectors have a high density (compared to gas detector) large energy loss in a short distance diffusion effect is smaller than in gas

More information

Module 7 (Lecture 27) RETAINING WALLS

Module 7 (Lecture 27) RETAINING WALLS Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Calculation of Active Horizontal and vertical Pressure Tie Force Factor of Safety Against Tie Failure

More information

Review for Exam Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa

Review for Exam Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa 57:020 Fluids Mechanics Fall2013 1 Review for Exam3 12. 11. 2013 Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa 57:020 Fluids Mechanics Fall2013 2 Chapter

More information

OBE solutions in the rotating frame

OBE solutions in the rotating frame OBE solutions in the rotating frame The light interaction with the 2-level system is VV iiiiii = μμ EE, where μμ is the dipole moment μμ 11 = 0 and μμ 22 = 0 because of parity. Therefore, light does not

More information

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra Worksheets for GCSE Mathematics Algebraic Expressions Mr Black 's Maths Resources for Teachers GCSE 1-9 Algebra Algebraic Expressions Worksheets Contents Differentiated Independent Learning Worksheets

More information

Secondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet

Secondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet Secondary H Unit Lesson Worksheet Simplify: mm + 2 mm 2 4 mm+6 mm + 2 mm 2 mm 20 mm+4 5 2 9+20 2 0+25 4 +2 2 + 2 8 2 6 5. 2 yy 2 + yy 6. +2 + 5 2 2 2 0 Lesson 6 Worksheet List all asymptotes, holes and

More information

SECTION 7: FAULT ANALYSIS. ESE 470 Energy Distribution Systems

SECTION 7: FAULT ANALYSIS. ESE 470 Energy Distribution Systems SECTION 7: FAULT ANALYSIS ESE 470 Energy Distribution Systems 2 Introduction Power System Faults 3 Faults in three-phase power systems are short circuits Line-to-ground Line-to-line Result in the flow

More information

CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I

CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I 1 5.1 X-Ray Scattering 5.2 De Broglie Waves 5.3 Electron Scattering 5.4 Wave Motion 5.5 Waves or Particles 5.6 Uncertainty Principle Topics 5.7

More information

PHY103A: Lecture # 9

PHY103A: Lecture # 9 Semester II, 2017-18 Department of Physics, IIT Kanpur PHY103A: Lecture # 9 (Text Book: Intro to Electrodynamics by Griffiths, 3 rd Ed.) Anand Kumar Jha 20-Jan-2018 Summary of Lecture # 8: Force per unit

More information

Variations. ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra

Variations. ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra Variations ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra Last Time Probability Density Functions Normal Distribution Expectation / Expectation of a function Independence Uncorrelated

More information

Elastic light scattering

Elastic light scattering Elastic light scattering 1. Introduction Elastic light scattering in quantum mechanics Elastic scattering is described in quantum mechanics by the Kramers Heisenberg formula for the differential cross

More information

Introduction to Electrical Theory and DC Circuits

Introduction to Electrical Theory and DC Circuits Introduction to Electrical Theory and DC Circuits For Engineers of All Disciplines by James Doane, PhD, PE Contents 1.0 Course Overview... 4 2.0 Fundamental Concepts... 4 2.1 Electric Charges... 4 2.1.1

More information

Supporting Information. for. Contactless photomagnetoelectric investigations of 2D

Supporting Information. for. Contactless photomagnetoelectric investigations of 2D Supporting Information for Contactless photomagnetoelectric investigations of 2D semiconductors Marian Nowak 1 *, Marcin Jesionek 1, Barbara Solecka 1, Piotr Szperlich 1, Piotr Duka 1 and Anna Starczewska

More information

Department of Engineering Science and Physics College of Staten Island. PHY315 Advanced Physics Laboratory. Lab Manuals

Department of Engineering Science and Physics College of Staten Island. PHY315 Advanced Physics Laboratory. Lab Manuals 1 Department of Engineering Science and Physics College of Staten Island PHY315 Advanced Physics Laboratory Lab Manuals 2 Content Notes about this Lab Course Safety First! Lab Reports Lab Works 1. Basic

More information

CHAPTER 2 Special Theory of Relativity

CHAPTER 2 Special Theory of Relativity CHAPTER 2 Special Theory of Relativity Fall 2018 Prof. Sergio B. Mendes 1 Topics 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 Inertial Frames of Reference Conceptual and Experimental

More information

(1) Introduction: a new basis set

(1) Introduction: a new basis set () Introduction: a new basis set In scattering, we are solving the S eq. for arbitrary VV in integral form We look for solutions to unbound states: certain boundary conditions (EE > 0, plane and spherical

More information

Math 171 Spring 2017 Final Exam. Problem Worth

Math 171 Spring 2017 Final Exam. Problem Worth Math 171 Spring 2017 Final Exam Problem 1 2 3 4 5 6 7 8 9 10 11 Worth 9 6 6 5 9 8 5 8 8 8 10 12 13 14 15 16 17 18 19 20 21 22 Total 8 5 5 6 6 8 6 6 6 6 6 150 Last Name: First Name: Student ID: Section:

More information

Electric Field and Electric Potential (A)

Electric Field and Electric Potential (A) Pre-Lab Quiz / PHYS 224 Electric Field and Electric Potential (A) Your Name Lab Section 1. What do you investigate in this lab? 2. In a uniform electric field between two parallel plates, a potential probe

More information

Atomic fluorescence. The intensity of a transition line can be described with a transition probability inversely

Atomic fluorescence. The intensity of a transition line can be described with a transition probability inversely Atomic fluorescence 1. Introduction Transitions in multi-electron atoms Energy levels of the single-electron hydrogen atom are well-described by EE nn = RR nn2, where RR = 13.6 eeee is the Rydberg constant.

More information

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra Worksheets for GCSE Mathematics Quadratics mr-mathematics.com Maths Resources for Teachers Algebra Quadratics Worksheets Contents Differentiated Independent Learning Worksheets Solving x + bx + c by factorisation

More information

Quantum Mechanics. An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc.

Quantum Mechanics. An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc. Quantum Mechanics An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc. Fall 2018 Prof. Sergio B. Mendes 1 CHAPTER 3 Experimental Basis of

More information

BHASVIC MαTHS. Skills 1

BHASVIC MαTHS. Skills 1 PART A: Integrate the following functions with respect to x: (a) cos 2 2xx (b) tan 2 xx (c) (d) 2 PART B: Find: (a) (b) (c) xx 1 2 cosec 2 2xx 2 cot 2xx (d) 2cccccccccc2 2xx 2 ccccccccc 5 dddd Skills 1

More information

Module 4 (Lecture 16) SHALLOW FOUNDATIONS: ALLOWABLE BEARING CAPACITY AND SETTLEMENT

Module 4 (Lecture 16) SHALLOW FOUNDATIONS: ALLOWABLE BEARING CAPACITY AND SETTLEMENT Topics Module 4 (Lecture 16) SHALLOW FOUNDATIONS: ALLOWABLE BEARING CAPACITY AND SETTLEMENT 1.1 STRIP FOUNDATION ON GRANULAR SOIL REINFORCED BY METALLIC STRIPS Mode of Failure Location of Failure Surface

More information

9. Switched Capacitor Filters. Electronic Circuits. Prof. Dr. Qiuting Huang Integrated Systems Laboratory

9. Switched Capacitor Filters. Electronic Circuits. Prof. Dr. Qiuting Huang Integrated Systems Laboratory 9. Switched Capacitor Filters Electronic Circuits Prof. Dr. Qiuting Huang Integrated Systems Laboratory Motivation Transmission of voice signals requires an active RC low-pass filter with very low ff cutoff

More information

CHAPTER 4 Structure of the Atom

CHAPTER 4 Structure of the Atom CHAPTER 4 Structure of the Atom Fall 2018 Prof. Sergio B. Mendes 1 Topics 4.1 The Atomic Models of Thomson and Rutherford 4.2 Rutherford Scattering 4.3 The Classic Atomic Model 4.4 The Bohr Model of the

More information

n i exp E g 2kT lnn i E g 2kT

n i exp E g 2kT lnn i E g 2kT HOMEWORK #10 12.19 For intrinsic semiconductors, the intrinsic carrier concentration n i depends on temperature as follows: n i exp E g 2kT (28.35a) or taking natural logarithms, lnn i E g 2kT (12.35b)

More information

The impact of hot charge carrier mobility on photocurrent losses

The impact of hot charge carrier mobility on photocurrent losses Supplementary Information for: The impact of hot charge carrier mobility on photocurrent losses in polymer-based solar cells Bronson Philippa 1, Martin Stolterfoht 2, Paul L. Burn 2, Gytis Juška 3, Paul

More information

SECTION 5: CAPACITANCE & INDUCTANCE. ENGR 201 Electrical Fundamentals I

SECTION 5: CAPACITANCE & INDUCTANCE. ENGR 201 Electrical Fundamentals I SECTION 5: CAPACITANCE & INDUCTANCE ENGR 201 Electrical Fundamentals I 2 Fluid Capacitor Fluid Capacitor 3 Consider the following device: Two rigid hemispherical shells Separated by an impermeable elastic

More information

Optical pumping and the Zeeman Effect

Optical pumping and the Zeeman Effect 1. Introduction Optical pumping and the Zeeman Effect The Hamiltonian of an atom with a single electron outside filled shells (as for rubidium) in a magnetic field is HH = HH 0 + ηηii JJ μμ JJ BB JJ μμ

More information

Dressing up for length gauge: Aspects of a debate in quantum optics

Dressing up for length gauge: Aspects of a debate in quantum optics Dressing up for length gauge: Aspects of a debate in quantum optics Rainer Dick Department of Physics & Engineering Physics University of Saskatchewan rainer.dick@usask.ca 1 Agenda: Attosecond spectroscopy

More information

Lecture 7 MOS Capacitor

Lecture 7 MOS Capacitor EE 471: Transport Phenomena in Solid State Devices Spring 2018 Lecture 7 MOS Capacitor Bryan Ackland Department of Electrical and Computer Engineering Stevens Institute of Technology Hoboken, NJ 07030

More information

Review for Exam Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa

Review for Exam Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa Review for Exam3 12. 9. 2015 Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa Assistant Research Scientist IIHR-Hydroscience & Engineering, University

More information

Quantization of electrical conductance

Quantization of electrical conductance 1 Introduction Quantization of electrical conductance Te resistance of a wire in te classical Drude model of metal conduction is given by RR = ρρρρ AA, were ρρ, AA and ll are te conductivity of te material,

More information

GaN and GaN/AlGaN Heterostructure Properties Investigation and Simulations. Ziyang (Christian) Xiao Neil Goldsman University of Maryland

GaN and GaN/AlGaN Heterostructure Properties Investigation and Simulations. Ziyang (Christian) Xiao Neil Goldsman University of Maryland GaN and GaN/AlGaN Heterostructure Properties Investigation and Simulations Ziyang (Christian) Xiao Neil Goldsman University of Maryland OUTLINE 1. GaN (bulk) 1.1 Crystal Structure 1.2 Band Structure Calculation

More information

Strand H Unit 3: Electromagnetic induction. Text Answers. Exercise H.3.1 Answers. a force of F = N. Since F = Bev,

Strand H Unit 3: Electromagnetic induction. Text Answers. Exercise H.3.1 Answers. a force of F = N. Since F = Bev, Exercise H.3.1 Answers 1. The magnetic field B = 0.6T and the electron of charge -1.6 10-19 C experiences a force of F = 2.88 10-15 N. Since F = Bev, vv = FF BBBB = 2.88 10 15 NN 1.6 10 19 CC 0.6TT = 30000mmss

More information

Analog Circuits Part 1 Circuit Theory

Analog Circuits Part 1 Circuit Theory Introductory Medical Device Prototyping Analog Circuits Part 1 Circuit Theory, http://saliterman.umn.edu/ Department of Biomedical Engineering, University of Minnesota Concepts to be Covered Circuit Theory

More information

CS Lecture 8 & 9. Lagrange Multipliers & Varitional Bounds

CS Lecture 8 & 9. Lagrange Multipliers & Varitional Bounds CS 6347 Lecture 8 & 9 Lagrange Multipliers & Varitional Bounds General Optimization subject to: min ff 0() R nn ff ii 0, h ii = 0, ii = 1,, mm ii = 1,, pp 2 General Optimization subject to: min ff 0()

More information

Photon Interactions in Matter

Photon Interactions in Matter Radiation Dosimetry Attix 7 Photon Interactions in Matter Ho Kyung Kim hokyung@pusan.ac.kr Pusan National University References F. H. Attix, Introduction to Radiological Physics and Radiation Dosimetry,

More information

Chemical Engineering 412

Chemical Engineering 412 Chemical Engineering 412 Introductory Nuclear Engineering Lecture 12 Radiation/Matter Interactions II 1 Neutron Flux The collisions of neutrons of all energies is given by FF = ΣΣ ii 0 EE φφ EE dddd All

More information

Acceleration to higher energies

Acceleration to higher energies Acceleration to higher energies While terminal voltages of 20 MV provide sufficient beam energy for nuclear structure research, most applications nowadays require beam energies > 1 GeV How do we attain

More information

C = V Q. To find the capacitance of two conductors:

C = V Q. To find the capacitance of two conductors: Capacitance Capacitance is a measure of the ability of two conductors to store charge when a given potential difference is established between them. Two conductors, on one of which is charge +Q and on

More information

" = Y(#,$) % R(r) = 1 4& % " = Y(#,$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V,

 = Y(#,$) % R(r) = 1 4& %  = Y(#,$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V, Recitation Problems: Week 4 1. Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom: n l m l m s 2 2 1! 3 1 0 -! 5 1 2! 4-1 0! 3 2 1 0 2 0 0 -! 7 2-2!

More information

Photons in the universe. Indian Institute of Technology Ropar

Photons in the universe. Indian Institute of Technology Ropar Photons in the universe Photons in the universe Element production on the sun Spectral lines of hydrogen absorption spectrum absorption hydrogen gas Hydrogen emission spectrum Element production on the

More information

GRADUATE WRITTEN EXAMINATION. Spring 2016 PART I

GRADUATE WRITTEN EXAMINATION. Spring 2016 PART I University of Minnesota School of Physics and Astronomy GRADUATE WRITTEN EXAMINATION Spring 2016 PART I Thursday, January 14 th, 2016 9:00 am to 1:00 pm Part 1 of this exam consists of 10 problems of equal

More information

Carrier Mobility and Hall Effect. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

Carrier Mobility and Hall Effect. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India Carrier Mobility and Hall Effect 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 calculation Calculate the hole and electron densities

More information

PHL424: Nuclear fusion

PHL424: Nuclear fusion PHL424: Nuclear fusion Hot Fusion 5 10 15 5 10 8 projectiles on target compound nuclei 1 atom Hot fusion (1961 1974) successful up to element 106 (Seaborgium) Coulomb barrier V C between projectile and

More information

Grover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick

Grover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick Grover s algorithm Search in an unordered database Example: phonebook, need to find a person from a phone number Actually, something else, like hard (e.g., NP-complete) problem 0, xx aa Black box ff xx

More information

Fluids in Rigid-Body Motion

Fluids in Rigid-Body Motion Fluids in Rigid-Body Motion 9. 14. 2016 Hyunse Yoon, Ph.D. Associate Research Scientist IIHR-Hydroscience & Engineering Newton s 2 nd Law of Motion In general, for a body of mass mm, mmaa = FF where, aa

More information

Last Name _Piatoles_ Given Name Americo ID Number

Last Name _Piatoles_ Given Name Americo ID Number Last Name _Piatoles_ Given Name Americo ID Number 20170908 Question n. 1 The "C-V curve" method can be used to test a MEMS in the electromechanical characterization phase. Describe how this procedure is

More information

Classification of Solids

Classification of Solids Classification of Solids Classification by conductivity, which is related to the band structure: (Filled bands are shown dark; D(E) = Density of states) Class Electron Density Density of States D(E) Examples

More information

Discrete scale invariance and Efimov bound states in Weyl systems with coexistence of electron and hole carriers

Discrete scale invariance and Efimov bound states in Weyl systems with coexistence of electron and hole carriers Institute of Advanced Study, Tsinghua, April 19, 017 Discrete scale invariance and Efimov bound states in Weyl systems with coexistence of electron and hole carriers Haiwen Liu ( 刘海文 ) Beijing Normal University

More information

Heat, Work, and the First Law of Thermodynamics. Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition

Heat, Work, and the First Law of Thermodynamics. Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition Heat, Work, and the First Law of Thermodynamics Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 Different ways to increase the internal energy of system: 2 Joule s apparatus

More information

ECE 6540, Lecture 06 Sufficient Statistics & Complete Statistics Variations

ECE 6540, Lecture 06 Sufficient Statistics & Complete Statistics Variations ECE 6540, Lecture 06 Sufficient Statistics & Complete Statistics Variations Last Time Minimum Variance Unbiased Estimators Sufficient Statistics Proving t = T(x) is sufficient Neyman-Fischer Factorization

More information

Radiation. Lecture40: Electromagnetic Theory. Professor D. K. Ghosh, Physics Department, I.I.T., Bombay

Radiation. Lecture40: Electromagnetic Theory. Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Radiation Zone Approximation We had seen that the expression for the vector potential for a localized cuent distribution is given by AA (xx, tt) = μμ 4ππ ee iiiiii dd xx eeiiii xx xx xx xx JJ (xx ) In

More information

Module 7 (Lecture 25) RETAINING WALLS

Module 7 (Lecture 25) RETAINING WALLS Module 7 (Lecture 25) RETAINING WALLS Topics Check for Bearing Capacity Failure Example Factor of Safety Against Overturning Factor of Safety Against Sliding Factor of Safety Against Bearing Capacity Failure

More information

Gradient expansion formalism for generic spin torques

Gradient expansion formalism for generic spin torques Gradient expansion formalism for generic spin torques Atsuo Shitade RIKEN Center for Emergent Matter Science Atsuo Shitade, arxiv:1708.03424. Outline 1. Spintronics a. Magnetoresistance and spin torques

More information

Magnetic Force and Current Balance

Magnetic Force and Current Balance Pre-Lab Quiz / PHYS 224 Magnetic Force and Current Balance Name Lab Section 1. What do you investigate in this lab? 2. Consider two parallel straight wires carrying electric current in opposite directions

More information

ME5286 Robotics Spring 2017 Quiz 2

ME5286 Robotics Spring 2017 Quiz 2 Page 1 of 5 ME5286 Robotics Spring 2017 Quiz 2 Total Points: 30 You are responsible for following these instructions. Please take a minute and read them completely. 1. Put your name on this page, any other

More information

From Hall Effect to TMR

From Hall Effect to TMR From Hall Effect to TMR 1 Abstract This paper compares the century old Hall effect technology to xmr technologies, specifically TMR (Tunnel Magneto-Resistance) from Crocus Technology. It covers the various

More information

Mathematics Ext 2. HSC 2014 Solutions. Suite 403, 410 Elizabeth St, Surry Hills NSW 2010 keystoneeducation.com.

Mathematics Ext 2. HSC 2014 Solutions. Suite 403, 410 Elizabeth St, Surry Hills NSW 2010 keystoneeducation.com. Mathematics Ext HSC 4 Solutions Suite 43, 4 Elizabeth St, Surry Hills NSW info@keystoneeducation.com.au keystoneeducation.com.au Mathematics Extension : HSC 4 Solutions Contents Multiple Choice... 3 Question...

More information

1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2,

1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2, 1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. x = 4, x = 3, x = 2, x = 1, x = 1, x = 2, x = 3, x = 4, x = 5 b. Find the value(s)

More information

Low-temperature physics

Low-temperature physics Low-temperature physics 1. Introduction Superconductors in magnetic fields Early transport measurement results were analyzed with the Drude classical scattering model, which may be viewed as the transport

More information

PHY103A: Lecture # 4

PHY103A: Lecture # 4 Semester II, 2017-18 Department of Physics, IIT Kanpur PHY103A: Lecture # 4 (Text Book: Intro to Electrodynamics by Griffiths, 3 rd Ed.) Anand Kumar Jha 10-Jan-2018 Notes The Solutions to HW # 1 have been

More information

Coulomb s Law and Coulomb s Constant

Coulomb s Law and Coulomb s Constant Pre-Lab Quiz / PHYS 224 Coulomb s Law and Coulomb s Constant Your Name: Lab Section: 1. What will you investigate in this lab? 2. Consider a capacitor created when two identical conducting plates are placed

More information

Revision : Thermodynamics

Revision : Thermodynamics Revision : Thermodynamics Formula sheet Formula sheet Formula sheet Thermodynamics key facts (1/9) Heat is an energy [measured in JJ] which flows from high to low temperature When two bodies are in thermal

More information

Lecture 2: Plasma particles with E and B fields

Lecture 2: Plasma particles with E and B fields Lecture 2: Plasma particles with E and B fields Today s Menu Magnetized plasma & Larmor radius Plasma s diamagnetism Charged particle in a multitude of EM fields: drift motion ExB drift, gradient drift,

More information

Pre-Lab Quiz / PHYS 224. R-C Circuits. Your Name Lab Section

Pre-Lab Quiz / PHYS 224. R-C Circuits. Your Name Lab Section Pre-Lab Quiz / PHYS 224 R-C Circuits Your Name Lab Section 1. What do we investigate in this lab? 2. For the R-C circuit shown in Figure 1 on Page 3, RR = 100 ΩΩ and CC = 1.00 FF. What is the time constant

More information

Fermi Surfaces and their Geometries

Fermi Surfaces and their Geometries Fermi Surfaces and their Geometries Didier Ndengeyintwali Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA (Dated: May 17, 2010) 1. Introduction The Pauli exclusion principle

More information

10.4 The Cross Product

10.4 The Cross Product Math 172 Chapter 10B notes Page 1 of 9 10.4 The Cross Product The cross product, or vector product, is defined in 3 dimensions only. Let aa = aa 1, aa 2, aa 3 bb = bb 1, bb 2, bb 3 then aa bb = aa 2 bb

More information

Diffusion modeling for Dip-pen Nanolithography Apoorv Kulkarni Graduate student, Michigan Technological University

Diffusion modeling for Dip-pen Nanolithography Apoorv Kulkarni Graduate student, Michigan Technological University Diffusion modeling for Dip-pen Nanolithography Apoorv Kulkarni Graduate student, Michigan Technological University Abstract The diffusion model for the dip pen nanolithography is similar to spreading an

More information

Problem 3.1 (Verdeyen 5.13) First, I calculate the ABCD matrix for beam traveling through the lens and space.

Problem 3.1 (Verdeyen 5.13) First, I calculate the ABCD matrix for beam traveling through the lens and space. Problem 3. (Verdeyen 5.3) First, I calculate the ABCD matrix for beam traveling through the lens and space. T = dd 0 0 dd 2 ff 0 = dd 2 dd ff 2 + dd ( dd 2 ff ) dd ff ff Aording to ABCD law, we can have

More information

Charged-Particle Interactions in Matter

Charged-Particle Interactions in Matter Radiation Dosimetry Attix 8 Charged-Particle Interactions in Matter Ho Kyung Kim hokyung@pusan.ac.kr Pusan National University References F. H. Attix, Introduction to Radiological Physics and Radiation

More information

Big Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation

Big Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation Big Bang Planck Era Source: http://www.crystalinks.com/bigbang.html Source: http://www.odec.ca/index.htm This theory: cosmological model of the universe that is best supported by several aspects of scientific

More information

Lecture 2 Electrons and Holes in Semiconductors

Lecture 2 Electrons and Holes in Semiconductors EE 471: Transport Phenomena in Solid State Devices Spring 2018 Lecture 2 Electrons and Holes in Semiconductors Bryan Ackland Department of Electrical and Computer Engineering Stevens Institute of Technology

More information

Specialist Mathematics 2019 v1.2

Specialist Mathematics 2019 v1.2 181314 Mensuration circumference of a circle area of a parallelogram CC = ππππ area of a circle AA = ππrr AA = h area of a trapezium AA = 1 ( + )h area of a triangle AA = 1 h total surface area of a cone

More information

Physics 371 Spring 2017 Prof. Anlage Review

Physics 371 Spring 2017 Prof. Anlage Review Physics 71 Spring 2017 Prof. Anlage Review Special Relativity Inertial vs. non-inertial reference frames Galilean relativity: Galilean transformation for relative motion along the xx xx direction: xx =

More information

Varying accelerating fields

Varying accelerating fields Varying accelerating fields Two approaches for accelerating with time-varying fields Linear Accelerators Circular Accelerators Use many accelerating cavities through which the particle beam passes once.

More information

Lesson 2. Homework Problem Set Sample Solutions S.19

Lesson 2. Homework Problem Set Sample Solutions S.19 Homework Problem Set Sample Solutions S.9. Below are formulas Britney Gallivan created when she was doing her paper-folding extra credit assignment. his formula determines the minimum width, WW, of a square

More information

Effect of First Order Chemical Reaction for Coriolis Force and Dust Particles for Small Reynolds Number in the Atmosphere Over Territory

Effect of First Order Chemical Reaction for Coriolis Force and Dust Particles for Small Reynolds Number in the Atmosphere Over Territory Global Journal of Science Frontier Research: H Environment & Earth Science Volume 16 Issue 1 Version 1.0 Year 2016 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals

More information

Control of Mobile Robots

Control of Mobile Robots Control of Mobile Robots Regulation and trajectory tracking Prof. Luca Bascetta (luca.bascetta@polimi.it) Politecnico di Milano Dipartimento di Elettronica, Informazione e Bioingegneria Organization and

More information

Work, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition

Work, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition Work, Energy, and Power Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 With the knowledge we got so far, we can handle the situation on the left but not the one on the right.

More information

A A A A A A A A A A A A. a a a a a a a a a a a a a a a. Apples taste amazingly good.

A A A A A A A A A A A A. a a a a a a a a a a a a a a a. Apples taste amazingly good. Victorian Handwriting Sheet Aa A A A A A A A A A A A A Aa Aa Aa Aa Aa Aa Aa a a a a a a a a a a a a a a a Apples taste amazingly good. Apples taste amazingly good. Now make up a sentence of your own using

More information

Fig. 1. Two common types of van der Pauw samples: clover leaf and square. Each sample has four symmetrical electrical contacts.

Fig. 1. Two common types of van der Pauw samples: clover leaf and square. Each sample has four symmetrical electrical contacts. 15 2. Basic Electrical Parameters of Semiconductors: Sheet Resistivity, Resistivity and Conduction Type 2.1 Objectives 1. Familiarizing with experimental techniques used for the measurements of electrical

More information

Phy207 Final Exam (Form1) Professor Zuo Fall Signature: Name:

Phy207 Final Exam (Form1) Professor Zuo Fall Signature: Name: #1-25 #26 Phy207 Final Exam (Form1) Professor Zuo Fall 2018 On my honor, I have neither received nor given aid on this examination #27 Total Signature: Name: ID number: Enter your name and Form 1 (FM1)

More information

Information Booklet of Formulae and Constants

Information Booklet of Formulae and Constants Pearson BTEC Level 3 Nationals Engineering Information Booklet of Formulae and Constants Unit 1: Engineering Principles Extended Certificate, Foundation Diploma, Diploma, Extended Diploma in Engineering

More information

PHL424: Feynman diagrams

PHL424: Feynman diagrams PHL424: Feynman diagrams In 1940s, R. Feynman developed a diagram technique to describe particle interactions in space-time. Feynman diagram example Richard Feynman time Particles are represented by lines

More information

Hall Effect Measurement in Germanium (Electrical Transport Option) Prof. Richard Averitt, UC San Diego

Hall Effect Measurement in Germanium (Electrical Transport Option) Prof. Richard Averitt, UC San Diego Hall Effect Measurement in Germanium (Electrical Transport Option) Prof. Richard Averitt, UC San Diego Description: The objective of this educational module is to measure the Hall effect germanium and

More information

EXPERIMENT 14. HALL EFFECT AND RESISTIVITY MEASUREMENTS IN DOPED GAAS 1. Hall Effect and Resistivity Measurements in Doped GaAs

EXPERIMENT 14. HALL EFFECT AND RESISTIVITY MEASUREMENTS IN DOPED GAAS 1. Hall Effect and Resistivity Measurements in Doped GaAs EXPERIMENT 14. HALL EFFECT AND RESISTIVITY MEASUREMENTS IN DOPED GAAS 1 Experiment 14 Hall Effect and Resistivity Measurements in Doped GaAs Note: This laboratory manual is based on a manual for a very

More information

Magnetism of materials

Magnetism of materials Magnetism of materials 1. Introduction Magnetism and quantum mechanics In the previous experiment, you witnessed a very special case of a diamagnetic material with magnetic susceptibility χχ = 1 (usually

More information

Wave Motion. Chapter 14 of Essential University Physics, Richard Wolfson, 3 rd Edition

Wave Motion. Chapter 14 of Essential University Physics, Richard Wolfson, 3 rd Edition Wave Motion Chapter 14 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 Waves: propagation of energy, not particles 2 Longitudinal Waves: disturbance is along the direction of wave propagation

More information

Metals: the Drude and Sommerfeld models p. 1 Introduction p. 1 What do we know about metals? p. 1 The Drude model p. 2 Assumptions p.

Metals: the Drude and Sommerfeld models p. 1 Introduction p. 1 What do we know about metals? p. 1 The Drude model p. 2 Assumptions p. Metals: the Drude and Sommerfeld models p. 1 Introduction p. 1 What do we know about metals? p. 1 The Drude model p. 2 Assumptions p. 2 The relaxation-time approximation p. 3 The failure of the Drude model

More information