UMEÅ UNIVERSITY Department of Physics Agnieszka Iwasiewicz Leif Hassmyr Ludvig Edman SOLID STATE PHYSICS HALL EFFECT
|
|
- Elmer Nash
- 5 years ago
- Views:
Transcription
1 UMEÅ UNIVERSITY Department of Physics Agnieszka Iwasiewicz Leif Hassmyr Ludvig Edman SOLID STATE PHYSICS HALL EFFECT
2 1. THE TASK To measure the electrical conductivity and the Hall voltage for InSb at different temperatures and from these data determine: band gap temperature dependence for the charge carriers' mobility. temperature dependence for the charge carriers' concentration. 2. ADDITIONAL LITERATURE 1. N.W. Ashcroft and N.D. Mermin, Solid State Physics (mainly chapter 28) 2. J. R. Hook and J. E. Hall, Solid State Physics 3. H. M. Rosenberg, The Solid State 3. AIM OF THE LAB The lab is providing you with a possibility to examine the Hall effect in a semiconductor. You will be asked to use the knowledge gained during the lectures in order to solve a practical task. On the way, you will work through some exercises to recall the important parts of the theory of conductivity mechanisms in a semiconductor. You will deepen the understanding of the phenomena taking place in a semiconductor at different temperatures. You will also practice the experimental skills by planning your measurements, using a thermocouple, a switch and a voltmeter, as well as you will learn how to work safely with liquid nitrogen. 4. THEORY 4.1. Electrical conductivity in a pure semiconductor For a semiconductor to conduct electrical current, the charge carriers have to be present. The charge carriers are electrons in the conduction band as well as holes in the valence band. When electron is being excited from the valence band to the conduction band, two charge carriers appear, since an electron-hole pair is created. The conductivity is determined both by the concentration of conduction electrons (n c ) and holes in the valence band (p v ), and by the charge carriers' mobility (μ c for electrons, μ v for holes). Exercise 1 Write down the expression for electrical conductivity of an intrinsic semiconductor, keeping in mind the two types of charge carriers: σ = The number of electrons thermally excited to the valence band depends on the temperature. The fraction of the total number of electrons excited across the gap at temperature T Eg 2kT B is roughly of the order e. 2
3 Exercise 2 What does the magnitude of the mobility depend on at different temperatures? An ideal, perfectly pure semiconductor (with no impurities) is called an intrinsic semiconductor. In such a semiconductor every excited electron leaves behind a hole in a valence band, and besides these there are no other charge carriers. Therefore, the charge carrier densities n ( T) = p T = n T. The charge carrier at each temperature for electrons and holes are equal: c h( ) i( ) density ni ( T ) can be determined using a formula: 32 Eg 34 2kT B 1 2kT B ni( T) = 2 ( mcmv) e, (1) 4 π h where m c and m v are the effective masses (products of the principal values of the effective mass tensor) for electrons and holes, respectively. A complete derivation of this formula can be found e.g. in the book by Ashcroft and Mermin. Exercise 3 E e kt B The Boltzmann factor (the term of type) appearing in the formula for the charge carriers concentration shows, that the energy of one thermally excited charge carrier equals half of the energy gap between the conduction and the valence band. Explain why: The temperature dependence of conductivity is completely determined by the temperature dependence of mobility and charge carriers density. For pure semiconductors at relatively high temperatures, the temperature dependence of mobility is proportional to T -3/2. This fact, together with ( ) Eg 32 2kT B ni T T e results in the temperature dependence of the conductivity: Eg 2kT B σ e. (2) The energy gap is also temperature dependent. There are two sources of this behavior: Thermal expansion of the lattice results in the expansion of the periodic potential experienced by electrons The effect of lattice vibrations varies with temperature, depending on the phonon distribution at each temperature. A typical temperature dependence of the energy gap is quadratic at very low temperatures and linear at higher temperatures. For the sake of our experiment it is correct to assume the dependence of the form: E g (T) = (1-αT) E g0. 3
4 Summarizing, one can write the formula for the conductivity in a form: σ = Ae E g0 α 2k B e E g0 2k B T (3) where A is a constant. Taking a logarithm of the above formula leads to: lnσ = ln Ae E g0 α E g0 2k B + ln 2k B T e = C E g 0 2k B T, (4) C being a constant. Exercise 4 What property of a semiconductor can be determined from the above formula? In which way? 4.2. Electrical conductivity in a doped semiconductor Usually, semiconductors are not free from impurities. One can also introduce the impurities (dopants) in order to influence the conductivity of a semiconductor. There can be two types of the impurities present: donor atoms, capable of donating an additional electron to the conduction band ( N d ionized atoms per unit volume) and/or acceptor atoms, able to absorb an electron from the valence band, and therefore creating a hole ( N atoms which accepted an electron per unit volume). a Both types can influence the conductivity and it is mostly visible in the low temperature range. The behavior caused by the presence of impurities is called the extrinsic behavior. The additional conduction electrons density, originating from the ionized donor atoms, will be denoted as n d. The additional holes density will be denoted by p a. The charge conservation and neutrality of a semiconductor as a whole demands: nc + nd + Na = pv + pa + Nd (5) where all the negatively charged contributions were collected on the left hand side of the equation, and positive-charged items on the right hand side. The above equation may be rewritten to get the expression for the (negative) charge carrier density: nc + nd = p. v + pa + Nd Na (6) n p Let us assume that the semiconductor is doped only with donor atoms. Then the charge carrier density formula gets a bit simplified. The character of the temperature dependence of the number of carriers in a unit volume is shown in figure 1 below: 4
5 Figure 1. The logarithm of a charge carrier density for a doped semiconductor, plotted versus the reciprocal temperature. Exercise 5 What is the physical origin of the temperature dependence of charge carrier density shown in figure 1? Consider the three distinct regions separately. Hint: A sketch of the energy levels in a semiconductor can be helpful. Exercise 6 Sketch the conductivity dependence on temperature. Chose the axes scales in a convenient way The Hall effect The Hall effect arises when a current I passes through a conductor exposed to a magnetic field. If the current density j is not parallel to the direction of the magnetic field B, an electric field E (Hall field) will arise in the direction of j B. The Hall field is maximal when the current is directed perpendicularly to the magnetic field. In this case, we may choose a convenient coordinate system, such that the magnetic field is pointing in the positive z-axis direction, and the current density is along the x-axis as shown on a figure 2. 5
6 Figure 2. The Hall effect geometry. The relation between the current density, electric and magnetic field vectors is now reduced to the equation binding their components: Ey = RH jxbz (7) where R is the Hall coefficient, a constant which value depends on the sample material. H In semiconductors there are two types of charge carriers, and for the relatively small magnetic fields the following equation holds: pμv nμc RH = (8) 2 e pμ + nμ ( ) The Hall effect is a direct consequence of the fact that the electric current consists of a number of moving charged particles, which experience the Lorentz force in a magnetic field. The sign of the Hall coefficient determines the type of the dominant charge carriers. Exercise 7 Check the table values of the mobility for electrons and holes in InSb (indium antimonide): μc =... μ =... v What can be said about these values? Can we assume something on the basis of this comparison? v c Exercise 8 Keeping in mind the outcome of the above exercise, write down the simplified equations for the conductivity and the Hall coefficient in case of InSb: σ = R H = 6
7 Exercise 9 How can we determine the mobility and the concentration of charge carriers? μ c = n = 5. EXPERIMENTAL SETUP The semiconductor sample to be examined is an InSb-plate with connection wires soldered onto it in accordance with figure 3. 7 Figure 3. The InSb-plate with connection wires. This plate is mounted vertically in a copper cylinder which can be placed between the poles of an electromagnet. Please do not dismount the copper cylinder. An identical InSb plate, not connected to the measurement setup is available in the lab as a model of your sample. The plate's vertical plane is parallel to the marking Ι-ΙΙ on the holder. The construction is such that the plate is in an area where the magnetic field is homogenous when the holder is at its lowest position. The temperature of the sample will be measured with a Chromel-Alumel thermocouple. One of the junctions of the thermocouple is in a close contact with the sample. The other should be placed in an ice bath, since the ice/water equilibrium point is used as a reference point for the thermocouple s voltage. The thermocouple voltage can be recalculated to the temperature by use of a calibration table, provided in the folder next to your experimental setup. The information about your sample dimensions and a wiring diagram can be also found in this folder. The sample is connected to a constant-current generator and a switch. The switch allows for the use of just one digital voltmeter (DVM) in order to measure the voltages from many sources, one after another. The voltages you can measure are (according to the labels on the switch box): HALL SP. the Hall voltage, measured between the contacts C and D on the sample (see figure 3) THERMOSP. the thermocouple voltage OHMSK SP. the Ohmic voltage along the current direction, measured between the contacts A and B on the sample (see figure 3)
8 STRÖM the voltage measured over a 10Ω resistor, use for the determination of the current The same box is additionally equipped with a switch for changing the current direction (below the voltage switching knob). The magnetic field is provided by an electromagnet. The electromagnet is supported by a stabilized DC-voltage aggregate. Set the current through the magnet coils to be 0.75 A. The current from the power supply should be controlled by the additional ampere meter for higher accuracy. The current must be maintained at a constant level throughout the experiment. The magnitude of the magnetic field can be determined with a Gauss meter. Exercise 10 Why must the current be maintained at a constant level? Liquid nitrogen (LN 2 ) will be used for cooling the sample. You will find a special insulating container for LN 2. It has a form of interconnected tubes, one thin and one thick. The container is attached to a foundation that can be slowly raised or lowered. The container is to be pre-cooled with a bit of LN 2, and filled with liquid nitrogen just a moment before the use. The thin tube is designed to fit between the poles of the magnet. When the container is raised, the copper cylinder is surrounded and filled by the liquid nitrogen and the sample is cooled. To warm up the sample, lower the container and the temperature will slowly increase. 6. EXPERIMENTAL TASKS Before you start the experiment, read through the tasks and the notes given below. Prepare a detailed plan of work and consult the measurement procedure with the lab supervisor. 1. Get familiar with the measurement equipment and prepare your workspace (e.g. fill the thermos with ice and let it rest for a moment to get a stable thermocouple s reference). 2. Determine the conductivity of the sample at different temperatures. What do you need to measure? Plot 1 lnσ = lnσ T (logarithm of conductivity versus the reciprocal temperature). 3. Determine the energy gap (band gap) E g. At which temperature can it be determined? 1 4. Plot n= n T 5. Plot 1 μc = μ c T 8
9 6. Plot ln μ ln μ ( ln ) Note 1: c = c T and determine the temperature dependence of mobility at higher temperatures. Compare your result with the theory. The conductivity of the semiconductor will unfortunately be affected by the magnetic field (magnetoresistance). In order to be able to compensate for this effect, two experiments must be made, both from 77 K to room temperature. In the first run the ohmic voltage is measured without any magnetic field (check that the Hall voltage is zero during this measurement). In the second run, the Hall voltage is determined for a constant magnetic field. Try to perform the measurements at the same temperature points (every 10 K) for both measurement series. Note 2: The sample is very small and it is possible that the Hall voltage contacts C and D are not exactly opposite to each other. Therefore, measuring the Hall voltage over the sample, one must consider that there exists an unwanted ohmic voltage component, a resistive voltage drop along the current direction. Exercise 11 Find a way how to eliminate the unwanted ohmic component from the Hall voltage measurement between the contacts C and D. Illustrate the problem with a right figure. GOOD LUCK! 9
Hall effect in germanium
Hall effect in germanium Principle The resistance and Hall voltage are measured on rectangular pieces of germanium as a function of the doping of the crystal, temperature and of magnetic field. From the
More informationADVANCED UNDERGRADUATE LABORATORY EXPERIMENT 20. Semiconductor Resistance, Band Gap, and Hall Effect
ADVANCED UNDERGRADUATE LABORATORY EXPERIMENT 20 Semiconductor Resistance, Band Gap, and Hall Effect Revised: November 1996 by David Bailey March 1990 by John Pitre & Taek-Soon Yoon Introduction Solid materials
More informationn 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 informationLast Revision: August,
A3-1 HALL EFFECT Last Revision: August, 21 2007 QUESTION TO BE INVESTIGATED How to individual charge carriers behave in an external magnetic field that is perpendicular to their motion? INTRODUCTION The
More informationSEMICONDUCTOR BEHAVIOR AND THE HALL EFFECT
5 Feb 14 Semi.1 SEMICONDUCTOR BEHAVIOR AND THE HALL EFFECT The object of this experiment is to study various properties of n- and p-doped germanium crystals. The temperature dependence of the electrical
More informationLecture 1. OUTLINE Basic Semiconductor Physics. Reading: Chapter 2.1. Semiconductors Intrinsic (undoped) silicon Doping Carrier concentrations
Lecture 1 OUTLINE Basic Semiconductor Physics Semiconductors Intrinsic (undoped) silicon Doping Carrier concentrations Reading: Chapter 2.1 EE105 Fall 2007 Lecture 1, Slide 1 What is a Semiconductor? Low
More informationCritical parameters of
Critical parameters of superconductors 2005-03-30 Why do this experiment? Superconductivity is a very interesting property from both commercial and basic scientific points of view. Superconductors are
More informationElectrical Resistance
Electrical Resistance I + V _ W Material with resistivity ρ t L Resistance R V I = L ρ Wt (Unit: ohms) where ρ is the electrical resistivity 1 Adding parts/billion to parts/thousand of dopants to pure
More informationPHY3901 PHY3905. Hall effect and semiconductors Laboratory protocol
PHY3901 PHY3905 Hall effect and semiconductors Laboratory protocol PHY3901 PHY3905 Hall effect and semiconductors Laboratory protocol Objectives Observe and qualitatively understand the phenomenon of transverse
More informationFig. 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 informationAfter successfully completing this laboratory assignment, including the assigned reading, the lab
University of California at Santa Cruz Jack Baskin School of Engineering Electrical Engineering Department EE-145L: Properties of Materials Laboratory Lab 6: Temperature Dependence of Semiconductor Conductivity
More informationFall 2014 Nobby Kobayashi
University of California at Santa Cruz Jack Baskin School of Engineering Electrical Engineering Department EE-145L: Properties of Materials Laboratory Lab 5: Temperature Dependence of Semiconductor Conductivity
More informationPhysical Structure of Matter. Hall effect in p-germanium Solid-state Physics, Plasma Physics. What you need:
Solid-state Physics, Plasma Physics Physical Structure of Matter What you can learn about Semiconductor Band theory Forbidden zone Intrinsic conductivity Extrinsic conductivity Valence band Conduction
More informationEngineering 2000 Chapter 8 Semiconductors. ENG2000: R.I. Hornsey Semi: 1
Engineering 2000 Chapter 8 Semiconductors ENG2000: R.I. Hornsey Semi: 1 Overview We need to know the electrical properties of Si To do this, we must also draw on some of the physical properties and we
More informationIntroduction to Semiconductor Devices
Physics 233 Experiment 48 Introduction to Semiconductor Devices References 1. G.W. Neudeck, The PN Junction Diode, Addison-Wesley MA 1989 2. Background notes (Appendix A) 3. Specification sheet for Diode
More informationIntroduction to Semiconductor Devices
Physics 233 Experiment 48 Introduction to Semiconductor Devices References 1. G.W. Neudeck, The PN Junction Diode, Addison-Wesley MA 1989 2. Background notes (Appendix A) 3. Specification sheet for Diode
More informationHALL EFFECT IN SEMICONDUCTORS
Warsaw University of Technology Faculty of Physics Physics Laboratory I P Andrzej Kubiaczyk 30 HALL EFFECT IN SEMICONDUCTORS 1. ackground 1.1. Electron motion in electric and magnetic fields A particle
More informationEXPERIMENT 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 informationSemiconductor Physics
Semiconductor Physics Motivation Is it possible that there might be current flowing in a conductor (or a semiconductor) even when there is no potential difference supplied across its ends? Look at the
More informationCLASS 12th. Semiconductors
CLASS 12th Semiconductors 01. Distinction Between Metals, Insulators and Semi-Conductors Metals are good conductors of electricity, insulators do not conduct electricity, while the semiconductors have
More informationPhysical Structure of Matter Hall effect in p-germanium with Cobra3. Solid-state Physics, Plasma Physics.
Physical Structure of Matter Solid-state Physics, Plasma Physics Hall effect in p-germanium with Cobra3 What you can learn about Semiconductor Band theory Forbidden zone Intrinsic conductivity Extrinsic
More informationEECS130 Integrated Circuit Devices
EECS130 Integrated Circuit Devices Professor Ali Javey 8/30/2007 Semiconductor Fundamentals Lecture 2 Read: Chapters 1 and 2 Last Lecture: Energy Band Diagram Conduction band E c E g Band gap E v Valence
More informationPhysical structure of matter Band gap of germanium with Cobra3. Solid-state Physics, Plasma Physics. What you need:
Physical structure of matter Solid-state Physics, Plasma Physics Band gap of germanium with Cobra3 What you can learn about Semiconductor Band theory Forbidden band Intrinsic conduction Extrinsic conduction
More informationSemiconductor Devices and Circuits Fall Midterm Exam. Instructor: Dr. Dietmar Knipp, Professor of Electrical Engineering. Name: Mat. -Nr.
Semiconductor Devices and Circuits Fall 2003 Midterm Exam Instructor: Dr. Dietmar Knipp, Professor of Electrical Engineering Name: Mat. -Nr.: Guidelines: Duration of the Midterm: 1 hour The exam is a closed
More informationElectro - Principles I
Electro - Principles I Page 10-1 Atomic Theory It is necessary to know what goes on at the atomic level of a semiconductor so the characteristics of the semiconductor can be understood. In many cases a
More informationSemiconductor Physics fall 2012 problems
Semiconductor Physics fall 2012 problems 1. An n-type sample of silicon has a uniform density N D = 10 16 atoms cm -3 of arsenic, and a p-type silicon sample has N A = 10 15 atoms cm -3 of boron. For each
More informationELECTRONIC I Lecture 1 Introduction to semiconductor. By Asst. Prof Dr. Jassim K. Hmood
ELECTRONIC I Lecture 1 Introduction to semiconductor By Asst. Prof Dr. Jassim K. Hmood SOLID-STATE ELECTRONIC MATERIALS Electronic materials generally can be divided into three categories: insulators,
More informationECE 142: Electronic Circuits Lecture 3: Semiconductors
Faculty of Engineering ECE 142: Electronic Circuits Lecture 3: Semiconductors Agenda Intrinsic Semiconductors Extrinsic Semiconductors N-type P-type Carrier Transport Drift Diffusion Semiconductors A semiconductor
More informationEXTRINSIC SEMICONDUCTOR
EXTRINSIC SEMICONDUCTOR EXTRINSIC SEMICONDUCTOR A semiconductor in which the impurity atoms are added by doping process is called Extrinsic semiconductor. The addition of impurities increases the carrier
More informationLecture 2. Semiconductor Physics. Sunday 4/10/2015 Semiconductor Physics 1-1
Lecture 2 Semiconductor Physics Sunday 4/10/2015 Semiconductor Physics 1-1 Outline Intrinsic bond model: electrons and holes Charge carrier generation and recombination Intrinsic semiconductor Doping:
More informationNote that it is traditional to draw the diagram for semiconductors rotated 90 degrees, i.e. the version on the right above.
5 Semiconductors The nearly free electron model applies equally in the case where the Fermi level lies within a small band gap (semiconductors), as it does when the Fermi level lies within a band (metal)
More informationECE 335: Electronic Engineering Lecture 2: Semiconductors
Faculty of Engineering ECE 335: Electronic Engineering Lecture 2: Semiconductors Agenda Intrinsic Semiconductors Extrinsic Semiconductors N-type P-type Carrier Transport Drift Diffusion Semiconductors
More informationUNIT - IV SEMICONDUCTORS AND MAGNETIC MATERIALS
1. What is intrinsic If a semiconductor is sufficiently pure, then it is known as intrinsic semiconductor. ex:: pure Ge, pure Si 2. Mention the expression for intrinsic carrier concentration of intrinsic
More informationSemiconductor Physics. Lecture 3
Semiconductor Physics Lecture 3 Intrinsic carrier density Intrinsic carrier density Law of mass action Valid also if we add an impurity which either donates extra electrons or holes the number of carriers
More informationHALL EFFECT. In a Ga!ium Arsenide Semiconductor. Jason Robin Fall 07 Phy Adv Lab. Ha! Effect 1
HALL EFFECT In a Ga!ium Arsenide Semiconductor Jason Robin Fall 07 Phy Adv Lab Ha! Effect 1 HALL EFFECT In a Ga!ium Arsenide Semiconductor Jason Robin University of Rochester Fall 07 PHY ADV LAB Introduction
More informationObservation of the Hall Effect, and measurement of the Hall constant of a few semi-conductors and metals samples.
H6-1 H6. Hall Effect I. OBJECTIVE OF THE EXPERIMENT Observation of the Hall Effect, and measurement of the Hall constant of a few semi-conductors and metals samples. II THEORETICAL BACKGROUND When a current
More informationExperiment The Hall Effect Physics 2150 Experiment No. 12 University of Colorado
Experiment 12 1 Introduction The Hall Effect Physics 2150 Experiment No. 12 University of Colorado The Hall Effect can be used to illustrate the effect of a magnetic field on a moving charge to investigate
More informationSemiconductor Physics Problems 2015
Semiconductor Physics Problems 2015 Page and figure numbers refer to Semiconductor Devices Physics and Technology, 3rd edition, by SM Sze and M-K Lee 1. The purest semiconductor crystals it is possible
More informationChapter 12: Semiconductors
Chapter 12: Semiconductors Bardeen & Shottky January 30, 2017 Contents 1 Band Structure 4 2 Charge Carrier Density in Intrinsic Semiconductors. 6 3 Doping of Semiconductors 12 4 Carrier Densities in Doped
More informationBasic Semiconductor Physics
6 Basic Semiconductor Physics 6.1 Introduction With this chapter we start with the discussion of some important concepts from semiconductor physics, which are required to understand the operation of solar
More informationUnit IV Semiconductors Engineering Physics
Introduction A semiconductor is a material that has a resistivity lies between that of a conductor and an insulator. The conductivity of a semiconductor material can be varied under an external electrical
More informationELECTRONIC DEVICES AND CIRCUITS SUMMARY
ELECTRONIC DEVICES AND CIRCUITS SUMMARY Classification of Materials: Insulator: An insulator is a material that offers a very low level (or negligible) of conductivity when voltage is applied. Eg: Paper,
More informationSemiconductors 1. Explain different types of semiconductors in detail with necessary bond diagrams. Intrinsic semiconductors:
Semiconductors 1. Explain different types of semiconductors in detail with necessary bond diagrams. There are two types of semi conductors. 1. Intrinsic semiconductors 2. Extrinsic semiconductors Intrinsic
More informationImpurity Content of a Semiconductor Crystal
Impurity Content of a Semiconductor Crystal Experiment F1/3 Contents Impurity Content of a Semiconductor Crystal... 2 1 Aims... 2 Background... 3 Doping... 3 Crystal Growth... 4 The 4-point probe... 6
More informationMat E 272 Lecture 25: Electrical properties of materials
Mat E 272 Lecture 25: Electrical properties of materials December 6, 2001 Introduction: Calcium and copper are both metals; Ca has a valence of +2 (2 electrons per atom) while Cu has a valence of +1 (1
More informationMicroscopic Ohm s Law
Microscopic Ohm s Law Outline Semiconductor Review Electron Scattering and Effective Mass Microscopic Derivation of Ohm s Law 1 TRUE / FALSE 1. Judging from the filled bands, material A is an insulator.
More informationSemiconductor Detectors
Semiconductor Detectors Summary of Last Lecture Band structure in Solids: Conduction band Conduction band thermal conductivity: E g > 5 ev Valence band Insulator Charge carrier in conductor: e - Charge
More informationConventional Paper I-2010
Conventional Paper I-010 1. (a) Sketch the covalent bonding of Si atoms in a intrinsic Si crystal Illustrate with sketches the formation of bonding in presence of donor and acceptor atoms. Sketch the energy
More informationCME 300 Properties of Materials. ANSWERS: Homework 9 November 26, As atoms approach each other in the solid state the quantized energy states:
CME 300 Properties of Materials ANSWERS: Homework 9 November 26, 2011 As atoms approach each other in the solid state the quantized energy states: are split. This splitting is associated with the wave
More informationMicron School of Materials Science and Engineering. Problem Set 9 Solutions
Problem Set 9 Solutions 1. Mobility in extrinsic semiconductors is affected by phonon scattering and impurity scattering. Thoroughly explain the mobility plots for the following figures from your textbook
More informationExperiment 11: Hall Effect & Energy Gap in Germanium
Experiment 11: Hall Effect & Energy Gap in Germanium We will see if the charge carrying particles are negative in n-doped germanium, and if they are positive in p-doped germanium. We will also measure
More informationPN Junction
P Junction 2017-05-04 Definition Power Electronics = semiconductor switches are used Analogue amplifier = high power loss 250 200 u x 150 100 u Udc i 50 0 0 50 100 150 200 250 300 350 400 i,u dc i,u u
More informationHALL. Semiconductor Resistance, Band Gap, and Hall Effect
ADVANCED UNDERGRADUATE LABORATORY HALL Semiconductor Resistance, Band Gap, and Hall Effect Revisions: September 2016, January 2018: Young-June Kim November 2011, January 2016: David Bailey October 2010:
More informationStanford University MatSci 152: Principles of Electronic Materials and Devices Spring Quarter, Final Exam, June 8, 2010
Stanford University MatSci 152: Principles of Electronic Materials and Devices Spring Quarter, 2009-2010 Final Exam, June 8, 2010 This is a closed book, closed notes exam. You are allowed two double-sided
More informationPractical 1P4 Energy Levels and Band Gaps
Practical 1P4 Energy Levels and Band Gaps What you should learn from this practical Science This practical illustrates some of the points from the lecture course on Elementary Quantum Mechanics and Bonding
More informationLecture 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 information4. I-V characteristics of electric
KL 4. - characteristics of electric conductors 4.1 ntroduction f an electric conductor is connected to a voltage source with voltage a current is produced. We define resistance being the ratio of the voltage
More informationEECS143 Microfabrication Technology
EECS143 Microfabrication Technology Professor Ali Javey Introduction to Materials Lecture 1 Evolution of Devices Yesterday s Transistor (1947) Today s Transistor (2006) Why Semiconductors? Conductors e.g
More informationPractical 1P4 Energy Levels and Band Gaps
Practical 1P4 Energy Levels and Band Gaps What you should learn from this practical Science This practical illustrates some of the points from the lecture course on Elementary Quantum Mechanics and Bonding
More informationSensing, Computing, Actuating
Sensing, Computing, ctuating Sander Stuijk (s.stuijk@tue.nl) Department of Electrical Engineering Electronic Systems 2 THERMOELECTRIC EFFECT (Chapter 5.11) 3 Thermocouple cylinder head temperature (thermocouple)
More informationFor the following statements, mark ( ) for true statement and (X) for wrong statement and correct it.
Benha University Faculty of Engineering Shoubra Electrical Engineering Department First Year communications. Answer all the following questions Illustrate your answers with sketches when necessary. The
More informationClassification 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 informationCarrier 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 informationEE301 Electronics I , Fall
EE301 Electronics I 2018-2019, Fall 1. Introduction to Microelectronics (1 Week/3 Hrs.) Introduction, Historical Background, Basic Consepts 2. Rewiev of Semiconductors (1 Week/3 Hrs.) Semiconductor materials
More informationEE143 Fall 2016 Microfabrication Technologies. Evolution of Devices
EE143 Fall 2016 Microfabrication Technologies Prof. Ming C. Wu wu@eecs.berkeley.edu 511 Sutardja Dai Hall (SDH) 1-1 Evolution of Devices Yesterday s Transistor (1947) Today s Transistor (2006) 1-2 1 Why
More informationThe Measurement of e/m
MSCD/UCD Physics Laboratories Lab II e/m The Measurement of e/m PURPOSE The objectives of this experiment are to measure the ratio between the charge and the mass of electrons, and then to find the mass
More informationSemiconductors. SEM and EDAX images of an integrated circuit. SEM EDAX: Si EDAX: Al. Institut für Werkstoffe der ElektrotechnikIWE
SEM and EDAX images of an integrated circuit SEM EDAX: Si EDAX: Al source: [Cal 99 / 605] M&D-.PPT, slide: 1, 12.02.02 Classification semiconductors electronic semiconductors mixed conductors ionic conductors
More informationV, I, R measurements: how to generate and measure quantities and then how to get data (resistivity, magnetoresistance, Hall). Makariy A.
V, I, R measurements: how to generate and measure quantities and then how to get data (resistivity, magnetoresistance, Hall). 590B Makariy A. Tanatar November 12, 2008 Resistivity Typical resistivity temperature
More informationREVISED HIGHER PHYSICS REVISION BOOKLET ELECTRONS AND ENERGY
REVSED HGHER PHYSCS REVSON BOOKLET ELECTRONS AND ENERGY Kinross High School Monitoring and measuring a.c. Alternating current: Mains supply a.c.; batteries/cells supply d.c. Electrons moving back and forth,
More informationThe Underground Experimental Investigation of Thermocouples
The Underground Experimental Investigation of Thermocouples April 14, 21 Abstract This experiment investigates a K-type thermocouple in order to demonstrate the Seebeck and Peltier coefficients. Temperature
More informationChemistry Instrumental Analysis Lecture 8. Chem 4631
Chemistry 4631 Instrumental Analysis Lecture 8 UV to IR Components of Optical Basic components of spectroscopic instruments: stable source of radiant energy transparent container to hold sample device
More informationSemiconductor physics I. The Crystal Structure of Solids
Lecture 3 Semiconductor physics I The Crystal Structure of Solids 1 Semiconductor materials Types of solids Space lattices Atomic Bonding Imperfection and doping in SOLIDS 2 Semiconductor Semiconductors
More informationSEMICONDUCTORS. Conductivity lies between conductors and insulators. The flow of charge in a metal results from the
SEMICONDUCTORS Conductivity lies between conductors and insulators The flow of charge in a metal results from the movement of electrons Electros are negatively charged particles (q=1.60x10-19 C ) The outermost
More informationThe Semiconductor in Equilibrium
Lecture 6 Semiconductor physics IV The Semiconductor in Equilibrium Equilibrium, or thermal equilibrium No external forces such as voltages, electric fields. Magnetic fields, or temperature gradients are
More informationX: The Hall Effect in Metals
X: The all Effect in Metals I. References C. Kittel: Introduction to Solid State Physics, pp. 148-151. Ashcroft and Mermin: Solid state Physics, pp. 6-15. Dekker: Solid State Physics, pp. 301-302. Yarwood:
More informationProcessing of Semiconducting Materials Prof. Pallab Banerji Department of Material Science Indian Institute of Technology, Kharagpur
Processing of Semiconducting Materials Prof. Pallab Banerji Department of Material Science Indian Institute of Technology, Kharagpur Lecture - 4 Doping in Semiconductors Good morning. Let us start with
More informationSemiconductor Physics fall 2012 problems
Semiconductor Physics fall 2012 problems 1. An n-type sample of silicon has a uniform density N D = 10 16 atoms cm -3 of arsenic, and a p-type silicon sample has N A = 10 15 atoms cm -3 of boron. For each
More informationDiamond. Covalent Insulators and Semiconductors. Silicon, Germanium, Gray Tin. Chem 462 September 24, 2004
Covalent Insulators and Chem 462 September 24, 2004 Diamond Pure sp 3 carbon All bonds staggered- ideal d(c-c) - 1.54 Å, like ethane Silicon, Germanium, Gray Tin Diamond structure Si and Ge: semiconductors
More informationChapter 1 Overview of Semiconductor Materials and Physics
Chapter 1 Overview of Semiconductor Materials and Physics Professor Paul K. Chu Conductivity / Resistivity of Insulators, Semiconductors, and Conductors Semiconductor Elements Period II III IV V VI 2 B
More informationChap. 1 (Introduction), Chap. 2 (Components and Circuits)
CHEM 455 The class describes the principles and applications of modern analytical instruments. Emphasis is placed upon the theoretical basis of each type of instrument, its optimal area of application,
More informationR measurements (resistivity, magnetoresistance, Hall). Makariy A. Tanatar
R measurements (resistivity, magnetoresistance, Hall). 590B Makariy A. Tanatar April 18, 2014 Resistivity Typical resistivity temperature dependence: metals, semiconductors Magnetic scattering Resistivities
More informationMost matter is electrically neutral; its atoms and molecules have the same number of electrons as protons.
Magnetism Electricity Magnetism Magnetic fields are produced by the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. -> permanent magnets Magnetic
More informationChapter 5. Carrier Transport Phenomena
Chapter 5 Carrier Transport Phenomena 1 We now study the effect of external fields (electric field, magnetic field) on semiconducting material 2 Objective Discuss drift and diffusion current densities
More informationChapter 1 Semiconductor basics
Chapter 1 Semiconductor basics ELEC-H402/CH1: Semiconductor basics 1 Basic semiconductor concepts Semiconductor basics Semiconductors, silicon and hole-electron pair Intrinsic silicon properties Doped
More informationSpring 2010 MSE 111. Midterm Exam. Prof. Eugene E. Haller. University of California at Berkeley Department of Materials Science and Engineering
Spring 00 MS Midterm xam Prof. ugene. Haller University of California at Berkeley Department of Materials Science and ngineering 3/6/0, 9:40 am 80 minutes, 74 points total, 0 pages ame: SID: Problem 3
More informationEE 446/646 Photovoltaic Devices I. Y. Baghzouz
EE 446/646 Photovoltaic Devices I Y. Baghzouz What is Photovoltaics? First used in about 1890, the word has two parts: photo, derived from the Greek word for light, volt, relating to electricity pioneer
More informationElectrical Properties
Electrical Properties Electrical Conduction R Ohm s law V = IR I l Area, A V where I is current (Ampere), V is voltage (Volts) and R is the resistance (Ohms or ) of the conductor Resistivity Resistivity,
More informationTHE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF PHYSICS FINAL EXAMINATION JUNE/JULY PHYS3080 Solid State Physics
THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF PHYSICS FINAL EXAMINATION JUNE/JULY 006 PHYS3080 Solid State Physics Time Allowed hours Total number of questions - 5 Answer ALL questions All questions are
More informationChapter 27. Current and Resistance
Chapter 27 Current and Resistance Electric Current Most practical applications of electricity deal with electric currents. The electric charges move through some region of space. The resistor is a new
More informationn N D n p = n i p N A
Summary of electron and hole concentration in semiconductors Intrinsic semiconductor: E G n kt i = pi = N e 2 0 Donor-doped semiconductor: n N D where N D is the concentration of donor impurity Acceptor-doped
More informationHigher Physics. Electricity. Summary Notes. Monitoring and measuring a.c. Current, potential difference, power and resistance
Higher Physics Electricity Summary Notes Monitoring and measuring a.c. Current, potential difference, power and resistance Electrical sources and internal resistance Capacitors Conductors, semiconductors
More informationNEEL Phase Change in Chromium At the Néel Temperature
University of Toronto ADVANCED PHYSICS LABOATOY NEEL Phase Change in Chromium At the Néel Temperature evisions: January 2018: January/August 2016: October 2005: Original: Young-June Kim David Bailey
More informationChap. 11 Semiconductor Diodes
Chap. 11 Semiconductor Diodes Semiconductor diodes provide the best resolution for energy measurements, silicon based devices are generally used for charged-particles, germanium for photons. Scintillators
More informationCh. 2: Energy Bands And Charge Carriers In Semiconductors
Ch. 2: Energy Bands And Charge Carriers In Semiconductors Discrete energy levels arise from balance of attraction force between electrons and nucleus and repulsion force between electrons each electron
More informationThe photovoltaic effect occurs in semiconductors where there are distinct valence and
How a Photovoltaic Cell Works The photovoltaic effect occurs in semiconductors where there are distinct valence and conduction bands. (There are energies at which electrons can not exist within the solid)
More informationExperiment 3. Electrical Energy. Calculate the electrical power dissipated in a resistor.
Experiment 3 Electrical Energy 3.1 Objectives Calculate the electrical power dissipated in a resistor. Determine the heat added to the water by an immersed heater. Determine if the energy dissipated by
More informationElectric Field Mapping
Electric Field Mapping Equipment: mapping board, U-probe, 5 resistive boards, templates, knob adjustable DC voltmeter, 4 long leads, 16 V DC for wall strip, 8 1/2 X 11 sheets of paper Reading: Topics of
More information1 Written and composed by: Prof. Muhammad Ali Malik (M. Phil. Physics), Govt. Degree College, Naushera
CURRENT ELECTRICITY Q # 1. What do you know about electric current? Ans. Electric Current The amount of electric charge that flows through a cross section of a conductor per unit time is known as electric
More informationReview of Semiconductor Fundamentals
ECE 541/ME 541 Microelectronic Fabrication Techniques Review of Semiconductor Fundamentals Zheng Yang (ERF 3017, email: yangzhen@uic.edu) Page 1 Semiconductor A semiconductor is an almost insulating material,
More informationDoped Semiconductors *
OpenStax-CNX module: m1002 1 Doped Semiconductors * Bill Wilson This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 1.0 To see how we can make silicon a useful
More information