# Mat E 272 Lecture 25: Electrical properties of materials

Size: px
Start display at page:

Transcription

1 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 electron per atom). Simply on the basis of numbers of charge carriers per unit volume, we might expect Ca to be a better conductor of electricity. However, this is not the case. Why then is Cu, with half as many valence electrons per atom, a far better electrical conductor than Ca? We will see that the answer lies in the nature of the electronic energy levels (or bands) that form when individual atoms coalesce into a solid. This energy band structure approach also describes the electrical behavior of semiconductors, one of the most technologically significant materials in the last 50 years. We begin with a review of some of the fundamental concepts such as Ohm s law and the nature of energy bands in solids. We will also see how solid solution alloying in metals can have a major impact on the motion of conduction electrons in the resulting alloy, in much the same way as solid solution strengthening affects dislocation motion.

2 Introduction Electrical conductivity: Did you know that electrical conductivity spans a greater range of values than any other material property? From insulators such as talc and sulfur on one extreme to highly conducting metals such as silver and copper and at the other extreme, this property spans over 20 orders of magnitude!!! Why is the propagation of electrical current so easy in some materials while almost non-existent in others?

3 Definitions Electrical conductivity: a quantitative measure of the ease with which electrical current is propagated in a material in response to an external electric field Suppose we place a material in an electric field, of magnitude E. In response to the applied field, charge carriers in the material will drift, or diffuse, down the field gradient. Empirically, we find that for any given material, the ratio of current density to applied field at constant temperature is a constant, called the electrical conductivity, σ (sigma) σ is a fundamental material property and varies with temperature The reciprocal of σ is called the electrical resistivity, and is abbreviated as ρ (rho)

4 Macroscopic conductivity - Ohm s law Ohm s law: The relationship between applied electric field and current density is more commonly known as Ohm s law: J = σe = σ(dv/dx) although you may be more familiar with another form of Ohm s law: I = (1/R)V where I is the electrical current, V is the voltage drop, and R is the electrical resistance (not resistivity in this equation). Current density can also be written as J = nev, where n is the density of current carriers, v is their drift velocity, and e is the charge of an electron, or 1.6x10-19 coulomb. Units of conductivity are (Ohm-m) -1, although (mohm-m) -1, and (mohm-cm) -1 are also frequently used. Ohm is given a special symbol: Ω (Omega)

5 Macroscopic conductivity - Ohm s law Ohm s law: What is the relationship between conductivity, σ, (or resistivity, ρ) and resistance, R? Resistance depends on the geometry of a material and is NOT a fundamental material property. Conductivity (or resistivity) does NOT depend on the size or shape of a material and IS a fundamental material property. R = V/I ρ = R(A/l), so ρ = (V/I)(A/l) so, σ = 1/ρ (the geometrical factor, A/l, accounts for the fact that resistance depends on cross sectional area and on length)

6 Electron propagation Energy bands: In order to understand how materials carry electrical current, we must look first at the allowed energy states for electrons, and how these allowed states are formed. We will use a metal to illustrate the point, but the basic argument applies equally well to any material. Recall that an isolated atom is characterized by a set of discrete energy shells, or orbitals, within which the electrons are constrained. As shown at right, there are actually three states corresponding to the 2p subshell.

7 Electron propagation Energy bands: When individual atoms come together to form a solid, these energy states split into discrete levels*, in accordance with the Pauli exclusion principle. If not for the splitting, there would be too many electrons trying to occupy too few energy levels. The splitting and coalescence of energy states is a consequence of the interaction between each atom s wavefunction. Notice how the discrete energy shells each split into bands. This example corresponds to a hypothetical situation in which 12 atoms coalesce, hence 12 bands for each quantum state. Imagine if we had atoms coming together, the number of bands would be immense and the energy spacing between them would be exceedingly small (but not continuous). * If there is one state per energy level, such as the 1s or 2s, there will be N bands. If there are 3 states per level, such as the 2p, then there will be 3N bands, and so on.

8 Electron propagation Energy bands: This is not a continuum of energy levels; this actually represents a huge number of discrete levels, each separated by a very small energy (~ kt) Note the presence of gaps between energy bands, and that the ground state is not split at the equilibrium atomic separation distance. Electrons cannot occupy energy levels within the gaps

9 Electron propagation Energy bands - metals: When energy bands are formed in solids, different arrangements are possible, depending on the initial distribution of electrons within the quantum states of the individual atoms. For example, the 4s subshell in copper is only half full, since it contains 1 valence electron. Thus, there are empty states within this level. In contrast, magnesium contains 2 electrons in its 3s subshell (which is thus filled), but when the individual Mg atoms form a solid, the s and p bands overlap, producing available energy states near the top-most filled band.

10 Electron propagation Energy bands - semiconductors and insulators: Notice in particular the two cases shown on the right. For these materials, there is a forbidden gap between the occupied valence bands and the unoccupied conduction bands. (Conduction bands run throughout the metal and account for electrical conductivity, whereas valence bands correspond to localized electrons). Such materials are called either semiconductors or insulators, depending on the magnitude of the forbidden energy gap. Energy (thermal or optical) is required to excite a valence electron across the gap into the conduction band.

11 Fermi level Way cool... Suppose we cool a material down to 0K (absolute zero). The electrons will fill up energy levels, starting with the lowest (1s), (consistent with the Pauli exclusion principle), until all electrons are accounted for. In this ground state configuration, we can identify a highest filled level (and a lowest unoccupied level). The energy level corresponding to the highest occupied level (at 0K) is given a special name; it is called the Fermi energy. The Fermi energy is just a fancy way of identifying the separation, or boundary, between occupied energy levels and unoccupied energy levels. The position of the Fermi energy is important, because it determines whether there are any nearby unoccupied conduction states for electrons to drift from atom to atom. If there are no available conduction states, then no matter how many electrons there are, conduction cannot take place and the electrons are localized. (Think about a classroom in which every seat is occupied; there may be a lot of students present, but none of them can move because there are no available seats.)

12 Fermi level - in a bit more detail Electronic conduction: Core electrons (those in low-lying energy states) find it difficult to participate in conduction because in order to move freely through the metal, they would have to push past all the other electrons lying in higher energy states. It would require a lot of energy for this to happen; consequently, core electrons remain localized. However, for those electrons near the top-most filled levels, only a little bit of energy is needed to push them into unoccupied states, if there are available states nearby (in terms of energy). We refer to the density of states (DOS) as the number of available energy states per unit volume. If the DOS near the top-most filled energy level is high, then there are plenty of places for electrons to become de-localized (or free) and drift throughout the material. However, if the DOS near the top-most filled band is low (or zero), then there are few available states and the electrons remain bound to their respective atoms.

13 Conduction states Electronic conduction: The top figure illustrates what happens when an electron occupying a state near the Fermi energy in a metal receives sufficient thermal energy to be excited into a higher energy state (e.g., in the conduction band). This electron now contributes to the bulk electrical current. The lower figure depicts the situation in semiconductors and insulators, where there is an energy gap between the valence and conduction bands. Much more energy must be imparted to the electron in order for it to overcome the barrier.

14 Metal systems Electrical conductivity of metals and alloys: Note how the resistivity increases (or how the conductivity decreases) with increasing solute concentration. This is because the solute atoms act as scattering sites, disrupting the otherwise regular periodicity of the lattice.

15 Semiconductors From electrons and holes to cell phones and PDAs Semiconductors form the backbone of our technological society all microchip processors are based on applications of Si, Ge, and other IIIA-VA and IIB-VIA compounds. In addition, many devices used as sensors are also based on these materials. What gives semiconductors their unique electrical behavior is the extreme sensitivity (exponential dependence) to the presence of minute quantities of solute, which we refer to as dopants. The next slide shows an example of how much the resistivity of Si changes upon addition of boron. Make note of the solute concentration; we re talking 13 parts per million (ppm) of boron; this is a fantastically small amount of additive, yet, it is enough to make the resistivity increase by over 4 orders of magnitude!

16 Semiconductors Effect of boron doping in silicon: This is amazing! Addition of only 13 ppm of B to Si increases the resistivity by several orders of magnitude! This means we have a way of fine-tuning the electrical properties of these materials simply by doping. How can this be?

17 Semiconductors The answer lies in the nature of the electronic structure of semiconductors Let s look at silicon as an example: Undoped (intrinsic) Si: Si doped with P: Each Si atom has 4 valence electrons which are covalently bonded to its nearest neighbors. When a phosphorus atom is substituted, since is has 5 valence electrons, all of the covalent bonds are satisfied and there is one electron left over. This extra electron is loosely bound; we say that the P doping introduces impurity states within the band gap, so it takes much less energy (on the order of a few mev, or 0.01 ev) for this extra electron to be promoted into the conduction band than for the other bound electrons.

18 Semiconductors Since the additional electron is loosely bound to its parent atom, only a minute amount of energy is needed to excite it into the conduction band (~ 0.01 ev). There, it can respond to an applied electric field and drift through the crystal. The loosely bound electron forms a donor state, and may reside only a few mev below the conduction band edge:

19 Semiconductors Similar behavior is obtained by doping with an element containing fewer valence electrons than the solvent, or host material. Such is the case with boron doping in silicon. The B atom produces an electron deficiency and results in formation of an impurity state within the band gap, close to the valence band. Thermal excitation of an electron from the valence band into this acceptor state forms a defect in the valence band, known as a hole. The hole is the active charge carrier and moves in opposite sense as an electron in the conduction band.

20 Semiconductors Temperature effects: What happens as a semiconductor is heated up? As more and more electrons acquire sufficient energy to overcome the band gap, the semiconductor becomes a better conductor of electricity. This is one key distinction between semiconductors and metals; as metals heat up, their electrical conductivity decreases. The conductivity of a semiconductor is described by an Arrhenius equation of the form E g kt σ = Ce 2 where E g is the magnitude of the band gap, k is Boltzman s constant, and T is the absolute temperature.

21 Example problem Problem: If the room temperature (298K) conductivity of intrinsic silicon is (Ohm-m) -1, estimate its conductivity at 150 o C (= 423K). Solution: If we know σ at one temperature, we can use this information to find the E value of the constant, C, in the Arrhenius equation for conductivity, g Then, we simply substitute this value back into the equation for the desired temperature : Starting with the given room temperature data: C = lnσ then, lnσ so σ = e Eg + 2kT Eg = C 2kT 0.69 = ln(0.0009) = = 0.50 (Ω-m) -1 5 ( x10 ev / K )( 298K ) 1.1eV 1.1eV 5 ( x10 ev / K )( 423K ) = 0.69 σ = Ce 2 = 14.4 kt

22 Appendix - useful electrical units information

### Lecture 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

### Introduction to Engineering Materials ENGR2000. Dr.Coates

Introduction to Engineering Materials ENGR2000 Chapter 18: Electrical Properties Dr.Coates 18.2 Ohm s Law V = IR where R is the resistance of the material, V is the voltage and I is the current. l R A

### CME 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

### FREQUENTLY ASKED QUESTIONS February 21, 2017

FREQUENTLY ASKED QUESTIONS February 21, 2017 Content Questions How do you place a single arsenic atom with the ratio 1 in 100 million? Sounds difficult to get evenly spread throughout. Yes, techniques

### Introduction to Semiconductor Physics. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

Introduction to Semiconductor Physics 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/cmp2013 Review of Semiconductor Physics Semiconductor fundamentals

### EE301 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

### DO PHYSICS ONLINE ELECTRIC CURRENT FROM IDEAS TO IMPLEMENTATION ATOMS TO TRANSISTORS ELECTRICAL PROPERTIES OF SOLIDS

DO PHYSICS ONLINE FROM IDEAS TO IMPLEMENTATION 9.4.3 ATOMS TO TRANSISTORS ELECTRICAL PROPERTIES OF SOLIDS ELECTRIC CURRENT Different substances vary considerably in their electrical properties. It is a

### EE 346: Semiconductor Devices

EE 346: Semiconductor Devices Lecture - 6 02/06/2017 Tewodros A. Zewde 1 DENSTY OF STATES FUNCTON Since current is due to the flow of charge, an important step in the process is to determine the number

### Engineering 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

### From Last Time Important new Quantum Mechanical Concepts. Atoms and Molecules. Today. Symmetry. Simple molecules.

Today From Last Time Important new Quantum Mechanical Concepts Indistinguishability: Symmetries of the wavefunction: Symmetric and Antisymmetric Pauli exclusion principle: only one fermion per state Spin

### Semiconductors 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

### Ch. 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

### Atoms? All matters on earth made of atoms (made up of elements or combination of elements).

Chapter 1 Atoms? All matters on earth made of atoms (made up of elements or combination of elements). Atomic Structure Atom is the smallest particle of an element that can exist in a stable or independent

### Semiconductors. Semiconductors also can collect and generate photons, so they are important in optoelectronic or photonic applications.

Semiconductors Semiconducting materials have electrical properties that fall between true conductors, (like metals) which are always highly conducting and insulators (like glass or plastic or common ceramics)

### Microscopic 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.

### A semiconductor is an almost insulating material, in which by contamination (doping) positive or negative charge carriers can be introduced.

Semiconductor A semiconductor is an almost insulating material, in which by contamination (doping) positive or negative charge carriers can be introduced. Page 2 Semiconductor materials Page 3 Energy levels

### ECE 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

### Doped 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

### Lecture 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:

### ELECTRONIC 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,

### EECS130 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

### Lecture 7: Extrinsic semiconductors - Fermi level

Lecture 7: Extrinsic semiconductors - Fermi level Contents 1 Dopant materials 1 2 E F in extrinsic semiconductors 5 3 Temperature dependence of carrier concentration 6 3.1 Low temperature regime (T < T

### Electronics The basics of semiconductor physics

Electronics The basics of semiconductor physics Prof. Márta Rencz, Gergely Nagy BME DED September 16, 2013 The basic properties of semiconductors Semiconductors conductance is between that of conductors

### Lecture Number - 01 Metals, Semiconductors and Insulators

Electronic Materials, Devices and Fabrication Dr. S. Parasuraman Department of Metallurgical and Materials Engineering Indian Institute of Technology, Madras Lecture Number - 01 Metals, Semiconductors

### ECE 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

### Electro - 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

### Electrons in materials. (where are they, what is their energy)

Electrons in materials (where are they, what is their energy) 1 Lone atoms A single atom has electrons in shells and sub shells. Each of these have a distinct energy level. The diagram shows an example

### CLASS 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

### Review 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,

### Semiconductor Physics and Devices Chapter 3.

Introduction to the Quantum Theory of Solids We applied quantum mechanics and Schrödinger s equation to determine the behavior of electrons in a potential. Important findings Semiconductor Physics and

### EE143 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

### Diamond. 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

### Free Electron Model for Metals

Free Electron Model for Metals Metals are very good at conducting both heat and electricity. A lattice of in a sea of electrons shared between all nuclei (moving freely between them): This is referred

### ECE 250 Electronic Devices 1. Electronic Device Modeling

ECE 250 Electronic Devices 1 ECE 250 Electronic Device Modeling ECE 250 Electronic Devices 2 Introduction to Semiconductor Physics You should really take a semiconductor device physics course. We can only

### EE 346: Semiconductor Devices

EE 346: Semiconductor Devices Lecture - 5 02/01/2017 Tewodros A. Zewde 1 The One-Electron Atom The potential function is due to the coulomb attraction between the proton and electron and is given by where

### Free Electron Model for Metals

Free Electron Model for Metals Metals are very good at conducting both heat and electricity. A lattice of in a sea of electrons shared between all nuclei (moving freely between them): This is referred

### Ga and P Atoms to Covalent Solid GaP

Ga and P Atoms to Covalent Solid GaP Band Gaps in Binary Group III-V Semiconductors Mixed Semiconductors Affect of replacing some of the As with P in GaAs Band Gap (ev) (nm) GaAs 1.35 919 (IR) GaP 2.24

### Charge Carriers in Semiconductor

Charge Carriers in Semiconductor To understand PN junction s IV characteristics, it is important to understand charge carriers behavior in solids, how to modify carrier densities, and different mechanisms

### HALL 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

### ITT Technical Institute ET215 Devices I Unit 1

ITT Technical Institute ET215 Devices I Unit 1 Chapter 1 Chapter 2, Sections 2.1-2.4 Chapter 1 Basic Concepts of Analog Circuits Recall ET115 & ET145 Ohms Law I = V/R If voltage across a resistor increases

### Due to the quantum nature of electrons, one energy state can be occupied only by one electron.

In crystalline solids, not all values of the electron energy are possible. The allowed intervals of energy are called allowed bands (shown as blue and chess-board blue). The forbidden intervals are called

### Session 0: Review of Solid State Devices. From Atom to Transistor

Session 0: Review of Solid State Devices From Atom to Transistor 1 Objective To Understand: how Diodes, and Transistors operate! p n p+ n p- n+ n+ p 2 21 Century Alchemy! Ohm s law resistivity Resistivity

### EECS143 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

### 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

Chapter 12: Electrical Properties School of Mechanical Engineering Choi, Hae-Jin Materials Science - Prof. Choi, Hae-Jin Chapter 12-1 ISSUES TO ADDRESS... How are electrical conductance and resistance

### From Last Time. Several important conceptual aspects of quantum mechanics Indistinguishability. Symmetry

From Last Time Several important conceptual aspects of quantum mechanics Indistinguishability particles are absolutely identical Leads to Pauli exclusion principle (one Fermion / quantum state). Symmetry

### 3.1 Introduction to Semiconductors. Y. Baghzouz ECE Department UNLV

3.1 Introduction to Semiconductors Y. Baghzouz ECE Department UNLV Introduction In this lecture, we will cover the basic aspects of semiconductor materials, and the physical mechanisms which are at the

### Calculating Band Structure

Calculating Band Structure Nearly free electron Assume plane wave solution for electrons Weak potential V(x) Brillouin zone edge Tight binding method Electrons in local atomic states (bound states) Interatomic

### ECE 442. Spring, Lecture -2

ECE 442 Power Semiconductor Devices and Integrated circuits Spring, 2006 University of Illinois at Chicago Lecture -2 Semiconductor physics band structures and charge carriers 1. What are the types of

### KATIHAL FİZİĞİ MNT-510

KATIHAL FİZİĞİ MNT-510 YARIİLETKENLER Kaynaklar: Katıhal Fiziği, Prof. Dr. Mustafa Dikici, Seçkin Yayıncılık Katıhal Fiziği, Şakir Aydoğan, Nobel Yayıncılık, Physics for Computer Science Students: With

### Chapter 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

### Electronic Circuits for Mechatronics ELCT 609 Lecture 2: PN Junctions (1)

Electronic Circuits for Mechatronics ELCT 609 Lecture 2: PN Junctions (1) Assistant Professor Office: C3.315 E-mail: eman.azab@guc.edu.eg 1 Electronic (Semiconductor) Devices P-N Junctions (Diodes): Physical

### LN 3 IDLE MIND SOLUTIONS

IDLE MIND SOLUTIONS 1. Let us first look in most general terms at the optical properties of solids with band gaps (E g ) of less than 4 ev, semiconductors by definition. The band gap energy (E g ) can

### Semiconductor 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

### Semiconductor 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

### n 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

### Basic 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

### Chapter 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

### Lecture 2. Introduction to semiconductors Structures and characteristics in semiconductors

Lecture 2 Introduction to semiconductors Structures and characteristics in semiconductors Semiconductor p-n junction Metal Oxide Silicon structure Semiconductor contact Literature Glen F. Knoll, Radiation

### Unit 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

### Lecture (02) Introduction to Electronics II, PN Junction and Diodes I

Lecture (02) Introduction to Electronics II, PN Junction and Diodes I By: Dr. Ahmed ElShafee ١ Agenda Current in semiconductors/conductors N type, P type semiconductors N Type Semiconductor P Type Semiconductor

### Chapter Two. Energy Bands and Effective Mass

Chapter Two Energy Bands and Effective Mass Energy Bands Formation At Low Temperature At Room Temperature Valence Band Insulators Metals Effective Mass Energy-Momentum Diagrams Direct and Indirect Semiconduction

### Chem 481 Lecture Material 3/20/09

Chem 481 Lecture Material 3/20/09 Radiation Detection and Measurement Semiconductor Detectors The electrons in a sample of silicon are each bound to specific silicon atoms (occupy the valence band). If

### Lecture 1 - Electrons, Photons and Phonons. September 4, 2002

6.720J/3.43J - Integrated Microelectronic Devices - Fall 2002 Lecture 1-1 Lecture 1 - Electrons, Photons and Phonons Contents: September 4, 2002 1. Electronic structure of semiconductors 2. Electron statistics

### Electrical 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,

### Minimal Update of Solid State Physics

Minimal Update of Solid State Physics It is expected that participants are acquainted with basics of solid state physics. Therefore here we will refresh only those aspects, which are absolutely necessary

### ESE 372 / Spring 2013 / Lecture 5 Metal Oxide Semiconductor Field Effect Transistor

Metal Oxide Semiconductor Field Effect Transistor V G V G 1 Metal Oxide Semiconductor Field Effect Transistor We will need to understand how this current flows through Si What is electric current? 2 Back

### ELEMENTARY BAND THEORY

ELEMENTARY BAND THEORY PHYSICIST Solid state band Valence band, VB Conduction band, CB Fermi energy, E F Bloch orbital, delocalized n-doping p-doping Band gap, E g Direct band gap Indirect band gap Phonon

### Chap. 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

### The 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)

### The 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

### David J. Starling Penn State Hazleton PHYS 214

Being virtually killed by a virtual laser in a virtual space is just as effective as the real thing, because you are as dead as you think you are. -Douglas Adams, Mostly Harmless David J. Starling Penn

### Unit III Free Electron Theory Engineering Physics

. Introduction The electron theory of metals aims to explain the structure and properties of solids through their electronic structure. The electron theory is applicable to all solids i.e., both metals

### Basic cell design. Si cell

Basic cell design Si cell 1 Concepts needed to describe photovoltaic device 1. energy bands in semiconductors: from bonds to bands 2. free carriers: holes and electrons, doping 3. electron and hole current:

### 12/10/09. Chapter 18: Electrical Properties. View of an Integrated Circuit. Electrical Conduction ISSUES TO ADDRESS...

Chapter 18: Electrical Properties ISSUES TO ADDRESS... How are electrical conductance and resistance characterized? What are the physical phenomena that distinguish? For metals, how is affected by and

### Bonding in solids The interaction of electrons in neighboring atoms of a solid serves the very important function of holding the crystal together.

Bonding in solids The interaction of electrons in neighboring atoms of a solid serves the very important function of holding the crystal together. For example Nacl In the Nacl lattice, each Na atom is

### CLASS 1 & 2 REVISION ON SEMICONDUCTOR PHYSICS. Reference: Electronic Devices by Floyd

CLASS 1 & 2 REVISION ON SEMICONDUCTOR PHYSICS Reference: Electronic Devices by Floyd 1 ELECTRONIC DEVICES Diodes, transistors and integrated circuits (IC) are typical devices in electronic circuits. All

### CHAPTER 2: ENERGY BANDS & CARRIER CONCENTRATION IN THERMAL EQUILIBRIUM. M.N.A. Halif & S.N. Sabki

CHAPTER 2: ENERGY BANDS & CARRIER CONCENTRATION IN THERMAL EQUILIBRIUM OUTLINE 2.1 INTRODUCTION: 2.1.1 Semiconductor Materials 2.1.2 Basic Crystal Structure 2.1.3 Basic Crystal Growth technique 2.1.4 Valence

### Chemistry 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

### First-Hand Investigation: Modeling of Semiconductors

perform an investigation to model the behaviour of semiconductors, including the creation of a hole or positive charge on the atom that has lost the electron and the movement of electrons and holes in

### Processing 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

### Solid State Physics. Lecture 10 Band Theory. Professor Stephen Sweeney

Solid State Physics Lecture 10 Band Theory Professor Stephen Sweeney Advanced Technology Institute and Department of Physics University of Surrey, Guildford, GU2 7XH, UK s.sweeney@surrey.ac.uk Recap from

### Lecture 2. Introduction to semiconductors Structures and characteristics in semiconductors

Lecture 2 Introduction to semiconductors Structures and characteristics in semiconductors Semiconductor p-n junction Metal Oxide Silicon structure Semiconductor contact Literature Glen F. Knoll, Radiation

### Electrical 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

### EE 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

### smal band gap Saturday, April 9, 2011

small band gap upper (conduction) band empty small gap valence band filled 2s 2p 2s 2p hybrid (s+p)band 2p no gap 2s (depend on the crystallographic orientation) extrinsic semiconductor semi-metal electron

### Lecture 3b. Bonding Model and Dopants. Reading: (Cont d) Notes and Anderson 2 sections

Lecture 3b Bonding Model and Dopants Reading: (Cont d) Notes and Anderson 2 sections 2.3-2.7 The need for more control over carrier concentration Without help the total number of carriers (electrons and

### Review of Optical Properties of Materials

Review of Optical Properties of Materials Review of optics Absorption in semiconductors: qualitative discussion Derivation of Optical Absorption Coefficient in Direct Semiconductors Photons When dealing

### Semiconductor 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

### Semiconductor Device Physics

1 Semiconductor Device Physics Lecture 1 http://zitompul.wordpress.com 2 0 1 3 2 Semiconductor Device Physics Textbook: Semiconductor Device Fundamentals, Robert F. Pierret, International Edition, Addison

### 3C3 Analogue Circuits

Department of Electronic & Electrical Engineering Trinity College Dublin, 2014 3C3 Analogue Circuits Prof J K Vij jvij@tcd.ie Lecture 1: Introduction/ Semiconductors & Doping 1 Course Outline (subject

### SEMICONDUCTORS. 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

### The Periodic Table III IV V

The Periodic Table III IV V Slide 1 Electronic Bonds in Silicon 2-D picture of perfect crystal of pure silicon; double line is a Si-Si bond with each line representing an electron Si ion (charge +4 q)

### ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems

ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Lec 6: September 14, 2015 MOS Model You are Here: Transistor Edition! Previously: simple models (0 and 1 st order) " Comfortable

### PN 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

### Lecture (02) PN Junctions and Diodes

Lecture (02) PN Junctions and Diodes By: Dr. Ahmed ElShafee ١ I Agenda N type, P type semiconductors N Type Semiconductor P Type Semiconductor PN junction Energy Diagrams of the PN Junction and Depletion

### ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems

ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Lec 6: September 18, 2017 MOS Model You are Here: Transistor Edition! Previously: simple models (0 and 1 st order) " Comfortable

### 7. FREE ELECTRON THEORY.

7. FREE ELECTRON THEORY. Aim: To introduce the free electron model for the physical properties of metals. It is the simplest theory for these materials, but still gives a very good description of many