Solid State Device Fundamentals

Size: px
Start display at page:

Download "Solid State Device Fundamentals"

Transcription

1 Solid State Device Fundamentals ES 345 Lecture Course by Alexander M. Zaitsev Tel: Oice 4101b 1

2 The ree electron model o metals The ree electron model o metals assumes that electrons are ree to move within the metal but are conined to the metal by potential barriers. The minimum energy W needed to extract an electron rom the metal equals ef M, where F M is the work unction. F M may vary rom 2.1 ev (or Cs) to 5.9 ev (Pt). This model ignores the periodic potential due to atoms and as such it does not work well or semiconductors. 5.3 ev 4.1 ev 2

3 Electrons in periodic potential Uniorm potential Periodic potential E E Energy o electron versus wavevector k (linear momentum p=ħk) or ree electron. Energy o electron versus wavevector k in monoatomic crystal lattice o lattice constant a. The energy gap E g is associated with the irst Bragg relection at k=±π/a ( = 2a). 3

4 Description o electrons in crystal A complete description o the electrons in a crystal is based on their wave characteristics, not just the particle characteristics. The electron wave unction is the solution o the three-dimensional Schrödinger wave equation: ħ2 2m 0 2 ψ + V(r)ψ = ψe Solution: = A exp(ik r), where k = 2π/ Acceleration = F = ee d 2 E m ħ 2 dk 2 For each k, there is a corresponding energy E. Eective mass, m = ħ 2 / d2 E dk 2 How much is eective mass o ree electron? 4

5 Eective mass o electron in semiconductors 5

6 Formation o energy bands o electrons in silicon hybridization a Energy levels in silicon as a unction o interatomic distance. The core levels (n = 1, 2) are completely illed with electrons. At the actual interatomic distance a o a crystal with atoms, the 2 electrons in the 3s subshell and the 2 electrons in the 3p subshell hybridize (sp 3 hybridization) producing 4 states o lower energy (valence energy band) and 4 states o higher energy (conduction energy band). 6

7 Electron energy bands in crystals electrons holes Possible energy band diagrams o a crystal: a) a hal illed band, b) two overlapping bands, c) an almost ull band separated by a small bandgap rom an almost empty band and d) a ull band and an empty band separated by a large bandgap. 7

8 Density o states The density o states in a semiconductor equals the density per unit volume and energy o the number o solutions to Schrödinger's equation. Assumptions: - Semiconductor is modeled as an ininite quantum well in which electrons have eective mass, m *, and are ree to move. - The energy in the well is set to zero. - The semiconductor is assumed a cube with side L. This assumption does not aect the result since the density o states per unit volume should not depend on the actual size or shape o the semiconductor. x = A exp(k x x), k x = n/l, n = 1, 2, 3, Calculation o the number o states with wavenumber less than k. g E = 8 2π h 3 m 3/2 E Density o states o electrons per unit volume per unit energy. 8

9 Density o states in semiconductor DE E c E v g c 8 mn 2mn E Ec 8 mp 2mp Ev E ( E) 3 h g v ( E) 3 h E c is the energy o the bottom o the conduction band E v is the energy o the top o the valence band 9

10 Electron energy bands in silicon and SiO 2 E c E g=1.1 ev E c Ev E g= 9 ev Si (Semiconductor) E v SiO 2 (Insulator) Totally illed bands and totally empty bands do not allow current low (just as there is no motion o liquid in a totally illed, or totally empty bottle). Semiconductors have smaller E g than insulators. 10

11 Measuring the Band Gap Energy by Light Absorption ree electron photons photon energy: h v > E g E g E c E v ree hole E g can be determined rom the minimum energy (hn) o photons that are absorbed by the semiconductor. Bandgap energies o selected semiconductors Semi-conductor InSb Ge Si GaAs GaP ZnSe Diamond Eg (ev)

12 Temperature dependence o the energy bandgap The temperature dependence o the energy bandgap, E g, has been experimentally determined yielding the ollowing expression or E g as a unction o the temperature, T: 12

13 Fermi unction Electrons are Fermions. The Pauli exclusion principle postulates that only one Fermion can occupy a single quantum state. Thereore, as Fermions are added to an energy band, they will ill the available states in an energy band just like water ills a bucket. The states with the lowest energy are illed irst, ollowed by the next higher ones. At absolute zero temperature (T = 0 K), the energy levels are all illed up to a maximum energy, which we call the Fermi level, E F. electrons holes E F Fermi unction provides the probability o occupancy o energy levels by electrons: The Fermi unction at three dierent temperatures 13

14 Fermi unction at high energies Boltzmann approximation: ( E) ( EE )/ kt 1 e 1 E E E E + 3kT + 2kT ( E) e EE kt ( E) e EE kt E E + kt E E kt E kt E E 2kT 3kT ( E) 1 e E E kt ( E) 1 e E E kt (E) E E kt 14

15 Homework Fermi unction 1. Calculate probability or an electron to have an energy o 3kT above the Fermi level. 2. Calculate probability or a hole to have an energy o 3kT below the Fermi level. 3. Compare this data with that calculated using Boltzmann approximation. 15

16 The density o occupied states per unit volume and energy, n(e), ), is simply the product o the density o states in the conduction band, g c (E) and the Fermi unction, (E): Density o electrons and holes Correspondingly or the density or holes, p(e), equals: The total density o charge carriers (concentration) is obtained by integrating the product o the density o states and the probability density unction over all possible states. For electrons in the conduction band the integral is taken rom the bottom o the conduction band, labeled, E c, to the top o the conduction band. n electron concentration, p hole concentration. A common unit is cm

17 Homework Density o states 1. Calculate density o states o ree electron and ree holes o an energy o 1 ev in Si, Ge and GaAs. 2. Calculate/Estimate concentration o electrons and holes in Si, Ge and GaAs at temperatures 100, 300 and 1000K. 17

18 on-degenerate semiconductors on-degenerate semiconductors are deined as semiconductors or which the Fermi energy is at least 3kT away rom either band edge. The approximation o non-degenerate semiconductors allows the Fermi unction to be replaced with a simple exponential unction. In many cases, solid state electronic devices operate on the principles o nondegenerate semiconductors 18

19 Electron and Hole Concentrations n c e ( E E c )/ kt c 2m nkt 2 2 h 3 2 c is the eective density o states o the conduction and. p v e ( E E v )/ kt v 2m pkt 2 2 h 3 2 v is the eective density o states o the valence band. The closer Fermi level moves up to E c, the larger n is. The closer Fermi level moves down to E v, the larger p is. For silicon, c = cm -3 and v = cm

20 Eective density o states in germanium Eective conduction band density o states cm -3 Eective valence band density o states cm -3 20

21 Homework Eective density o states 1. Calculate eective density o states oe electrons and holes in Ge and GaAs. 2. Compare the obtained data with c and v in silicon. 21

22 The np product and the intrinsic carrier concentration n c e ( E E c )/ kt p v e ( E E v )/ kt np c v e ( E E kt E c v )/ cve g / kt np n i 2 n i c v e E g / 2kT In an intrinsic (undoped) semiconductor, n = p = n i n i is the intrinsic carrier concentration n i ~10 10 cm -3 or Si at room temperature 22

23 Intrinsic electron and hole concentration versus temperature n c e ( E E c )/ kt p v e ( E E v )/ kt Intrinsic carrier density versus temperature in: GaAs (red), Silicon (blue), Germanium (black). 23

24 Homework Intrinsic carrier concentration 1. Calculate intrinsic carrier concentration or Si, Ge and GaAs at temperatures 100K and 1000K. 2. Compare the obtained data with c and v shown on previous slide Estimate the temperature at which intrinsic carrier concentration or Si, Ge and GaAs become comparable. 4. At the temperature calculated in 3, can Si, Ge and GaAs be considered as non-degenerate semiconductors? 24

25 Position o Fermi level versus temperature n c e ( E E c )/ kt p v e ( E E )/ kt v E F * E C EV 3 me k ln BT * 2 4 mh m e * > m h * m e * < m h * Red line shows the middle o the bandgap In intrinsic semiconductors, in a broad temperature range, the Fermi level remains close to the middle o the bandgap. 25

26 Homework Position o Fermi level 1. Calculate position o Fermi level in Si, Ge and GaAs at temperatures 100K and 1000K. 2. At what temperature Fermi level crosses E c /E v in these semiconductors? 26

27 27

Solid State Device Fundamentals

Solid State Device Fundamentals Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 The free electron model of metals The free electron model

More information

Solid State Device Fundamentals

Solid State Device Fundamentals 4. lectrons and Holes Solid State Device Fundamentals NS 45 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 4N101b 1 4. lectrons and Holes Free electrons and holes

More information

EECS130 Integrated Circuit Devices

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

More information

EE143 Fall 2016 Microfabrication Technologies. Evolution of Devices

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

More information

Bohr s Model, Energy Bands, Electrons and Holes

Bohr s Model, Energy Bands, Electrons and Holes Dual Character of Material Particles Experimental physics before 1900 demonstrated that most of the physical phenomena can be explained by Newton's equation of motion of material particles or bodies and

More information

EECS143 Microfabrication Technology

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

More information

Calculating Band Structure

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

More information

Semiconductor Physics and Devices Chapter 3.

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

More information

Three Most Important Topics (MIT) Today

Three Most Important Topics (MIT) Today Three Most Important Topics (MIT) Today Electrons in periodic potential Energy gap nearly free electron Bloch Theorem Energy gap tight binding Chapter 1 1 Electrons in Periodic Potential We now know the

More information

Chapter 12: Semiconductors

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

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

Basic cell design. Si cell

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:

More information

Lecture 1. OUTLINE Basic Semiconductor Physics. Reading: Chapter 2.1. Semiconductors Intrinsic (undoped) silicon Doping Carrier concentrations

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

More information

Ch. 2: Energy Bands And Charge Carriers In Semiconductors

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

More information

Chapter Two. Energy Bands and Effective Mass

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

More information

Introduction to Quantum Theory of Solids

Introduction to Quantum Theory of Solids Lecture 5 Semiconductor physics III Introduction to Quantum Theory of Solids 1 Goals To determine the properties of electrons in a crystal lattice To determine the statistical characteristics of the very

More information

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, 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 information

Semiconductor Device Physics

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

More information

半導體元件與物理. Semiconductor Devices and physics 許正興國立聯合大學電機工程學系 聯大電機系電子材料與元件應用實驗室

半導體元件與物理. Semiconductor Devices and physics 許正興國立聯合大學電機工程學系 聯大電機系電子材料與元件應用實驗室 半導體元件與物理 Semiconductor Devices and physics 許正興國立聯合大學電機工程學系 1. Crystal Structure of Solids 2. Quantum Theory of Solids 3. Semiconductor in Equilibrium and Carrier Transport phenomena 4. PN Junction and

More information

ECE 442. Spring, Lecture -2

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

More information

The Semiconductor in Equilibrium

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

More information

Lecture 2. Unit Cells and Miller Indexes. Reading: (Cont d) Anderson 2 1.8,

Lecture 2. Unit Cells and Miller Indexes. Reading: (Cont d) Anderson 2 1.8, Lecture 2 Unit Cells and Miller Indexes Reading: (Cont d) Anderson 2 1.8, 2.1-2.7 Unit Cell Concept The crystal lattice consists of a periodic array of atoms. Unit Cell Concept A building block that can

More information

EE 346: Semiconductor Devices

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

More information

smal band gap Saturday, April 9, 2011

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

More information

Course overview. Me: Dr Luke Wilson. The course: Physics and applications of semiconductors. Office: E17 open door policy

Course overview. Me: Dr Luke Wilson. The course: Physics and applications of semiconductors. Office: E17 open door policy Course overview Me: Dr Luke Wilson Office: E17 open door policy email: luke.wilson@sheffield.ac.uk The course: Physics and applications of semiconductors 10 lectures aim is to allow time for at least one

More information

Unit III Free Electron Theory Engineering Physics

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

More information

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. 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

More information

Variation of Energy Bands with Alloy Composition E

Variation of Energy Bands with Alloy Composition E Variation of Energy Bands with Alloy Composition E 3.0 E.8.6 L 0.3eV Al x GaAs AlAs 1- xas 1.43eV.16eV X k.4 L. X.0 X 1.8 L 1.6 1.4 0 0. 0.4 0.6 X 0.8 1 1 Carriers in intrinsic Semiconductors Ec 4º 1º

More information

EE 346: Semiconductor Devices

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

More information

Lecture 3: Electron statistics in a solid

Lecture 3: Electron statistics in a solid Lecture 3: Electron statistics in a solid Contents Density of states. DOS in a 3D uniform solid.................... 3.2 DOS for a 2D solid........................ 4.3 DOS for a D solid........................

More information

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

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

More information

I. Introduction II. Solid State Physics Detection of Light Bernhard Brandl 1

I. Introduction II. Solid State Physics Detection of Light Bernhard Brandl 1 Detection of Light I. Introduction II. Solid State Physics 4-2-2015 Detection of Light Bernhard Brandl 1 4-2-2015 Detection of Light Bernhard Brandl 2 Blabla Recommended 4-2-2015 Detection of Light Bernhard

More information

Review of Semiconductor Fundamentals

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,

More information

Semiconductor Physics

Semiconductor Physics 1 Semiconductor Physics 1.1 Introduction 2 1.2 The Band Theory of Solids 2 1.3 The Kronig Penney Model 3 1.4 The Bragg Model 8 1.5 Effective Mass 8 1.6 Number of States in a Band 10 1.7 Band Filling 12

More information

Charge Carriers in Semiconductor

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

More information

Note that it is traditional to draw the diagram for semiconductors rotated 90 degrees, i.e. the version on the right above.

Note 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 information

Solid State Device Fundamentals

Solid State Device Fundamentals Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 Outline - Goals of the course. What is electronic device?

More information

Mat E 272 Lecture 25: Electrical properties of materials

Mat 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 information

Semiconductor Physics and Devices

Semiconductor Physics and Devices EE321 Fall 2015 September 28, 2015 Semiconductor Physics and Devices Weiwen Zou ( 邹卫文 ) Ph.D., Associate Prof. State Key Lab of advanced optical communication systems and networks, Dept. of Electronic

More information

ELEMENTARY BAND THEORY

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

More information

Chapter 2. Semiconductor Fundamentals

Chapter 2. Semiconductor Fundamentals hapter Semiconductor Fundamentals.0 Introduction There are altogether 9 types of natural occurring elements, of which only few types are important in semiconductor physics and technology. They are the

More information

Semiconductors and Optoelectronics. Today Semiconductors Acoustics. Tomorrow Come to CH325 Exercises Tours

Semiconductors and Optoelectronics. Today Semiconductors Acoustics. Tomorrow Come to CH325 Exercises Tours Semiconductors and Optoelectronics Advanced Physics Lab, PHYS 3600 Don Heiman, Northeastern University, 2017 Today Semiconductors Acoustics Tomorrow Come to CH325 Exercises Tours Semiconductors and Optoelectronics

More information

Chapter 1 Overview of Semiconductor Materials and Physics

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

More information

Chapter 4: Bonding in Solids and Electronic Properties. Free electron theory

Chapter 4: Bonding in Solids and Electronic Properties. Free electron theory Chapter 4: Bonding in Solids and Electronic Properties Free electron theory Consider free electrons in a metal an electron gas. regards a metal as a box in which electrons are free to move. assumes nuclei

More information

7.4. Why we have two different types of materials: conductors and insulators?

7.4. Why we have two different types of materials: conductors and insulators? Phys463.nb 55 7.3.5. Folding, Reduced Brillouin zone and extended Brillouin zone for free particles without lattices In the presence of a lattice, we can also unfold the extended Brillouin zone to get

More information

CLASS 12th. Semiconductors

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

More information

Mark Lundstrom 2/10/2013. SOLUTIONS: ECE 606 Homework Week 5 Mark Lundstrom Purdue University (corrected 3/26/13)

Mark Lundstrom 2/10/2013. SOLUTIONS: ECE 606 Homework Week 5 Mark Lundstrom Purdue University (corrected 3/26/13) SOLUIONS: ECE 606 Homework Week 5 Mark Lundstrom Purdue University corrected 6/13) Some of the problems below are taken/adapted from Chapter 4 in Advanced Semiconductor Fundamentals, nd. Ed. By R.F. Pierret.

More information

Chemistry Instrumental Analysis Lecture 8. Chem 4631

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

More information

Semiconductors. SEM and EDAX images of an integrated circuit. SEM EDAX: Si EDAX: Al. Institut für Werkstoffe der ElektrotechnikIWE

Semiconductors. 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 information

Crystal Properties. MS415 Lec. 2. High performance, high current. ZnO. GaN

Crystal Properties. MS415 Lec. 2. High performance, high current. ZnO. GaN Crystal Properties Crystal Lattices: Periodic arrangement of atoms Repeated unit cells (solid-state) Stuffing atoms into unit cells Determine mechanical & electrical properties High performance, high current

More information

ECE 340 Lecture 6 : Intrinsic and Extrinsic Material I Class Outline:

ECE 340 Lecture 6 : Intrinsic and Extrinsic Material I Class Outline: ECE 340 Lecture 6 : Intrinsic and Extrinsic Material I Class Outline: Effective Mass Intrinsic Material Extrinsic Material Things you should know when you leave Key Questions What is the physical meaning

More information

David J. Starling Penn State Hazleton PHYS 214

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

More information

ECE 250 Electronic Devices 1. Electronic Device Modeling

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

More information

LN 3 IDLE MIND SOLUTIONS

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

More information

Free Electron Model for Metals

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

More information

Lecture 7: Extrinsic semiconductors - Fermi level

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

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

SEMICONDUCTOR PHYSICS

SEMICONDUCTOR PHYSICS SEMICONDUCTOR PHYSICS by Dibyendu Chowdhury Semiconductors The materials whose electrical conductivity lies between those of conductors and insulators, are known as semiconductors. Silicon Germanium Cadmium

More information

The potential is minimum at the positive ion sites and maximum between the two ions.

The potential is minimum at the positive ion sites and maximum between the two ions. 1. Bloch theorem: - A crystalline solid consists of a lattice, which is composed of a large number of ion cores at regular intervals, and the conduction electrons that can move freely through out the lattice.

More information

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

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

More information

Module - 01 Assignment - 02 Intrinsic Semiconductors. In today's assignment class, we will be looking fully at intrinsic semiconductors.

Module - 01 Assignment - 02 Intrinsic Semiconductors. In today's assignment class, we will be looking fully at intrinsic semiconductors. Electronic Materials, Devices and Fabrication Dr. S. Parasuraman Department of Metallurgical and Materials Engineering Indian Institute of Technology, Madras Module - 01 Assignment - 02 Intrinsic Semiconductors

More information

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

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

More information

Solid State Device Fundamentals

Solid State Device Fundamentals Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 Outline - Goals of the course. What is electronic device?

More information

Spring 2005 MSE111 Midterm. Prof. Eugene Haller. 3/15/05, 9:40 am

Spring 2005 MSE111 Midterm. Prof. Eugene Haller. 3/15/05, 9:40 am Spring 005 MSE111 Midterm Prof. Eugene Haller 3/15/05, 9:40 am University of California at Berkeley Department of Materials Science and Engineering 80 minutes, 68 points total, 10 pages Name: SID: Problem

More information

Metals and Insulators

Metals and Insulators Metals and Insulators Covalent bonds, weak U seen by e-, with E F being in mid-band area: free e-, metallic Covalent or slightly ionic bonds, weak U to medium U, with E F near band edge E F in or near

More information

ENERGY BANDS AND GAPS IN SEMICONDUCTOR. Muhammad Hafeez Javed

ENERGY BANDS AND GAPS IN SEMICONDUCTOR. Muhammad Hafeez Javed ENERGY BANDS AND GAPS IN SEMICONDUCTOR Muhammad Hafeez Javed www.rmhjaved.com rmhjaved@gmail.com Out Line Introduction Energy band Classification of materials Direct and indirect band gap of SC Classification

More information

EE495/695 Introduction to Semiconductors I. Y. Baghzouz ECE Department UNLV

EE495/695 Introduction to Semiconductors I. Y. Baghzouz ECE Department UNLV EE495/695 Introduction to Semiconductors I Y. Baghzouz ECE Department UNLV Introduction Solar cells have always been aligned closely with other electronic devices. We will cover the basic aspects of semiconductor

More information

Physics of Semiconductor Devices. Unit 2: Revision of Semiconductor Band Theory

Physics of Semiconductor Devices. Unit 2: Revision of Semiconductor Band Theory Physics of Semiconductor Devices Unit : Revision of Semiconductor Band Theory Unit Revision of Semiconductor Band Theory Contents Introduction... 5 Learning outcomes... 5 The Effective Mass... 6 Electrons

More information

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. 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

More information

Semiconductor Detectors

Semiconductor 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 information

Review of Optical Properties of Materials

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

More information

ELEC311( 물리전자, Physical Electronics) Course Outlines:

ELEC311( 물리전자, Physical Electronics) Course Outlines: ELEC311( 물리전자, Physical Electronics) Course Outlines: by Professor Jung-Hee Lee Lecture notes are prepared with PPT and available before the class (http://abeek.knu.ac.kr). The topics in the notes are

More information

Diamond. Covalent Insulators and Semiconductors. Silicon, Germanium, Gray Tin. Chem 462 September 24, 2004

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

More information

2. Thermodynamics of native point defects in GaAs

2. Thermodynamics of native point defects in GaAs 2. Thermodynamics o native point deects in The totality o point deects in a crystal comprise those existing in a perectly chemically pure crystal, so called intrinsic deects, and those associated with

More information

Free Electron Model for Metals

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

More information

Introduction to Condensed Matter Physics

Introduction to Condensed Matter Physics Introduction to Condensed Matter Physics Crystalline Solids - Introduction M.P. Vaughan Overview Overview of course Crystal solids Crystal structure Crystal symmetry The reciprocal lattice Band theory

More information

Introduction to Engineering Materials ENGR2000. Dr.Coates

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

More information

When I hear of Schrödinger s cat, I reach for my gun. --Stephen W. Hawking. Lecture 21, p 1

When I hear of Schrödinger s cat, I reach for my gun. --Stephen W. Hawking. Lecture 21, p 1 When I hear of Schrödinger s cat, I reach for my gun. --Stephen W. Hawking Lecture 21, p 1 Lecture 21: Lasers, Schrödinger s Cat, Atoms, Molecules, Solids, etc. Review and Examples Lecture 21, p 2 Act

More information

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

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

More information

Lecture 21: Lasers, Schrödinger s Cat, Atoms, Molecules, Solids, etc. Review and Examples. Lecture 21, p 1

Lecture 21: Lasers, Schrödinger s Cat, Atoms, Molecules, Solids, etc. Review and Examples. Lecture 21, p 1 Lecture 21: Lasers, Schrödinger s Cat, Atoms, Molecules, Solids, etc. Review and Examples Lecture 21, p 1 Act 1 The Pauli exclusion principle applies to all fermions in all situations (not just to electrons

More information

Conductivity and Semi-Conductors

Conductivity and Semi-Conductors Conductivity and Semi-Conductors J = current density = I/A E = Electric field intensity = V/l where l is the distance between two points Metals: Semiconductors: Many Polymers and Glasses 1 Electrical Conduction

More information

Silicon. tetrahedron diamond structure

Silicon. tetrahedron diamond structure Silicon a tetrahedron a a diamond structure Tetrahedral bonding Hund s Rule 14Si [e] 3s 3p [e] hybridize 3sp 3 Hybridized level has higher energy for an isolated atom, but allows overall reduction in energy

More information

3.1 Introduction to Semiconductors. Y. Baghzouz ECE Department UNLV

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

More information

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

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

More information

Basic Principles of Light Emission in Semiconductors

Basic Principles of Light Emission in Semiconductors Basic Principles of Light Emission in Semiconductors Class: Integrated Photonic Devices Time: Fri. 8:00am ~ 11:00am. Classroom: 資電 06 Lecturer: Prof. 李明昌 (Ming-Chang Lee) Model for Light Generation and

More information

Introduction to Sources: Radiative Processes and Population Inversion in Atoms, Molecules, and Semiconductors Atoms and Molecules

Introduction to Sources: Radiative Processes and Population Inversion in Atoms, Molecules, and Semiconductors Atoms and Molecules OPTI 500 DEF, Spring 2012, Lecture 2 Introduction to Sources: Radiative Processes and Population Inversion in Atoms, Molecules, and Semiconductors Atoms and Molecules Energy Levels Every atom or molecule

More information

MTLE-6120: Advanced Electronic Properties of Materials. Intrinsic and extrinsic semiconductors. Reading: Kasap:

MTLE-6120: Advanced Electronic Properties of Materials. Intrinsic and extrinsic semiconductors. Reading: Kasap: MTLE-6120: Advanced Electronic Properties of Materials 1 Intrinsic and extrinsic semiconductors Reading: Kasap: 5.1-5.6 Band structure and conduction 2 Metals: partially filled band(s) i.e. bands cross

More information

Nearly Free Electron Gas model - I

Nearly Free Electron Gas model - I Nearly Free Electron Gas model - I Contents 1 Free electron gas model summary 1 2 Electron effective mass 3 2.1 FEG model for sodium...................... 4 3 Nearly free electron model 5 3.1 Primitive

More information

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

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

More information

Lecture. Ref. Ihn Ch. 3, Yu&Cardona Ch. 2

Lecture. Ref. Ihn Ch. 3, Yu&Cardona Ch. 2 Lecture Review of quantum mechanics, statistical physics, and solid state Band structure of materials Semiconductor band structure Semiconductor nanostructures Ref. Ihn Ch. 3, Yu&Cardona Ch. 2 Reminder

More information

Complete nomenclature for electron orbitals

Complete nomenclature for electron orbitals Complete nomenclature for electron orbitals Bohr s model worked but it lacked a satisfactory reason why. De Broglie suggested that all particles have a wave nature. u l=h/p Enter de Broglie again It was

More information

We have arrived to the question: how do molecular bonds determine the band gap? We have discussed that the silicon atom has four outer electrons.

We have arrived to the question: how do molecular bonds determine the band gap? We have discussed that the silicon atom has four outer electrons. ET3034Tux - 2.2.2 - Band Gap 2 - Electrons in Molecular Bonds We have arrived to the question: how do molecular bonds determine the band gap? We have discussed that the silicon atom has four outer electrons.

More information

Fundamentals of Semiconductor Devices Prof. Digbijoy N. Nath Centre for Nano Science and Engineering Indian Institute of Science, Bangalore

Fundamentals of Semiconductor Devices Prof. Digbijoy N. Nath Centre for Nano Science and Engineering Indian Institute of Science, Bangalore Fundamentals of Semiconductor Devices Prof. Digbijoy N. Nath Centre for Nano Science and Engineering Indian Institute of Science, Bangalore Lecture - 05 Density of states Welcome back. So, today is the

More information

Quantum Condensed Matter Physics Lecture 9

Quantum Condensed Matter Physics Lecture 9 Quantum Condensed Matter Physics Lecture 9 David Ritchie QCMP Lent/Easter 2018 http://www.sp.phy.cam.ac.uk/drp2/home 9.1 Quantum Condensed Matter Physics 1. Classical and Semi-classical models for electrons

More information

5 Problems Chapter 5: Electrons Subject to a Periodic Potential Band Theory of Solids

5 Problems Chapter 5: Electrons Subject to a Periodic Potential Band Theory of Solids E n = :75, so E cont = E E n = :75 = :479. Using E =!, :479 = m e k z =! j e j m e k z! k z = r :479 je j m e = :55 9 (44) (v g ) z = @! @k z = m e k z = m e :55 9 = :95 5 m/s. 4.. A ev electron is to

More information

Optical Properties of Lattice Vibrations

Optical Properties of Lattice Vibrations Optical Properties of Lattice Vibrations For a collection of classical charged Simple Harmonic Oscillators, the dielectric function is given by: Where N i is the number of oscillators with frequency ω

More information

Semiconductor device structures are traditionally divided into homojunction devices

Semiconductor device structures are traditionally divided into homojunction devices 0. Introduction: Semiconductor device structures are traditionally divided into homojunction devices (devices consisting of only one type of semiconductor material) and heterojunction devices (consisting

More information

Semiconductor physics I. The Crystal Structure of Solids

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

More information

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

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

More information

Physics of Semiconductors. Exercises. The Evaluation of the Fermi Level in Semiconductors.

Physics of Semiconductors. Exercises. The Evaluation of the Fermi Level in Semiconductors. Physics of Semiconductors. Exercises. The Evaluation of the Fermi Level in Semiconductors. B.I.Lembrikov Department of Communication Engineering Holon Academic Institute of Technology I. Problem 8. The

More information