# EE 346: Semiconductor Devices

Size: px
Start display at page:

Transcription

1 EE 346: Semiconductor Devices Lecture /06/2017 Tewodros A. Zewde 1

2 DENSTY OF STATES FUNCTON Since current is due to the flow of charge, an important step in the process is to determine the number of electrons and holes in the semiconductor that will be available for conduction. The number of carriers that can contribute to the conduction process is a function of the number of available energy or quantum states since, by the Pauli exclusion principle, only one electron can occupy a given quantum state. Hence, we must determine the density of discrete energy levels, or allowed energy states as a function of energy in order to calculate the electron and hole concentrations. As the energy of this free electron becomes small, the number of available quantum states decreases.

3 A general expression for the density of allowed electron quantum states can be derived using the model of a free electron with mass m bounded in a three-dimensional infinite potential wall. The same general model can be extended to a semiconductor to determine the density of quantum states in the conduction band and the density of quantum states in the valence band. The density of allowed electronic energy states in the conduction and valance band are given as follow: where m * is effective mass that takes into account the effect of internal forces in the crystal. As the energy of the electron in the conduction band decreases, the number of available quantum states also decreases.

4 The plot of the density of quantum states as a function of energy. Quantum states do not exist within the forbidden energy band, so g(e)=0 for E v <E <E c. f the electron and hole effective masses were equal, then the functions g c (E) and g v (E) would be symmetrical about the energy midway between E c and E v.

5 Now that we know the number of available states at each energy, or n dealing with large numbers of particles, we are interested only in the statistical behavior of the group as a whole rather than in the behavior of each individual particle. n a crystal, the electrical characteristics will be determined y the statistical behavior of a large number of electrons. Electrons in a crystal follow the probability function, i.e., one particle is permitted in each quantum state. 1 f (E) = where k Boltzman constant,t Temperature in Kelvin ( E E F ) kt 1+e and E F Fermi energy the energy below which all states are filled with electrons and above which all states are empty at T = 0 K. The function, f(e) is called the Fermi-Dirac distribution or probability function, and it gives the probability that a quantum state at the energy E will be occupied by an electron. f(e) is the probability that a state at energy E is occupied

6 Hence, the number density N(E) is the number of particles per unit volume per unit energy, i.e., filled quantum states, at any energy E becomes N(E) = g(e) f(e) where the function g(e) is the number of quantum states per unit volume per unit energy, and f(e) is the probability that a state at energy E is occupied. At T=0K, no occupation of states above E F and complete occupation of states below E F At T > 0K, occupation probability is reduced with increasing energy. f(e=e F ) = 1/2 regardless of temperature. At higher temperatures, higher energy states can be occupied, leaving more lower energy states unoccupied (1-f(E)).

7 For temperatures above absolute zero, there is a nonzero probability that some energy states above E F will be occupied by electrons and some energy states below E F will be empty. This result again means that some electrons have jumped to higher energy levels with increasing thermal energy. Exercise Given that T = 300K, determine the probability that an energy level (a) 1kT above the Fermi energy is occupied by an electron. (b) 2kT above the Fermi energy is occupied by an electron. (c) 3kT above the Fermi energy is occupied by an electron. Note that k is Boltzmann constant, and k=1.381x10-23 J/K.

8 f(e) f ( E) ( E EF ) kt 1 e 1 For E < (E f -3kT): f(e) ~ 1-e -(E-Ef)/kT ~1 +/-3 kt 3 kt 3 kt 3 kt 3 kt E f =0.55 ev For E > (E f +3kT): f(e) ~ e -(E-Ef)/kT ~0 T=10 K, kt= ev T=300K, kt= T=450K, kt= E [ev]

9 The Semiconductor in Equilibrium Equilibrium, or thermal equilibrium, implies that no external forces such as voltages, electric fields. magnetic fields, or temperature gradients are acting on the semiconductor. n this section, we will use the density the density of quantum states in the conduction band and the density of quantum states in the valence band along with the Fermi-dirac probability function to determine the concentration of electrons and holes in the conduction and valence bands, respectively. We will initially consider the properties of an intrinsic semiconductor, that is, a pure crystal with no impurity atoms or defects. We will see that the electrical properties of a semiconductor can be altered in desirable ways by adding controlled amounts of specific impurity atoms. called dopant atoms, to the crystal.

10 Equilibrium Distribution of Electrons and Holes Since the current in a semiconductor is determined largely by the number of electrons in the conduction band and the number of holes in the valence hand, an important characteristic of the semiconductor is the density of these charge carriers. The distribution (with respect to energy) of electrons in the conduction band is given by n(e) = g c (E) f(e) where g c (E) is the density of quantum states in the conduction band and f(e) if the Fermi-Dirac probability function. Similarly, the distribution (with respect to energy) of holes in the valence band is given by p(e) = g v (E) [1- f(e)]

11 Energy band Density Occupancy diagram of states factors E e - EF E v LL_ gc( E) 8 v(e) E t 1 - f(e) f(e) E e E V Carrier distributions gc(e)f(e) : 8v(E)[ 1 - /( )] (a) EF above midgap E e 8c(E) - E F gv(e) E v E t Electrons E _.{.-:.. e, E v r' k Holes (b) E p near midgap Ee -EF E v LL- E 8v( E) K 8e(E) t E e (c) E p below midgap

12 \1-fF(t)J Figure 4.1 (a)density of states fimctions, Fenni-Dirac probability fonction,and areas representing electron and hole concen1ratioa5 for the case when,- is near the midgap energy; (b) expanded vie w near the conduction band energy; and (c) e-xpanded view near the valence band energy.

13 The thermal-equilibrium concentration of electron per unit volume is found by integrating the density functions over the entire conduction-band energy, or For electrons in conduction band, E>E c, and if E c -E F >>kt where the exponential term in the denominator of f (E) 1 (E E F ) kt 1+e is much greater than unity, so the Femi-Dirac distribution function reduces to the Maxwell-Boltzmann approximation (Boltzmann approximation), which is f (E ) E E F ) kt ē ( N c == is effective density of state in conduction band.

14 The thermal-equilibrium concentration of holes in the valence band is found by Following similar steps, we have where N v = valence band. is effective density of states function in the For an intrinsic semiconductor, the concentration of electrons in the conduction band is equal to the concentration of holes in the valence band. Let E F =E Fi for the Fermi energy level for the intrinsic semiconductor, and then

15 which leads to where E g is the bandgap energy. For a given semiconductor material at a constant temperature, the value of n i is a constant, and independent of the Fermi energy. The intrinsic carrier concentration is a very strong function of temperature. The figure shows the intrinsic carrier concentration of Ge, Si, and GaAs as a function of temperature.

16 The intrinsic Fermi-level position can be determined using the fact that the electron and hole concentrations are equal, i.e., which leads to where f m * p = m* n, then the intrinsic Fermi level is exactly in the center of the bandgap. f m* p > m* n, the intrinsic Fermi level is slightly above the center, and f m* p < m* n, it is slightly below the center of the bandgap. The intrinsic Fermi level must shift away from the band with the larger density of states in order to maintain equal numbers of electrons and holes.

17 DOPANT ATOMS AND ENERGY LEVELS Without help the total number of carriers (electrons and holes) is limited to 2ni. For most materials, this is not that much, and leads to very high resistance and few useful applications. The intrinsic semiconductor may be an interesting material, but the real power of semiconductors is realized by adding small, controlled amounts of specific dopant, or impurity, atoms. This process is known as doping the crystal. Adding controlled amounts of dopant atoms, either donors or acceptors, creates a material called an extrinsic semiconductor. An extrinsic semiconductor will have either excess electrons (n-type) or excess holes (ptype).

18 Donor impurity atom: Consider adding a group V element as a substitutional impurity to silicon. Example: P, As, Sb in Si The fifth valence electron is denoted as a donor electron, and a donor impurity atom donates an electron to the conduction band.

19 The electron in the conduction band can now move through the crystal generating a current, while the positively charged ion is fixed in the crystal.

20 Concept of a Donor adding extra electrons: Band diagram equivalent view The energy level, E D, is the energy state of the donor electron. The donor impurity atoms add electrons to the conduction band without creating holes in the valence band. The resulting material is referred to as an n-type semiconductor (n for the negatively charged electron).

21 Acceptor impurity atom: consider adding a group element as a substitutional impurity to silicon. One covalent bonding position appears to be empty. Example: B, Al, n in Si One less bond means the acceptor is electrically satisfied One less bond means the neighboring silicon is left with an empty state.

22

23 The "empty" position associated with the boron atom becomes occupied, and other valence electron positions become vacated. These other vacated electron positions can be thought of as holes in the semiconductor material. +

24 The hole can move through the crystal generating a current, while the negatively charged boron atom is fixed in the crystal. +

25 The hole can move through the crystal generating a current, while the negatively charged boron atom is fixed in the crystal. +

26 Concept of an Acceptor adding extra hole : Band diagram equivalent view The electron occupying the "empty" position does not have sufficient energy to be in the conduction band, so its energy is far smaller than the conductionband energy. The energy level, E A, is the energy state of the acceptor electron. The group atom accepts an electron from the valence band and so is referred to as an acceptor impurity atom. This type of material is referred to as a p-type semiconductor (p for the positively charged hole).

### EE 346: Semiconductor Devices. 02/08/2017 Tewodros A. Zewde 1

EE 346: Semiconductor Devices 02/08/2017 Tewodros A. Zewde 1 DOPANT ATOMS AND ENERGY LEVELS Without help the total number of carriers (electrons and holes) is limited to 2ni. For most materials, this is

### 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

### 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

### Lecture 4. Density of States and Fermi Energy Concepts. Reading: (Cont d) Pierret

C 3040 Dr. Alan Doolittle Lecture 4 Density of States and Fermi nergy Concepts Reading: (Cont d Pierret 2.1-2.6 C 3040 Dr. Alan Doolittle Density of States Concept Quantum Mechanics tells us that the number

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Carriers Concentration in Semiconductors - V. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

Carriers Concentration in Semiconductors - V 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 Motion and Recombination of Electrons and

### 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,

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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:

### 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

### 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

### 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

### 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

### Lecture 2 - Carrier Statistics in Equilibrium. September 5, 2002

6.720J/3.43J Integrated Microelectronic Devices Fall 2002 Lecture 21 Lecture 2 Carrier Statistics in Equilibrium Contents: September 5, 2002 1. Conduction and valence bands, bandgap, holes 2. Intrinsic

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Semiconductor 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

### Key Questions. ECE 340 Lecture 6 : Intrinsic and Extrinsic Material I 9/10/12. Class Outline: Effective Mass Intrinsic Material

9/1/1 ECE 34 Lecture 6 : Intrinsic and Extrinsic Material I Class Outline: Things you should know when you leave Key Questions What is the physical meaning of the effective mass What does a negative effective

### 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

### EXTRINSIC 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

### 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

### 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,

### 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

### 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

### Recitation 2: Equilibrium Electron and Hole Concentration from Doping

Recitation : Equilibrium Electron and Hole Concentration from Doping Here is a list of new things we learned yesterday: 1. Electrons and Holes. Generation and Recombination 3. Thermal Equilibrium 4. Law

### 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

### Electrons, Holes, and Defect ionization

Electrons, Holes, and Defect ionization The process of forming intrinsic electron-hole pairs is excitation a cross the band gap ( formation energy ). intrinsic electronic reaction : null e + h When electrons

### 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

### * motif: a single or repeated design or color

Chapter 2. Structure A. Electronic structure vs. Geometric structure B. Clean surface vs. Adsorbate covered surface (substrate + overlayer) C. Adsorbate structure - how are the adsorbed molecules bound

### 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

### 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)

### 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

### Intrinsic Semiconductors

Technische Universität Graz Institute of Solid State Physics Intrinsic Semiconductors ermi function f(e) is the probability that a state at energy E is occupied. f( E) 1 E E 1 exp kt B ermi energy The

### 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

### Chapter 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

### 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)

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Solid State Device Fundamentals

Solid State Device Fundamentals ES 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Oice 4101b 1 The ree electron model o metals The ree electron model o metals

### 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

### 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.

### 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

### UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. EECS 130 Professor Ali Javey Fall 2006

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 130 Professor Ali Javey Fall 2006 Midterm I Name: Closed book. One sheet of notes is allowed.

### 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

### 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

### Lecture 2 - Carrier Statistics in Equilibrium. February 8, 2007

6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 21 Lecture 2 Carrier Statistics in Equilibrium Contents: February 8, 2007 1. Conduction and valence bands, bandgap, holes 2. Intrinsic

### 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

### 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

### PHYS208 p-n junction. January 15, 2010

1 PHYS208 p-n junction January 15, 2010 List of topics (1) Density of states Fermi-Dirac distribution Law of mass action Doped semiconductors Dopinglevel p-n-junctions 1 Intrinsic semiconductors List of

### 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

### 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

### 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

### Solid State Electronics EC210 Arab Academy for Science and Technology AAST Cairo Fall Lecture 10: Semiconductors

Solid State Electronics EC210 Arab Academy for Science and Technology AAST Cairo Fall 2014 Lecture 10: Semiconductors Lecture Notes Prepared by: Dr. Amr Bayoumi, Dr. Nadia Rafat These PowerPoint color

### Determination of properties in semiconductor materials by applying Matlab

Determination of properties in semiconductor materials by applying Matlab Carlos Figueroa. 1, Raúl Riera A. 2 1 Departamento de Ingeniería Industrial. Universidad de Sonora A.P. 5-088, Hermosillo, Sonora.

### Concept of Semiconductor Physics

Concept of Semiconductor Physics Prof. (Dr.) Pradeep Kumar Sharma Department of Physics University of Engineering & Management, Jaipur OBJECTIVES: This course deals with an introduction to semiconductor

### 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

### 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

### 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

### 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........................

### 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

### 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

### 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

### Lecture 02 Semiconductor Physics

Lecture 02 Semiconductor Physics Prepared By Dr. Eng. Sherif Hekal Assistant Professor, CCE department Lecture 02 Semiconductors 10/15/201 7 1 ILOS In this section, we will learn: The basic properties

### UConn ECE 4211, Semiconductor Devices and Nanostructures Lecture Week 1 January 17, 2017

UConn ECE 411, Semiconductor Devices and Nanostructures Lecture Week 1 January 17, 017 Device Operation: One of the objectives of this course is to understand operation of carrier transport in semiconductor

### 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

### Electron Energy, E E = 0. Free electron. 3s Band 2p Band Overlapping energy bands. 3p 3s 2p 2s. 2s Band. Electrons. 1s ATOM SOLID.

Electron Energy, E Free electron Vacuum level 3p 3s 2p 2s 2s Band 3s Band 2p Band Overlapping energy bands Electrons E = 0 1s ATOM 1s SOLID In a metal the various energy bands overlap to give a single

### Ch/ChE 140a Problem Set #3 2007/2008 SHOW ALL OF YOUR WORK! (190 Points Total) Due Thursday, February 28 th, 2008

Ch/ChE 140a Problem Set #3 2007/2008 SHOW ALL OF YOUR WORK! (190 Points Total) Due Thursday, February 28 th, 2008 Please read chapter 6 (pp. 175-209) of Advanced Semiconductor Fundamentals by Pierret.