# Carriers Concentration and Current in Semiconductors

Size: px
Start display at page:

Transcription

1 Carriers Concentration and Current in Semiconductors

2 Carrier Transport Two driving forces for carrier transport: electric field and spatial variation of the carrier concentration. Both driving forces lead to a directional motion of carriers superimposed on the random thermal motion. To calculate the directional carrier motion and the currents in a semiconductor, classical & nonclassical models can be used. The classical models assume that variation of E-field in time is sufficiently slow so that the transport properties of carriers (mobility or diffusivity) can follow the changes of the field immediately. If carriers are exposed to a fast-varying field, they may not be able to adjust their transport properties instantaneously to variations of the field, and carrier mobility and diffusivity may be different from their steady-state values nonstationary Nonstationary carrier transport can occur in electron devices under both dc and ac bias conditions. 2

3 Classical Description of Carrier Transport Assume thermal equilibrium for a semiconductor having a spatially homogeneous carrier concentration with no applied E-field. No driving force for directional carrier motion. The carriers not in standstill condition but in continuous motion due to kinetic energy. For electron in the conduction band, * 3 mn 2 Ekin kbt vth where v th is the thermal velocity, m n * is the conductivity 2 2 effective electron mass. The average time between two scattering events is the mean free time and the average distance a carrier travels between collisions is the mean free path. Fig. 2.5 (a) Applying V, the E-fields adds a directional component to the random motion of the electron. Fig. 2.5 (b) 3

4 The mean electron velocity: v n = -μ n E The directed unilateral motion of carriers caused by E-field is drift velocity. Similarly, v p = μ p E A change in E-field instantaneously results in a change of the drift velocity. 4

5 Fick s First Law: relating diffusion current to carrier concentration gradient. e D e dn dx e = electron flux, D e = diffusion coefficient of electrons, dn/dx = electron concentration gradient Electron Diffusion Current Density dn J D,e e e ed e dx J D, e = electric current density due to electron diffusion, e = electron flux, e = electronic charge, Where: D e = diffusion coefficient of electrons, dn/dx = electron concentration gradient

6 Hole Diffusion Current Density dp J D,h e h ed h dx J D, h = electric current density due to hole diffusion, e = electronic charge, h = hole flux, D h = diffusion coefficient of holes, dp/dx = hole concentration gradient Total Electron Current Due to Drift and Diffusion J e en e E x ed e dn dx J e = electron current due to drift and diffusion, n = electron concentration, e = electron drift mobility, E x = electric field in the x direction, D e = diffusion coefficient of electrons, dn/dx = electron concentration gradient

7 Total Currents Due to Drift and Diffusion J h = hole current due to drift and diffusion, p = hole concentration, h = hole drift mobility, E x = electric field in the x direction, D h = diffusion coefficient of holes, dp/dx = hole concentration gradient J h ep h E x ed h dp dx J e en e E x ed e dn dx J e = electron current due to drift and diffusion, n = electron concentration e = electron drift mobility, E x = electric field in the x direction, D e = diffusion coefficient of electrons, dn/dx = electron concentration gradient J total = J h +J e

8 Einstein Relation: diffusion coefficient and mobility are related! D e e kt e and D h h kt e D e = diffusion coefficient of electrons, e = electron drift mobility, D h = diffusion coefficient of the holes, h = hole drift mobility

9 Carrier diffusion due to doping level gradient. This is a common device fabrication step. Exposed As + Donor n 2 n 1 V o E x represents electrons (majority carriers in this case) Note: the As + are fixed, non-mobile charges! Diffusion Flux Drift Net current = 0 Diffusion occurs until an electric field builds up! We call this the built-in potential. Fig. 5.32: Non-uniform doping profile results in electron diffusion towards the less concentrated regions. This exposes positively charged donors and sets up a built-in field Ex. In the steady state, the diffusion of electrons towards the right is balanced by their drift towards the left. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

10 Built-In Potential and Concentration V 2 = potential at point 2, V 1 = potential at point 1, n 2 = electron concentration at point 2, n 1 = electron concentration at point 1 V 2 V 1 kt e ln n 2 Built-In Field in Nonuniform Doping E x = electric field in the x direction, b = characteristic of the exponential doping profile, e = electronic charge. E x kt be n 1 Exposed As + Donor n 2 n 1 V o E x Diffusion Flux Drift Net current = 0 Fig. 5.32: Non-uniform doping profile results in electron diffusio towards the less concentrated regions. This exposes positively ch donors and sets up a built-in field Ex. In the steady state, the dif electrons towards the right is balanced by their drift towards the From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

11 Carrier creation: Photoinjected charge carriers If we shine light on a semiconductor, we will generate new charge carriers (in addition to those thermally generated) if E photon >E gap. If the light is always on and of constant intensity, some steady state concentration of electrons and holes will result.

12 Carrier creation: Photoinjected charge carriers Let s consider the case of n-type material Consider an n-type semiconductor with a doping concentration of 5 x cm -3. What are the carrier concentrations? Let s define some terms; n no majority carrier concentration in the n-type (only thermally ionized carriers) (i.e. the electron concentration in n-type) p no minority carrier concentration in the n-type (only thermally ionized carriers) (i.e. the hole concentration in n-type) semiconductor in the dark semiconductor in the dark Note: the no subscript implies that mass action law is valid!

13 When we have light: With light of E photon >E gap hitting the semiconductor, we get photogeneration of excess charge carriers. n n excess electron concentration such that:: n n = n n -n n0 p n excess hole concentration such that:: p n = p n -p n0 & Note that photogenerated carriers excited across the gap can only be created in pairs i.e. p n = n n and now (in light) n n p n n i2 i.e. mass action not valid!

14 Carrier density change under illumination If the temperature is constant, n n0 and p n0 are not time dependent, so dn n dt d n n dt and dp n dt d p n dt Consider the case of weak illumination, which creates a 10% change in n n0 i.e. n n = 0.1n n0 Or if the doping level is n no =5 x cm -3, then n n = 0.1n n0 = 0.5 x cm -3 And p n = n n = 0.5 x cm -3 Which change is more important? Majority or minority?

15 Recall the intrinsic carrier concentration For Si n i is roughly 1.5x10 10 cm -3 At room temperature Since p no =n i2 /n n0 = (1.5x10 10 ) 2 /5x10 16 p no =4500 cm -3

16 p n = n n = 0.5 x cm -3 An extremely important concept! Minority carrier concentration can be controlled over many orders of magnitude with only a small change in majority concentration.

17 Carrier creation followed by recombination

18 Carrier creation followed by recombination Mostly majority carriers in the dark Almost equal Carrier concentration In light The extra minority carriers recombine once the generation source is removed. How quickly do the carriers recombine?

19 Minority carrier lifetime h for n-type h = average time a hole exists in the valance band from its generation until its recombination And so 1/ h is the average probability (per unit time) that a hole will recombine with an electron. h depends on impurities, defects and temperature. The recombination process in a real semiconductor usually involves a carrier being localized at a recombination center. can be short (nanoseconds) allowing fast response (e.g. switch) or slow (seconds) for a photoconductor or solar cell

20 Excess Minority Carrier Concentration d p n dt G ph p n h p n = excess hole (minority carrier) concentration, t = time, G ph = rate of photogeneration, h = minority carrier lifetime (mean recombination time) h = average time a hole exists in the valance band from its generation until its recombination

21 Carrier concentration versus time with pulsed illumination t is time after illumination is removed

22 Continuous illumination provides increased conductivity Often used as a switch or motion detector

23 Carrier diffusion away from high concentration holes in this p-type example

24 Carrier motion: via diffusion (due to concentration gradient) and drift (due to electric field) Both diffusion and drift occur in semiconductors. Note here that holes (minority carriers) drift and diffuse in the same direction; but electrons (majority carriers) do not! With light we alter minority carrier concentration

### Lecture 15: Optoelectronic devices: Introduction

Lecture 15: Optoelectronic devices: Introduction Contents 1 Optical absorption 1 1.1 Absorption coefficient....................... 2 2 Optical recombination 5 3 Recombination and carrier lifetime 6 3.1

### Carriers Concentration, Current & Hall Effect in Semiconductors. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

Carriers Concentration, Current & Hall Effect in Semiconductors 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 Conductivity Charge

### Session 5: Solid State Physics. Charge Mobility Drift Diffusion Recombination-Generation

Session 5: Solid State Physics Charge Mobility Drift Diffusion Recombination-Generation 1 Outline A B C D E F G H I J 2 Mobile Charge Carriers in Semiconductors Three primary types of carrier action occur

### 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

### collisions of electrons. In semiconductor, in certain temperature ranges the conductivity increases rapidly by increasing temperature

1.9. Temperature Dependence of Semiconductor Conductivity Such dependence is one most important in semiconductor. In metals, Conductivity decreases by increasing temperature due to greater frequency of

### In this block the two transport mechanisms will be discussed: diffusion and drift.

ET3034TUx - 2.3.3 Transport of charge carriers What are the charge carrier transport principles? In this block the two transport mechanisms will be discussed: diffusion and drift. We will discuss that

### 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

### The German University in Cairo. Faculty of Information Engineering & Technology Semiconductors (Elct 503) Electronics Department Fall 2014

The German University in Cairo th Electronics 5 Semester Faculty of Information Engineering & Technology Semiconductors (Elct 503) Electronics Department Fall 2014 Problem Set 3 1- a) Find the resistivity

### Uniform excitation: applied field and optical generation. Non-uniform doping/excitation: diffusion, continuity

6.012 - Electronic Devices and Circuits Lecture 2 - Uniform Excitation; Non-uniform conditions Announcements Review Carrier concentrations in TE given the doping level What happens above and below room

### 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

### pn JUNCTION THE SHOCKLEY MODEL

The pn Junction: The Shockley Model ( S. O. Kasap, 1990-001) 1 pn JUNCTION THE SHOCKLEY MODEL Safa Kasap Department of Electrical Engineering University of Saskatchewan Canada Although the hole and its

### Semiconductor Device Physics

1 Semiconductor Device Physics Lecture 3 http://zitompul.wordpress.com 2 0 1 3 Semiconductor Device Physics 2 Three primary types of carrier action occur inside a semiconductor: Drift: charged particle

### This is the 15th lecture of this course in which we begin a new topic, Excess Carriers. This topic will be covered in two lectures.

Solid State Devices Dr. S. Karmalkar Department of Electronics and Communication Engineering Indian Institute of Technology, Madras Lecture - 15 Excess Carriers This is the 15th lecture of this course

### 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

### PHYS208 P-N Junction. Olav Torheim. May 30, 2007

1 PHYS208 P-N Junction Olav Torheim May 30, 2007 1 Intrinsic semiconductors The lower end of the conduction band is a parabola, just like in the quadratic free electron case (E = h2 k 2 2m ). The density

### 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

### 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

### - A free electron in CB "meets" a hole in VB: the excess energy -> a photon energy.

5.4. Recombination and Minority Carrier Injection 5.4.1 Direct and Indirect Recombination A free electron in CB "meets" a hole in VB: the excess energy > a photon energy. Energy CB ψ cb (k cb ) ψ vb (k

### 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

### Chapter 5. Carrier Transport Phenomena

Chapter 5 Carrier Transport Phenomena 1 We now study the effect of external fields (electric field, magnetic field) on semiconducting material 2 Objective Discuss drift and diffusion current densities

### Excess carriers: extra carriers of values that exist at thermal equilibrium

Ch. 4: Excess carriers In Semiconductors Excess carriers: extra carriers of values that exist at thermal equilibrium Excess carriers can be created by many methods. In this chapter the optical absorption

### Semiconductor Physics fall 2012 problems

Semiconductor Physics fall 2012 problems 1. An n-type sample of silicon has a uniform density N D = 10 16 atoms cm -3 of arsenic, and a p-type silicon sample has N A = 10 15 atoms cm -3 of boron. For each

### ECE 340 Lecture 21 : P-N Junction II Class Outline:

ECE 340 Lecture 21 : P-N Junction II Class Outline: Contact Potential Equilibrium Fermi Levels Things you should know when you leave Key Questions What is the contact potential? Where does the transition

### 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

### Solid State Physics SEMICONDUCTORS - IV. Lecture 25. A.H. Harker. Physics and Astronomy UCL

Solid State Physics SEMICONDUCTORS - IV Lecture 25 A.H. Harker Physics and Astronomy UCL 9.9 Carrier diffusion and recombination Suppose we have a p-type semiconductor, i.e. n h >> n e. (1) Create a local

### MTLE-6120: Advanced Electronic Properties of Materials. Semiconductor p-n junction diodes. Reading: Kasap ,

MTLE-6120: Advanced Electronic Properties of Materials 1 Semiconductor p-n junction diodes Reading: Kasap 6.1-6.5, 6.9-6.12 Metal-semiconductor contact potential 2 p-type n-type p-type n-type Same semiconductor

### Carrier Action: Motion, Recombination and Generation. What happens after we figure out how many electrons and holes are in the semiconductor?

Carrier Action: Motion, Recombination and Generation. What happens after we figure out how many electrons and holes are in the semiconductor? 1 Carrier Motion I Described by 2 concepts: Conductivity: σ

### Lecture 3 Semiconductor Physics (II) Carrier Transport

Lecture 3 Semiconductor Physics (II) Carrier Transport Thermal Motion Carrier Drift Carrier Diffusion Outline Reading Assignment: Howe and Sodini; Chapter 2, Sect. 2.4-2.6 6.012 Spring 2009 Lecture 3 1

### ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 2/25/13) e E i! E T

ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 2/25/13) 1) Consider an n- type semiconductor for which the only states in the bandgap are donor levels (i.e. ( E T = E D ). Begin with

### The 5 basic equations of semiconductor device physics: We will in general be faced with finding 5 quantities:

6.012 - Electronic Devices and Circuits Solving the 5 basic equations - 2/12/08 Version The 5 basic equations of semiconductor device physics: We will in general be faced with finding 5 quantities: n(x,t),

### SEMICONDUCTOR PHYSICS REVIEW BONDS,

SEMICONDUCTOR PHYSICS REVIEW BONDS, BANDS, EFFECTIVE MASS, DRIFT, DIFFUSION, GENERATION, RECOMBINATION February 3, 2011 The University of Toledo, Department of Physics and Astronomy SSARE, PVIC Principles

### Classification of Solids

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

### 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)

### 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

### 3.1 Absorption and Transparency

3.1 Absorption and Transparency 3.1.1 Optical Devices (definitions) 3.1.2 Photon and Semiconductor Interactions 3.1.3 Photon Intensity 3.1.4 Absorption 3.1 Absorption and Transparency Objective 1: Recall

### Semiconductor Physics and Devices

The pn Junction 1) Charge carriers crossing the junction. 3) Barrier potential Semiconductor Physics and Devices Chapter 8. The pn Junction Diode 2) Formation of positive and negative ions. 4) Formation

### Chapter 2. Electronics I - Semiconductors

Chapter 2 Electronics I - Semiconductors Fall 2017 talarico@gonzaga.edu 1 Charged Particles The operation of all electronic devices is based on controlling the flow of charged particles There are two type

### OPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626

OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona kkieu@optics.arizona.edu Meinel building R.626 Announcements Homework #6 is assigned, due May 1 st Final exam May 8, 10:30-12:30pm

### 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

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

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

### 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

### ( )! N D ( x) ) and equilibrium

ECE 66: SOLUTIONS: ECE 66 Homework Week 8 Mark Lundstrom March 7, 13 1) The doping profile for an n- type silicon wafer ( N D = 1 15 cm - 3 ) with a heavily doped thin layer at the surface (surface concentration,

### Diodes. anode. cathode. cut-off. Can be approximated by a piecewise-linear-like characteristic. Lecture 9-1

Diodes mplest nonlinear circuit element Basic operation sets the foundation for Bipolar Junction Transistors (BJTs) Also present in Field Effect Transistors (FETs) Ideal diode characteristic anode cathode

### Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction, and the transistors.

- 1-1/15/02C:\lec320.doc H.L.Kwok SEMICONDUCTOR MATERIALS AND DEVICES by H.L. Kwok Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction,

### PN Junction and MOS structure

PN Junction and MOS structure Basic electrostatic equations We will use simple one-dimensional electrostatic equations to develop insight and basic understanding of how semiconductor devices operate Gauss's

### 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:

### Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction, and the transistors.

- 1-3/4/02C:\lec320.doc H.L.Kwok SEMICONDUCTOR MATERIALS AND DEVICES by H.L. Kwok Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction,

### Semiconductor Physics Problems 2015

Semiconductor Physics Problems 2015 Page and figure numbers refer to Semiconductor Devices Physics and Technology, 3rd edition, by SM Sze and M-K Lee 1. The purest semiconductor crystals it is possible

### 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

### ECE 440 Lecture 20 : PN Junction Electrostatics II Class Outline:

ECE 440 Lecture 20 : PN Junction Electrostatics II Class Outline: Depletion Approximation Step Junction Things you should know when you leave Key Questions What is the space charge region? What are the

### Lecture 8. Equations of State, Equilibrium and Einstein Relationships and Generation/Recombination

Lecture 8 Equations of State, Equilibrium and Einstein Relationships and Generation/Recombination Reading: (Cont d) Notes and Anderson 2 sections 3.4-3.11 Energy Equilibrium Concept Consider a non-uniformly

### Lecture 9 - Carrier Drift and Diffusion (cont.), Carrier Flow. September 24, 2001

6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 9-1 Lecture 9 - Carrier Drift and Diffusion (cont.), Carrier Flow September 24, 2001 Contents: 1. Quasi-Fermi levels 2. Continuity

### 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

### Carrier Recombination

Notes for ECE-606: Spring 013 Carrier Recombination Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA lundstro@purdue.edu /19/13 1 carrier recombination-generation

### Spring Semester 2012 Final Exam

Spring Semester 2012 Final Exam Note: Show your work, underline results, and always show units. Official exam time: 2.0 hours; an extension of at least 1.0 hour will be granted to anyone. Materials parameters

### 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

### Single Photon detectors

Single Photon detectors Outline Motivation for single photon detection Semiconductor; general knowledge and important background Photon detectors: internal and external photoeffect Properties of semiconductor

### 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

### 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

### 1 Name: Student number: DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY MEMORIAL UNIVERSITY OF NEWFOUNDLAND. Fall :00-11:00

1 Name: DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY MEMORIAL UNIVERSITY OF NEWFOUNDLAND Final Exam Physics 3000 December 11, 2012 Fall 2012 9:00-11:00 INSTRUCTIONS: 1. Answer all seven (7) questions.

### Lecture 8 - Carrier Drift and Diffusion (cont.), Carrier Flow. February 21, 2007

6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 8-1 Lecture 8 - Carrier Drift and Diffusion (cont.), Carrier Flow February 21, 2007 Contents: 1. Quasi-Fermi levels 2. Continuity

### Isolated atoms Hydrogen Energy Levels. Neuromorphic Engineering I. Solids Energy bands. Metals, semiconductors and insulators Energy bands

Isolated atoms Hydrogen Energy Levels Neuromorphic Engineering I INI-404 227-1033-00 Electron in atoms have quantized energy levels Material courtesy of Elisabetta Chicca Bielefeld University, Germany

### 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

### Session 6: Solid State Physics. Diode

Session 6: Solid State Physics Diode 1 Outline A B C D E F G H I J 2 Definitions / Assumptions Homojunction: the junction is between two regions of the same material Heterojunction: the junction is between

### Radiation Detection for the Beta- Delayed Alpha and Gamma Decay of 20 Na. Ellen Simmons

Radiation Detection for the Beta- Delayed Alpha and Gamma Decay of 20 Na Ellen Simmons 1 Contents Introduction Review of the Types of Radiation Charged Particle Radiation Detection Review of Semiconductor

### Semiconductor Junctions

8 Semiconductor Junctions Almost all solar cells contain junctions between different materials of different doping. Since these junctions are crucial to the operation of the solar cell, we will discuss

### Electronic PRINCIPLES

MALVINO & BATES Electronic PRINCIPLES SEVENTH EDITION Chapter 2 Semiconductors Topics Covered in Chapter 2 Conductors Semiconductors Silicon crystals Intrinsic semiconductors Two types of flow Doping a

### 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.

### Getting J e (x), J h (x), E(x), and p'(x), knowing n'(x) Solving the diffusion equation for n'(x) (using p-type example)

6.012 - Electronic Devices and Circuits Lecture 4 - Non-uniform Injection (Flow) Problems - Outline Announcements Handouts - 1. Lecture Outline and Summary; 2. Thermoelectrics Review Thermoelectricity:

### UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. Professor Chenming Hu.

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 130 Spring 2009 Professor Chenming Hu Midterm I Name: Closed book. One sheet of notes is

### For the following statements, mark ( ) for true statement and (X) for wrong statement and correct it.

Benha University Faculty of Engineering Shoubra Electrical Engineering Department First Year communications. Answer all the following questions Illustrate your answers with sketches when necessary. The

### 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

### Peak Electric Field. Junction breakdown occurs when the peak electric field in the PN junction reaches a critical value. For the N + P junction,

Peak Electric Field Junction breakdown occurs when the peak electric field in the P junction reaches a critical value. For the + P junction, qa E ( x) ( xp x), s W dep 2 s ( bi Vr ) 2 s potential barrier

### Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium September 20, 2005

6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-1 Contents: Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium September 20, 2005

### Quiz #1 Practice Problem Set

Name: Student Number: ELEC 3908 Physical Electronics Quiz #1 Practice Problem Set? Minutes January 22, 2016 - No aids except a non-programmable calculator - All questions must be answered - All questions

### PHYSICAL ELECTRONICS(ECE3540) CHAPTER 9 METAL SEMICONDUCTOR AND SEMICONDUCTOR HETERO-JUNCTIONS

PHYSICAL ELECTRONICS(ECE3540) CHAPTER 9 METAL SEMICONDUCTOR AND SEMICONDUCTOR HETERO-JUNCTIONS Tennessee Technological University Wednesday, October 30, 013 1 Introduction Chapter 4: we considered the

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

### 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

### ADVANCED UNDERGRADUATE LABORATORY EXPERIMENT 20. Semiconductor Resistance, Band Gap, and Hall Effect

ADVANCED UNDERGRADUATE LABORATORY EXPERIMENT 20 Semiconductor Resistance, Band Gap, and Hall Effect Revised: November 1996 by David Bailey March 1990 by John Pitre & Taek-Soon Yoon Introduction Solid materials

### 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

### ECE 440 Lecture 28 : P-N Junction II Class Outline:

ECE 440 Lecture 28 : P-N Junction II Class Outline: Contact Potential Equilibrium Fermi Levels Things you should know when you leave Key Questions What is the contact potential? Where does the transition

### 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

### 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

### Carrier transport: Drift and Diffusion

. Carrier transport: Drift and INEL 5209 - Solid State Devices - Spring 2012 Manuel Toledo April 10, 2012 Manuel Toledo Transport 1/ 32 Outline...1 Drift Drift current Mobility Resistivity Resistance Hall

### 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

### L5: Surface Recombination, Continuity Equation & Extended Topics tanford University

L5: Surface Recombination, Continuity Equation & Extended Topics EE 216 : Aneesh Nainani 1 Announcements Project Select topic by Jan 29 (Tuesday) 9 topics, maximum 4 students per topic Quiz Thursday (Jan

### Lecture 12. Semiconductor Detectors - Photodetectors

Lecture 12 Semiconductor Detectors - Photodetectors Principle of the pn junction photodiode Absorption coefficient and photodiode materials Properties of semiconductor detectors The pin photodiodes Avalanche

### 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

### 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)

### Metal Semiconductor Contacts

Metal Semiconductor Contacts The investigation of rectification in metal-semiconductor contacts was first described by Braun [33-35], who discovered in 1874 the asymmetric nature of electrical conduction

### Semiconductors CHAPTER 3. Introduction The pn Junction with an Applied Voltage Intrinsic Semiconductors 136

CHAPTER 3 Semiconductors Introduction 135 3.1 Intrinsic Semiconductors 136 3.2 Doped Semiconductors 139 3.3 Current Flow in Semiconductors 142 3.4 The pn Junction 148 3.5 The pn Junction with an Applied

### 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,

### 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

### Direct and Indirect Semiconductor

Direct and Indirect Semiconductor Allowed values of energy can be plotted vs. the propagation constant, k. Since the periodicity of most lattices is different in various direction, the E-k diagram must

### Lecture 15 - The pn Junction Diode (I) I-V Characteristics. November 1, 2005

6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 15-1 Lecture 15 - The pn Junction Diode (I) I-V Characteristics November 1, 2005 Contents: 1. pn junction under bias 2. I-V characteristics

### CLASS 3&4. BJT currents, parameters and circuit configurations

CLASS 3&4 BJT currents, parameters and circuit configurations I E =I Ep +I En I C =I Cp +I Cn I B =I BB +I En -I Cn I BB =I Ep -I Cp I E = I B + I C I En = current produced by the electrons injected from

### Lecture 7 - Carrier Drift and Diffusion (cont.) February 20, Non-uniformly doped semiconductor in thermal equilibrium

6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 7-1 Lecture 7 - Carrier Drift and Diffusion (cont.) February 20, 2007 Contents: 1. Non-uniformly doped semiconductor in thermal equilibrium

### 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