Key Questions. ECE 340 Lecture 16 and 17: Diffusion of Carriers 2/28/14
|
|
- Oscar Chapman
- 6 years ago
- Views:
Transcription
1 /8/4 C 340 eure 6 ad 7: iffusio of Carriers Class Oulie: iffusio roesses iffusio ad rif of Carriers Thigs you should kow whe you leave Key Quesios Why do arriers use? Wha haes whe we add a eleri field o our arrier gradie? How a I visualize his from a ad diagram? Wha is he geeral effe of iludig reomiaio i our osideraios? Wha is he relaioshi ewee usio ad moiliy? M.. Giler C 340 eure 6 ad 7 iffusio roesses Wha haes whe we have a oeraio disoiuiy?? Cosider a siuaio where we sray erfume i he orer of a room If here is o oveio or moio of air he he se sreads y usio. This is due o he radom moio of ariles. ariles move radomly uil hey ollide wih a air moleule whih hages i s direio. If he moio is ruly radom he a arile siig i some volume has eual roailiies of movig io or ou of he volume a some ime ierval. Should he same hig hae i a semioduor if we have saial gradies of arriers? M.. Giler C 340 eure 6 ad 7 T 0 T 0 T 0 T 3 0 iffusio roesses e s shie ligh o a loalized ar of a semioduor ow le s moior he sysem Assume hermal moio. Carriers move y ieraig wih he laie or imuriies. Thermal moio auses ariles o jum o a adjae omarme. Afer he mea-free ime ( half of ariles will leave ad half will remai a erai volume M.. Giler C 340 eure 6 ad 7 3 roess oiues uil uiform oeraio. We mus have a oeraio gradie for usio o sar.
2 /8/4 iffusio roesses How do we desrie his hysial roess?? We wa o alulae he rae a whih eleros use i a simle oedimesioal eamle. Cosider a arirary elero disriuio e # of eleros movig from lef o righ i oe. M.. Giler C 340 eure 6 ad 7 ivide he disriuio io iremeal disaes of he mea-free ah (. valuae ( i he eer of he segmes. leros o he lef of 0 have a 50% hae of movig lef or righ i a ime. Same is rue for eleros o he righ of 0. ( A ( A iffusio roesses So we have a flu of ariles The rae of elero flow i he + direio (er ui area: ( Sie he mea-free ah is a small ereial legh we a wrie he elero eree as: ( + I he limi of small or small mea-free ah ewee ollisios lim 0 d ( + d iffusio oeffiie (m /se M.. Giler C 340 eure 6 ad 7 iffusio roesses Bu we already eeed his iffusio ad rif of Carriers How do we hadle a oeraio gradie ad a eleri field? efie he arrier flu for eleros ad holes: d d d d Ad he orresodig urre desiies assoiaed wih usio d d d d e- The oal urre mus e he sum of he elero ad hole urres resulig from he drif ad usio roesses h+ ( d + d ( d d rif iffusio Where are he ariles ad urres flowig? ( ad drif ( ( ad drif ( + leros (drif (drif Carriers move ogeher urres oosie direios. M.. Giler C 340 eure 6 ad 7 ashed Arrows arile Flow!!Solid Arrows Resulig Curres!!! M.. Giler C 340 eure 6 ad 7
3 /8/4 iffusio ad rif of Carriers A few era oservaios iffusio ad rif of Carriers Ca we relae he usio oeffiie o he moiliy? ( ad drif ( (drif We a y usig wha we kow aou drif usio ad ad edig ( ad drif ( ashed Arrows arile Flow!!Solid Arrows Resulig Curres!!! iffusio urres are i oosie direios. rif urres are i he same direio. Curres deed o: Relaive elero ad hole oeraios. Magiude ad direios of eleri field. Carrier gradies. d M.. Giler C 340 eure 6 ad 7 (drif d + iffusio urres a e large eve d if he arriers are i he mioriy y several orders of magiude. d o rue for drif urres. d i e d k T I euilirium o urre flows. Ay fluuaio ha would egi a usio urre also ses u a eleri field whih redisriues he arriers y drif. d + 0 M.. Giler C 340 eure 6 ad 7 d Solve for he eleri field (: I s euilirium so we kow (: ( F i k T di d Assumig is o-zero ( F i ie ( ( 0 k T d d iffusio ad rif of Carriers These relaios are alled he isei relaios The alae of drif ad usio urres reaes a uil-i eleri field o aomay ay gradie i he ads. Gradies i he ads a our a euilirium whe: he ad ga varies. alloy oeraio varies. doa oeraios vary. V M.. Giler C 340 eure 6 ad 7 d dv di d d d iffusio ad rif of Carriers Reall he revious eamle Assume ha: I is silio maiaied a 300 K. i g /4 a ± ad i g /4 a 0. Choose he Fermi level as he referee eergy. ( V V ref M.. Giler C 340 eure 6 ad 7 i V d dv di d d d 3
4 /8/4 iffusio ad rif of Carriers iffusio ad rif of Carriers Quesio: Is i i euilirium? ergy i Wha are he elero ad hole urre desiies a ± /: i Maerial OS ( F f ( Maerial OS ( F f ( Assume wo maerials i iimae oa. I hermal euilirium. o urre. o e eergy rasfer. Carriers movig from o mus e alaed y arriers movig from o. Rae ( f( ( [ f( ] - Rae ( f ( ( [ f ( - ] Rae - Rae - I is i euilirium so ad 0. Roughly skeh ad iside he samle: i d F Therefore f ( f ( 0 f d M.. Giler C 340 eure 6 ad 7 YS M.. Giler C 340 eure 6 ad 7 iffusio ad rif of Carriers iffusio ad Reomiaio Wha are he elero usio urre a ± /? If so i wha direio? There is a usio urre a oh / ad /. A /: d > 0 d d A /: < 0 d Wha are he elero drif urre a ± /? If so i wha direio? A /: A /: drif drif Wha is he usio oeffiie? Use isei relaio M.. Giler C 340 eure 6 ad 7 i drif vd.9 m /se So wha does his mea? Cosider his semioduor: The hole urre desiy leavig he ereial area may e larger or smaller ha he urre desiy ha eers he area. This is a resul of reomiaio ad geeraio. e irease i hole oeraio er ui ime d/d is eree ewee hole flu er ui volume eerig ad leavig mius he reomiaio rae. M.. Giler C 340 eure 6 ad 7 4
5 /8/4 5 M.. Giler C 340 eure 6 ad 7 iffusio ad Reomiaio How a we elai his? The e irease i hole oeraio er ui ime is he eree ewee he hole flu eerig ad leavig mius he reomiaio rae + + ( Rae of hole uildu. Irease i hole oeraio i A er ui ime. Reomiaio rae As goes o zero we a wrie he hage i hole oeraio as a derivaive jus like i usio leros These relaios form he oiuiy euaios. M.. Giler C 340 eure 6 ad 7 iffusio ad Reomiaio Are here ay simlifiaios? If he urre is arried maily y usio (small drif we a relae he urres i he oiuiy euaio We u his ak io he oiuiy euaios iffusio euaio for eleros d d d d + iffusio euaio for holes Useful mahemaial euaio for may ere hysial siuaios M.. Giler C 340 eure 6 ad 7 Seady Sae Carrier Ijeio To his oi we ee assumig ha he eruraio was removed Wha haes if we kee he eruraio? The ime derivaives disaear d d d d leros Where iffusio egh
ECE 340 Lecture 15 and 16: Diffusion of Carriers Class Outline:
ECE 340 Lecure 5 ad 6: iffusio of Carriers Class Oulie: iffusio rocesses iffusio ad rif of Carriers Thigs you should kow whe you leave Key Quesios Why do carriers diffuse? Wha haes whe we add a elecric
More informationECE 340 Lecture 19 : Steady State Carrier Injection Class Outline:
ECE 340 ecure 19 : Seady Sae Carrier Ijecio Class Oulie: iffusio ad Recombiaio Seady Sae Carrier Ijecio Thigs you should kow whe you leave Key Quesios Wha are he major mechaisms of recombiaio? How do we
More informationComplementi di Fisica Lecture 6
Comlemei di Fisica Lecure 6 Livio Laceri Uiversià di Triese Triese, 15/17-10-2006 Course Oulie - Remider The hysics of semicoducor devices: a iroducio Basic roeries; eergy bads, desiy of saes Equilibrium
More informationK3 p K2 p Kp 0 p 2 p 3 p
Mah 80-00 Mo Ar 0 Chaer 9 Fourier Series ad alicaios o differeial equaios (ad arial differeial equaios) 9.-9. Fourier series defiiio ad covergece. The idea of Fourier series is relaed o he liear algebra
More informationSTK4080/9080 Survival and event history analysis
STK48/98 Survival ad eve hisory aalysis Marigales i discree ime Cosider a sochasic process The process M is a marigale if Lecure 3: Marigales ad oher sochasic processes i discree ime (recap) where (formally
More information1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
More informationLecture 15: Three-tank Mixing and Lead Poisoning
Lecure 15: Three-ak Miig ad Lead Poisoig Eigevalues ad eigevecors will be used o fid he soluio of a sysem for ukow fucios ha saisfy differeial equaios The ukow fucios will be wrie as a 1 colum vecor [
More informationChapter 10. Laser Oscillation : Gain and Threshold
Chaper 0. aser Osillaio : Gai ad hreshold Deailed desripio of laser osillaio 0. Gai Cosider a quasi-moohromai plae wave of frequey propaai i he + direio ; u A he rae a whih
More informationC(p, ) 13 N. Nuclear reactions generate energy create new isotopes and elements. Notation for stellar rates: p 12
Iroducio o sellar reacio raes Nuclear reacios geerae eergy creae ew isoopes ad elemes Noaio for sellar raes: p C 3 N C(p,) 3 N The heavier arge ucleus (Lab: arge) he ligher icomig projecile (Lab: beam)
More informationMoment Generating Function
1 Mome Geeraig Fucio m h mome m m m E[ ] x f ( x) dx m h ceral mome m m m E[( ) ] ( ) ( x ) f ( x) dx Mome Geeraig Fucio For a real, M () E[ e ] e k x k e p ( x ) discree x k e f ( x) dx coiuous Example
More informationExercise 3 Stochastic Models of Manufacturing Systems 4T400, 6 May
Exercise 3 Sochasic Models of Maufacurig Sysems 4T4, 6 May. Each week a very popular loery i Adorra pris 4 ickes. Each ickes has wo 4-digi umbers o i, oe visible ad he oher covered. The umbers are radomly
More informationEnergy Density / Energy Flux / Total Energy in 1D. Key Mathematics: density, flux, and the continuity equation.
ecure Phys 375 Eergy Desiy / Eergy Flu / oal Eergy i D Overview ad Moivaio: Fro your sudy of waves i iroducory physics you should be aware ha waves ca raspor eergy fro oe place o aoher cosider he geeraio
More informationECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
More informationME 501A Seminar in Engineering Analysis Page 1
Seod ad igher Order Liear Differeial Equaios Oober 9, 7 Seod ad igher Order Liear Differeial Equaios Larr areo Mehaial Egieerig 5 Seiar i Egieerig alsis Oober 9, 7 Oulie Reiew las lass ad hoewor ppl aerial
More informationClass 36. Thin-film interference. Thin Film Interference. Thin Film Interference. Thin-film interference
Thi Film Ierferece Thi- ierferece Ierferece ewee ligh waves is he reaso ha hi s, such as soap ules, show colorful paers. Phoo credi: Mila Zikova, via Wikipedia Thi- ierferece This is kow as hi- ierferece
More informationCalculus BC 2015 Scoring Guidelines
AP Calculus BC 5 Scorig Guidelies 5 The College Board. College Board, Advaced Placeme Program, AP, AP Ceral, ad he acor logo are regisered rademarks of he College Board. AP Ceral is he official olie home
More informationPure Math 30: Explained!
ure Mah : Explaied! www.puremah.com 6 Logarihms Lesso ar Basic Expoeial Applicaios Expoeial Growh & Decay: Siuaios followig his ype of chage ca be modeled usig he formula: (b) A = Fuure Amou A o = iial
More informationth m m m m central moment : E[( X X) ] ( X X) ( x X) f ( x)
1 Trasform Techiques h m m m m mome : E[ ] x f ( x) dx h m m m m ceral mome : E[( ) ] ( ) ( x) f ( x) dx A coveie wa of fidig he momes of a radom variable is he mome geeraig fucio (MGF). Oher rasform echiques
More informationLinear System Theory
Naioal Tsig Hua Uiversiy Dearme of Power Mechaical Egieerig Mid-Term Eamiaio 3 November 11.5 Hours Liear Sysem Theory (Secio B o Secio E) [11PME 51] This aer coais eigh quesios You may aswer he quesios
More informationB. Maddah INDE 504 Simulation 09/02/17
B. Maddah INDE 54 Simulaio 9/2/7 Queueig Primer Wha is a queueig sysem? A queueig sysem cosiss of servers (resources) ha provide service o cusomers (eiies). A Cusomer requesig service will sar service
More informationProblems and Solutions for Section 3.2 (3.15 through 3.25)
3-7 Problems ad Soluios for Secio 3 35 hrough 35 35 Calculae he respose of a overdamped sigle-degree-of-freedom sysem o a arbirary o-periodic exciaio Soluio: From Equaio 3: x = # F! h "! d! For a overdamped
More information2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)
Mah PracTes Be sure o review Lab (ad all labs) There are los of good quesios o i a) Sae he Mea Value Theorem ad draw a graph ha illusraes b) Name a impora heorem where he Mea Value Theorem was used i he
More informationLecture contents Macroscopic Electrodynamics Propagation of EM Waves in dielectrics and metals
Leure oes Marosopi lerodyamis Propagaio of M Waves i dieleris ad meals NNS 58 M Leure #4 Maxwell quaios Maxwell equaios desribig he ouplig of eleri ad magei fields D q ev B D J [SI] [CGS] D 4 B D 4 J B
More informationFresnel Dragging Explained
Fresel Draggig Explaied 07/05/008 Decla Traill Decla@espace.e.au The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field
More information5.74 Introductory Quantum Mechanics II
MIT OpeCourseWare hp://ocw.mi.edu 5.74 Iroducory Quaum Mechaics II Sprig 009 For iformaio aou ciig hese maerials or our Terms of Use, visi: hp://ocw.mi.edu/erms. drei Tokmakoff, MIT Deparme of Chemisry,
More informationThe Eigen Function of Linear Systems
1/25/211 The Eige Fucio of Liear Sysems.doc 1/7 The Eige Fucio of Liear Sysems Recall ha ha we ca express (expad) a ime-limied sigal wih a weighed summaio of basis fucios: v ( ) a ψ ( ) = where v ( ) =
More informationReview Exercises for Chapter 9
0_090R.qd //0 : PM Page 88 88 CHAPTER 9 Ifiie Series I Eercises ad, wrie a epressio for he h erm of he sequece..,., 5, 0,,,, 0,... 7,... I Eercises, mach he sequece wih is graph. [The graphs are labeled
More informationMAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPALLI
MAHALAKSHMI EGIEERIG COLLEGE TIRUCHIRAALLI 6 QUESTIO BAK - ASWERS -SEMESTER: V MA 6 - ROBABILITY AD QUEUEIG THEORY UIT IV:QUEUEIG THEORY ART-A Quesio : AUC M / J Wha are he haraerisis of a queueig heory?
More informationMATH 507a ASSIGNMENT 4 SOLUTIONS FALL 2018 Prof. Alexander. g (x) dx = g(b) g(0) = g(b),
MATH 57a ASSIGNMENT 4 SOLUTIONS FALL 28 Prof. Alexader (2.3.8)(a) Le g(x) = x/( + x) for x. The g (x) = /( + x) 2 is decreasig, so for a, b, g(a + b) g(a) = a+b a g (x) dx b so g(a + b) g(a) + g(b). Sice
More informationChapter 2: Time-Domain Representations of Linear Time-Invariant Systems. Chih-Wei Liu
Caper : Time-Domai Represeaios of Liear Time-Ivaria Sysems Ci-Wei Liu Oulie Iroucio Te Covoluio Sum Covoluio Sum Evaluaio Proceure Te Covoluio Iegral Covoluio Iegral Evaluaio Proceure Iercoecios of LTI
More informationSolutions Manual 4.1. nonlinear. 4.2 The Fourier Series is: and the fundamental frequency is ω 2π
Soluios Maual. (a) (b) (c) (d) (e) (f) (g) liear oliear liear liear oliear oliear liear. The Fourier Series is: F () 5si( ) ad he fudameal frequecy is ω f ----- H z.3 Sice V rms V ad f 6Hz, he Fourier
More informationExtremal graph theory II: K t and K t,t
Exremal graph heory II: K ad K, Lecure Graph Theory 06 EPFL Frak de Zeeuw I his lecure, we geeralize he wo mai heorems from he las lecure, from riagles K 3 o complee graphs K, ad from squares K, o complee
More informationLecture 3. Electron and Hole Transport in Semiconductors
Lecture 3 lectro ad Hole Trasort i Semicoductors I this lecture you will lear: How electros ad holes move i semicoductors Thermal motio of electros ad holes lectric curret via lectric curret via usio Semicoductor
More informationSolution. The straightforward approach is surprisingly difficult because one has to be careful about the limits.
ose ad Varably Homewor # (8), aswers Q: Power spera of some smple oses A Posso ose A Posso ose () s a sequee of dela-fuo pulses, eah ourrg depedely, a some rae r (More formally, s a sum of pulses of wdh
More informationELEG 205 Fall Lecture #13. Mark Mirotznik, Ph.D. Professor The University of Delaware Tel: (302)
ELEG 205 Fall 2017 Leure #13 Mark Miroznik, Ph.D. Professor The Universiy of Delaware Tel: (302831-4221 Email: mirozni@ee.udel.edu Chaper 8: RL and RC Ciruis 1. Soure-free RL iruis (naural response 2.
More informationBEST LINEAR FORECASTS VS. BEST POSSIBLE FORECASTS
BEST LINEAR FORECASTS VS. BEST POSSIBLE FORECASTS Opimal ear Forecasig Alhough we have o meioed hem explicily so far i he course, here are geeral saisical priciples for derivig he bes liear forecas, ad
More informationSUMMATION OF INFINITE SERIES REVISITED
SUMMATION OF INFINITE SERIES REVISITED I several aricles over he las decade o his web page we have show how o sum cerai iiie series icludig he geomeric series. We wa here o eed his discussio o he geeral
More informationChemistry 1B, Fall 2016 Topics 21-22
Cheisry B, Fall 6 Topics - STRUCTURE ad DYNAMICS Cheisry B Fall 6 Cheisry B so far: STRUCTURE of aos ad olecules Topics - Cheical Kieics Cheisry B ow: DYNAMICS cheical kieics herodyaics (che C, 6B) ad
More information14.02 Principles of Macroeconomics Fall 2005
14.02 Priciples of Macroecoomics Fall 2005 Quiz 2 Tuesday, November 8, 2005 7:30 PM 9 PM Please, aswer he followig quesios. Wrie your aswers direcly o he quiz. You ca achieve a oal of 100 pois. There are
More information8. Queueing systems lect08.ppt S Introduction to Teletraffic Theory - Fall
8. Queueg sysems lec8. S-38.45 - Iroduco o Teleraffc Theory - Fall 8. Queueg sysems Coes Refresher: Smle eleraffc model M/M/ server wag laces M/M/ servers wag laces 8. Queueg sysems Smle eleraffc model
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More informationLecture 15 First Properties of the Brownian Motion
Lecure 15: Firs Properies 1 of 8 Course: Theory of Probabiliy II Term: Sprig 2015 Isrucor: Gorda Zikovic Lecure 15 Firs Properies of he Browia Moio This lecure deals wih some of he more immediae properies
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.265/15.070J Fall 2013 Lecture 4 9/16/2013. Applications of the large deviation technique
MASSACHUSETTS ISTITUTE OF TECHOLOGY 6.265/5.070J Fall 203 Lecure 4 9/6/203 Applicaios of he large deviaio echique Coe.. Isurace problem 2. Queueig problem 3. Buffer overflow probabiliy Safey capial for
More informationChemical Engineering 374
Chemical Egieerig 374 Fluid Mechaics NoNeoia Fluids Oulie 2 Types ad properies of o-neoia Fluids Pipe flos for o-neoia fluids Velociy profile / flo rae Pressure op Fricio facor Pump poer Rheological Parameers
More informationCOMBUSTION. TA : Donggi Lee ROOM: Building N7-2 #3315 TELEPHONE : 3754 Cellphone : PROF.
COMBUSIO ROF. SEUG WOOK BAEK DEARME OF AEROSACE EGIEERIG, KAIS, I KOREA ROOM: Buldng 7- #334 ELEHOE : 3714 Cellphone : 1-53 - 5934 swbaek@kast.a.kr http://proom.kast.a.kr A : Dongg Lee ROOM: Buldng 7-
More informationEconomics 8723 Macroeconomic Theory Problem Set 2 Professor Sanjay Chugh Spring 2017
Deparme of Ecoomics The Ohio Sae Uiversiy Ecoomics 8723 Macroecoomic Theory Problem Se 2 Professor Sajay Chugh Sprig 207 Labor Icome Taxes, Nash-Bargaied Wages, ad Proporioally-Bargaied Wages. I a ecoomy
More informationClock Skew and Signal Representation
Clock Skew ad Sigal Represeaio Ch. 7 IBM Power 4 Chip 0/7/004 08 frequecy domai Program Iroducio ad moivaio Sequeial circuis, clock imig, Basic ools for frequecy domai aalysis Fourier series sigal represeaio
More informationt = s D Overview of Tests Two-Sample t-test: Independent Samples Independent Samples t-test Difference between Means in a Two-sample Experiment
Overview of Te Two-Sample -Te: Idepede Sample Chaper 4 z-te Oe Sample -Te Relaed Sample -Te Idepede Sample -Te Compare oe ample o a populaio Compare wo ample Differece bewee Mea i a Two-ample Experime
More informationCalculus Limits. Limit of a function.. 1. One-Sided Limits...1. Infinite limits 2. Vertical Asymptotes...3. Calculating Limits Using the Limit Laws.
Limi of a fucio.. Oe-Sided..... Ifiie limis Verical Asympoes... Calculaig Usig he Limi Laws.5 The Squeeze Theorem.6 The Precise Defiiio of a Limi......7 Coiuiy.8 Iermediae Value Theorem..9 Refereces..
More information2007 Spring VLSI Design Mid-term Exam 2:20-4:20pm, 2007/05/11
7 ri VLI esi Mid-erm xam :-4:m, 7/5/11 efieτ R, where R ad deoe he chael resisace ad he ae caaciace of a ui MO ( W / L μm 1μm ), resecively., he chael resisace of a ui PMO, is wo R P imes R. i.e., R R.
More informationPhysics for Scientists & Engineers 2
Direc Curren Physics for Scieniss & Engineers 2 Spring Semeser 2005 Lecure 16 This week we will sudy charges in moion Elecric charge moving from one region o anoher is called elecric curren Curren is all
More informationa 10.0 (m/s 2 ) 5.0 Name: Date: 1. The graph below describes the motion of a fly that starts out going right V(m/s)
Name: Dae: Kinemaics Review (Honors. Physics) Complee he following on a separae shee of paper o be urned in on he day of he es. ALL WORK MUST BE SHOWN TO RECEIVE CREDIT. 1. The graph below describes he
More informationA Two-Level Quantum Analysis of ERP Data for Mock-Interrogation Trials. Michael Schillaci Jennifer Vendemia Robert Buzan Eric Green
A Two-Level Quaum Aalysis of ERP Daa for Mock-Ierrogaio Trials Michael Schillaci Jeifer Vedemia Rober Buza Eric Gree Oulie Experimeal Paradigm 4 Low Workload; Sigle Sessio; 39 8 High Workload; Muliple
More informationCHAPTER 2 TORSIONAL VIBRATIONS
Dr Tiwari, Associae Professor, De. of Mechaical Egg., T Guwahai, (riwari@iig.ere.i) CHAPTE TOSONAL VBATONS Torsioal vibraios is redomia wheever here is large discs o relaively hi shafs (e.g. flywheel of
More informationKEY. Math 334 Midterm I Fall 2008 sections 001 and 003 Instructor: Scott Glasgow
1 KEY Mah 4 Miderm I Fall 8 secions 1 and Insrucor: Sco Glasgow Please do NOT wrie on his eam. No credi will be given for such work. Raher wrie in a blue book, or on our own paper, preferabl engineering
More information6.302 Feedback Systems Recitation : Phase-locked Loops Prof. Joel L. Dawson
6.32 Feedback Syem Phae-locked loop are a foundaional building block for analog circui deign, paricularly for communicaion circui. They provide a good example yem for hi cla becaue hey are an excellen
More informationBig O Notation for Time Complexity of Algorithms
BRONX COMMUNITY COLLEGE of he Ciy Uiversiy of New York DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE CSI 33 Secio E01 Hadou 1 Fall 2014 Sepember 3, 2014 Big O Noaio for Time Complexiy of Algorihms Time
More informationSection 5: Chain Rule
Chaper The Derivaive Applie Calculus 11 Secion 5: Chain Rule There is one more ype of complicae funcion ha we will wan o know how o iffereniae: composiion. The Chain Rule will le us fin he erivaive of
More informationModule 2 F c i k c s la l w a s o s f dif di fusi s o i n
Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms
More informationMath 2414 Homework Set 7 Solutions 10 Points
Mah Homework Se 7 Soluios 0 Pois #. ( ps) Firs verify ha we ca use he iegral es. The erms are clearly posiive (he epoeial is always posiive ad + is posiive if >, which i is i his case). For decreasig we
More information2.1 (a) The mean free time between collisions using Equation (2.2.4b) is. The distance traveled by drift between collisions is
Chater Mobility (a) The mea ree time betwee ollisios usig Euatio (4b) is m m m m 850 3 se where is gie to be 500 m /Vse (= 005 m /Vse), a m is assume to be m 0 (b) We ee to i the rit eloity irst: 50000m
More information( ) ( ) ( ) ( ) (b) (a) sin. (c) sin sin 0. 2 π = + (d) k l k l (e) if x = 3 is a solution of the equation x 5x+ 12=
Eesio Mahemaics Soluios HSC Quesio Oe (a) d 6 si 4 6 si si (b) (c) 7 4 ( si ).si +. ( si ) si + 56 (d) k + l ky + ly P is, k l k l + + + 5 + 7, + + 5 9, ( 5,9) if is a soluio of he equaio 5+ Therefore
More informationTransverse Wave Motion
Trasverse Wave Moio Defiiio of Waves wave is a disurbae ha moves hrough a medium wihou givig he medium, as a whole, a permae displaeme. The geeral ame for hese waves is progressive wave. If he disurbae
More information6/10/2014. Definition. Time series Data. Time series Graph. Components of time series. Time series Seasonal. Time series Trend
6//4 Defiiio Time series Daa A ime series Measures he same pheomeo a equal iervals of ime Time series Graph Compoes of ime series 5 5 5-5 7 Q 7 Q 7 Q 3 7 Q 4 8 Q 8 Q 8 Q 3 8 Q 4 9 Q 9 Q 9 Q 3 9 Q 4 Q Q
More informationDavid Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =
More informationINDEX. Transient analysis 1 Initial Conditions 1
INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera
More informationLet s express the absorption of radiation by dipoles as a dipole correlation function.
MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles
More information3.6 Derivatives as Rates of Change
3.6 Derivaives as Raes of Change Problem 1 John is walking along a sraigh pah. His posiion a he ime >0 is given by s = f(). He sars a =0from his house (f(0) = 0) and he graph of f is given below. (a) Describe
More informationReading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4.
PHY1 Elecriciy Topic 7 (Lecures 1 & 11) Elecric Circuis n his opic, we will cover: 1) Elecromoive Force (EMF) ) Series and parallel resisor combinaions 3) Kirchhoff s rules for circuis 4) Time dependence
More informationME 3210 Mechatronics II Laboratory Lab 6: Second-Order Dynamic Response
Iroucio ME 30 Mecharoics II Laboraory Lab 6: Seco-Orer Dyamic Respose Seco orer iffereial equaios approimae he yamic respose of may sysems. I his lab you will moel a alumium bar as a seco orer Mass-Sprig-Damper
More information12 Getting Started With Fourier Analysis
Commuicaios Egieerig MSc - Prelimiary Readig Geig Sared Wih Fourier Aalysis Fourier aalysis is cocered wih he represeaio of sigals i erms of he sums of sie, cosie or complex oscillaio waveforms. We ll
More informationChapter 2 The Derivative Applied Calculus 107. We ll need a rule for finding the derivative of a product so we don t have to multiply everything out.
Chaper The Derivaive Applie Calculus 107 Secion 4: Prouc an Quoien Rules The basic rules will le us ackle simple funcions. Bu wha happens if we nee he erivaive of a combinaion of hese funcions? Eample
More informationBasic Results in Functional Analysis
Preared by: F.. ewis Udaed: Suday, Augus 7, 4 Basic Resuls i Fucioal Aalysis f ( ): X Y is coiuous o X if X, (, ) z f( z) f( ) f ( ): X Y is uiformly coiuous o X if i is coiuous ad ( ) does o deed o. f
More informationRATE LAWS AND STOICHIOMETRY (3) Marcel Lacroix Université de Sherbrooke
RE LWS D SOIHIOMERY (3 Marcel Lacroix Uniersité de Sherbrooke RE LWS D SOIHIOMERY: RELIOSHIS EWEE j D HUS R, WE HE SEE H I IS OSSILE O SIZE IDEL REORS I HE RE EQUIO IS KOW S UIO O OERSIO,i.e., r g( M.
More informationOn Similarity Transformations A Classical Approach
O Similari rasformaios A Classial Aroah Edard M. Rose EMR eholo Gro Irodio Similari rasformaios are ofe ilized o oer arial differeial eqaios o a se of ordiar differeial eqaios []. he ordiar differeial
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More informationCircuit Variables. AP 1.1 Use a product of ratios to convert two-thirds the speed of light from meters per second to miles per second: 1 ft 12 in
Circui Variables 1 Assessmen Problems AP 1.1 Use a produc of raios o conver wo-hirds he speed of ligh from meers per second o miles per second: ( ) 2 3 1 8 m 3 1 s 1 cm 1 m 1 in 2.54 cm 1 f 12 in 1 mile
More informationSolutions Problem Set 3 Macro II (14.452)
Soluions Problem Se 3 Macro II (14.452) Francisco A. Gallego 04/27/2005 1 Q heory of invesmen in coninuous ime and no uncerainy Consider he in nie horizon model of a rm facing adjusmen coss o invesmen.
More informationLocalization. MEM456/800 Localization: Bayes Filter. Week 4 Ani Hsieh
Localiaio MEM456/800 Localiaio: Baes Filer Where am I? Week 4 i Hsieh Evirome Sesors cuaors Sofware Ucerai is Everwhere Level of ucerai deeds o he alicaio How do we hadle ucerai? Eamle roblem Esimaig a
More informationREVERSIBLE NON-FLOW PROCESS CONSTANT VOLUME PROCESS (ISOCHORIC PROCESS) In a constant volume process, he working substance is contained in a rigid
REVERSIBLE NON-FLOW PROCESS CONSTANT VOLUME PROCESS (ISOCHORIC PROCESS) I a ostat olume roess, he workig substae is otaied i a rigid essel, hee the boudaries of the system are immoable, so work aot be
More informationSolutions to Assignment 1
MA 2326 Differenial Equaions Insrucor: Peronela Radu Friday, February 8, 203 Soluions o Assignmen. Find he general soluions of he following ODEs: (a) 2 x = an x Soluion: I is a separable equaion as we
More information10.3 Autocorrelation Function of Ergodic RP 10.4 Power Spectral Density of Ergodic RP 10.5 Normal RP (Gaussian RP)
ENGG450 Probabiliy ad Saisics for Egieers Iroducio 3 Probabiliy 4 Probabiliy disribuios 5 Probabiliy Desiies Orgaizaio ad descripio of daa 6 Samplig disribuios 7 Ifereces cocerig a mea 8 Comparig wo reames
More informationOutline. simplest HMM (1) simple HMMs? simplest HMM (2) Parameter estimation for discrete hidden Markov models
Oulie Parameer esimaio for discree idde Markov models Juko Murakami () ad Tomas Taylor (2). Vicoria Uiversiy of Welligo 2. Arizoa Sae Uiversiy Descripio of simple idde Markov models Maximum likeliood esimae
More informationF.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics
F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mahemaics Prelim Quesio Paper Soluio Q. Aemp ay FIVE of he followig : [0] Q.(a) Defie Eve ad odd fucios. [] As.: A fucio f() is said o be eve fucio if
More informationRCT Worksheets/Quizzes 1.06 Radioactivity and Radioactive Decay
RCT Workshees/Quizzes.06 Radioaciviy ad Radioacive Decay.06 WORKSHEET #. worker accideally igesed oe millicurie of I3. I3 has a half-life of 8 days. How may disiegraios per secod of I3 are i he workers
More informationEE650R: Reliability Physics of Nanoelectronic Devices Lecture 9:
EE65R: Reliabiliy Physics of anoelecronic Devices Lecure 9: Feaures of Time-Dependen BTI Degradaion Dae: Sep. 9, 6 Classnoe Lufe Siddique Review Animesh Daa 9. Background/Review: BTI is observed when he
More informationt is a basis for the solution space to this system, then the matrix having these solutions as columns, t x 1 t, x 2 t,... x n t x 2 t...
Mah 228- Fri Mar 24 5.6 Marix exponenials and linear sysems: The analogy beween firs order sysems of linear differenial equaions (Chaper 5) and scalar linear differenial equaions (Chaper ) is much sronger
More informationSection 8 Convolution and Deconvolution
APPLICATIONS IN SIGNAL PROCESSING Secio 8 Covoluio ad Decovoluio This docume illusraes several echiques for carryig ou covoluio ad decovoluio i Mahcad. There are several operaors available for hese fucios:
More informationECE Semiconductor Device and Material Characterization
ECE 483 Semicoducor Device ad Maerial Characerizaio Dr. Ala Doolile School of Elecrical ad Comuer Egieerig Georgia Isiue of Techology As wih all of hese lecure slides, I am idebed o Dr. Dieer Schroder
More informationλiv Av = 0 or ( λi Av ) = 0. In order for a vector v to be an eigenvector, it must be in the kernel of λi
Liear lgebra Lecure #9 Noes This week s lecure focuses o wha migh be called he srucural aalysis of liear rasformaios Wha are he irisic properies of a liear rasformaio? re here ay fixed direcios? The discussio
More informationChapter 18: Sampling Distribution Models
Chater 18: Samlig Distributio Models This is the last bit of theory before we get back to real-world methods. Samlig Distributios: The Big Idea Take a samle ad summarize it with a statistic. Now take aother
More informationModeling Micromixing Effects in a CSTR
delig irixig Effes i a STR STR, f all well behaved rears, has he wides RTD i.e. This eas ha large differees i perfrae a exis bewee segregaed flw ad perais a axiu ixedess diis. The easies hig rea is he
More informationRhythm of the Heart. Megan Levine. Abstract
Rhyhm of he Hear Megan Levine Asrac An overlook of he hear and how i works as a pump wih an eplanaion of how o uild a mahemaical model using differenial equaions. The Hear. The Hear Bea The hear ea is
More informationMathematical Statistics. 1 Introduction to the materials to be covered in this course
Mahemaical Saisics Iroducio o he maerials o be covered i his course. Uivariae & Mulivariae r.v s 2. Borl-Caelli Lemma Large Deviaios. e.g. X,, X are iid r.v s, P ( X + + X where I(A) is a umber depedig
More informationKinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.
Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages
More informationN! AND THE GAMMA FUNCTION
N! AND THE GAMMA FUNCTION Cosider he produc of he firs posiive iegers- 3 4 5 6 (-) =! Oe calls his produc he facorial ad has ha produc of he firs five iegers equals 5!=0. Direcly relaed o he discree! fucio
More informationCarriers in a semiconductor diffuse in a carrier gradient by random thermal motion and scattering from the lattice and impurities.
Diffusio of Carriers Wheever there is a cocetratio gradiet of mobile articles, they will diffuse from the regios of high cocetratio to the regios of low cocetratio, due to the radom motio. The diffusio
More informationThe Change of the Distances between the Wave Fronts
Joural of Physical Mahemaics IN: 9-9 Research Aricle Aricle Joural of Physical Mahemaics Geadiy ad iali, J Phys Mah 7, 8: DOI: 47/9-97 OMI Ope Ieraioal Access Opical Fizeau Experime wih Movig Waer is Explaied
More information4.6 One Dimensional Kinematics and Integration
4.6 One Dimensional Kinemaics and Inegraion When he acceleraion a( of an objec is a non-consan funcion of ime, we would like o deermine he ime dependence of he posiion funcion x( and he x -componen of
More information( ) a system of differential equations with continuous parametrization ( T = R + These look like, respectively:
XIII. DIFFERENCE AND DIFFERENTIAL EQUATIONS Ofen funcions, or a sysem of funcion, are paramerized in erms of some variable, usually denoed as and inerpreed as ime. The variable is wrien as a funcion of
More information