Electronic Properties of TANOS Flash Memory

Size: px
Start display at page:

Download "Electronic Properties of TANOS Flash Memory"

Transcription

1 Elecroic Proeries of TANOS Flash Memory Vladimir Griseko Isiue of Semicoducor Physics Siberia Brach of Russia Academy of Scieces Novosibirsk

2 Oulook Marke of flash memory Pricial of flash memory High-k dielecric i flash memory Scalig of flash memory Microscoic hysics of flash Coclusio

3 Flash memory is ow drivig force i microelecroics The hisory of semicoducor busiess. Sice 1990 he FLASH memory domiaes o semicoducor marke.

4 Flash marke Flash memory is used for he savig ad rasfer of iformaio esecially i orable devices. Curre marke: digial camera ad video USB flash memory MP3 layer mobile hoe biomerical assor smar cards orable elecroics oys PC rier scaer auo commuicaio avigaio sace miliary. Fuure marke: oebooks e books elecroic aer elecroic books elecroic ebook elecroic ecycloedia. Flash memory marke er year ~ USD

5 Oeraio ricile of flash memory The basic ricile of flash memory is differe charge value accumulaed i memory ode. As memory ode i curre flash memory is used silico floaig gae or silico iride Iformaio mus be saved i flash device durig 10 years a 85 o C wihou eergy cosumio.

6 Scalig of flash memory The subsaioal disadvaage of floaig gae flash memory is arasiic ierferece durig iformaio wriig. Ierefece resuls i low reliabiliy of flash memory ad resricio for scalig o icrease memory volume > 64Gbie. This disadvaage is overcame i charge ra memory based o silico iride. Our oic for coracs bewee SEC ad ISP if he charge ra memory.

7 Saeme of a roblem The mai ricile of flash memory oeraio is he charge caure i he sorage medium of meal- oide - semicoducor field-effec rasisor. The silico iride is used as sorage maerial. The silico iride has a roery o localize a elecros ad holes wih gigaic lifeime o he dee ras. The memory eleme has srucure: oly-silico- oide- irideoide- semicoducor SONOS. The uel oide hickess of SONOS srucure is m. The disadvaage such memory eleme is a bad reliabiliy durig reeio. To elimiae his disadvaage he Al 2 O 3 dielecric ermiiviy ε=1o was roosed isead of SiO2 SANOS srucure see figure o he righ had.

8 Memory Flash Trasisor SONOS/TANOS High-k blockig dielecric allows o icrease he hickess of uel oide ad imrove he reeio of flash eleme увеличить a 85 С. Griseko VA Nasyrov KA Novikov YuN. A ew low volage fas SONOS memory wih high-k dielecrics. Absrac of he 12h Worksho o dielecrics i microelecroics November Greoble Frace V. A. Griseko K. A. Nasyrov Yu. N. Novikov A. L. Aseev S. Y. Yoo J.-W. Lee E.-H. Lee C. W. Kim A ew low volage fas SONOS memory wih high-k dielecric Solid-Sae Elecroics 47 N aes Russia Federaio o ew flash memory based o high-k dielecrics

9 The advaages of he SANOS i comariso wih SONOS The usig of high-k dielecrics wih high dielecric cosa as blockig oide lead o followig advaages: 1. he icreasig of elecric field i he uel oide lead o icreasig of curre ijecio figure o he righ had. This roery allows o use hicker uel oide whe he memory widow is fied which ca rovide he larger reeio ime i.e. reliabiliy ad decrease of rejecio rae of flash memory. 2. he decreasig of volage dro o he blockig oide leads o decreasig of arasiic ijecio of elecros ad holes form oly silico gae durig wrie/erase oeraios see figure o he righ had

10 Mahemaical model for simulaio of flash devices memory roeries ad charge rasor 1 P N j e r r υ σ υ σ + = P N r υ συ σ = 1 v P N v j e r σ σ + = P N r υ συ σ = 0 εε e F = 2 / sih 2 coh 2 e h T i h h h W W P kt W S I kt W S kt W P + = + = h T o i W W W S W ef m W m ef W P = = e * / h

11 Program Code STRUCTURE develoed i ISP for SEC These arameers defie he disribuios of door ad acceor sies o o oide/gae ierface These arameers defie he disribuios of door ad acceor sies o Si/boom oide ierface Now STRUCTURE ca simulae curreemeraure deedece ad TSC Srucure shows he iiial CV characerisic of samle

12 Wrie ad erase iformaio i TANOS: eerime ad simulaio 8 U FB V V 200 us + 17 V Si- SiO 2 35A Si 3 N 4 70A Al 2 O 3 160A TaN 200A V 20 ms -18 V T=20 C s

13 Comariso eerime ad ra assised hole ijecio model V U FB V V -14 V V -22 V -18 V -16 V sec K.A. Nasyrov S.S. Shaimeev V.A. Griseko Tra-Assised Tuelig Hole Ijecio i SiO2: Eerime ad Theory JETP v

14 Frekel model of ra ad hoo couled ra model K. A. Nasyrov V. A. Griseko Yu. N. Novikov E.-H. Lee S. Y. Yoo C. W. Kim Two- Bads Charge Trasor i Silico Niride due o Phoo-Assised Tra Ioizaio J. Al. Phys. V. 96 N

15 Curre as fucio of emeraure i silico iride: eerime ad simulaio K. A. Nasyrov V. A. Griseko M. K. Kim H. S. Chae S. D. Chae W. I. Ryu J. H. Sok J. W. Lee B. M. Kim Charge Trasor Mechaism i Meal-Niride-Oide Silico Srucures IEEE Elecro Device Leers V. 23 N

16 Curre-volage characerisics of memory ode-silico iride i TANOS A.V. Vishyakov Yu.N. Novikov V.A. Griseko K.A. Nasyrov The charge rasor mechaism i silico iride: Muli-hoo ra ioizaio Solid- Sae Elecroics V. 53 N

17 Naure of memory ras i silico iride of flash devices Elecro localizaio Hole localizaio S.S. Nekrashevich V.V. VasilevA.V. Shaoshikov V.A. Griseko Elecroic srucure of memory ras i silico iride Microelecroic Egieerig 86 N

18 Charge rasor i Al2O3 N. Novikov V.A. Griseko K.A. Nasyrov Charge rasor mechaism i amorhous alumia Al. Phys. Le

19 Poolumiescece of Al2O3 eied by sychroro radiaio DESY Gamburg Germay Phoolumiescece eergy idicae o eisece of oyge vacacies i Al2O3 T.V. Perevalov O.E. Teresheko V.A. Griseko V.A. Pusovarov A.P. Yelisseyev Chaji Park Jeog Hee Ha Choogma Lee Oyge Deficiecy Defecs i Amorhous Al2O3 J. Al. Phys. v

20 Elecro Eergy Loss Secroscoy of a-al2o3 T.V. Perevalov A.V. Shaoshikov V.A. Griseko Elecroic srucure of bulk ad defecs alfa- ad gamma-al2o3 Microelecroic Egieerig March 2009.

21 Elecroic Srucure of Al2O3

22 Bad Srucure ad Effecive masses i α-al2o3 Bad Srucure of α-al2o m * m 0 Effecive masses ofelecros m e ad holes m h Direcio * m e * m h Г-А [ Г-А ] 0.39 Г-А Г-K

23 Coclusio The localizaio effec i silico iride of TANOS is relaed o ecess silico Si-Si bods or Si clusers The defecs resosible for he lumiescece of amorhous Al2O3 are oyge vacacies The elecro ras resosible for he charge The elecro ras resosible for he charge rasor i amorhous Al2O3 are oyge vacacies

24 Thak You

V.A. Gritsenko. Ins/tute of Semiconductor Physics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia

V.A. Gritsenko. Ins/tute of Semiconductor Physics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia The charge ranspor mechanism and he naure of raps in charge rap flash ReRAM and FeRAM devices V.A. Grisenko Ins/ue of Semiconducor Physics of Siberian Branch of Russian Academy of Sciences Novosibirsk

More information

Complementi di Fisica Lecture 6

Complementi 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 information

ECE 340 Lecture 19 : Steady State Carrier Injection Class Outline:

ECE 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 information

ECE 340 Lecture 15 and 16: Diffusion of Carriers Class Outline:

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 information

Thyristors. Vitezslav Benda Dept. of Electrotechnology Czech Technical University in Prague Czech Republic

Thyristors. Vitezslav Benda Dept. of Electrotechnology Czech Technical University in Prague Czech Republic Thyrisors iezslav Beda De. of Elecroechology Czech Techical Uiversiy i rague Czech Reublic Thyrisors - family of swichig devices cosisig of four layers of semicoducor of aleraig doa ye (). Three-ermial

More information

REVERSE CHARACTERISTICS OF PN JUNCTION

REVERSE CHARACTERISTICS OF PN JUNCTION EESE CHAACESCS O N JUNCON Whe ucio reverse biased, sace charge regio creaed by ioised doors ad acceors exeds. Elecric field ad volage disribuio ca be fid solvig oisso equaio e( ND NA ) div E div grad ε

More information

3.8. Other Unipolar Junctions

3.8. Other Unipolar Junctions 3.8. Oher Uipolar ucios The meal-semicoducor jucio is he mos sudied uipolar jucio, be o he oly oe ha occurs i semicoducor devices. Two oher uipolar jucios are he - homojucio ad he - Heerojucio. The - homojucio

More information

Thin MLCC (Multi-Layer Ceramic Capacitor) Reliability Evaluation Using an Accelerated Ramp Voltage Test

Thin MLCC (Multi-Layer Ceramic Capacitor) Reliability Evaluation Using an Accelerated Ramp Voltage Test cceleraed Sress Tesig ad Reliabiliy Thi MLCC (Muli-Layer Ceramic Capacior) Reliabiliy Evaluaio Usig a cceleraed Ramp olage Tes Joh Scarpulla The erospace Corporaio joh.scarpulla@aero.org Jauary-4-7 Sepember

More information

Radiation Experiments and New Materials. T. Paulmier, B. Dirassen, R. Rey

Radiation Experiments and New Materials. T. Paulmier, B. Dirassen, R. Rey Radiaio Exerimes ad New Maerials T. Paulmier, B. Dirasse, R. Rey The research leadig o hese resuls fuded i ar by he Euroea Uio Seveh Framework Programme (FP7) uder gra agreeme No 6676 SPACESTORM Close

More information

Linear System Theory

Linear 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 information

Optimization of the Dielectric Constant of a Blocking Dielectric in the Nonvolatile Memory Based on Silicon Nitride

Optimization of the Dielectric Constant of a Blocking Dielectric in the Nonvolatile Memory Based on Silicon Nitride ISSN 8756-699, Optoelectronics, Instrumentation and Data Processing, 9, Vol. 45, No. 4, pp. 48 5. c Allerton Press, Inc., 9. Original Russian Text c Y. N. Novikov, V. A. Gritsenko, K. A. Nasyrov, 9, published

More information

A TRANSIENT MODEL FOR INSULATED GATE BIPOLAR. TRANSISTORS (IGBTs) Mohsen A Hajji. B.S. in E.E., University of Pittsburgh, 1988

A TRANSIENT MODEL FOR INSULATED GATE BIPOLAR. TRANSISTORS (IGBTs) Mohsen A Hajji. B.S. in E.E., University of Pittsburgh, 1988 A ANSEN MODEL FO NSULAED GAE OLA ANSSOS Gs y Mohse A Hajji.S. i E.E., Uiversiy of isburgh, 988 M.S. i E.E., Uiversiy of isburgh, 996 Submied o he Graduae Faculy of he school of Egieerig arial fulfillme

More information

NUMERICAL SIMULATION OF NANOSCALE DOUBLE-GATE MOSFETS

NUMERICAL SIMULATION OF NANOSCALE DOUBLE-GATE MOSFETS NUMEICAL SIMULAION OF NANOSCALE DOULE-AE MOSFES olad Sezel, Leif Müller, om Herrma, Wilfried Klix Dearme of Elecrical Egieerig Uiversiy of Alied Scieces Dresde Friedrich-Lis-Plaz, D-69 Dresde ermay ASAC

More information

Review Answers for E&CE 700T02

Review Answers for E&CE 700T02 Review Aswers for E&CE 700T0 . Deermie he curre soluio, all possible direcios, ad sepsizes wheher improvig or o for he simple able below: 4 b ma c 0 0 0-4 6 0 - B N B N ^0 0 0 curre sol =, = Ch for - -

More information

Lecture 15: Three-tank Mixing and Lead Poisoning

Lecture 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 information

The analysis of the method on the one variable function s limit Ke Wu

The analysis of the method on the one variable function s limit Ke Wu Ieraioal Coferece o Advaces i Mechaical Egieerig ad Idusrial Iformaics (AMEII 5) The aalysis of he mehod o he oe variable fucio s i Ke Wu Deparme of Mahemaics ad Saisics Zaozhuag Uiversiy Zaozhuag 776

More information

Let s express the absorption of radiation by dipoles as a dipole correlation function.

Let 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 information

Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space via Compatible Mappings of Type (K)

Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space via Compatible Mappings of Type (K) Ieraioal Joural of ahemaics Treds ad Techology (IJTT) Volume 35 umber 4- July 016 Commo Fixed Poi Theorem i Iuiioisic Fuzzy eric Sace via Comaible aigs of Tye (K) Dr. Ramaa Reddy Assisa Professor De. of

More information

Moment Generating Function

Moment 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 information

th m m m m central moment : E[( X X) ] ( X X) ( x X) f ( x)

th 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 information

Ideal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory

Ideal 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 information

PI3B V, 16-Bit to 32-Bit FET Mux/DeMux NanoSwitch. Features. Description. Pin Configuration. Block Diagram.

PI3B V, 16-Bit to 32-Bit FET Mux/DeMux NanoSwitch. Features. Description. Pin Configuration. Block Diagram. 33V, 6-Bi o 32-Bi FET Mux/DeMux NaoSwich Feaures -ohm Swich Coecio Bewee Two Pors Near-Zero Propagaio Delay Fas Swichig Speed: 4s (max) Ulra -Low Quiesce Power (02mA yp) Ideal for oebook applicaios Idusrial

More information

COMBUSTION. TA : Donggi Lee ROOM: Building N7-2 #3315 TELEPHONE : 3754 Cellphone : PROF.

COMBUSTION. 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 information

RCT Worksheets/Quizzes 1.06 Radioactivity and Radioactive Decay

RCT 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 information

Electrical Engineering Department Network Lab.

Electrical Engineering Department Network Lab. Par:- Elecrical Egieerig Deparme Nework Lab. Deermiaio of differe parameers of -por eworks ad verificaio of heir ierrelaio ships. Objecive: - To deermie Y, ad ABD parameers of sigle ad cascaded wo Por

More information

ECE Semiconductor Device and Material Characterization

ECE 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 information

Comparative analysis of existing disinfection models

Comparative analysis of existing disinfection models Comparaive aalysis of exisig disifecio models T. ANDRIANARISON, H. JUPSIN, A OUALI* ad J-L. VASEL Uié Assaiisseme e Eviroeme Uiversié de Liège Campus d Arlo *CERTE, BP 273 Solima, 8020 Tuisia Iroducio

More information

Procedia - Social and Behavioral Sciences 230 ( 2016 ) Joint Probability Distribution and the Minimum of a Set of Normalized Random Variables

Procedia - Social and Behavioral Sciences 230 ( 2016 ) Joint Probability Distribution and the Minimum of a Set of Normalized Random Variables Available olie a wwwsciecedireccom ScieceDirec Procedia - Social ad Behavioral Scieces 30 ( 016 ) 35 39 3 rd Ieraioal Coferece o New Challeges i Maageme ad Orgaizaio: Orgaizaio ad Leadership, May 016,

More information

F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics

F.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 information

Lecture 15 First Properties of the Brownian Motion

Lecture 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 information

Calculus Limits. Limit of a function.. 1. One-Sided Limits...1. Infinite limits 2. Vertical Asymptotes...3. Calculating Limits Using the Limit Laws.

Calculus 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 information

BEST LINEAR FORECASTS VS. BEST POSSIBLE FORECASTS

BEST 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 information

ES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017)

ES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017) Pae1 Nae Soluios ES 330 Elecroics II Hoework 03 (Fall 017 ue Wedesday, Sepeber 0, 017 Proble 1 You are ive a NMOS aplifier wih drai load resisor R = 0 k. The volae (R appeari across resisor R = 1.5 vols

More information

FIXED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE

FIXED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE Mohia & Samaa, Vol. 1, No. II, December, 016, pp 34-49. ORIGINAL RESEARCH ARTICLE OPEN ACCESS FIED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE 1 Mohia S. *, Samaa T. K. 1 Deparme of Mahemaics, Sudhir Memorial

More information

Calculus BC 2015 Scoring Guidelines

Calculus 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 information

Comparison between Fourier and Corrected Fourier Series Methods

Comparison between Fourier and Corrected Fourier Series Methods Malaysia Joural of Mahemaical Scieces 7(): 73-8 (13) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural homepage: hp://eispem.upm.edu.my/oural Compariso bewee Fourier ad Correced Fourier Series Mehods 1

More information

EGR 544 Communication Theory

EGR 544 Communication Theory EGR 544 Commuicaio heory 7. Represeaio of Digially Modulaed Sigals II Z. Aliyazicioglu Elecrical ad Compuer Egieerig Deparme Cal Poly Pomoa Represeaio of Digial Modulaio wih Memory Liear Digial Modulaio

More information

Dynamic h-index: the Hirsch index in function of time

Dynamic h-index: the Hirsch index in function of time Dyamic h-idex: he Hirsch idex i fucio of ime by L. Egghe Uiversiei Hassel (UHassel), Campus Diepebeek, Agoralaa, B-3590 Diepebeek, Belgium ad Uiversiei Awerpe (UA), Campus Drie Eike, Uiversieisplei, B-260

More information

Adaptive sampling based on the motion

Adaptive sampling based on the motion Adaive samlig based o he moio Soglao, Whoi-Yul Kim School of Elecrical ad Comuer Egieerig Hayag Uiversiy Seoul, Korea 33 79 Email: sliao@visio.hayag.ac.kr wykim@hayag.ac.kr Absrac Moio based adaive samlig

More information

ECE 442. Spring, Lecture - 4

ECE 442. Spring, Lecture - 4 ECE 44 Power Semicoductor Devices ad Itegrated circuits Srig, 6 Uiversity of Illiois at Chicago Lecture - 4 ecombiatio, geeratio, ad cotiuity equatio 1. Geeratio thermal, electrical, otical. ecombiatio

More information

PI3B

PI3B 234789023478902347890223478902347890234789022347890234789023478902234789023478902347890223478902 Feaures Near-Zero propagaio delay -ohm swiches coec ipus o oupus Fas Swichig Speed - 4s max Permis Ho Iserio

More information

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)

2 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 information

METHOD OF THE EQUIVALENT BOUNDARY CONDITIONS IN THE UNSTEADY PROBLEM FOR ELASTIC DIFFUSION LAYER

METHOD OF THE EQUIVALENT BOUNDARY CONDITIONS IN THE UNSTEADY PROBLEM FOR ELASTIC DIFFUSION LAYER Maerials Physics ad Mechaics 3 (5) 36-4 Received: March 7 5 METHOD OF THE EQUIVAENT BOUNDARY CONDITIONS IN THE UNSTEADY PROBEM FOR EASTIC DIFFUSION AYER A.V. Zemsov * D.V. Tarlaovsiy Moscow Aviaio Isiue

More information

Solutions Manual 4.1. nonlinear. 4.2 The Fourier Series is: and the fundamental frequency is ω 2π

Solutions 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 information

Discrete-Time Signals and Systems. Introduction to Digital Signal Processing. Independent Variable. What is a Signal? What is a System?

Discrete-Time Signals and Systems. Introduction to Digital Signal Processing. Independent Variable. What is a Signal? What is a System? Discree-Time Sigals ad Sysems Iroducio o Digial Sigal Processig Professor Deepa Kudur Uiversiy of Toroo Referece: Secios. -.4 of Joh G. Proakis ad Dimiris G. Maolakis, Digial Sigal Processig: Priciples,

More information

INVESTMENT PROJECT EFFICIENCY EVALUATION

INVESTMENT PROJECT EFFICIENCY EVALUATION 368 Miljeko Crjac Domiika Crjac INVESTMENT PROJECT EFFICIENCY EVALUATION Miljeko Crjac Professor Faculy of Ecoomics Drsc Domiika Crjac Faculy of Elecrical Egieerig Osijek Summary Fiacial efficiecy of ivesme

More information

OLS bias for econometric models with errors-in-variables. The Lucas-critique Supplementary note to Lecture 17

OLS bias for econometric models with errors-in-variables. The Lucas-critique Supplementary note to Lecture 17 OLS bias for ecoomeric models wih errors-i-variables. The Lucas-criique Supplemeary oe o Lecure 7 RNy May 6, 03 Properies of OLS i RE models I Lecure 7 we discussed he followig example of a raioal expecaios

More information

July 24-25, Overview. Why the Reliability Issue is Important? Some Well-known Reliability Measures. Weibull and lognormal Probability Plots

July 24-25, Overview. Why the Reliability Issue is Important? Some Well-known Reliability Measures. Weibull and lognormal Probability Plots Par I: July 24-25, 204 Overview Why he Reliabiliy Issue is Impora? Reliabiliy Daa Paer Some Well-kow Reliabiliy Measures Weibull ad logormal Probabiliy Plos Maximum Likelihood Esimaor 2 Wha is Reliabiliy?

More information

5.74 Introductory Quantum Mechanics II

5.74 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 information

Department of Electrical and Computer Engineering COEN 451 April 25, 2008

Department of Electrical and Computer Engineering COEN 451 April 25, 2008 Deparme of Elecrical ad ompuer Egieerig OEN 45 April 5, 008 Aswer all Quesios. All Quesios carry equal marks Exam Duraio 3 hour You may use he crib shee ad MOSIS5B parameers aached. Oly recommeded calculaors

More information

Institute of Actuaries of India

Institute of Actuaries of India Isiue of cuaries of Idia Subjec CT3-robabiliy ad Mahemaical Saisics May 008 Eamiaio INDICTIVE SOLUTION Iroducio The idicaive soluio has bee wrie by he Eamiers wih he aim of helig cadidaes. The soluios

More information

Prakash Chandra Rautaray 1, Ellipse 2

Prakash Chandra Rautaray 1, Ellipse 2 Prakash Chadra Rauara, Ellise / Ieraioal Joural of Egieerig Research ad Alicaios (IJERA) ISSN: 48-96 www.ijera.com Vol. 3, Issue, Jauar -Februar 3,.36-337 Degree Of Aroimaio Of Fucios B Modified Parial

More information

Application of Fixed Point Theorem of Convex-power Operators to Nonlinear Volterra Type Integral Equations

Application of Fixed Point Theorem of Convex-power Operators to Nonlinear Volterra Type Integral Equations Ieraioal Mahemaical Forum, Vol 9, 4, o 9, 47-47 HIKRI Ld, wwwm-hikaricom h://dxdoiorg/988/imf4333 licaio of Fixed Poi Theorem of Covex-ower Oeraors o Noliear Volerra Tye Iegral Equaios Ya Chao-dog Huaiyi

More information

The Inverter. References:

The Inverter. References: The Iverer Refereces: Adaped from: Digial Iegraed Circuis: A Desig Perspecive, J. Rabaey UCB Priciples of CMOS LSI Desig: A Sysems Perspecive, d Ed., N. H. E. Wese ad K. Eshraghia Regios of Operaio Cuoff

More information

Doped semiconductors: donor impurities

Doped semiconductors: donor impurities Doped semicoductors: door impurities A silico lattice with a sigle impurity atom (Phosphorus, P) added. As compared to Si, the Phosphorus has oe extra valece electro which, after all bods are made, has

More information

An interesting result about subset sums. Nitu Kitchloo. Lior Pachter. November 27, Abstract

An interesting result about subset sums. Nitu Kitchloo. Lior Pachter. November 27, Abstract A ieresig resul abou subse sums Niu Kichloo Lior Pacher November 27, 1993 Absrac We cosider he problem of deermiig he umber of subses B f1; 2; : : :; g such ha P b2b b k mod, where k is a residue class

More information

ELEG5693 Wireless Communications Propagation and Noise Part II

ELEG5693 Wireless Communications Propagation and Noise Part II Deparme of Elecrical Egieerig Uiversiy of Arkasas ELEG5693 Wireless Commuicaios Propagaio ad Noise Par II Dr. Jigxia Wu wuj@uark.edu OUTLINE Wireless chael Pah loss Shadowig Small scale fadig Simulaio

More information

MODERN CONTROL SYSTEMS

MODERN CONTROL SYSTEMS MODERN CONTROL SYSTEMS Lecure 9, Sae Space Repreeaio Emam Fahy Deparme of Elecrical ad Corol Egieerig email: emfmz@aa.edu hp://www.aa.edu/cv.php?dip_ui=346&er=6855 Trafer Fucio Limiaio TF = O/P I/P ZIC

More information

14.02 Principles of Macroeconomics Fall 2005

14.02 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 information

Constrained Codes for Phase-change Memories

Constrained Codes for Phase-change Memories 2010 IEEE Iformaio Theory Workshop - ITW 2010 Dubli Cosraied Codes for Phase-chage Memories Axiao Adrew Jiag Compuer Sciece ad Eg. Dep. Texas A&M Uiversiy College Saio, TX 7784 Email: ajiag@cse.amu.edu

More information

Convergence Analysis of Multi-innovation Learning Algorithm Based on PID Neural Network

Convergence Analysis of Multi-innovation Learning Algorithm Based on PID Neural Network Sesors & rasducers, Vol., Secial Issue, May 03,. 4-46 Sesors & rasducers 03 by IFSA h://www.sesorsoral.com Coergece Aalysis of Muli-ioaio Learig Algorihm Based o PID Neural Nework Gag Re,, Pile Qi, Mimi

More information

2007 Spring VLSI Design Mid-term Exam 2:20-4:20pm, 2007/05/11

2007 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 information

Fluctuation and Flow Probes of Early-Time Correlations

Fluctuation and Flow Probes of Early-Time Correlations Flucuaio ad Flow Probes of Early-Time Correlaios WPCF 0 Frakfur am Mai, Seember 0 George Moschelli Frakfur Isiue for Adaced Sudies & Sea Gai Waye Sae Uiersiy Moiaio Two Paricle Correlaios: d d d Pair Disribuio

More information

Comparisons Between RV, ARV and WRV

Comparisons Between RV, ARV and WRV Comparisos Bewee RV, ARV ad WRV Cao Gag,Guo Migyua School of Maageme ad Ecoomics, Tiaji Uiversiy, Tiaji,30007 Absrac: Realized Volailiy (RV) have bee widely used sice i was pu forward by Aderso ad Bollerslev

More information

IV. COMPARISON of CHARGE-CARRIER POPULATION at EACH SIDE of the JUNCTION V. FORWARD BIAS, REVERSE BIAS

IV. COMPARISON of CHARGE-CARRIER POPULATION at EACH SIDE of the JUNCTION V. FORWARD BIAS, REVERSE BIAS Fall-2003 PH-31 A. La Rosa JUNCTIONS I. HARNESSING ELECTRICAL CONDUCTIVITY IN SEMICONDUCTOR MATERIALS Itrisic coductivity (Pure silico) Extrisic coductivity (Silico doed with selected differet atoms) II.

More information

N! AND THE GAMMA FUNCTION

N! 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 information

EECS130 Integrated Circuit Devices

EECS130 Integrated Circuit Devices EECS130 Itegrated Circuit Devices Professor Ali Javey 9/04/2007 Semicoductor Fudametals Lecture 3 Readig: fiish chapter 2 ad begi chapter 3 Aoucemets HW 1 is due ext Tuesday, at the begiig of the class.

More information

12 Getting Started With Fourier Analysis

12 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 information

MATH 507a ASSIGNMENT 4 SOLUTIONS FALL 2018 Prof. Alexander. g (x) dx = g(b) g(0) = g(b),

MATH 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 information

Pure Math 30: Explained!

Pure 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 information

Fresnel Dragging Explained

Fresnel 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 information

A Hilbert-type fractal integral inequality and its applications

A Hilbert-type fractal integral inequality and its applications Liu ad Su Joural of Ieualiies ad Alicaios 7) 7:83 DOI.86/s366-7-36-9 R E S E A R C H Oe Access A Hilber-e fracal iegral ieuali ad is alicaios Qiog Liu ad Webig Su * * Corresodece: swb5@63.com Dearme of

More information

1 Notes on Little s Law (l = λw)

1 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 information

Class 36. Thin-film interference. Thin Film Interference. Thin Film Interference. Thin-film interference

Class 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 information

Mathematical Statistics. 1 Introduction to the materials to be covered in this course

Mathematical 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 information

Outline. simplest HMM (1) simple HMMs? simplest HMM (2) Parameter estimation for discrete hidden Markov models

Outline. 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 information

King Fahd University of Petroleum & Minerals Computer Engineering g Dept

King Fahd University of Petroleum & Minerals Computer Engineering g Dept Kig Fahd Uiversiy of Peroleum & Mierals Compuer Egieerig g Dep COE 4 Daa ad Compuer Commuicaios erm Dr. shraf S. Hasa Mahmoud Rm -4 Ex. 74 Email: ashraf@kfupm.edu.sa 9/8/ Dr. shraf S. Hasa Mahmoud Lecure

More information

6.003: Signals and Systems Lecture 20 April 22, 2010

6.003: Signals and Systems Lecture 20 April 22, 2010 6.003: Sigals ad Sysems Lecure 0 April, 00 6.003: Sigals ad Sysems Relaios amog Fourier Represeaios Mid-erm Examiaio #3 Wedesday, April 8, 7:30-9:30pm. No reciaios o he day of he exam. Coverage: Lecures

More information

ECE-314 Fall 2012 Review Questions

ECE-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 information

NARAYANA. C o m m o n P r a c t i c e T e s t 1 2 XII STD BATCHES [CF] Date: PHYSICS CHEMISTRY MATHEMATICS 18. (A) 33. (C) 48. (B) 63.

NARAYANA. C o m m o n P r a c t i c e T e s t 1 2 XII STD BATCHES [CF] Date: PHYSICS CHEMISTRY MATHEMATICS 18. (A) 33. (C) 48. (B) 63. NARAYANA I I T / N E E T A C A D E M Y. (D). (A). (D). (A). (C). (B) 7. (C) 8. (A) 9. (B) 0. (C). (B). (C). (B). (C). (D) C o m m o P r a c i c e T e s XII STD BATCES [CF] Dae: 0.07.7 ANSWER PYSICS CEMISTRY

More information

Clock Skew and Signal Representation

Clock 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 information

Spintronics of Nanomechanical Shuttle

Spintronics of Nanomechanical Shuttle * Spinronics of Nanomechanical Shule Rober Shekher In collaboraion wih: D.Fedores,. Gorelik, M. Jonson Göeborg Universiy / Chalmers Universiy of Technology Elecromechanics of Coulomb Blockade srucures

More information

The universal vector. Open Access Journal of Mathematical and Theoretical Physics [ ] Introduction [ ] ( 1)

The universal vector. Open Access Journal of Mathematical and Theoretical Physics [ ] Introduction [ ] ( 1) Ope Access Joural of Mahemaical ad Theoreical Physics Mii Review The uiversal vecor Ope Access Absrac This paper akes Asroheology mahemaics ad pus some of i i erms of liear algebra. All of physics ca be

More information

Design and Application Notes for AP3765 System Solution

Design and Application Notes for AP3765 System Solution licaio oe 064 Desig ad licaio oes for 3765 ysem oluio reared by u Ju Jie ysem Egeerg De.. roducio The 3765 uses ulse Frequecy Modulaio (FM) mehod o realize Discouous Coducio Mode (DCM) oeraio for flyback

More information

q=2π/d BNL-NSLS NSLS d = α β b β c Long d Spacing small Bragg angle 2L wide Bragg angle Though this be madness yet there is method in t X rays

q=2π/d BNL-NSLS NSLS d = α β b β c Long d Spacing small Bragg angle 2L wide Bragg angle Though this be madness yet there is method in t X rays Crysallizaio of fas uder shear: X-ray diffracio ad NMR daa Crysallie srucure of fas Log d Spacig small ragg agle 2L 3L Giafraco Mazzai Dalhousie Uiversiy, Halifax, Caada Shor d Spacig wide ragg agle a

More information

H033 A New Pseudo-acoustic Wave Equation for VTI Media

H033 A New Pseudo-acoustic Wave Equation for VTI Media H033 A New Pseudo-acousic Wae Euaio for VTI Media X. Du* WeserGeco Schlumberger R.P. Flecher WeserGeco Schlumberger & P.J. Fowler WeserGeco Schlumberger SUMMARY We roose a ew aroimae arial differeial euaio

More information

Effect of Heat Exchangers Connection on Effectiveness

Effect of Heat Exchangers Connection on Effectiveness Joural of Roboics ad Mechaical Egieerig Research Effec of Hea Exchagers oecio o Effeciveess Voio W Koiaho Maru J Lampie ad M El Haj Assad * Aalo Uiversiy School of Sciece ad echology P O Box 00 FIN-00076

More information

Vibration damping of the cantilever beam with the use of the parametric excitation

Vibration damping of the cantilever beam with the use of the parametric excitation The s Ieraioal Cogress o Soud ad Vibraio 3-7 Jul, 4, Beijig/Chia Vibraio dampig of he cailever beam wih he use of he parameric exciaio Jiří TŮMA, Pavel ŠURÁNE, Miroslav MAHDA VSB Techical Uiversi of Osrava

More information

Journal of Chemical and Pharmaceutical Research, 2015, 7(3): Research Article

Journal of Chemical and Pharmaceutical Research, 2015, 7(3): Research Article Available olie www.jocr.com Joural of Chemical ad Pharmaceuical Researc 05, 7(3):0-0 Research Aricle ISSN : 0975-7384 CODEN(USA) : JCPRC5 Research o iceive ad cosrai model of miliar erus o eerrise age

More information

When both wages and prices are sticky

When both wages and prices are sticky Whe boh ages ad rices are sicy Previously, i he basic models, oly roduc rices ere alloed o be sicy. I racice, i is ossible ha oher rices are sicy as ell. I addiio, some rices migh be more or less sicy

More information

Chapter 2 Motion and Recombination of Electrons and Holes

Chapter 2 Motion and Recombination of Electrons and Holes Chapter 2 Motio ad Recombiatio of Electros ad Holes 2.1 Thermal Eergy ad Thermal Velocity Average electro or hole kietic eergy 3 2 kt 1 2 2 mv th v th 3kT m eff 3 23 1.38 10 JK 0.26 9.1 10 1 31 300 kg

More information

CHAP.4 Circuit Characteristics and Performance Estimation

CHAP.4 Circuit Characteristics and Performance Estimation HAP.4 ircui haracerisics ad Performace Esimaio 4. Resisace esimaio ρ l R w (ohms) where ρ resisiviy hickess l coducor legh w coducor widh l R Rs w where Rs shee resisace (Ω/square) i 0.5µm o.0µm MOS processes

More information

12 th Mathematics Objective Test Solutions

12 th Mathematics Objective Test Solutions Maemaics Objecive Tes Soluios Differeiaio & H.O.D A oes idividual is saisfied wi imself as muc as oer are saisfied wi im. Name: Roll. No. Bac [Moda/Tuesda] Maimum Time: 90 Miues [Eac rig aswer carries

More information

More Digital Logic. t p output. Low-to-high and high-to-low transitions could have different t p. V in (t)

More Digital Logic. t p output. Low-to-high and high-to-low transitions could have different t p. V in (t) EECS 4 Spring 23 Lecure 2 EECS 4 Spring 23 Lecure 2 More igial Logic Gae delay and signal propagaion Clocked circui elemens (flip-flop) Wriing a word o memory Simplifying digial circuis: Karnaugh maps

More information

Big O Notation for Time Complexity of Algorithms

Big 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 information

The Eigen Function of Linear Systems

The 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 information

Chapter 5: The pn Junction

Chapter 5: The pn Junction Cher 5: The ucio Noequilibrium ecess crriers i semicoducors Crrier geerio d recombiio Mhemicl lysis of ecess crriers Ambiolr rsor The jucio Bsic srucure of he jucio Zero lied bis Reverse lied bis No-uiformly

More information

ECE 570 Session 7 IC 752-E Computer Aided Engineering for Integrated Circuits. Transient analysis. Discuss time marching methods used in SPICE

ECE 570 Session 7 IC 752-E Computer Aided Engineering for Integrated Circuits. Transient analysis. Discuss time marching methods used in SPICE ECE 570 Sessio 7 IC 75-E Compuer Aided Egieerig for Iegraed Circuis Trasie aalysis Discuss ime marcig meods used i SPICE. Time marcig meods. Explici ad implici iegraio meods 3. Implici meods used i circui

More information

BAYESIAN ESTIMATION METHOD FOR PARAMETER OF EPIDEMIC SIR REED-FROST MODEL. Puji Kurniawan M

BAYESIAN ESTIMATION METHOD FOR PARAMETER OF EPIDEMIC SIR REED-FROST MODEL. Puji Kurniawan M BAYESAN ESTMATON METHOD FOR PARAMETER OF EPDEMC SR REED-FROST MODEL Puji Kuriawa M447 ABSTRACT. fecious diseases is a impora healh problem i he mos of couries, belogig o doesia. Some of ifecious diseases

More information

Key Questions. ECE 340 Lecture 16 and 17: Diffusion of Carriers 2/28/14

Key Questions. ECE 340 Lecture 16 and 17: Diffusion of Carriers 2/28/14 /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

More information