Semiconductor Optical Communication Components and Devices Lecture 15: Light Emitting Diode (LED)

Size: px
Start display at page:

Download "Semiconductor Optical Communication Components and Devices Lecture 15: Light Emitting Diode (LED)"

Transcription

1 Semicoducto Otical Commuicatio Comoets ad Devices Lectue 15: Light mittig Diode (LD) Pof. Utal Das Pofesso, Deatmet of lectical gieeig, Lase Techology Pogam, Idia Istitute of Techology, Kau htt://

2 Doig fo P-N juctio LD hece F c m kt e 3 e ~ m C 3 kt lectos N f O C C F V Holes V 3 h ~ m V F V V V F V

3 LD Mateial Poeties: Fo efficiet light emissio, diect bad-ga semicoductos ae efeed (e.g. GaAs). As caies ecombie acoss the active egio of the P-N juctio device, the active egio caot be eithe - o -tye as thee ae a lot of electo as well as a lot of holes. The Femi eegy, theefoe, has to slit ad have seaate quasi-femi eegy fo electos ( F ) ad quasi- Femi eegy fo holes ( f ). The wavelegth of the light emitted is the ootioal to this bad-ga ( g = h). X valley gi1 G valley gd egy L valley gi Light Hole Heavy Hole Slit Bad K

4 Diect ad Idiect tasitio i Semicoductos - LD s - (k ) 1 Diect Bad Ga c Absotio Recombiatio missio egy + + Sotaeous missio g h (k) h v k g elec. khole 0 Reduced Plak s Costat Fequecy of the Photo 0 h k 0 Idiect Bad Ga Recombiatio emissio k c OP g k k h g AP v a k k 0 h k

5 (a) quilibium (V=0) - juctio LD I O alied V (b) Fowad Bias (V=V f ) V f V V V O I I e qv k T B (c) Revese Bias (V=-V ) V 1 R s () ( C )... kt 1.5 Itegatio of eegies fom the bad ga to all electo ad hole eegies g lecto h egy v F V V O Diffusio e Diffusio h Dift e qv o Dift h v F V V v O C F V V f Diffusio e Fh F Diffusio h Dift e v Q(V o -V f ) Dift h V C F O V v F V V Dift h Dift e Q(V o +V f ) g egy Bad tails due to heavy doig of - ad - tye mateial v V V ( ).. kt Caie Cocetatio R ( ) A(, ) f ( )[1 f ( )] d s 1 1 C V 1 CV C 3 ( m ) 1 CV ( ) 3 g F ( kbt) ( ) u s 4 u du c h V e 1 0

6 Light Outut (Powe) Light Outut (mw) Light Outut (mw) LD Powe as a fuctio of Dive Cuet The excess ijected caie P Ohmic Cotact cocetatio deceases t 0e as Dielectic Isulato tot (Oxide/Nitide) + GaAsP egio The ate of chage fo a cuet d J + GaAsP P = 40% desity J ad deletio width d is dt qd J tot m qd I R tot, q P it + GaAs substate N Ohmic Cotact it hci q Cuet (I) 3 R it R tot Ideal: Liea tot Whee the 1s tem o the ight is the ate of ijected chage caie coc. ad the d is the ate of sotaeous decay. J At steady state the: tot qd Assumig each e-h ai oduces oe hoto P it = R tot.h O P it =(I/q)h(c/)=(hc/q)I=[1.396/(mm)]I 1 10 Not all ecombiatios oduce hotos. Hece P it = it (hc/q)i High Sloe but Satuatio effects at high cuets Due to oadiative ecombiatio effects aisig out of Auge Recombiatio Cuet (ma) Low Sloe due to oadiative ecombiatio ate lage i comaiso to adiative ecombiatio ate Cuet (ma)

7 LD xtactio fficiecy 1 F q c I I 1 cosq c q q q I Cost. siqdqd siqdqd F q c 1 F = 1- =η 1 1 si 1 1 q q c q Poit Light Souce 1 - juctio e(xtactio) Note that 1 is the semicoducto efactive idex ad is usually ai o lastic ecasulatio Plastic ecasulatio lectical Cotacts 3

8 ij 1 m m LD xteal fficiecy ve eglectig citical agle, still e = ½ due to loss i the substate h L o e L o e h 1 (mobility, majoity caie cocetatio, ad diffusio legth) The fial fficiecy is the give by tot ij e lectical Cotacts To icease e oe could use a hemisheical dome, but it is exesive. So a cheae alteative is to use lastic ecasulatio whee o =1, of the semicoducto is ~3.5-4, ad 1 is usually ~1.5

9 Stuctues of LD (Imotat oes) - I: Light Outut Light Outut Dome LD tye eitaxial laye tye substate Plaa LD Diffused -tye Ohmic cotacts Ohmic cotacts Dome ad laa LD ae used i most dislay devices whee the iteest is i extactig the maximum amout of light fom the device. =>Light is emittig i all diectios ad usig a les aagemet to focus the light Buus ad edge-emittig LD ae used maily i otical fibe commuicatio systems

10 Stuctues of LD (Imotat oes) - II: A ossible device stuctue is show i Fig. Ufotuately, the ecombiatio ocess that leads to hoto oductio ivolves the Z imuity cetes, ad hoto emissio ocesses ivolvig imuity cetes ae much less efficiet tha bad to bad ocesses. i - GaN Blue Photos Ohmic Cotacts + - GaN Sahie Substate (Tasaet) Dielectic (Oxide o Nitide)

11 Review Poblems 1. Photos of wavelegth =813 m ae absobed i IP at oom temeatue (g=1.344ev, m e *=0.08m o, m h *=0.60m o ) ad excites electo-hole ais (HP). Calculate the aveage kietic eegy of the electos ad holes befoe they elax to the bottom of the bads. [Hit: they will ot be the same]. Fid the eak emissio wavelegth ( o ) fo a Al 0. Ga 0.8 As LD oeatig at 400 o K, give the bad gas AlAs G =3.03eV, AlAs X =.15eV, AlAs L =.36eV, GaAs G =1.43eV, GaAs X =1.73eV, ad GaAs L =1.89eV. (assume liea iteolatio to be valid) 3. Deive the factio of adiatio escaig fom a LD (oit souce) imbedded i a medium of efactive idex 1 ito the ue medium of efactive idex, assumig thee is o absotio i the medium. Also assume the tasmissio coefficiet is that of omal icidece at the iteface. 4. A LD at oom temeatue ude 0.8V fowad bias coducts a cuet of I =1mA ad emits light at a eak wavelegth of 1.0µm. The adiative ad the o-adiative time costats ae 0.1s ad 1s, esectively. Assumig that the uity extactio efficiecy ad the ijectio efficiecy is 0.9, calculate the owe covesio efficiecy of the diode. Is this calculated efficiecy geate tha o less tha uity? Does it suise you, exlai. What is the ew covesio efficiecy, if fo the same set of coditios, the emissio wavelegth is ow 1.3µm?

Nonequilibrium Excess Carriers in Semiconductors

Nonequilibrium Excess Carriers in Semiconductors Lecture 8 Semicoductor Physics VI Noequilibrium Excess Carriers i Semicoductors Noequilibrium coditios. Excess electros i the coductio bad ad excess holes i the valece bad Ambiolar trasort : Excess electros

More information

1. pn junction under bias 2. I-Vcharacteristics

1. pn junction under bias 2. I-Vcharacteristics Lecture 10 The p Juctio (II) 1 Cotets 1. p juctio uder bias 2. I-Vcharacteristics 2 Key questios Why does the p juctio diode exhibit curret rectificatio? Why does the juctio curret i forward bias icrease

More information

Photo-Voltaics and Solar Cells. Photo-Voltaic Cells

Photo-Voltaics and Solar Cells. Photo-Voltaic Cells Photo-Voltaics ad Solar Cells this lecture you will lear: Photo-Voltaic Cells Carrier Trasort, Curret, ad Efficiecy Solar Cells Practical Photo-Voltaics ad Solar Cells ECE 407 Srig 009 Farha aa Corell

More information

Solar Photovoltaic Technologies

Solar Photovoltaic Technologies Solar Photovoltaic Techologies ecture-17 Prof. C.S. Solaki Eergy Systems Egieerig T Bombay ecture-17 Cotets Brief summary of the revious lecture Total curret i diode: Quatitative aalysis Carrier flow uder

More information

Photodiodes. 1. Current and Voltage in an Illuminated Junction 2. Solar Cells

Photodiodes. 1. Current and Voltage in an Illuminated Junction 2. Solar Cells Photodiodes 1. Curret ad Voltae i a llumiated Juctio 2. olar Cells Diode Equatio D (e.) ( e qv / kt 1) V D o ( e qv / kt 1) Particle Flow uder Reversed Bias Particle Flow uder llumiatio W -tye -tye Otical

More information

Nanomaterials for Photovoltaics (v11) 10. Bulk-Heterojunction Solar Cells

Nanomaterials for Photovoltaics (v11) 10. Bulk-Heterojunction Solar Cells 1 10. Bulk-Heteojuctio Sola Cells Naostuctued sola cells We ca imagie a spectum of aostuctue sola cells agig fom a ogaic, bulk heteojuctio type just discussed to a iogaic, 3-D ogaized type. Example: CuSCN/TiO

More information

EE415/515 Fundamentals of Semiconductor Devices Fall 2012

EE415/515 Fundamentals of Semiconductor Devices Fall 2012 11/18/1 EE415/515 Fudametals of Semicoductor Devices Fall 1 ecture 16: PVs, PDs, & EDs Chater 14.1-14.6 Photo absortio Trasaret or oaque Photo eergy relatioshis c hc 1.4 m E E E i ev 11/18/1 ECE 415/515

More information

Bipolar Junction Transistors

Bipolar Junction Transistors ipolar Juctio Trasistors ipolar juctio trasistor (JT) was iveted i 948 at ell Telephoe Laboratories Sice 97, the high desity ad low power advatage of the MOS techology steadily eroded the JT s early domiace.

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 Motio 3 1 2 Average electro or hole kietic eergy kt mv th 2 2 v th 3kT m eff 23 3 1.38 10 JK 0.26 9.1 10 1 31 300 kg K 5 7 2.310 m/s 2.310

More information

The aim of the course is to give an introduction to semiconductor device physics. The syllabus for the course is:

The aim of the course is to give an introduction to semiconductor device physics. The syllabus for the course is: Semicoductor evices Prof. Rb Robert tat A. Taylor The aim of the course is to give a itroductio to semicoductor device physics. The syllabus for the course is: Simple treatmet of p- juctio, p- ad p-i-

More information

p/n junction Isolated p, n regions: no electric contact, not in equilibrium E vac E i E A E F E V E C E D

p/n junction Isolated p, n regions: no electric contact, not in equilibrium E vac E i E A E F E V E C E D / juctio Isolated, regios: o electric cotact, ot i equilibrium E vac E C E C E E F E i E i E F E E V E V / juctio I equilibrium, the Fermi level must be costat. Shift the eergy levels i ad regios u/dow

More information

ECEN 5014, Spring 2013 Special Topics: Active Microwave Circuits and MMICs Zoya Popovic, University of Colorado, Boulder

ECEN 5014, Spring 2013 Special Topics: Active Microwave Circuits and MMICs Zoya Popovic, University of Colorado, Boulder ECEN 5014, Spig 013 Special Topics: Active Micowave Cicuits ad MMICs Zoya Popovic, Uivesity of Coloado, Boulde LECTURE 7 THERMAL NOISE L7.1. INTRODUCTION Electical oise is a adom voltage o cuet which is

More information

Greatest term (numerically) in the expansion of (1 + x) Method 1 Let T

Greatest term (numerically) in the expansion of (1 + x) Method 1 Let T BINOMIAL THEOREM_SYNOPSIS Geatest tem (umeically) i the epasio of ( + ) Method Let T ( The th tem) be the geatest tem. Fid T, T, T fom the give epasio. Put T T T ad. Th will give a iequality fom whee value

More information

Week 03 Discussion. 30% are serious, and 50% are stable. Of the critical ones, 30% die; of the serious, 10% die; and of the stable, 2% die.

Week 03 Discussion. 30% are serious, and 50% are stable. Of the critical ones, 30% die; of the serious, 10% die; and of the stable, 2% die. STAT 400 Wee 03 Discussio Fall 07. ~.5- ~.6- At the begiig of a cetai study of a gou of esos, 5% wee classified as heavy smoes, 30% as light smoes, ad 55% as osmoes. I the five-yea study, it was detemied

More information

Diode in electronic circuits. (+) (-) i D

Diode in electronic circuits. (+) (-) i D iode i electroic circuits Symbolic reresetatio of a iode i circuits ode Cathode () (-) i ideal diode coducts the curret oly i oe directio rrow shows directio of the curret i circuit Positive olarity of

More information

JEE(MAIN) 2018 TEST PAPER WITH ANSWER (HELD ON SUNDAY 08 th APRIL, 2018) PART C PHYSICS. 64. The density of a material in the shape of a cube ALLEN

JEE(MAIN) 2018 TEST PAPER WITH ANSWER (HELD ON SUNDAY 08 th APRIL, 2018) PART C PHYSICS. 64. The density of a material in the shape of a cube ALLEN 6. The agula width of the cetal maximum i a sigle slit diffactio patte is 60. The width of the slit is mm. The slit is illumiated by moochomatic plae waves. If aothe slit of same width is made ea it, Youg

More information

Semiconductors. PN junction. n- type

Semiconductors. PN junction. n- type Semicoductors. PN juctio We have reviously looked at the electroic roerties of itrisic, - tye ad - time semicoductors. Now we will look at what haes to the electroic structure ad macroscoic characteristics

More information

I PUC MATHEMATICS CHAPTER - 08 Binomial Theorem. x 1. Expand x + using binomial theorem and hence find the coefficient of

I PUC MATHEMATICS CHAPTER - 08 Binomial Theorem. x 1. Expand x + using binomial theorem and hence find the coefficient of Two Maks Questios I PU MATHEMATIS HAPTER - 08 Biomial Theoem. Epad + usig biomial theoem ad hece fid the coefficiet of y y. Epad usig biomial theoem. Hece fid the costat tem of the epasio.. Simplify +

More information

Lecture 2-5. Optical Fiber

Lecture 2-5. Optical Fiber We use qualitative desciptio athe tha quatitative desciptio. What is fibe? - Best aswe is cicula ad vey log waveguide. - Geeal ideas fo guidig i a plaa waveguide is exteded to a cylidical waveguide - Fibe

More information

EE105 Fall 2015 Microelectronic Devices and Circuits. pn Junction

EE105 Fall 2015 Microelectronic Devices and Circuits. pn Junction EE105 Fall 015 Microelectroic Devices ad Circuits Prof. Mig C. Wu wu@eecs.berkeley.edu 511 Sutardja Dai Hall (SDH 6-1 Juctio -tye semicoductor i cotact with -tye Basic buildig blocks of semicoductor devices

More information

Introduction to Microelectronics

Introduction to Microelectronics The iolar Juctio Trasistor Physical Structure of the iolar Trasistor Oeratio of the NPN Trasistor i the Active Mode Trasit Time ad Diffusio aacitace Ijectio fficiecy ad ase Trasort Factor The bers-moll

More information

SOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T

SOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T SOUIONS: ECE 606 Homework Week 7 Mark udstrom Purdue Uiversity (revised 3/27/13) 1) Cosider a - type semicoductor for which the oly states i the badgap are door levels (i.e. ( E = E D ). Begi with the

More information

5.1 Introduction 5.2 Equilibrium condition Contact potential Equilibrium Fermi level Space charge at a junction 5.

5.1 Introduction 5.2 Equilibrium condition Contact potential Equilibrium Fermi level Space charge at a junction 5. 5.1 troductio 5.2 Equilibrium coditio 5.2.1 Cotact otetial 5.2.2 Equilibrium Fermi level 5.2.3 Sace charge at a juctio 5.3 Forward- ad Reverse-biased juctios; steady state coditios 5.3.1 Qualitative descritio

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

Electron states in a periodic potential. Assume the electrons do not interact with each other. Solve the single electron Schrodinger equation: KJ =

Electron states in a periodic potential. Assume the electrons do not interact with each other. Solve the single electron Schrodinger equation: KJ = Electo states i a peiodic potetial Assume the electos do ot iteact with each othe Solve the sigle electo Schodige equatio: 2 F h 2 + I U ( ) Ψ( ) EΨ( ). 2m HG KJ = whee U(+R)=U(), R is ay Bavais lattice

More information

CHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method

CHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method CHAPTER 5 : SERIES 5.1 Seies 5. The Sum of a Seies 5..1 Sum of Powe of Positive Iteges 5.. Sum of Seies of Patial Factio 5..3 Diffeece Method 5.3 Test of covegece 5.3.1 Divegece Test 5.3. Itegal Test 5.3.3

More information

2012 GCE A Level H2 Maths Solution Paper Let x,

2012 GCE A Level H2 Maths Solution Paper Let x, GCE A Level H Maths Solutio Pape. Let, y ad z be the cost of a ticet fo ude yeas, betwee ad 5 yeas, ad ove 5 yeas categoies espectively. 9 + y + 4z =. 7 + 5y + z = 8. + 4y + 5z = 58.5 Fo ude, ticet costs

More information

(a) Unde zeo-bias conditions, thee ae no lled states on one side of the junction which ae at the same enegy as the empty allowed states on the othe si

(a) Unde zeo-bias conditions, thee ae no lled states on one side of the junction which ae at the same enegy as the empty allowed states on the othe si 1 Esaki Diode hen the concentation of impuity atoms in a pn-diode is vey high, the depletion laye width is educed to about 1 nm. Classically, a caie must have an enegy at least equal to the potential-baie

More information

Carriers in a semiconductor diffuse in a carrier gradient by random thermal motion and scattering from the lattice and impurities.

Carriers 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 information

Complementi di Fisica Lecture 24

Complementi di Fisica Lecture 24 Comlemeti di Fisica - Lecture 24 18-11-2015 Comlemeti di Fisica Lecture 24 Livio Laceri Uiversità di Trieste Trieste, 18-11-2015 I this lecture Cotets Drift of electros ad holes i ractice (umbers ): coductivity

More information

Technical Report: Bessel Filter Analysis

Technical Report: Bessel Filter Analysis Sasa Mahmoodi 1 Techical Repot: Bessel Filte Aalysis 1 School of Electoics ad Compute Sciece, Buildig 1, Southampto Uivesity, Southampto, S17 1BJ, UK, Email: sm3@ecs.soto.ac.uk I this techical epot, we

More information

Mark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University

Mark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University Mark udstrom Sprig 2015 SOUTIONS: ECE 305 Homework: Week 5 Mark udstrom Purdue Uiversity The followig problems cocer the Miority Carrier Diffusio Equatio (MCDE) for electros: Δ t = D Δ + G For all the

More information

ECE606: Solid State Devices Lecture 9 Recombination Processes and Rates

ECE606: Solid State Devices Lecture 9 Recombination Processes and Rates ECE606: Solid State Devices Lecture 9 Recombiatio Processes ad Rates Gerhard Klimeck gekco@urdue.edu Outlie ) No-equilibrium systems ) Recombiatio geeratio evets 3) Steady-state ad trasiet resose ) Motivatio

More information

Phys 102 Lecture 25 The quantum mechanical model of light

Phys 102 Lecture 25 The quantum mechanical model of light Phys 102 Lecture 25 The quatum mechaical model of light 1 Recall last time Problems with classical physics Stability of atoms Atomic spectra Photoelectric effect Quatum model of the atom Bohr model oly

More information

BINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a

BINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a BINOMIAL THEOREM hapte 8 8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4 5y, etc., ae all biomial epessios. 8.. Biomial theoem If

More information

Maxwell s equations. in differential form. r J

Maxwell s equations. in differential form. r J Bacgoud Maell s equatios C 46/566 Guided Wave Optics Mawell s equatios i diffeetial fom B t D H t B D ρ J Faaday s law Ampee s law No mag. moopoles Gauss law lectic field [V/m] H Magetic field [A/m] D

More information

2. Characteristics of Synchrotron Radiation

2. Characteristics of Synchrotron Radiation . Chaacteistics of Schoto Radiatio. Itoductio The adiatio i geeal is chaacteized b the followig tems: spectal age, photo flu, photo flu desit, billiace, ad the polaizatio. The photo flu is the oveall flu

More information

BINOMIAL THEOREM NCERT An expression consisting of two terms, connected by + or sign is called a

BINOMIAL THEOREM NCERT An expression consisting of two terms, connected by + or sign is called a 8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4, etc., ae all biomial 5y epessios. 8.. Biomial theoem BINOMIAL THEOREM If a ad b ae

More information

ANSWERS, HINTS & SOLUTIONS HALF COURSE TEST VII (Main)

ANSWERS, HINTS & SOLUTIONS HALF COURSE TEST VII (Main) AIITS-HT-VII-PM-JEE(Mai)-Sol./7 I JEE Advaced 06, FIITJEE Studets bag 6 i Top 00 AIR, 7 i Top 00 AIR, 8 i Top 00 AIR. Studets fom Log Tem lassoom/ Itegated School Pogam & Studets fom All Pogams have qualified

More information

Introduction to Semiconductor Devices and Circuit Model

Introduction to Semiconductor Devices and Circuit Model Itroductio to Semicoductor Devices ad Circuit Model Readig: Chater 2 of Howe ad Sodii Electrical Resistace I + V _ W homogeeous samle t L Resistace R V I L = ρ Wt (Uits: Ω) where ρ is the resistivity (Uits:

More information

The Pigeonhole Principle 3.4 Binomial Coefficients

The Pigeonhole Principle 3.4 Binomial Coefficients Discete M athematic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Ageda Ch 3. The Pigeohole Piciple

More information

( ) 1 Comparison Functions. α is strictly increasing since ( r) ( r ) α = for any positive real number c. = 0. It is said to belong to

( ) 1 Comparison Functions. α is strictly increasing since ( r) ( r ) α = for any positive real number c. = 0. It is said to belong to Compaiso Fuctios I this lesso, we study stability popeties of the oautoomous system = f t, x The difficulty is that ay solutio of this system statig at x( t ) depeds o both t ad t = x Thee ae thee special

More information

SYMMETRY ENERGY FOR NUCLEI BEYOND THE STABILITY VALLEY. V.M. Kolomietz and A.I.Sanzhur

SYMMETRY ENERGY FOR NUCLEI BEYOND THE STABILITY VALLEY. V.M. Kolomietz and A.I.Sanzhur SYMMETRY ENERGY FOR NULEI BEYOND THE STBILITY VLLEY V.M. Kolomietz ad.i.sazhu Istitute fo Nuclea Reseach, 368 Kiev, Ukaie We aly the diect vaiatioal method to deive the equatio of state fo fiite uclei

More information

a) The average (mean) of the two fractions is halfway between them: b) The answer is yes. Assume without loss of generality that p < r.

a) The average (mean) of the two fractions is halfway between them: b) The answer is yes. Assume without loss of generality that p < r. Solutios to MAML Olympiad Level 00. Factioated a) The aveage (mea) of the two factios is halfway betwee them: p ps+ q ps+ q + q s qs qs b) The aswe is yes. Assume without loss of geeality that p

More information

Basic Physics of Semiconductors

Basic Physics of Semiconductors Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1 Semicoductor Physics Semicoductor devices serve as heart of microelectroics.

More information

Lecture 10: P-N Diodes. Announcements

Lecture 10: P-N Diodes. Announcements EECS 15 Sprig 4, Lecture 1 Lecture 1: P-N Diodes EECS 15 Sprig 4, Lecture 1 Aoucemets The Thursday lab sectio will be moved a hour later startig this week, so that the TA s ca atted lecture i aother class

More information

Nanomaterials for Photovoltaics (v11) 6. Homojunctions

Nanomaterials for Photovoltaics (v11) 6. Homojunctions Naomaterials for Photovoltaics (v11) 1 6. Homojuctios / juctio diode The most imortat device cocet for the coversio of light ito electrical curret is the / juctio diode. We first cosider isolated ad regios

More information

Basic Physics of Semiconductors

Basic Physics of Semiconductors Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1 Semicoductor Physics Semicoductor devices serve as heart of microelectroics.

More information

Quiz #3 Practice Problem Set

Quiz #3 Practice Problem Set Name: Studet Number: ELEC 3908 Physical Electroics Quiz #3 Practice Problem Set? Miutes March 11, 2016 - No aids excet a o-rogrammable calculator - ll questios must be aswered - ll questios have equal

More information

MATH Midterm Solutions

MATH Midterm Solutions MATH 2113 - Midtem Solutios Febuay 18 1. A bag of mables cotais 4 which ae ed, 4 which ae blue ad 4 which ae gee. a How may mables must be chose fom the bag to guaatee that thee ae the same colou? We ca

More information

Lecture 24: Observability and Constructibility

Lecture 24: Observability and Constructibility ectue 24: Obsevability ad Costuctibility 7 Obsevability ad Costuctibility Motivatio: State feedback laws deped o a kowledge of the cuet state. I some systems, xt () ca be measued diectly, e.g., positio

More information

THE ANALYTIC LARGE SIEVE

THE ANALYTIC LARGE SIEVE THE ANALYTIC LAGE SIEVE 1. The aalytic lage sieve I the last lectue we saw how to apply the aalytic lage sieve to deive a aithmetic fomulatio of the lage sieve, which we applied to the poblem of boudig

More information

Discussion 02 Solutions

Discussion 02 Solutions STAT 400 Discussio 0 Solutios Spig 08. ~.5 ~.6 At the begiig of a cetai study of a goup of pesos, 5% wee classified as heavy smoes, 30% as light smoes, ad 55% as osmoes. I the fiveyea study, it was detemied

More information

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : , MB BINOMIAL THEOREM Biomial Epessio : A algebaic epessio which cotais two dissimila tems is called biomial epessio Fo eample :,,, etc / ( ) Statemet of Biomial theoem : If, R ad N, the : ( + ) = a b +

More information

Overview of Silicon p-n Junctions

Overview of Silicon p-n Junctions Overview of Silico - Juctios r. avid W. Graham West irgiia Uiversity Lae eartmet of omuter Sciece ad Electrical Egieerig 9 avid W. Graham 1 - Juctios (iodes) - Juctios (iodes) Fudametal semicoductor device

More information

Ch 3.4 Binomial Coefficients. Pascal's Identit y and Triangle. Chapter 3.2 & 3.4. South China University of Technology

Ch 3.4 Binomial Coefficients. Pascal's Identit y and Triangle. Chapter 3.2 & 3.4. South China University of Technology Disc ete Mathem atic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Pigeohole Piciple Suppose that a

More information

4. Biasing Transistor Circuits

4. Biasing Transistor Circuits Lectue 5: toductio to electoic aalog cicuits 361-1-3661 1 4. iasig Tasisto icuits ugee Papeo, 2008 Ou mai aim is to aalyze the dawbacks of the bias i the elemetay tasisto cicuits ad to suggest a betteolutio

More information

CHAPTER 3 MICROSTRIP PATCH ANTENNA

CHAPTER 3 MICROSTRIP PATCH ANTENNA CHAPTER 3 MICROSTRIP PATCH ANTENNA I this chapte, a itoductio to the Micostip Patch Atea is followed by its advatages ad disadvatages. Next, some feed modelig techiques ae discussed. Fially, a detailed

More information

Progression. CATsyllabus.com. CATsyllabus.com. Sequence & Series. Arithmetic Progression (A.P.) n th term of an A.P.

Progression. CATsyllabus.com. CATsyllabus.com. Sequence & Series. Arithmetic Progression (A.P.) n th term of an A.P. Pogessio Sequece & Seies A set of umbes whose domai is a eal umbe is called a SEQUENCE ad sum of the sequece is called a SERIES. If a, a, a, a 4,., a, is a sequece, the the expessio a + a + a + a 4 + a

More information

Early 1900 s Max Planck derives the blackbody intensity spectrum assuming each atom to be an oscillator emitting and absorbing photons discretely.

Early 1900 s Max Planck derives the blackbody intensity spectrum assuming each atom to be an oscillator emitting and absorbing photons discretely. Peludes to Quatum Mechaics ~ 900 90 Blackbody Radiatio A blackbody absobs all icidet adiatio without eflectio o scatteig. The adiatio emitted fom a blackbody adiato by vitue of its tempeatue shows a chaacteistic

More information

Introduction to Solid State Physics

Introduction to Solid State Physics Itroductio to Solid State Physics Class: Itegrated Photoic Devices Time: Fri. 8:00am ~ 11:00am. Classroom: 資電 206 Lecturer: Prof. 李明昌 (Mig-Chag Lee) Electros i A Atom Electros i A Atom Electros i Two atoms

More information

Two arbitrary semiconductors generally have different electron affinities, bandgaps, and effective DOSs. An arbitrary example is shown below.

Two arbitrary semiconductors generally have different electron affinities, bandgaps, and effective DOSs. An arbitrary example is shown below. 9. Heterojuctios Semicoductor heterojuctios A heterojuctio cosists of two differet materials i electrical equilibrium separated by a iterface. There are various reasos these are eeded for solar cells:

More information

Photodetectors; Receivers

Photodetectors; Receivers Photoetectors; Receivers They covert a otical sigal to a electrical sigal through absortio of hotos a creatio of HP. Their esig is more comlicate tha the otical trasmitters because the receivers must first

More information

RECIPROCAL POWER SUMS. Anthony Sofo Victoria University, Melbourne City, Australia.

RECIPROCAL POWER SUMS. Anthony Sofo Victoria University, Melbourne City, Australia. #A39 INTEGERS () RECIPROCAL POWER SUMS Athoy Sofo Victoia Uivesity, Melboue City, Austalia. athoy.sofo@vu.edu.au Received: /8/, Acceted: 6//, Published: 6/5/ Abstact I this ae we give a alteative oof ad

More information

On composite conformal mapping of an annulus to a plane with two holes

On composite conformal mapping of an annulus to a plane with two holes O composite cofomal mappig of a aulus to a plae with two holes Mila Batista (July 07) Abstact I the aticle we coside the composite cofomal map which maps aulus to ifiite egio with symmetic hole ad ealy

More information

Supplementary materials. Suzuki reaction: mechanistic multiplicity versus exclusive homogeneous or exclusive heterogeneous catalysis

Supplementary materials. Suzuki reaction: mechanistic multiplicity versus exclusive homogeneous or exclusive heterogeneous catalysis Geeal Pape ARKIVOC 009 (xi 85-03 Supplemetay mateials Suzui eactio: mechaistic multiplicity vesus exclusive homogeeous o exclusive heteogeeous catalysis Aa A. Kuohtia, Alexade F. Schmidt* Depatmet of Chemisty

More information

Lecture 3-7 Semiconductor Lasers.

Lecture 3-7 Semiconductor Lasers. Laser LED Stimulated emissio Spotaeous emissio Laser I th I Typical output optical power vs. diode curret (I) characteristics ad the correspodig output spectrum of a laser diode.?1999 S.O. Kasap, Optoelectroics

More information

International Journal of Mathematics Trends and Technology (IJMTT) Volume 47 Number 1 July 2017

International Journal of Mathematics Trends and Technology (IJMTT) Volume 47 Number 1 July 2017 Iteatioal Joual of Matheatics Teds ad Techology (IJMTT) Volue 47 Nube July 07 Coe Metic Saces, Coe Rectagula Metic Saces ad Coo Fixed Poit Theoes M. Sivastava; S.C. Ghosh Deatet of Matheatics, D.A.V. College

More information

Analysis of Arithmetic. Analysis of Arithmetic. Analysis of Arithmetic Round-Off Errors. Analysis of Arithmetic. Analysis of Arithmetic

Analysis of Arithmetic. Analysis of Arithmetic. Analysis of Arithmetic Round-Off Errors. Analysis of Arithmetic. Analysis of Arithmetic In the fixed-oint imlementation of a digital filte only the esult of the multilication oeation is quantied The eesentation of a actical multilie with the quantie at its outut is shown below u v Q ^v The

More information

r, this equation is graphed in figure 1.

r, this equation is graphed in figure 1. Washigto Uivesity i St Louis Spig 8 Depatmet of Ecoomics Pof James Moley Ecoomics 4 Homewok # 3 Suggested Solutio Note: This is a suggested solutio i the sese that it outlies oe of the may possible aswes

More information

Minimal order perfect functional observers for singular linear systems

Minimal order perfect functional observers for singular linear systems Miimal ode efect fuctioal obseves fo sigula liea systems Tadeusz aczoek Istitute of Cotol Idustial lectoics Wasaw Uivesity of Techology, -66 Waszawa, oszykowa 75, POLAND Abstact. A ew method fo desigig

More information

ECEN Microelectronics. Semiconductor Physics and P/N junctions 2/05/19

ECEN Microelectronics. Semiconductor Physics and P/N junctions 2/05/19 ECEN 3250 Microelectroics Semicoductor Physics ad P/N juctios 2/05/19 Professor J. Gopiath Professor J. Gopiath Uiversity of Colorado at Boulder Microelectroics Sprig 2014 Overview Eergy bads Atomic eergy

More information

Digital Integrated Circuit Design

Digital Integrated Circuit Design Digital Itegrated Circuit Desig Lecture 4 PN Juctio -tye -tye Adib Abrishamifar EE Deartmet IUST Diffusio (Majority Carriers) Cotets PN Juctio Overview PN Juctios i Equilibrium Forward-biased PN Juctios

More information

Semiconductors a brief introduction

Semiconductors a brief introduction Semicoductors a brief itroductio Bad structure from atom to crystal Fermi level carrier cocetratio Dopig Readig: (Sedra/Smith 7 th editio) 1.7-1.9 Trasport (drift-diffusio) Hyperphysics (lik o course homepage)

More information

Masses and orbits of minor planets with the GAIA mission

Masses and orbits of minor planets with the GAIA mission asses ad obits of io laets with the GAIA issio Sege ouet Suevisos : F.igad D.Hestoffe PLAN Itoductio Puose of the PhD Iotace of asses The diffeet ethods to estiate these asses Descitio of close aoach Diffeet

More information

FAR FIELD SOLUTION OF SH-WAVE BY CIRCULAR INCLUSION AND LINEAR CRACK

FAR FIELD SOLUTION OF SH-WAVE BY CIRCULAR INCLUSION AND LINEAR CRACK The 4 th Wold Cofeece o Eathquake Egieeig Octobe -7, 8, Beijig, Chia FAR FIELD SOLUTION OF SH-WAVE BY CIRCULAR INCLUSION AND LINEAR CRACK HogLiag Li,GuoHui Wu, Associate Pofesso, Depatmet of Egieeig Mechaics,

More information

Heterojunctions. Heterojunctions

Heterojunctions. Heterojunctions Heterojuctios Heterojuctios Heterojuctio biolar trasistor SiGe GaAs 4 96, 007-008, Ch. 9 3 Defiitios eφ s eχ s lemet Ge, germaium lectro affiity, χ (ev) 4.13 Si, silico 4.01 GaAs, gallium arseide 4.07

More information

Chapter 9. Spintransport in Semiconductors. Spinelektronik: Grundlagen und Anwendung spinabhängiger Transportphänomene 1

Chapter 9. Spintransport in Semiconductors. Spinelektronik: Grundlagen und Anwendung spinabhängiger Transportphänomene 1 Chapte 9 Spintanspot in Semiconductos : Gundlagen und Anwendung spinabhängige Tanspotphänomene 1 Winte 05/06 Why ae semiconductos of inteest in spintonics? They povide a contol of the chage as in conventional

More information

Parameter Extraction Procedure for Ion Implantation Profiles to Establish Robust Database based on Tail Function

Parameter Extraction Procedure for Ion Implantation Profiles to Establish Robust Database based on Tail Function JOUNAL OF SEMICONDUCTO TECHNOLOGY AND SCIENCE, VOL., NO., DECEMBE, 5 Paamete Extactio Pocedue fo Io Implatatio Pofiles to Establish obust Database based o Tail Fuctio Kuihio SUZUKI* ad Shuichi KOJIMA**

More information

Minimization of the quadratic test function

Minimization of the quadratic test function Miimizatio of the quadatic test fuctio A quadatic fom is a scala quadatic fuctio of a vecto with the fom f ( ) A b c with b R A R whee A is assumed to be SPD ad c is a scala costat Note: A symmetic mati

More information

Lecture 9: Diffusion, Electrostatics review, and Capacitors. Context

Lecture 9: Diffusion, Electrostatics review, and Capacitors. Context EECS 5 Sprig 4, Lecture 9 Lecture 9: Diffusio, Electrostatics review, ad Capacitors EECS 5 Sprig 4, Lecture 9 Cotext I the last lecture, we looked at the carriers i a eutral semicoductor, ad drift currets

More information

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70 SAMPL PAPR I Time Allowed : 3 hous Maximum Maks : 70 Note : Attempt All questions. Maks allotted to each question ae indicated against it. 1. The magnetic field lines fom closed cuves. Why? 1 2. What is

More information

MATH 10550, EXAM 3 SOLUTIONS

MATH 10550, EXAM 3 SOLUTIONS MATH 155, EXAM 3 SOLUTIONS 1. I fidig a approximate solutio to the equatio x 3 +x 4 = usig Newto s method with iitial approximatio x 1 = 1, what is x? Solutio. Recall that x +1 = x f(x ) f (x ). Hece,

More information

Auchmuty High School Mathematics Department Sequences & Series Notes Teacher Version

Auchmuty High School Mathematics Department Sequences & Series Notes Teacher Version equeces ad eies Auchmuty High chool Mathematics Depatmet equeces & eies Notes Teache Vesio A sequece takes the fom,,7,0,, while 7 0 is a seies. Thee ae two types of sequece/seies aithmetic ad geometic.

More information

Advanced Higher Formula List

Advanced Higher Formula List Advaced Highe Fomula List Note: o fomulae give i eam emembe eveythig! Uit Biomial Theoem Factoial! ( ) ( ) Biomial Coefficiet C!! ( )! Symmety Idetity Khayyam-Pascal Idetity Biomial Theoem ( y) C y 0 0

More information

Current, Resistance and

Current, Resistance and Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity

More information

P-N Junction in equilibrium. Diode. Diode bias. Forward and reverse bias. Diode current-voltage characteristics. Models. Applications.

P-N Junction in equilibrium. Diode. Diode bias. Forward and reverse bias. Diode current-voltage characteristics. Models. Applications. Unit 12: Semiconducto devices. Diode. P-N Junction in equilibium. Diode. Diode bias. Fowad and evese bias. Diode cuent-voltage chaacteistics. Models. Applications. PN junction in equilibium Electons Holes

More information

FYS Vår 2016 (Kondenserte fasers fysikk)

FYS Vår 2016 (Kondenserte fasers fysikk) FYS3410 - Vår 2016 (Kodeserte fasers fysikk) http://www.uio.o/studier/emer/matat/fys/fys3410/v16/idex.html Pesum: Itroductio to Solid State Physics by Charles Kittel (Chapters 1-9 ad 17, 18, 20) Adrej

More information

ECE606: Solid State Devices Lecture 14 Electrostatics of p-n junctions

ECE606: Solid State Devices Lecture 14 Electrostatics of p-n junctions ECE606: Solid State evices Lecture 14 Electrostatics of - juctios Gerhard Klimeck gekco@urdue.edu Outlie 1) Itroductio to - juctios ) rawig bad-diagrams 3) ccurate solutio i equilibrium 4) Bad-diagram

More information

Schottky diodes: I-V characteristics

Schottky diodes: I-V characteristics chottky diodes: - characteristics The geeral shape of the - curve i the M (-type) diode are very similar to that i the p + diode. However the domiat curret compoets are decidedly differet i the two diodes.

More information

Lecture 6: October 16, 2017

Lecture 6: October 16, 2017 Ifomatio ad Codig Theoy Autum 207 Lectue: Madhu Tulsiai Lectue 6: Octobe 6, 207 The Method of Types Fo this lectue, we will take U to be a fiite uivese U, ad use x (x, x 2,..., x to deote a sequece of

More information

Counting Functions and Subsets

Counting Functions and Subsets CHAPTER 1 Coutig Fuctios ad Subsets This chapte of the otes is based o Chapte 12 of PJE See PJE p144 Hee ad below, the efeeces to the PJEccles book ae give as PJE The goal of this shot chapte is to itoduce

More information

THE ANALYSIS OF SOME MODELS FOR CLAIM PROCESSING IN INSURANCE COMPANIES

THE ANALYSIS OF SOME MODELS FOR CLAIM PROCESSING IN INSURANCE COMPANIES Please cite this atle as: Mhal Matalyck Tacaa Romaiuk The aalysis of some models fo claim pocessig i isuace compaies Scietif Reseach of the Istitute of Mathemats ad Compute Sciece 004 Volume 3 Issue pages

More information

Special Modeling Techniques

Special Modeling Techniques Colorado School of Mies CHEN43 Secial Modelig Techiques Secial Modelig Techiques Summary of Toics Deviatio Variables No-Liear Differetial Equatios 3 Liearizatio of ODEs for Aroximate Solutios 4 Coversio

More information

4. PERMUTATIONS AND COMBINATIONS Quick Review

4. PERMUTATIONS AND COMBINATIONS Quick Review 4 ERMUTATIONS AND COMBINATIONS Quick Review A aagemet that ca be fomed by takig some o all of a fiite set of thigs (o objects) is called a emutatio A emutatio is said to be a liea emutatio if the objects

More information

Mapping Radius of Regular Function and Center of Convex Region. Duan Wenxi

Mapping Radius of Regular Function and Center of Convex Region. Duan Wenxi d Iteatioal Cofeece o Electical Compute Egieeig ad Electoics (ICECEE 5 Mappig adius of egula Fuctio ad Cete of Covex egio Dua Wexi School of Applied Mathematics Beijig Nomal Uivesity Zhuhai Chia 363463@qqcom

More information

INTEGRATION BY PARTS (TABLE METHOD)

INTEGRATION BY PARTS (TABLE METHOD) INTEGRATION BY PARTS (TABLE METHOD) Suppose you wat to evaluate cos d usig itegratio by parts. Usig the u dv otatio, we get So, u dv d cos du d v si cos d si si d or si si d We see that it is ecessary

More information

physicsandmathstutor.com

physicsandmathstutor.com physicsadmathstuto.com physicsadmathstuto.com Jue 005 5x 3 3. (a) Expess i patial factios. (x 3)( x ) (3) (b) Hece fid the exact value of logaithm. 6 5x 3 dx, givig you aswe as a sigle (x 3)( x ) (5) blak

More information

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3

More information

Solid State Device Fundamentals

Solid State Device Fundamentals Solid State Device Fudametals ENS 345 Lecture Course by Alexader M. Zaitsev alexader.zaitsev@csi.cuy.edu Tel: 718 982 2812 4N101b 1 Thermal motio of electros Average kietic eergy of electro or hole (thermal

More information