ebook img

Semiconductor photonics. Principles and Applications PDF

247 Pages·2016·169.563 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Semiconductor photonics. Principles and Applications

Mauro Nisoli Semiconductor Photonics Principles and applications git su|:|ET.& EDITRICE I =—'§ ESCULAPIO Contents Preface Band structure of semiconductors 1.1 Crystals. latticesandcells 1.1.1 TheWigner-Seltzcell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Thereciprocal lattice ~16- 1.3 Electrons in a periodic crystal 10 1.4 Theconceptoteitective mass 13 1.5 Energy bands 14 1.5.1 Electronsand holesinasemiconductor . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Calculationoithebandstructure 15 1.6.1 Tight-bindingmethod . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6.2 Crystalwithone-atombasisandsingleatomicorbital 18 1.6.3 Linearlattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.6.4 Slmplecubiclattice . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.6.5 BandstructureofsemiconductorscalculatedbyTBM 22 1.7 Thek - p method 25 1.8 Bandstructuresofafewsemiconductors 28 1.8.1 Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.8.2 GalliumArsenlde . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.8.3 Gallium Nitride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - - - . . . . - - i i ' - - - - 30 Electrons in semiconductors 2.1 introduction 33 5.7 Competition between radiativeand nonradiative recombination QLlCJl‘iii.ll*.“ ‘1‘.’e-ll=1 6.1 introduction 6.2 Electronic states 6.2.1 Electronicstatesinthevalence band . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Density ofstates 6.4 Electron density 6.5 Transition selection rules 6.5.1 lntersubbandtransitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Absorption and gain in a quantum well 6.7 lntersubband absorption 6.8 Strained quantum wells 6.9 Transparency densityanddifferentialgain 6.9.1 Differential gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10 Excitons 6.10.1 Absorptionspectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10.2 Excltonsin quantumwells . . . Light i:r‘r\-iitin:.; -T.=iP»<:iei~' 7.1 Basic concepts 7.2 Double heterostructure LEDs 7.3 Carrierleakage over barrier 7.4 External efficiencyofa LED 7.5 Emission pattern of a LED 7.6 Luminousefficiency 7.7 Blue Light Emitting Diodes Se-:"Yiici'_»n<tu<;i;_\' L~;‘?sK.=-.'$ 8.1 introduction 8.2 Rateequationsandthresholdconditionsfor laseraction 8.3 Temperature dependence 8.4 Output power 8.5 Quantum well lasers 8.6 Laserstructures " 8.7 Spectral and spatial characteristicsofdiode laseremission Disti'iti-liteu t"E*F3diDCJ(t14. Lasers 9.1 Basic concepts 9.2 Coupled-modetheory 9.2.1 Thresholdconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 DFB laserwith uniform grating 9.3.1 Approxlmated evaluation ofoscillatingfrequenciesandthreshold gain 9.4 DFB laserwith ,\/4-shiftedgrating 9.5 Distributed Bragg Reflector (DBR) laser Vertical Cavity Surlace~~Emitting Lasers 10.1 Basic structure 10.2 Threshold conditions 10.3 Distributed Bragg reflectorsforVCSELs 10.4 Threshold conditionsandcurrentconfinement 10.5 Advantagesandapplications Quantum cascade lasers 11.1 Quantum cascade lasers 11.2 Gain coefficient 11.3 Rateequationsand threshold conditions 11.4 Outputpower, slope- and wall-plug efflciency 11.4.1 Wall-plug efflciency . . . . . . . . . . . . . . . . . . . . . . . . 11.5 Numerical example 11.6 Applications Fundamental constants index Preface The termphotonics was introduced in the late sixties by PierreAigrain, who gave the following definition: "Photonics is the science ofthe harnessing oflight. Pho- tonics encompasses the generationoflight, thedetectionoflight, themanagement oflight through guidance, manipulation and amplification and, most importantly, its utilisation for the benefit ofmankind." In the last decades impressive progress in the field ofphotonics hasbeen achieved, thanks to remarkable advances in the understandingofthe physical processes at the heart oflight-matter interaction in photonic applications and tothe introduction ofcrucial technological innovations. Photonics is anextremelylarge field, as clearlypointedoutbythe above definition, since it refers to all types oftechnological device and process, where photons are involved. Thisbookdoes notaim toanalyseallaspectsofphotonics: afewexcellenttextbooks alreadyexist,whichpresentseveraltopicsrelevantforphotonicapplications. Theaim ofthisbookistointroduce and explain importantphysicalprocesses attheheartof the opticalpropertiesofsemiconductordevices, suchaslightemittingdiodes (LEDs) andsemiconductorlasers. Itissuitableforahalf-semester (oraone-semester) course inPhotonicsorOptoelectronicsatthegraduatelevelinengineeringphysics, electrical engineeringormaterialscience. ltoriginated froma graduatecourse (PhotonicsI) which I amteachingatthe PolitecnicodiMi1ano since 2006. The concepts ofsolid statephysicsandquantum mechanicswhichare required tounderstand thesubjects discussed in thisbookare addressed in the introductorychapters. Itis assumed that the reader hashadcourses onelementaryquantum mechanics, solid-state physics, andelectromagnetictheoryatthe undergraduatelevel. The book presents a selection oftopics, which I consider essential to understand the operation ofsemiconductordevices. Itoffers a relativelyadvanced analysisof the photo-physics ofsemiconductors, trying toavoid the use ofexceedinglycomplex formalisms. Particularattentionwas devoted toofferaclearphysicalinterpretation ofallthe obtained results. Variousworked examples are added throughoutall the chapters to illustrate the application ofthe various formulas: the solved exercises are evidenced bythe coloured boxes in the text. The numerical examples are also importantsince theyallowthe reader to have a direct feeling ofthe orderofmagni- tude ofthe parameters used in the formulas discussed in the text. The greyboxes containconcise discussions ofsupplementarytopics ormore advanced derivations of particularresults reported in the maintext, which maynotbe easilyderived bythe reader. SemiconductorPhotonics isorganizedas follows. Chapter 1 focuses onthe description ofa fewconcepts ofsolid state physics, which are relevantforthe calculation and analysis ofthe band structure ofsemiconductors. The Bloch theorem is introduced, which describes the wavefunction of electrons in periodic structures. The tight- binding method is considered, with a few simple examples, and the k ~ p method, which are used tocalculated the band structure ofsemiconductors. Chapter2 deals with the discussion ofthe main properties ofcharged particles (electrons and holes) inintrinsicanddopedsemiconductors. The densityofstatesis firstcalculated andthe essentialconceptsofcarrierstatistics insemiconductorsare discussed. Basicconcepts ofquantum mechanics are contained inChapter3. In particular, the densitymatrix formalism is introduced, which is used in the book forthe calculation ofthe optical susceptibility ofa semiconductor. After a veryshort overview ofessential aspects ofclassicalelectromagnetic theory, Chapter4 analyses the interaction ofelectrons with an electromagnetic field. The expressions ofthe interaction Hamiltonian, which are extensively used throughout the book, are derived in this chapter. Chapters 5 and 6 build on the previous chapters. in particular, Chapter S deals with the opti- calpropertiesofbulksemiconductors, i.e., semiconductorswithspatial dimensions muchlargerthan the de Broglie wavelengthofthe electrons involved in the relevant physical processes. Absorption and gaincoefficients are calculated and the radiative and non-radiative recombination processes insemiconductors are analysed. Chapter 6 analyses the principles ofthe photo-physics in semiconductorquantumwells, i.e., insemiconductorstructureswhere the electrons are confined in one direction bya potentialwell,with a thickness smallerthan the electron de Brogliewavelength. In the remaining five chapters the general results obtained in the first part ofthe bookare applied to the investigation ofthe main optical properties ofsemiconduc- tor devices: light-emitting diodes and lasers. The general philosophy adopted in these chapters is the following: the fundamentalphysical processes are investigated, ratherthan the technological characteristics ofthe devices. Aftera shortand general analysis ofsemiconductorlasers inChapter8, based on the rate equation approach, Chapter9 contains a detailed theoretical analysis ofthe Distributed Feedback (DFB) lasers, based on the use ofthe coupled-modeequations. Byusinga simpleperturba- tive approach, the threshold laserconditions are obtained. Vertical CavitySurface EmittingLasers (VCSELs) and Quantum Cascade Lasers are analysed in thefinal two chapters. Final note: whyEschefs “Skyand WaterI" on the bookcover? This print suggested me various connections with photonics in semiconductors. It is light which, by playingwith shapes, gives rise to an evolutionwhich transforms fishes inwaterinto birds inthe skyand the transformationis closelyrelated to the reciprocal interaction among elements. In a similar manner, it is lightwhich, by playingwith electrons, triggers dynamical processes inside matter, with the generation ofnew properties and functions, where complex interactions among particles and surrounding envi- ronment play a crucial role. The analogy can be pushed even more considering that in Escher’s print the transition from skytowaterstarts and ends with realistic shapes ofbirds and fishes, respectively, and moves from one real shape to theother through a sequence ofshapes that, in particularin the central portion ofthe print, resemble but are not exactly neither birds nor fishes. Forcing a little the analogy, we can saythat typical photonic processes in semiconductors evolve from a given physical (real) state to anotherphysical (real) state through a sequence ofquantum superpositionofstates,whichdonothaveananalogyinthe realmofclassicalphysics. Milano, 11 November2016 MauroNisoli l. Band structure of semiconductors Crystals, latticesand cells Acrystal is composedbyaperiodic repetitionofidenticalgroupsofatoms: agroup is calledbasis. The correspondingcrystallattice isobtainedbyreplacingeachgroupof atoms bya representative point, asshown in Fig. 1.1. Acrystal can be also called latticewitha basis. Whenthebasis is composedbyasingle atom thecorresponding lattice is called monoatomic. In aBravais lattice the position Rofall points in the latticecanbewritten as : R=T1181 +71,282 +71.383, (1.1) where a1, a2 and a3 are three non-coplanar translation vectors, called primitive vectorsandn1, ‘fig andn3 are arbitrary (positive ornegative) integers. This definition ofBravaislattice implies thatthislatticelooksexactlythe samewhenviewed from anylattice point. Notonlythe arrangementofpointsbutalsotheorientation must be exactlythe same from everypoint in a Bravais lattice. Therefore, two points in o'o'o'o' - - - O. 0.0.0.0. ' . _ _ o'o'o'o' - - - - la) rs) (cl Figure 1.1: (a) Basiscomposedbytwodifferentatoms; (b) bidimensionalcrystaland (c) correspondinglattice. the lattice, whose positions vectors are given byr and r’ = r+ R are completely equivalentenvironmentally. Forexample, the two-dimensional honeycomb lattice

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.