Semiconductor nanowires. I, Growth and theory PDF
Preview Semiconductor nanowires. I, Growth and theory
SERIES EDITORS EICKE R. WEBER Director Fraunhofer-Institut für SolareEnergiesysteme ISE Vorsitzender, Fraunhofer-Allianz Energie Heidenhofstr. 2,79110 Freiburg, Germany CHENNUPATI JAGADISH Australian Laureate Fellow andDistinguished Professor Department ofElectronic MaterialsEngineering Research Schoolof Physics andEngineering Australian National University Canberra,ACT0200 Australia AcademicPressisanimprintofElsevier 225WymanStreet,Waltham,MA02451,USA 525BStreet,Suite1800,SanDiego,CA92101-4495,USA TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK 125LondonWall,London,EC2Y5AS,UK Firstedition2015 ©2015ElsevierInc.Allrightsreserved Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans, electronicormechanical,includingphotocopying,recording,oranyinformationstorageand retrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseek permission,furtherinformationaboutthePublisher’spermissionspoliciesandour arrangementswithorganizationssuchastheCopyrightClearanceCenterandtheCopyright LicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. 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ISBN:978-0-12-803027-1 ISSN:0080-8784 ForinformationonallAcademicPresspublications visitourwebsiteathttp://store.elsevier.com/ CONTRIBUTORS ErikBakkers EindhovenUniversityofTechnology,Eindhoven,andKavliInstituteofNanoscience, DelftUniversityofTechnology,Delft,TheNetherlands.(ch5) SoniaConesa-Boj EindhovenUniversityofTechnology,Eindhoven,TheNetherlands.(ch5) VladimirG.Dubrovskii St.PetersburgAcademicUniversity,St.Petersburg,andIoffePhysicalTechnicalInstitute RAS,St.Petersburg,Russia.(ch1) FrankGlas CNRS—LaboratoiredePhotoniqueetdeNanostructures,Marcoussis,France.(ch2) Mo¨ıraHocevar InstitutNe´elCNRS/UJF,Grenoble,France.(ch5) YoungJoonHong FacultyofNanotechnology&AdvancedMaterialsEngineering,GrapheneResearch Institute,SejongUniversity,Seoul,SouthKorea.(ch3) NariJeon DepartmentofMaterialsScienceandEngineering,NorthwesternUniversity,Evanston, Illinois,USA.(ch6) LincolnJ.Lauhon DepartmentofMaterialsScienceandEngineering,NorthwesternUniversity,Evanston, Illinois,USA.(ch6) Chul-HoLee KU-KISTGraduateSchoolofConvergingScienceandTechnology,KoreaUniversity, Seoul,SouthKorea.(ch3) Gyu-ChulYi DepartmentofPhysicsandAstronomy,SeoulNationalUniversity,Seoul,SouthKorea. (ch4) HosangYoon DepartmentofPhysicsandAstronomy,SeoulNationalUniversity,Seoul,SouthKorea. (ch4) vii PREFACE Prior to 1990 known as whiskers and nowadays as nanowires, filamentary crystalswithadiameterinthenanoscalerrangehaverecentlyinspiredmany scientistsandengineers.Thankstothesmalldimensionsandparticularlydue to their special shape, nanowires have enabled novel applications and improvedexistingonesinabroadrangeoffields.Theseincludethediscov- ery of new phenomena in one-dimensional physics, next-generation solar cells, lasers, solid-state lighting, biosensing, and integrated circuits. Addi- tionally, they have provided an excellent platform to study crystal growth in 1D and to synthesize materials in new phases, combinations, and archi- tectures that are not possibly attained otherwise. Obtaining nanowires with the tailored size, shape, crystal phase, orien- tation, and composition profile is the key requisite for enabling any appli- cation. Today, exquisite control on many of these properties has already beendemonstrated,thankstothefocusedandextensiveeffortsofthescien- tificcommunityinthelastdecadeswhichdevelopedimpressiveunderstand- ingoftheirgrowthandoftailoringtheirproperties.Itisthereforetimelyto disseminatetheseresultsandtoprovideacomprehensivetreatmentofnano- wire growth and theory, particularly for the III–V and II–VI compound semiconductor materials. In this first volume, we review important aspects of nanowire growth. The first chapter concerns with the theory of VLS growth in compound semiconductors which is influenced by complex contributions of many growth parameters that are not typically present in elemental whisker or nanowiregrowth.Thesecondchaptertreatstheroleofstraininnanowires andrelatedheterostructures,akeycharacteristicfortuningboththegrowth and properties of semiconductor nanowires. The third chapter discusses a recently emerging growth mechanism of 1D nanowires on 2D materials: van der Waals heteroepitaxy. The fourth chapter comprises a summary on the studies of position-controlled growth of ZnO nanostructures. The fifth chapter provides one archetypical example of what nanowires enable in contrast to thin-film technology: the quasi defect-free integration of groupIVandIII–Vsemiconductorsinasinglestructure.Thesixthandlast chapterreviewsatomprobetomographystudiesonnanowires,animportant techniqueforthethree-dimensionalmappingofthechemicalcomposition innanowires.Ourexamplesconcernsemiconductormaterials.Nevertheless, ix x Preface the implications are in fact much more general and concern many more materials systems. AnnaFontcubertaiMorral,EcolePolytechniqueFe´de´raledeLausanne Shadi A. Dayeh, University of California, San Diego Chennupati Jagadish, Australian National University Editors CHAPTER ONE Theory of VLS Growth of Compound Semiconductors Vladimir G. Dubrovskii1 St.PetersburgAcademicUniversity,St.Petersburg,Russia IoffePhysicalTechnicalInstituteRAS,St.Petersburg,Russia 1Correspondingauthor:e-mailaddress:[email protected] Contents 1. Introduction 1 2. FundamentalsofVLSGrowth 2 3. ChemicalPotentialsforAu-CatalyzedVLSGrowthofIII–VNanowires 11 4. GrowthKineticsofIII–VNanowires 15 5. Transport-LimitedGrowthofNanowires 18 6. NucleationRateinVLSNanowires 33 7. Position-DependentNucleationinNanowires 40 8. Self-consistentGrowthEquation 42 9. Ga-CatalyzedGrowthofGaAsNanowires 47 10. FormationofTernaryAu-CatalyzedIII–VNanowires 56 11. ImpactofGrowthConditionsontheCrystalStructureofIII–VNanowires 62 References 73 1. INTRODUCTION This chapter deals with growth and structural modeling of vapor– liquid–solid (VLS) III–V nanowires catalyzed by either Au or group III metals. We have tried to balance a semi-quantitative description of the VLSgrowthprocessandpresentationofthewell-knownresultswithsome newlydevelopedmodels.Consequently,theexpositionofthechapteristhe following.Section2containsanintroductiontotheVLSgrowthmethodin the case of III–V nanowires, which should be helpful to the beginners. Section 3describesthe drivingforce—the liquid chemical potential in ter- naryAu-III–Valloys.InSection4,webrieflydescribetheVLSgrowthkinet- icsinthesteadystatewheresignificantsimplificationsinmodelingbecome possible. Section 5 presents a detailedanalysis of the transport-limited axial SemiconductorsandSemimetals,Volume93 #2015ElsevierInc. 1 ISSN0080-8784 Allrightsreserved. http://dx.doi.org/10.1016/bs.semsem.2015.09.002 2 VladimirG.Dubrovskii and radial growth rates, with some refinements of the existing models. In Section 6, we consider our recently published results on the Zeldovich nucleation rate in Au-catalyzed III–V nanowires along with a self- consistency renormalization which appears very important in applications. Section 7 describes the position-dependent nucleation in nanowires. In Section8,wepresentasimpleself-consistentgrowthequationwhichallows onetodescribethevastvarietyofexperimentaldata. Thenextsectionscontainmainlynewresults.InSection9,weconsider somenewdataonGa-catalyzedgrowthofGaAsnanowiresandinparticular theeffectoftheradiusself-equilibration.Section10dealswithAu-catalyzed ternary InGaAs nanowires where we develop a new atomistic growth picture.Despiteitssimplicity,ithelpstoimproveourunderstandingofcom- plex growth phenomena in ternary nanowires. Finally, Section11 presents a refined model of crystallographic polytypism in Au-catalyzed III–V nanowires. This model is capable of describing the thresholds between mononucleation, polynucleation, and atomistic growth, and explains very welltherecentlyobservednonmonotonicbehaviorsofthepreferredcrystal structure versus different parameters such as the group V flux. 2. FUNDAMENTALS OF VLS GROWTH Insimpleterms,theVLSmethod(WagnerandEllis,1964)makesuse of catalytic effect of a liquid metal droplet (e.g., Au) to fabricate semicon- ductor nanowires that grow away from the substrate with the position and width determined by the initial location and size of this droplet, as showninFig.1.Usually,nanowiresgrowinh111idirectionperpendicular to(111)substrate.Parasiticgrowthon nonactivatedparts ofthesubstrateis eithercompletelysuppressedorproceedsatalowerratethanthatofnano- wires.Fastelongationofnanowiresoccursbecausemuchmoresemiconduc- tormaterialarrivestothedropletthantothesubstrate.Inchemicalepitaxies such as metal organic chemical vapor deposition (MOCVD) or hydride vapor phase epitaxy (HVPE), a liquid metal largely enhances the cracking efficiency of semiconductor precursors, while in molecular beam epitaxy (MBE)thedropletactsasamaterialcollectorthatdirectsthediffusionfluxes tothenanowiretop(Dubrovskii,2014a).Whateveristheepitaxytechnique usedtoproducenanowires,theVLSprocessnecessarilyinvolvestwophase transitionsofasemiconductormaterial:fromvapor(e.g.,GaandAs beams 2 inMBE)toliquid(Au–Ga–Asliquidalloyinthedroplet)andfromliquidto solid (GaAs nanowire), which explains the term “vapor–liquid–solid.” TheoryofVLSGrowthofCompoundSemiconductors 3 Au film (1) Deposition of GaAs buffer layer solid Au film GaAs (111B) substrate Au–Ga–As droplets (2) Anneal above the GaAs buffer layer melting temperature GaAs (111B) substrate 2D layer (3) Epitaxial growth of GaAs nanowires GaAs buffer layer GaAs (111B) substrate Figure1 Au-assistedVLSgrowthofGaAsnanowiresonGaAs(111)BsubstratebyMBE with predeposition of (cid:2)1-nm-thick solid Au layer. Atomic force microscopy images show the surface after Au deposition (first stage) and 3D droplets after annealing (secondstage).Scanningelectronmicroscopy(SEM)imageshowstheverticallyaligned GaAsnanowires(thirdstage).Thesenanowireshaveratherbroadlengthanddiameter distributionsduetoirregularityoftheinitialensembleofdropletsachievedbythermal dewetting. The VLS growth usually consists of the following steps schematized in Fig. 1: (1) Preparationoftheinitialcatalystlayerorcatalystparticleswhichcanbe organized into regular arrays by lithographical surface patterning. (2) Annealofthesurfaceabovethemeltingtemperatureofagivenmetal– semiconductor alloy to produce liquid droplets. (3) Materialdepositionwherethestructuralpropertiesofnanowireensem- bles(length,width,shape,andeventhecrystalphase)canbetunedby depositionconditionssuchasthegrowthtime,temperature,groupIII and V fluxes. Figure2presentstheexamplesofregulararraysofInPnanowiresgrownby chemical beam epitaxy (CBE) from organized Au seeds in the openings of inertSiN masklayeronInP(111)B(Kelrichetal.,2013,2015).Sincever- x ticalandradialgrowthratesaredeterminedbythedropletdiameter,lateral spacing, and deposition conditions while fluctuations within the nanowire ensemble(e.g.,randomnessofstartingtimesforgrowthorinhomogeneityof material influxes into different nanowires) are usually negligible, all nano- wires can be made almost exactly identical. This feature of catalytic 4 VladimirG.Dubrovskii A B 500 nm Figure2 (A)PlanviewSEMimageofaregular2DarrayofAunanoparticlesinsidethe SiN openingspriortoCBEgrowth.(B)45°tiltedSEMimageofaregulararraysofInP x nanowires grown from 127-nm diameter openings at T¼420°С, TMI flow correspondingto110nm/h2DgrowthrateonInP(100)at500°С,andPH flowrate 3 of3sccm(Kelrichetal.,2013).Taperingandcrystalstructureofthesenanowirescan becontrolledbythegrowthtemperatureandphosphorusflux(Kelrichetal.,2015). nanostructures is very advantageous for applications. Such a level of size uniformity cannot be achieved in self-induced approaches due to random characterofnucleation.Itshouldbenoted,however,thatperfectlyregular nanowirescanalsobeobtainedbyselectivearea(SA)methods(Noborisaka etal.,2005)sothattheVLStechniqueisnotexclusiveinthisrespect.Onthe other hand, SA growth can acquire the VLS character under the excessive group III influx to the nanowire top. TheVLSmechanismappliesonlywhenthealloyofmetalandsemicon- ductorremainsliquidduringgrowth.Thestateofcatalystparticlesdepends onmanyfactorssuchasthegrowthtemperature,dropletcomposition,and particlesize.Alternatively,theso-calledvapor–solid–solid(VSS)mechanism ofIII–VcompoundsintroducedbyPerssonetal.(2004)andfurtherdevel- opedbyDicketal.(2005)suggeststhatthecatalystparticleatthenanowire tipissolidduringgrowth.InPerssonetal.(2004),throughinsitutransmis- sionelectronmicroscopy(TEM)analysisandenergy-dispersiveX-rayspec- troscopy (EDXS) measurements of GaAs nanowires grown by CBE, the authors observedthecrystallinity oftheAu–Gaparticleand alowGacon- centrationbelowtheeutecticmelt.TheanalysisofDicketal.(2005)refers tothecaseofAu-catalyzedInAsnanowiresgrownbyMOCVDbelowthe eutectic temperature of bulk Au–In alloy at 454.3°С. Indeed, the VLS growth mechanism is always guaranteed for self-catalyzed III–V nanowires with group III metal catalysts, while in Au-catalyzed III–V nanowires the interplay between VLS and VSS modes requires close examination. In particular, the Au–Ga–As droplets should be liquid at typical MBE TheoryofVLSGrowthofCompoundSemiconductors 5 temperatures above 500°C (Harmand et al., 2005), while Au-catalyzed MBE growth of InAs nanowires within the temperature window from 380 to 430°C most probably yields partly solidified catalyst particles (Tchernycheva et al., 2007). As any epitaxial growth, the VLS process should occur at a positive difference of the effective chemical potentials of a semiconductor material in the vapor (V) and solid (S) phases, Δμ ¼μ (cid:3)μ . However, the VLS VS V S growthnecessarilyinvolvesanintermediateliquid(L)stateofthissemicon- ductor at the chemical potential μ . The latter should be larger than μ to L S ensure solidification but smaller than μ to drive the vapor-to-liquid tran- V sition.Therefore,theclassicaladsorption-inducedVLSgrowthoccurswhen μ >μ >μ or Δμ >μ >0: (1) V L S VS LS For III–V semiconductors, the definitions of these chemical potentials requiresomecare.First,weneedtoconsideratomicchemicalpotentialsof IIIandVelementsinvaporsuchthatμ ¼μV+μV(hereandbelow,thesub- V 3 5 script“3”standsforgroupIII,“5”forgroupV,and“35”forasolidIII–Vpair). Thesearegivenbytheatomic fluxesofgroupIIIandV elementsontothe droplet surface—I and I , respectively, MBE growth geometry or the 3 5 correspondingcrackingefficienciesinchemicalepitaxies(seeFig.3forillus- tration of the main parameters in VLS III–V nanowires). For Au-catalyzed VLSgrowth,theliquidchemicalpotentialatthesurfacetemperatureTisgen- erally defined as (Glas, 2010a): μ ðc ,c ,TÞ¼ μLðc ,c ,TÞ+μLðc ,c ,TÞ. L 3 5 3 3 5 5 3 5 Here, c and c are the relative atomic concentrations of group III and 3 5 V atoms dissolved in gold such that the atomic concentration of Au equals c ¼1(cid:3)c (cid:3)c . The solid chemical potential refers to a bound III–V pair Au 3 5 instoichiometriczincblende(ZB)crystal:μ ¼μS ðTÞandgenerallycannot S 35 bedecoupledtothesumofthegroupIIIandVcontributions.Ifthenanowire phaseiswurtzite(WZ),thesolidchemicalpotentialchangestoμ +ψ,withψ S asthebulkenergydifferencebetweentheWZandZBphases(Dubrovskii, 2014a)(forconventionalIII–Vmaterials,ψ ispositive).Duetotheknown low solubility of most group V elements such as As in liquid metals, the VLSprocessusuallyproceedsatc ≪c .Inthiscase,wecanneglectthedepen- 5 3 denceofμLonc andwriteapproximately(Dubrovskii,2014b) 3 5 Δμ ðc ,c ,TÞ¼μLðc ,TÞ+μLðc ,c ,TÞ(cid:3)μS ðTÞ: (2) LS 3 5 3 3 5 3 5 35 Therefore,thegroupVchemicalpotentialinliquidisthemostdifficult one since it depends on concentrations of both growth species.
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